Publications

Rubisco is the main gateway through which inorganic carbon enters the biosphere, catalyzing the vast majority of carbon fixation on Earth. This pivotal enzyme has long been observed to be kinetically constrained. Yet, this impression is based on kinetic measurements heavily focused on eukaryotic rubiscos, a rather conserved group of low genetic diversity. Moreover, the fastest rubiscos that we know of so far were found among the sparsely sampled prokaryotes. Could there be yet faster rubiscos among the uncharted regions of rubiscos phylogenetic diversity? Here, we perform a characterization of more than 250 rubiscos from a wide range of bacteria and archaea, thereby doubling the coverage of the diversity of this key enzyme. We assess the distribution of the carboxylation rates at saturating levels of CO₂, and establish that rubisco is a relatively slow enzyme across the tree of life, never exceeding ≈30 reactions per second at 30 °C. We show that relatively faster subclades share similar evolutionary contexts, involving micro-oxygenic environments or a CO₂ concentrating mechanism. Leveraging a simple machine learning model trained on this dataset, we predict the carboxylation rate for all ≈68,000 sequenced rubisco variants found in nature to date. This study provides the largest and most diverse dataset of natural variants for an enzyme and their associated rates, establishing a solid benchmark for future efforts to predict catalytic rates from sequence data.

Can we build a living cell from non-living molecular components? This foundational question drives the field of synthetic cell engineering, having already reconstituted key cellular processes within synthetic environments, and now advancing toward their integration into systems of increasing complexity. At this stage of gradual complexification, it is essential to construct a general quantitative picture of synthetic cells that can clarify the capabilities and limitations of current systems and help guide future design efforts. Here, we adopt the \u201cby the numbers\u201d approach to provide a quantitative and intuitive overview of synthetic cell properties. Focusing on liposome-based systems, we compile and contextualize numerical estimates from the literature and use them to reason about the structural, biochemical, and functional characteristics of these synthetic constructs. Through this quantitative lens, we aim to highlight both the current performance achieved and the key challenges that remain in the path toward building autonomous synthetic cells.

Earth is teeming with life on the move, shaping ecosystems and human civilizations alike. However, the magnitude of movement by humans and other animals has yet to be assessed holistically. Here we quantify the movement of biomass across all animal life and in comparison to humanity. We show that the combined biomass movement of all wild birds, land arthropods and wild land mammals is about one-sixth that of humans walking and about 40 times smaller than all the biomass movement of humans. The biomass movement of marine animals, which we find to be the living worlds largest, has been halved since 1850 due to industrial fishing and whaling, while human biomass movement has increased by about 40-fold. This study gives a quantitative perspective on global mobility in the Anthropocene and sharpens our perception regarding the extent of human versus animal activity.

Mammals are of central interest in ecology and conservation science. Here, we estimate the trajectory of mammal biomass globally over time including humans, domesticated and wild mammals. According to our estimates, in the 1850s, the combined biomass of wild mammals was ≈200 Mt (million tonnes), roughly equal to that of humanity and its domesticated mammals at that time. Since then, human and domesticated mammal populations have grown rapidly, reaching their current combined biomass of ≈1100 Mt. During the same period, the total biomass of wild mammals decreased by more than 2-fold. We estimate that, despite a moderate increase in the recent decades, the global biomass of wild marine mammals has declined by ≈70% since the 1850s. This provides a broader perspective to observed species extinctions, with ≈2% of marine mammal species recorded as extinct during the same period. While historical wild mammal biomass estimates rely on limited data and have various uncertainties, they provide a complementary perspective to species extinctions and other metrics in tracking the status of wildlife. This work additionally provides a quantitative view on the rapid human-induced shift in the composition of mammalian biomass over the past two centuries.

Mapping ecosystem integrity is a key task of the planetary-boundaries framework. Two new control variables have been suggested for the core planetary boundary for functional biosphere integrity: (1) human appropriation of net primary production (HANPP) and (2) a metric for ecological disruption (EcoRisk). However they have not yet been mapped spatially and temporally explicitly. Here, we use simulations with the dynamic global vegetation model LPJmL to map the status of these variables at a spatial resolution of 0.5° × 0.5° for every year since 1600. We additionally quantify local degradation thresholds by comparison with independent biosphere integrity indicators. We finally aggregate results globally to a planetary boundary status as the land area transgressing the local thresholds. We find that the local boundary is currently transgressed on 60% of the global land area, with 38% already at high risk of degradation. This study provides an important first step and opens the opportunity for further research, especially for finding a planetary-scale threshold.

Improving food security and reducing the environmental footprint of food production is urgently needed to satisfy the growing global population in a time of climate, biodiversity, and water pressures. Indoor vertical farming is largely independent of environmental conditions and is reported to reduce the land and water required for food production. However, vertical farming requires large amounts of energy. Based on the vertical farming energy cost, we derive from basic considerations a current minimum cost of approximate to$10/kg dry plant matter. Vertical farming is therefore not currently competitive with dried cereals or pulses (e.g. wheat, rice, and soybeans). We also show limited current competitiveness for products like tomatoes and lettuce, despite a low dry matter content. Whereas the environmental implications of vertical farming depend on the electricity source. Using the average newly installed electricity mix in recent years (predominantly solar and wind, with some coal, natural gas, and bioenergy), vertical farming could substantially increase greenhouse gas emissions and has limited land benefits compared with conventional agriculture. Using exclusively electricity from photovoltaics, some environmental benefits could be achieved for crops with a low dry matter content like lettuce, but this is more limited for dried crops like wheat. The transparent calculations we provide here set out challenges for vertical farming and highlight that improvements in both the overall vertical farming energetic efficiency (approximate to 1% to 2%), as well as low-impact electricity sources are needed in the future.

There is a strong need to develop technologies that reduce anthropogenic pollution and the dependence on nonrenewable Earth resources. One way of doing so is by harnessing biological systems for replacing the production of fossil-fuel based goods with low-environmental-impact alternatives. Recently, progress was made in engineering the model organism E. coli to grow using CO₂ and formate as its only carbon and energy sources using the reductive glycine pathway (rGlyP). Here, we use this engineered strain of E. coli as a host system for the production of polyhydroxybutyrate (PHB), a biologically derived and biodegradable plastic. The production of PHB in this strain was confirmed using Nile red fluorescence microscopy, transmission electron microscopy, and HPLC analysis, with a yield of 0.172 ± 0.005 mg/L of PHB after 120 hours of incubation. Since formate can be efficiently generated from CO₂ by electrochemical reduction using renewable energy sources, this study serves as a proof of concept for the emerging field of electro-bioproduction.

Producing goods, such as foods and fuels, with minimal environmental impacts is urgently needed. Although advances in bioproduction are promising, there is often a noticeable gap in our understanding of whether and where new processes can compete with existing methods on an economic and environmental basis. Transparent lower bound calculations from basic principles highlight potential benefits of producing foods, but not fuels, from electro-microbial production of biomass.

Rubisco is the primary CO₂-fixing enzyme of the biosphere¹, yet it has slow kinetics². The roles of evolution and chemical mechanism in constraining its biochemical function remain debated^3,4. Engineering efforts aimed at adjusting the biochemical parameters of rubisco have largely failed⁵, although recent results indicate that the functional potential of rubisco has a wider scope than previously known⁶. Here we developed a massively parallel assay, using an engineered Escherichia coli⁷ in which enzyme activity is coupled to growth, to systematically map the sequencefunction landscape of rubisco. Composite assay of more than 99% of single-amino acid mutants versus CO₂ concentration enabled inference of enzyme velocity and apparent CO₂ affinity parameters for thousands of substitutions. This approach identified many highly conserved positions that tolerate mutation and rare mutations that improve CO₂ affinity. These data indicate that non-trivial biochemical changes are readily accessible and that the functional distance between rubiscos from diverse organisms can be traversed, laying the groundwork for further enzyme engineering efforts.

The framework presented in the Dublin Declaration has generated controversy by advocating for maintaining or increasing livestock numbers. The serious and acute harms associated with global livestock production today bring the goals of the declaration into dispute.

Autotrophy is the basis for complex life on Earth. Central to this process is rubiscothe enzyme that catalyzes almost all carbon fixation on the planet. Yet, with only a small fraction of rubisco diversity kinetically characterized so far, the underlying biological factors driving the evolution of fast rubiscos in nature remain unclear. We conducted a high-throughput kinetic characterization of over 100 bacterial form I rubiscos, the most ubiquitous group of rubisco sequences in nature, to uncover the determinants of rubiscos carboxylation velocity. We show that the presence of a carboxysome CO₂ concentrating mechanism correlates with faster rubiscos with a median fivefold higher rate. In contrast to prior studies, we find that rubiscos originating from α-cyanobacteria exhibit the highest carboxylation rates among form I enzymes (≈10 s⁻¹ median versus

Cell-free DNA (cfDNA) tests use small amounts of DNA in the bloodstream as biomarkers. While it is thought that cfDNA is largely released by dying cells, the proportion of dying cells' DNA that reaches the bloodstream is unknown. Here, we integrate estimates of cellular turnover rates to calculate the expected amount of cfDNA. By comparing this to the actual amount of cell type-specific cfDNA, we estimate the proportion of DNA reaching plasma as cfDNA. We demonstrate that

Synthetic autotrophy is a promising avenue to sustainable bioproduction from CO2. Here, we use iterative laboratory evolution to generate several distinct autotrophic strains. Utilising this genetic diversity, we identify that just three mutations are sufficient for Escherichia coli to grow autotrophically, when introduced alongside non-native energy (formate dehydrogenase) and carbon-fixing (RuBisCO, phosphoribulokinase, carbonic anhydrase) modules. The mutated genes are involved in glycolysis (pgi), central-carbon regulation (crp), and RNA transcription (rpoB). The pgi mutation reduces the enzyme's activity, thereby stabilising the carbon-fixing cycle by capping a major branching flux. For the other two mutations, we observe down-regulation of several metabolic pathways and increased expression of native genes associated with the carbon-fixing module (rpiB) and the energy module (fdoGH), as well as an increased ratio of NADH/NAD+ - the cycle's electron-donor. This study demonstrates the malleability of metabolism and its capacity to switch trophic modes using only a small number of genetic changes and could facilitate transforming other heterotrophic organisms into autotrophs.

Following evidence of waning immunity against both infection and severe disease after 2 doses of the BNT162b2 vaccine, Israel began administering a 3rd BNT162b2 dose (booster) in July 2021. Recent studies showed that the 3rd dose provides a much lower protection against infection with the Omicron variant compared to the Delta variant and that this protection wanes quickly. However, there is little evidence regarding the protection of the 3rd dose against Omicron (BA.1/BA.2) severe disease. In this study, we estimate the preservation of immunity from severe disease up to 7 months after receiving the booster dose. We calculate rates of severe SARS-CoV-2 disease between groups of individuals aged 60 and above, comparing those who received two doses at least 4 months previously to those who received the 3rd dose (stratified by the time from vaccination), and to those who received a 4th dose. The analysis shows that protection conferred by the 3rd dose against Omicron severe disease did not wane over a 7-month period. Moreover, a 4th dose further improved protection, with a severe disease rate approximately 3-fold lower than in the 3-dose cohorts.

The rate of primary productivity is a keystone variable in driving biogeochemical cycles today and has been throughout Earth's past.¹ For example, it plays a critical role in determining nutrient stoichiometry in the oceans,² the amount of global biomass,³ and the composition of Earth's atmosphere.⁴ Modern estimates suggest that terrestrial and marine realms contribute near-equal amounts to global gross primary productivity (GPP).⁵ However, this productivity balance has shifted significantly in both recent times⁶ and through deep time.^7,8 Combining the marine and terrestrial components, modern GPP fixes ≈250 billion tonnes of carbon per year (Gt C year⁻¹).^5,9,10,11 A grand challenge in the study of the history of life on Earth has been to constrain the trajectory that connects present-day productivity to the origin of life. Here, we address this gap by piecing together estimates of primary productivity from the origin of life to the present day. We estimate that ∼10¹¹10¹² Gt C has cumulatively been fixed through GPP (≈100 times greater than Earth's entire carbon stock). We further estimate that 10³⁹10⁴⁰ cells have occupied the Earth to date, that more autotrophs than heterotrophs have ever existed, and that cyanobacteria likely account for a larger proportion than any other group in terms of the number of cells. We discuss implications for evolutionary trajectories and highlight the early Proterozoic, which encompasses the Great Oxidation Event (GOE), as the time where most uncertainty exists regarding the quantitative census presented here.

Objectives: This study aims to address limitations in assessing vaccine protection using the classical vaccine effectiveness (VE) measure, especially in contexts where a significant portion of the population is already vaccinated or infected. Study Design and Setting: We propose using the adjusted number of cases (ANC) as a building block for deriving vaccine effectiveness measures. This approach accounts for biases arising from small and unrepresentative unvaccinated reference groups with incomplete data. We demonstrate the use of these measures for assessing the protection conferred by a booster dose against severe COVID-19 using data from Israel. Results: The use of ANC and the derived measures reveals a more comprehensive understanding of the complex immunity landscape compared to traditional VE measures. This approach enables meaningful comparisons between different vaccination categories and provides insights to inform policy decisions. Conclusion: In situations with widespread vaccination and prior infections, traditional VE measures can be limited in their informative value. Using the ANC offers a more robust and insightful assessment of vaccine effectiveness. A demonstration of the evaluation of booster dose protection against severe COVID-19 in Israel underscores the importance of adopting complementary measures to guide public health strategies.

The immune system is a complex network of cells with critical functions in health and disease. However, a comprehensive census of the cells comprising the immune system is lacking. Here, we estimated the abundance of the primary immune cell types throughout all tissues in the human body. We conducted a literature survey and integrated data from multiplexed imaging and methylome-based deconvolution. We also considered cellular mass to determine the distribution of immune cells in terms of both number and total mass. Our results indicate that the immune system of a reference 73 kg man consists of 1.8 x 10¹² cells (95% CI 1.5-2.3 x 10¹²), weighing 1.2 kg (95% CI 0.8-1.9). Lymphocytes constitute 40% of the total number of immune cells and 15% of the mass and are mainly located in the lymph nodes and spleen. Neutrophils account for similar proportions of both the number and total mass of immune cells, with most neutrophils residing in the bone marrow. Macrophages, present in most tissues, account for 10% of immune cells but contribute nearly 50% of the total cellular mass due to their large size. The quantification of immune cells within the human body presented here can serve to understand the immune function better and facilitate quantitative modeling of this vital system.

The daily activities of ≈8 billion people occupy exactly 24 h per day, placing a strict physical limit on what changes can be achieved in the world. These activities form the basis of human behavior, and because of the global integration of societies and economies, many of these activities interact across national borders. Yet, there is no comprehensive overview of how the finite resource of time is allocated at the global scale. Here, we estimate how all humans spend their time using a generalized, physical outcome-based categorization that facilitates the integration of data from hundreds of diverse datasets. Our compilation shows that most waking hours are spent on activities intended to achieve direct outcomes for human minds and bodies (9.4 h/d), while 3.4 h/d are spent modifying our inhabited environments and the world beyond. The remaining 2.1 h/d are devoted to organizing social processes and transportation. We distinguish activities that vary strongly with GDP per capita, including the time allocated to food provision and infrastructure, vs. those that do not vary consistently, such as meals and transportation time. Globally, the time spent directly extracting materials and energy from the Earth system is small, on the order of 5 min per average human day, while the time directly dealing with waste is on the order of 1 min per day, suggesting a large potential scope to modify the allocation of time to these activities. Our results provide a baseline quantification of the temporal composition of global human life that can be expanded and applied to multiple fields of research.

Wild mammals are icons of conservation efforts, yet there is no rigorous estimate available for their overall global biomass. Biomass as a metric allows us to compare species with very different body sizes, and can serve as an indicator of wild mammal presence, trends, and impacts, on a global scale. Here, we compiled estimates of the total abundance (i.e., the number of individuals) of several hundred mammal species from the available data, and used these to build a model that infers the total biomass of terrestrial mammal species for which the global abundance is unknown. We present a detailed assessment, arriving at a total wet biomass of ≈20 million tonnes (Mt) for all terrestrial wild mammals (95% CI 13-38 Mt), i.e., ≈3 kg per person on earth. The primary contributors to the biomass of wild land mammals are large herbivores such as the white-tailed deer, wild boar, and African elephant. We find that even-hoofed mammals (artiodactyls, such as deer and boars) represent about half of the combined mass of terrestrial wild mammals. In addition, we estimated the total biomass of wild marine mammals at ≈40 Mt (95% CI 20-80 Mt), with baleen whales comprising more than half of this mass. In order to put wild mammal biomass into perspective, we additionally estimate the biomass of the remaining members of the class Mammalia. The total mammal biomass is overwhelmingly dominated by livestock (≈630 Mt) and humans (≈390 Mt). This work is a provisional census of wild mammal biomass on Earth and can serve as a benchmark for human impacts.

Insects and other arthropods are central to terrestrial ecosystems. However, data are lacking regarding their global population abundance. We synthesized thousands of evaluations from around 500 sites worldwide, estimating the absolute biomass and abundance of terrestrial arthropods across different taxa and habitats. We found that there are approximate to 1 x 10(19) (twofold uncertainty range) soil arthropods on Earth, approximate to 95% of which are soil mites and springtails. The soil contains approximate to 200 (twofold uncertainty range) million metric tons (Mt) of dry biomass. Termites contribute approximate to 40% of the soil biomass, much more than ants at approximate to 10%. Our estimate for the global biomass of above-ground arthropods is more uncertain, highlighting a knowledge gap that future research should aim to close. We estimate the combined dry biomass of all terrestrial arthropods at approximate to 300 Mt (uncertainty range, 100 to 500), similar to the mass of humanity and its livestock. These estimates enhance the quantitative understanding of arthropods in terrestrial ecosystems and provide an initial holistic benchmark on their decline.

Background: The BNT162b2 (Pfizer-BioNTech) two-dose vaccine regiment for children and the BNT162b2 third dose for adolescents were approved shortly before the SARS-CoV-2 omicron (B.1.1.529) outbreak in Israel. We aimed to estimate the effects of these vaccines on the rates of confirmed infection against the omicron variant in children and adolescents. Methods: In this observational cohort study, we extracted data for the omicron-dominated (sublineage BA.1) period. We compared rates of confirmed SARS-CoV-2 infection between children aged 510 years 1435 days after receiving the second vaccine dose with an internal control group of children 37 days after receiving the first dose (when the vaccine is not yet effective). Similarly, we compared confirmed infection rates in adolescents aged 1215 years 1460 days after receiving a booster dose with an internal control group of adolescents 37 days after receiving the booster dose. We used Poisson regression, adjusting for age, sex, socioeconomic status, calendar week, and exposure. Findings: Between Dec 26, 2021, and Jan 8, 2022, we included 1 158 289 participants. In children aged 510 years, the adjusted rate of confirmed infection was 2·3 times (95% CI 2·02·5) lower in children who received a second dose than in the internal control group. The adjusted infection rate in children who received a second dose was 102 infections per 100 000 risk-days (94110) compared with 231 infections per 100 000 risk-days (215248) in the corresponding internal control cohort. In adolescents aged 1215 years, the booster dose decreased confirmed infection rates by 3·3 times (2·84·0) compared with in the internal control group. The adjusted infection rate of the booster cohort was 70 per 100 000 risk-days (6081) compared with 232 per 100 000 risk-days (212254) in the internal control cohort. Interpretation: A recent two-dose vaccination regimen with BNT162b2 and a recent booster dose in adolescents substantially reduced the rate of confirmed infection compared with the internal control groups. Future studies are needed to assess the duration of this protection and protection against other outcomes such as paediatric inflammatory multisystem syndrome temporally associated with SARS-CoV-2 and long-COVID. Funding: None.

Israel began administering a BNT162b2 booster dose to restore protection following the waning of the 2-dose vaccine. Biological studies have shown that a "fresh" booster dose leads to increased antibody levels compared to a fresh 2-dose vaccine, which may suggest increased effectiveness. To compare the real-world effectiveness of a fresh (up to 60 days) booster dose with that of a fresh 2-dose vaccine, we took advantage of a quasi-experimental study that compares populations that were eligible to receive the vaccine at different times due to age-dependent policies. Specifically, we compared the confirmed infection rates in adolescents aged 12-14 (215,653 individuals) who received the 2-dose vaccine and in adolescents aged 16-18 (103,454 individuals) who received the booster dose. Our analysis shows that the confirmed infection rate was lower by a factor of 3.7 (95% CI: 2.7 to 5.2) in the booster group.

The Human Impacts Database (www.anthroponumbers.org) is a curated, searchable resource housing quantitative data relating to the diverse anthropogenic impacts on our planet, with topics ranging from sea-level rise to livestock populations, greenhouse gas emissions, fertilizer use, and beyond. Each entry in the database reports a quantitative value (or a time series of values) along with clear referencing of the primary source, the method of measurement or estimation, an assessment of uncertainty, and links to the underlying data, as well as a permanent identifier called a Human Impacts ID (HuID). While there are other databases that house some of these values, they are typically focused on a single topic area, like energy usage or greenhouse gas emissions. The Human Impacts Database facilitates access to carefully curated data, acting as a quantitative resource pertaining to the myriad ways in which humans have an impact on the Earth, for practicing scientists, the general public, and those involved in education for sustainable development alike. We outline the structure of the database, describe our curation procedures, and use this database to generate a graphical summary of the current state of human impacts on the Earth, illustrating both their numerical values and their intimate interconnections.

Quantifying the temporal dynamics of infectiousness of individuals infected with SARS-CoV-2 is crucial for understanding the spread of COVID-19 and for evaluating the effectiveness of mitigation strategies. Many studies have estimated the infectiousness profile using observed serial intervals. However, statistical and epidemiological biases could lead to underestimation of the duration of infectiousness. We correct for these biases by curating data from the initial outbreak of the pandemic in China (when mitigation was minimal), and find that the infectiousness profile of the original strain is longer than previously thought. Sensitivity analysis shows our results are robust to model structure, assumed growth rate and potential observational biases. Although unmitigated transmission data is lacking for variants of concern (VOCs), previous analyses suggest that the alpha and delta variants have faster within-host kinetics, which we extrapolate to crude estimates of variant-specific unmitigated generation intervals. Knowing the unmitigated infectiousness profile of infected individuals can inform estimates of the effectiveness of isolation and quarantine measures. The framework presented here can help design better quarantine policies in early stages of future epidemics.

The extent to which Omicron infection¹⁹, with or without previous vaccination, elicits protection against the previously dominant Delta (B.1.617.2) variant is unclear. Here we measured the neutralization capacity against variants of severe acute respiratory syndrome coronavirus 2 in 39 individuals in South Africa infected with the Omicron sublineage BA.1 starting at a median of 6 (interquartile range 39) days post symptom onset and continuing until last follow-up sample available, a median of 23 (interquartile range 1927) days post symptoms to allow BA.1-elicited neutralizing immunity time to develop. Fifteen participants were vaccinated with Pfizer's BNT162b2 or Johnson & Johnson's Ad26.CoV2.S and had BA.1 breakthrough infections, and 24 were unvaccinated. BA.1 neutralization increased from a geometric mean 50% focus reduction neutralization test titre of 42 at enrolment to 575 at the last follow-up time point (13.6-fold) in vaccinated participants and from 46 to 272 (6.0-fold) in unvaccinated participants. Delta virus neutralization also increased, from 192 to 1,091 (5.7-fold) in vaccinated participants and from 28 to 91 (3.0-fold) in unvaccinated participants. At the last time point, unvaccinated individuals infected with BA.1 had low absolute levels of neutralization for the non-BA.1 viruses and 2.2-fold lower BA.1 neutralization, 12.0-fold lower Delta neutralization, 9.6-fold lower Beta variant neutralization, 17.9-fold lower ancestral virus neutralization and 4.8-fold lower Omicron sublineage BA.2 neutralization relative to vaccinated individuals infected with BA.1. These results indicate that hybrid immunity formed by vaccination and Omicron BA.1 infection should be protective against Delta and other variants. By contrast, infection with Omicron BA.1 alone offers limited cross-protection despite moderate enhancement.

BACKGROUND Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) provides natural immunity against reinfection. Recent studies have shown waning of the immunity provided by the BNT162b2 vaccine. The time course of natural and hybrid immunity is unknown. METHODS Using the Israeli Ministry of Health database, we extracted data for August and September 2021, when the B.1.617.2 (delta) variant was predominant, on all persons who had been previously infected with SARS-CoV-2 or who had received coronavirus 2019 vaccine. We used Poisson regression with adjustment for confounding factors to compare the rates of infection as a function of time since the last immunity-conferring event. RESULTS The number of cases of SARS-CoV-2 infection per 100,000 person-days at risk (adjusted rate) increased with the time that had elapsed since vaccination with BNT162b2 or since previous infection. Among unvaccinated persons who had recovered from infection, this rate increased from 10.5 among those who had been infected 4 to less than 6 months previously to 30.2 among those who had been infected 1 year or more previously. Among persons who had received a single dose of vaccine after previous infection, the adjusted rate was low (3.7) among those who had been vaccinated less than 2 months previously but increased to 11.6 among those who had been vaccinated at least 6 months previously. Among previously uninfected persons who had received two doses of vaccine, the adjusted rate increased from 21.1 among those who had been vaccinated less than 2 months previously to 88.9 among those who had been vaccinated at least 6 months previously. CONCLUSIONS Among persons who had been previously infected with SARS-CoV-2 (regardless of whether they had received any dose of vaccine or whether they had received one dose before or after infection), protection against reinfection decreased as the time increased since the last immunity-conferring event; however, this protection was higher than that conferred after the same time had elapsed since receipt of a second dose of vaccine among previously uninfected persons. A single dose of vaccine after infection reinforced protection against reinfection.

The spread of the omicron variant produced an increase in Covid-19 in Israel in late 2021, and a second boost of BNT162b2 vaccine was authorized in early January 2022. This article reports the efficacy of the fourth dose among Israeli citizens 60 years of age or older. Rates of severe illness were reduced by a factor of 3.5 in the fourth week after the second boost.

The Omicron variant of SARS-CoV-2 has been reported to cause milder disease in adults but lead to increased hospital admissions in children. How can we compare disease severity in Omicron and Delta infections, and how should differences be interpreted?

eQuilibrator (equilibrator.weizmann.ac.il) is a database of biochemical equilibrium constants and Gibbs free energies, originally designed as a web-based interface. While the website now counts around 1,000 distinct monthly users, its design could not accommodate larger compound databases and it lacked a scalable Application Programming Interface (API) for integration into other tools developed by the systems biology community. Here, we report on the recent updates to the database as well as the addition of a new Python-based interface to eQuilibrator that adds many new features such as a 100-fold larger compound database, the ability to add novel compounds, improvements in speed and memory use, and correction for Mg2+ ion concentrations. Moreover, the new interface can compute the covariance matrix of the uncertainty between estimates, for which we show the advantages and describe the application in metabolic modelling. We foresee that these improvements will make thermodynamic modelling more accessible and facilitate the integration of eQuilibrator into other software platforms.

BACKGROUND In December 2020, Israel began a mass vaccination campaign against coronavirus disease 2019 (Covid-19) by administering the BNT162b2 vaccine, which led to a sharp curtailing of the outbreak. After a period with almost no cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, a resurgent Covid-19 outbreak began in mid-June 2021. Possible reasons for the resurgence were reduced vaccine effectiveness against the delta (B.1.617.2) variant and waning immunity. The extent of waning immunity of the vaccine against the delta variant in Israel is unclear. METHODS We used data on confirmed infection and severe disease collected from an Israeli national database for the period of July 11 to 31, 2021, for all Israeli residents who had been fully vaccinated before June 2021. We used a Poisson regression model to compare rates of confirmed SARS-CoV-2 infection and severe Covid-19 among persons vaccinated during different time periods, with stratification according to age group and with adjustment for possible confounding factors. RESULTS Among persons 60 years of age or older, the rate of infection in the July 1131 period was higher among persons who became fully vaccinated in January 2021 (when they were first eligible) than among those fully vaccinated 2 months later, in March (rate ratio, 1.6; 95% confidence interval [CI], 1.3 to 2.0). Among persons 40 to 59 years of age, the rate ratio for infection among those fully vaccinated in February (when they were first eligible), as compared with 2 months later, in April, was 1.7 (95% CI, 1.4 to 2.1). Among persons 16 to 39 years of age, the rate ratio for infection among those fully vaccinated in March (when they were first eligible), as compared with 2 months later, in May, was 1.6 (95% CI, 1.3 to 2.0). The rate ratio for severe disease among persons fully vaccinated in the month when they were first eligible, as compared with those fully vaccinated in March, was 1.8 (95% CI, 1.1 to 2.9) among persons 60 years of age or older and 2.2 (95% CI, 0.6 to 7.7) among those 40 to 59 years of age; owing to small numbers, the rate ratio could not be calculated among persons 16 to 39 years of age. CONCLUSIONS These findings indicate that immunity against the delta variant of SARS-CoV-2 waned in all age groups a few months after receipt of the second dose of vaccine.

BACKGROUND After promising initial results from the administration of a third (booster) dose of the BNT162b2 messenger RNA vaccine (PfizerBioNTech) to persons 60 years of age or older, the booster campaign in Israel was gradually expanded to persons in younger age groups who had received a second dose at least 5 months earlier. METHODS We extracted data for the period from July 30 to October 10, 2021, from the Israel Ministry of Health database regarding 4,696,865 persons 16 years of age or older who had received two doses of BNT162b2 at least 5 months earlier. In the primary analysis, we compared the rates of confirmed coronavirus disease 2019 (Covid-19), severe illness, and death among those who had received a booster dose at least 12 days earlier (booster group) with the rates among those who had not received a booster (nonbooster group). In a secondary analysis, we compared the rates in the booster group with the rates among those who had received a booster 3 to 7 days earlier (early postbooster group). We used Poisson regression models to estimate rate ratios after adjusting for possible confounding factors. RESULTS The rate of confirmed infection was lower in the booster group than in the nonbooster group by a factor of approximately 10 (range across five age groups, 9.0 to 17.2) and was lower in the booster group than in the early postbooster group by a factor of 4.9 to 10.8. The adjusted rate difference ranged from 57.0 to 89.5 infections per 100,000 person-days in the primary analysis and from 34.4 to 38.3 in the secondary analysis. The rates of severe illness in the primary and secondary analyses were lower in the booster group by a factor of 17.9 (95% confidence interval [CI], 15.1 to 21.2) and 6.5 (95% CI, 5.1 to 8.2), respectively, among those 60 years of age or older and by a factor of 21.7 (95% CI, 10.6 to 44.2) and 3.7 (95% CI, 1.3 to 10.2) among those 40 to 59 years of age. The adjusted rate difference in the primary and secondary analyses was 5.4 and 1.9 cases of severe illness per 100,000 person-days among those 60 years of age or older and 0.6 and 0.1 among those 40 to 59 years of age. Among those 60 years of age or older, mortality was lower by a factor of 14.7 (95% CI, 10.0 to 21.4) in the primary analysis and 4.9 (95% CI, 3.1 to 7.9) in the secondary analysis. The adjusted rate difference in the primary and secondary analyses was 2.1 and 0.8 deaths per 100,000 person-days. CONCLUSIONS Across the age groups studied, rates of confirmed Covid-19 and severe illness were substantially lower among participants who received a booster dose of the BNT162b2 vaccine than among those who did not.

BACKGROUND On July 30, 2021, the administration of a third (booster) dose of the BNT162b2 messenger RNA vaccine (Pfizer-BioNTech) was approved in Israel for persons who were 60 years of age or older and who had received a second dose of vaccine at least 5 months earlier. Data are needed regarding the effect of the booster dose on the rate of confirmed coronavirus 2019 disease (Covid-19) and the rate of severe illness. METHODS We extracted data for the period from July 30 through August 31, 2021, from the Israeli Ministry of Health database regarding 1,137,804 persons who were 60 years of age or older and had been fully vaccinated (i.e., had received two doses of BNT162b2) at least 5 months earlier. In the primary analysis, we compared the rate of confirmed Covid-19 and the rate of severe illness between those who had received a booster injection at least 12 days earlier (booster group) and those who had not received a booster injection (nonbooster group). In a secondary analysis, we evaluated the rate of infection 4 to 6 days after the booster dose as compared with the rate at least 12 days after the booster. In all the analyses, we used Poisson regression after adjusting for possible confounding factors. RESULTS At least 12 days after the booster dose, the rate of confirmed infection was lower in the booster group than in the nonbooster group by a factor of 11.3 (95% confidence interval [CI], 10.4 to 12.3); the rate of severe illness was lower by a factor of 19.5 (95% CI, 12.9 to 29.5). In a secondary analysis, the rate of confirmed infection at least 12 days after vaccination was lower than the rate after 4 to 6 days by a factor of 5.4 (95% CI, 4.8 to 6.1). CONCLUSIONS In this study involving participants who were 60 years of age or older and had received two doses of the BNT162b2 vaccine at least 5 months earlier, we found that the rates of confirmed Covid-19 and severe illness were substantially lower among those who received a booster (third) dose of the BNT162b2 vaccine.

Cet ouvrage est destiné aux étudiants de licence en sciences de la vie, et constitue un support pédagogique pour les enseignants

Population growth and changes in dietary patterns place an evergrowing pressure on the environment. Feeding the world within sustainable boundaries therefore requires revolutionizing the way we harness natural resources. Microbial biomass can be cultivated to yield protein-rich feed and food supplements, collectively termed single-cell protein (SCP). Yet, we still lack a quantitative comparison between traditional agriculture and photovoltaic-driven SCP systems in terms of land use and energetic efficiency. Here, we analyze the energetic efficiency of harnessing solar energy to produce SCP from air and water. Ourmodel includes photovoltaic electricity generation, direct air capture of carbon dioxide, electrosynthesis of an electron donor and/or carbon source for microbial growth (hydrogen, formate, or methanol), microbial cultivation, and the processing of biomass and proteins. We show that, per unit of land, SCP production can reach an over 10-fold higher protein yield and at least twice the caloric yield compared with any staple crop. Altogether, this quantitative analysis offers an assessment of the future potential of photovoltaic-driven microbial foods to supplement conventional agricultural production and support resource-efficient protein supply on a global scale.

Quantitatively describing the time course of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection within an infected individual is important for understanding the current global pandemic and possible ways to combat it. Here we integrate the best current knowledge about the typical viral load of SARS-CoV-2 in bodily fluids and host tissues to estimate the total number and mass of SARS-CoV-2 virions in an infected person. We estimate that each infected person carries 10⁹ to 10¹¹ virions during peak infection, with a total mass in the range of 1 μg to 100 μg, which curiously implies that all SARS-CoV-2 virions currently circulating within human hosts have a collective mass of only 0.1 kg to 10 kg. We combine our estimates with the available literature on host immune response and viral mutation rates to demonstrate how antibodies markedly outnumber the spike proteins, and the genetic diversity of virions in an infected host covers all possible single nucleotide substitutions.

Background: Cervical discopathy and demyelinating lesions often co-exist in patients with multiple sclerosis (MS). Our study examines the possible association between these two pathologies. Methods: Medical records and cervical magnetic resonance imaging scans of MS patients with cervical discopathy who were seen at our MS clinic during 2018 were retrospectively reviewed. The severity of the disc disease was classified as grade I (no compression), grade II (compression of the dural sac) and grade III (cord compression). The spinal cord in each scan was divided into six segments corresponding to the intervertebral space of the spine (C1C6). Each segment was defined as containing demyelinating lesion and disc pathology (group 1), demyelinating lesion without disc pathology (group 2), disc pathology without demyelinating lesion (group 3) and no demyelinating lesion or disc pathology (group 4). Fishers exact test was used to test the association between demyelinating lesions and disc pathology. Results: Thirty-four MS patients with cervical discopathy were included in the study (26 females; average age 42.9 ± 13.7 years; average disease duration 8.4 ± 5.4 years). A total of 204 spinal cord segments were evaluated. Twenty-four segments were classified as group 1, 27 segments as group 2, 52 segments as group 3 and 101 segments as group 4. There was no association between demyelinating lesions and the grade of disc disease (p = 0.1 for grade I, p = 0.3 for grade II and p = 1 for grade III disc disease). Conclusion: Our study did not find any association between cervical disc disease and demyelinating spinal cord lesion.

Phosphorelays are signal transduction circuits that sense environmental changes and adjust cellular metabolism. Five different circuit architectures account for 99% of all phosphorelay operons annotated in over 9,000 fully sequenced genomes. Here we asked what biological design principles, if any, could explain selection among those architectures in nature. We began by studying kinetically well characterized phosphorelays (Spo0 of Bacillus subtilis and Sln1 of Saccharomyces cerevisiae). We find that natural circuit architecture maximizes information transmission in both cases. We use mathematical models to compare information transmission among the architectures for a realistic range of concentration and parameter values. Mapping experimentally determined phosphorelay protein concentrations onto that range reveals that the native architecture maximizes information transmission in sixteen out of seventeen analyzed phosphorelays. These results suggest that maximization of information transmission is important in the selection of native phosphorelay architectures, parameter values and protein concentrations.

Secondary progressive multiple sclerosis (SPMS) is a debilitating condition characterized by gradual worsening after an initial relapsing disease course. Despite the recent advances in our understanding of the disease, the diagnosis and treatment of SPMS continue to be challenging in routine clinical practice. The aim of this review article is to present the views of leading MS experts on the challenges in the diagnosis and management of SPMS and clinicians perspectives in Central and Eastern Europe. This article also provides recommendations of MS experts to improve the situation with diagnosis and management of SPMS. Many countries within Central and Eastern Europe have high prevalence of MS (>100 per 100,000 population). Consistent with the global trend, in the absence of reliable tests or biomarkers, SPMS at early stage remains undiagnosed. Due to diagnostic uncertainty and lack of a universally accepted disease definition, clinicians rely more on retrospective analysis of the clinical symptoms to confirm the diagnosis. With the lack of awareness and poor understanding of the timing of the onset of SPMS, clinicians may tend to direct attention to relapses than the symptoms of progression, which leads to underestimation of SPMS. Although several predictors of progression to SPMS have been identified, their predictive value is highly variable. Therefore, defining the transitioning period as a separate stage of MS is essential. According to experts opinion, frequent follow-up of patients and periodic assessment of progression are recommended for the timely identification of patients transitioning from RRMS to SPMS. MSProDiscuss Tool is an example of a quick assessment tool for identifying patients progressing from RRMS to SPMS. MS progression is usually assessed by changes in Expanded Disability Status Scale (EDSS) scores. As EDSS scores tend to fluctuate when measured in the short term (36 months), a longer period (≥12 months) may be needed to confirm the progression. Assessment of cognitive function is also important for evaluating secondary progression. Compartmentalization of inflammation within the central nervous system is an important reason behind the limited success of disease-modifying therapies (DMTs) for treating SPMS. Most of the DMTs fail to cross the blood-brain barrier; only 38% of the tested DMTs achieved their primary endpoint in SPMS. In Europe, siponimod is the first oral treatment for adults with active SPMS. Particularly, in Central and Eastern Europe, patients with SPMS are still being prescribed less efficacious DMTs and interferons. The absence of alternative treatments in SPMS supports the use of new products (siponimod and others); however the decision to initiate siponimod therapy in more severe patients (EDSS score of 7 or higher) should be individualized in consultation with the payers. The focus should be on early treatment initiation to delay disease progression.

We integrated ubiquity, mass and lifespan of all major cell types to achieve a comprehensive quantitative description of cellular turnover. We found a total cellular mass turnover of 80 ± 20 grams per day, dominated by blood cells and gut epithelial cells. In terms of cell numbers, close to 90% of the (0.33 ± 0.02) × 10¹² cells per day turnover was blood cells.

Humanity has become a dominant force in shaping the face of Earth(1-9). An emerging question is how the overall material output of human activities compares to the overall natural biomass. Here we quantify the human-made mass, referred to as 'anthropogenic mass', and compare it to the overall living biomass on Earth, which currently equals approximately 1.1 teratonnes(10,11). We find that Earth is exactly at the crossover point; in the year 2020 (+/- 6), the anthropogenic mass, which has recently doubled roughly every 20 years, will surpass all global living biomass. On average, for each person on the globe, anthropogenic mass equal to more than his or her bodyweight is produced every week. This quantification of the human enterprise gives a mass-based quantitative and symbolic characterization of the human-induced epoch of the Anthropocene.

Summary Humanity is facing two major challenges the need to feed a growing population with limited land and freshwater resources and global warming, caused by anthropogenic greenhouse gas emissions. The capture of CO2 from the atmosphere and its subsequent utilization lies at the heart of these challenges. Biological systems for CO2 conversion to organic molecules present a promising avenue due to their high product specificity and modularity. The possibility of combining renewable-energy-harvesting systems along with synthetic-CO2-using microorganisms is especially promising. In this article, we discuss recent major advances in engineering microbes to use CO2 and other one-carbon molecules as the feedstock. We portray the gap in cost that integrated abiotic-biotic systems for CO2 conversion should close to become cost competitive by using the techno-economic data of algae as an existing reference solution.

Many photosynthetic organisms employ a CO2 concentrating mechanism (CCM) to increase the rate of CO2 fixation via the Calvin cycle. CCMs catalyze approximate to 50% of global photosynthesis, yet it remains unclear which genes and proteins are required to produce this complex adaptation. We describe the construction of a functional CCM in a non-native host, achieved by expressing genes from an autotrophic bacterium in an Escherichia coli strain engineered to depend on rubisco carboxylation for growth. Expression of 20 CCM genes enabled E. coli to grow by fixing CO2 from ambient air into biomass, with growth in ambient air depending on the components of the CCM. Bacterial CCMs are therefore genetically compact and readily transplanted, rationalizing their presence in diverse bacteria. Reconstitution enabled genetic experiments refining our understanding of the CCM, thereby laying the groundwork for deeper study and engineering of the cell biology supporting CO2 assimilation in diverse organisms.

CO 2 is converted into biomass almost solely by the enzyme rubisco. The poor carboxylation properties of plant rubiscos have led to efforts that made it the most kinetically characterized enzyme, yet these studies focused on < 5% of its natural diversity. Here, we searched for fastcarboxylating variants by systematically mining genomic and metagenomic data. Approximately 33,000 unique rubisco sequences were identified and clustered into ≈ 1,000 similarity groups. We then synthesized, purified, and biochemically tested the carboxylation rates of 143 representatives, spanning all clusters of formII and formII /III rubiscos. Most variants (> 100) were active in vitro , with the fastest having a turnover number of 22 ± 1 s−1sixfold faster than the median plant rubisco and nearly twofold faster than the fastest measured rubisco to date. Unlike rubiscos from plants and cyanobacteria, the fastest variants discovered here are homodimers and exhibit a much simpler folding and activation kinetics. Our pipeline can be utilized to explore the kinetic space of other enzymes of interest, allowing us to get a better view of the biosynthetic potential of the biosphere.

The current SARS-CoV-2 pandemic is a harsh reminder of the fact that, whether in a single human host or a wave of infection across continents, viral dynamics is often a story about the numbers. In this snapshot, our aim is to provide a one-stop, curated graphical source for the key numbers that help us understand the virus driving our current global crisis. The discussion is framed around two broad themes: 1) the biology of the virus itself and 2) the characteristics of the infection of a single human host. Our one-page summary provides the key numbers pertaining to SARS-CoV-2, based mostly on peer-reviewed literature. The numbers reported in summary format are substantiated by the annotated references below. Readers are urged to remember that much uncertainty remains and knowledge of this pandemic and the virus driving it is rapidly evolving. In the paragraphs below we provide \u201cback of the envelope\u201d calculations that exemplify the insights that can be gained from knowing some key numbers and using quantitative logic. These calculations serve to improve our intuition through sanity checks, but do not replace detailed epidemiological analysis.

Identifying the molecular mechanisms that give rise to genetic variation is essential for the understanding of evolutionary processes. Previously, we have used adaptive laboratory evolution to enable biomass synthesis from CO2 in Escherichia coli. Genetic analysis of adapted clones from two independently evolving populations revealed distinct enrichment for insertion and deletion mutational events. Here, we follow these observations to show that mutations in the gene encoding for DNA topoisomerase I (topA) give rise to mutator phenotypes with characteristic mutational spectra. Using genetic assays and mutation accumulation lines, we find that point mutations in topA increase the rate of sequence deletion and duplication events. Interestingly, we observe that a single residue substitution (R168C) results in a high rate of head-to-tail (tandem) short sequence duplications, which are independent of existing sequence repeats. Finally, we show that the unique mutation spectrum of topA mutants enhances the emergence of antibiotic resistance in comparison to mismatch-repair (mutS) mutators, and leads to new resistance genotypes. Our findings highlight a potential link between the catalytic activity of topoisomerases and the fundamental question regarding the emergence of de novo tandem repeats, which are known modulators of bacterial evolution.

The long atmospheric residence time of CO2 creates an urgent need to add atmospheric carbon drawdown to CO2 regulatory strategies. Synthetic and systems biology (SSB), which enables manipulation of cellular phenotypes, offers a powerful approach to amplifying and adding new possibilities to current land management practices aimed at reducing atmospheric carbon. The participants (in attendance: Christina Agapakis, George Annas, Adam Arkin, George Church, Robert Cook-Deegan, Charles DeLisi, Dan Drell, Sheldon Glashow, Steve Hamburg, Henry Jacoby, Henry Kelly, Mark Kon, Todd Kuiken, Mary Lidstrom, Mike MacCracken, June Medford, Jerry Melillo, Ron Milo, Pilar Ossorio, Ari Patrinos, Keith Paustian, Kristala Jones Prather, Kent Redford, David Resnik, John Reilly, Richard J. Roberts, Daniel Segre, Susan Solomon, Elizabeth Strychalski, Chris Voigt, Dominic Woolf, Stan Wullschleger, and Xiaohan Yang) identified a range of possibilities by which SSB might help reduce greenhouse gas concentrations and which might also contribute to environmental sustainability and adaptation. These include, among other possibilities, engineering plants to convert CO2 produced by respiration into a stable carbonate, designing plants with an increased root-to-shoot ratio, and creating plants with the ability to self-fertilize. A number of serious ecological and societal challenges must, however, be confronted and resolved before any such application can be fully assessed, realized, and deployed.

Obtaining a quantitative global picture of life in the great expanses of the oceans is a challenging task. By integrating data from across existing literature, we provide a comprehensive view of the distribution of marine biomass between taxonomic groups, modes of life, and habitats.

The living world is largely divided into autotrophs that convert CO2 into biomass and heterotrophs that consume organic compounds. In spite of widespread interest in renewable energy storage and more sustainable food production, the engineering of industrially relevant heterotrophic model organisms to use CO2 as their sole carbon source has so far remained an outstanding challenge. Here, we report the achievement of this transformation on laboratory timescales. We constructed and evolved Escherichia coli to produce all its biomass carbon from CO2. Reducing power and energy, but not carbon, are supplied via the one-carbon molecule formate, which can be produced electrochemically. Rubisco and phosphoribulokinase were co-expressed with formate dehydrogenase to enable CO2 fixation and reduction via the Calvin-Benson-Bassham cycle. Autotrophic growth was achieved following several months of continuous laboratory evolution in a chemostat under intensifying organic carbon limitation and confirmed via isotopic labeling.

Rubisco is the primary carboxylase of the Calvin cycle, the most abundant enzyme in the biosphere, and one of the best-characterized enzymes. On the basis of correlations between Rubisco kinetic parameters, it is widely posited that constraints embedded in the catalytic mechanism enforce trade-offs between CO2 specificity, S-C/O, and maximum carboxylation rate, k(cat,C). However, the reasoning that established this view was based on data from approximate to 20 organisms. Here, we re-examine models of trade-offs in Rubisco catalysis using a data set from approximate to 300 organisms. Correlations between kinetic parameters are substantially attenuated in this larger data set, with the inverse relationship between k(cat,C) and S-C/O being a key example. Nonetheless, measured kinetic parameters display extremely limited variation, consistent with a view of Rubisco as a highly constrained enzyme. More than 95% of k(cat,C) values are between 1 and 10 s(-1), and no measured k(cat,C) exceeds 15 s(-1). Similarly, S-C/O varies by only 30% among Form I Rubiscos and

Biofilms are a fundamental form of microbial life and occur in diverse environments, ranging from the mammalian gut to deep subsurface rocks. It is often claimed that most bacteria and archaea live in biofilms, but this claim awaits quantification. Recent updates on global microbial cell numbers prompt a revisiting of this question.

Photosynthetic carbon assimilation enables energy storage in the living world and produces most of the biomass in the biosphere. Rubisco (D-ribulose 1,5-bisphosphate carboxylase/oxygenase) is responsible for the vast majority of global carbon fixation and has been claimed to be the most abundant protein on Earth. Here we provide an updated and rigorous estimate for the total mass of Rubisco on Earth, concluding it is approximate to 0.7 Gt, more than an order of magnitude higher than previously thought. We find that > 90% of Rubisco enzymes are found in the approximate to 2 x 10(14) m(2) of leaves of terrestrial plants, and that Rubisco accounts for approximate to 3% of the total mass of leaves, which we estimate at approximate to 30 Gt dry weight. We use our estimate for the total mass of Rubisco to derive the effective time-averaged catalytic rate of Rubisco of approximate to 0.03 s(-1) on land and approximate to 0.6 s(-1) in the ocean. Compared with the maximal catalytic rate observed in vitro at 25 degrees C, the effective rate in the wild is approximate to 100-fold slower on land and sevenfold slower in the ocean. The lower ambient temperature, and Rubisco not working at night, can explain most of the difference from laboratory conditions in the ocean but not on land, where quantification of many more factors on a global scale is needed. Our analysis helps sharpen the dramatic difference between laboratory and wild environments and between the terrestrial and marine environments.

While protein tags are ubiquitously utilized in molecular biology, they harbor the potential to interfere with functional traits of their fusion counterparts. Systematic evaluation of the effect of protein tags on function would promote accurate use of tags in experimental setups. Here we examine the effect of green fluorescent protein tagging at either the N or C terminus of budding yeast proteins on subcellular localization and functionality. We use a competition-based approach to decipher the relative fitness of two strains tagged on the same protein but on opposite termini and from that infer the correct, physiological localization for each protein and the optimal position for tagging. Our study provides a first of a kind systematic assessment of the effect of tags on the functionality of proteins and provides a step toward broad investigation of protein fusion libraries.

Enzymes catalyze a vast range of reactions. Their catalytic performances, mechanisms, global folds, and active-site architectures are also highly diverse, suggesting that enzymes are shaped by an entire range of physiological demands and evolutionary constraints, as well as by chemical and physicochemical constraints. We have attempted to identify signatures of these shaping demands and constraints. To this end, we describe a bird's-eye view of the enzyme space from two angles: evolution and chemistry. We examine various chemical reaction parameters that may have shaped the catalytic performances and active-site architectures of enzymes. We test and weigh these considerations against physiological and evolutionary factors. Although the catalytic properties of the "average" enzyme correlate with cellular metabolic demands and enzyme expression levels, at the level of individual enzymes, a multitude of physiological demands and constraints, combined with the coincidental nature of evolutionary processes, result in a complex picture. Indeed, neither reaction type (a chemical constraint) nor evolutionary origin alone can explain enzyme rates. Nevertheless, chemical constraints are apparent in the convergence of active site architectures in independently evolved enzymes, although significant variations within an architecture are common.

A census of the biomass on Earth is key for understanding the structure and dynamics of the biosphere. However, a global, quantitative view of how the biomass of different taxa compare with one another is still lacking. Here, we assemble the overall biomass composition of the biosphere, establishing a census of the ≈550 gigatons of carbon (Gt C) of biomass distributed among all of the kingdoms of life. We find that the kingdoms of life concentrate at different locations on the planet; plants (≈450 Gt C, the dominant kingdom) are primarily terrestrial, whereas animals (≈2 Gt C) are mainly marine, and bacteria (≈70 Gt C) and archaea (≈7 Gt C) are predominantly located in deep subsurface environments. We show that terrestrial biomass is about two orders of magnitude higher than marine biomass and estimate a total of ≈6 Gt C of marine biota, doubling the previous estimated quantity. Our analysis reveals that the global marine biomass pyramid contains more consumers than producers, thus increasing the scope of previous observations on inverse food pyramids. Finally, we highlight that the mass of humans is an order of magnitude higher than that of all wild mammals combined and report the historical impact of humanity on the global biomass of prominent taxa, including mammals, fish, and plants.

Food loss is widely recognized as undermining food security and environmental sustainability. However, consumption of resource-intensive food items instead of more efficient, equally nutritious alternatives can also be considered as an effective food loss. Here we define and quantify these opportunity food losses as the food loss associated with consuming resource-intensive animal-based items instead of plant-based alternatives which are nutritionally comparable, e.g., in terms of protein content. We consider replacements that minimize cropland use for each of the main US animal-based food categories. We find that although the characteristic conventional retail-to-consumer food losses are approximate to 30% for plant and animal products, the opportunity food losses of beef, pork, dairy, poultry, and eggs are 96%, 90%, 75%, 50%, and 40%, respectively. This arises because plant-based replacement diets can produce 20-fold and twofold more nutritionally similar food per cropland than beef and eggs, the most and least resource-intensive animal categories, respectively. Although conventional and opportunity food losses are both targets for improvement, the high opportunity food losses highlight the large potential savings beyond conventionally defined food losses. Concurrently replacing all animal-based items in the US diet with plant-based alternatives will add enough food to feed, in full, 350 million additional people, well above the expected benefits of eliminating all supply chain food waste. These results highlight the importance of dietary shifts to improving food availability and security.

Food production dominates land, water and fertilizer use and is a greenhouse gas source. In the United States, beef production is the main agricultural resource user overall, as well as per kcal or g of protein. Here, we offer a possible, non-unique, definition of 'sustainable' beef as that subsisting exclusively on grass and by-products, and quantify its expected US production as a function of pastureland use. Assuming today's pastureland characteristics, all of the pastureland that US beef currently use can sustainably deliver ≈45% of current production. Rewilding this pastureland's less productive half (≈135 million ha) can still deliver ≈43% of current beef production. In all considered scenarios, the ≈32 million ha of high-quality cropland that beef currently use are reallocated for plant-based food production. These plant items deliver 2- to 20-fold more calories and protein than the replaced beef and increase the delivery of protective nutrients, but deliver no B₁₂. Increased deployment of rapid rotational grazing or grassland multi-purposing may increase beef production capacity.

Understanding the evolution of a new metabolic capability in full mechanistic detail is challenging, as causative mutations may be masked by non-essential "hitchhiking" mutations accumulated during the evolutionary trajectory. We have previously used adaptive laboratory evolution of a rationally engineered ancestor to generate an Escherichia coli strain able to utilize CO2 fixation for sugar synthesis. Here, we reveal the genetic basis underlying this metabolic transition. Five mutations are sufficient to enable robust growth when a non-native Calvin-Benson-Bassham cycle provides all the sugar-derived metabolic building blocks. These mutations are found either in enzymes that affect the efflux of intermediates from the autocatalytic CO2 fixation cycle toward biomass (prs, serA, and pgi), or in key regulators of carbon metabolism (crp and ppsR). Using suppressor analysis, we show that a decrease in catalytic capacity is a common feature of all mutations found in enzymes. These findings highlight the enzymatic constraints that are essential to the metabolic stability of autocatalytic cycles and are relevant to future efforts in constructing non-native carbon fixation pathways.

Carbon fixation is the gateway of inorganic carbon into the biosphere. Our ability to engineer carbon fixation pathways in living organisms is expected to play a crucial role in the quest towards agricultural and energetic sustainability. Recent successes to introduce non-native carbon fixation pathways into heterotrophic hosts offer novel platforms for manipulating these pathways in genetically malleable organisms. Here, we focus on past efforts and future directions for engineering the dominant carbon fixation pathway in the biosphere, the Calvin-Benson cycle, into the well-known model organism Escherichia coli. We describe how central carbon metabolism of this heterotrophic bacterium can be manipulated to allow directed evolution of carbon fixing enzymes. Finally, we highlight future directions towards synthetic autotrophy.

Enzyme kinetics are fundamental to an understanding of cellular metabolism and for crafting synthetic biology applications. For decades, enzyme characterization has been based on in vitro enzyme assays. However, kinetic parameters are only available for

Viruses are incapable of autonomous energy production. Although many experimental studies make it clear that viruses are parasitic entities that hijack the molecular resources of the host, a detailed estimate for the energetic cost of viral synthesis is largely lacking. To quantify the energetic cost of viruses to their hosts, we enumerated the costs associated with two very distinct but representative DNA and RNA viruses, namely, T4 and influenza. We found that, for these viruses, translation of viral proteins is the most energetically expensive process. Interestingly, the costs of building a T4 phage and a single influenza virus are nearly the same. Due to influenza's higher burst size, however, the overall cost of a T4 phage infection is only 2.3% of the cost of an influenza infection. The costs of these infections relative to their host's estimated energy budget during the infection reveal that a T4 infection consumes about a third of its host's energy budget, whereas an influenza infection consumes only ≈ 1%. Building on our estimates for T4, we show how the energetic costs of double-stranded DNA phages scale with the capsid size, revealing that the dominant cost of building a virus can switch from translation to genome replication above a critical size. Last, using our predictions for the energetic cost of viruses, we provide estimates for the strengths of selection and genetic drift acting on newly incorporated genetic elements in viral genomes, under conditions of energy limitation.

A set of chemical reactions that require a metabolite to synthesize more of that metabolite is an autocatalytic cycle. Here, we show that most of the reactions in the core of central carbon metabolism are part of compact autocatalytic cycles. Such metabolic designs must meet specific conditions to support stable fluxes, hence avoiding depletion of intermediate metabolites. As such, they are subjected to constraints that may seem counter-intuitive: the enzymes of branch reactions out of the cycle must be overexpressed and the affinity of these enzymes to their substrates must be relatively weak. We use recent quantitative proteomics and fluxomics measurements to show that the above conditions hold for functioning cycles in central carbon metabolism of E. coli. This work demonstrates that the topology of a metabolic network can shape kinetic parameters of enzymes and lead to seemingly wasteful enzyme usage.

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cells capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as k_cat and K_M constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 4.1 and 2.6, respectively, for the two kinds of data. This result from the cost-optimized metabolic state is significantly better than randomly sampled metabolite profiles, supporting the hypothesis that enzyme cost is important for the fitness of E. coli. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, and could be a valuable computational tool to assist metabolic engineering projects. Furthermore, it establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified.

Feeding a growing population while minimizing environmental degradation is a global challenge requiring thoroughly rethinking food production and consumption. Dietary choices control food availability and natural resource demands. In particular, reducing or avoiding consumption of low production efficiency animal-based products can spare resources that can then yield more food. In quantifying the potential food gains of specific dietary shifts, most earlier research focused on calories, with less attention to other important nutrients, notably protein. Moreover, despite the well-known environmental burdens of livestock, only a handful of national level feed-to-food conversion efficiency estimates of dairy, beef, poultry, pork, and eggs exist. Yet such high level estimates are essential for reducing diet related environmental impacts and identifying optimal food gain paths. Here we quantify caloric and protein conversion efficiencies for US livestock categories. We then use these efficiencies to calculate the food availability gains expected from replacing beef in the US diet with poultry, a more efficient meat, and a plant-based alternative. Averaged over all categories, caloric and protein efficiencies are 7%-8%. At 3% in both metrics, beef is by far the least efficient. We find that reallocating the agricultural land used for beef feed to poultry feed production can meet the caloric and protein demands of ≈120 and ≈140 million additional people consuming the mean American diet, respectively, roughly 40% of current US population.

Many carbon-fixing bacteria rely on a CO₂ concentrating mechanism (CCM) to elevate the CO₂ concentration around the carboxylating enzyme ribulose bisphosphate carboxylase/oxygenase (RuBisCO). The CCM is postulated to simultaneously enhance the rate of carboxylation and minimize oxygenation, a competitive reaction with O₂ also catalyzed by RuBisCO. To achieve this effect, the CCM combines two features: active transport of inorganic carbon into the cell and colocalization of carbonic anhydrase and RuBisCO inside proteinaceous microcompartments called carboxysomes. Understanding the significance of the various CCM components requires reconciling biochemical intuition with a quantitative description of the system. To this end, we have developed a mathematical model of the CCM to analyze its energetic costs and the inherent intertwining of physiology and pH. We find that intracellular pH greatly affects the cost of inorganic carbon accumulation. At low pH the inorganic carbon pool contains more of the highly cellpermeable H₂ CO₃ , necessitating a substantial expenditure of energy on transport to maintain internal inorganic carbon levels. An intracellular pH ≈8 reduces leakage, making the CCM significantly more energetically efficient. This pH prediction coincides well with our measurement of intracellular pH in a model cyanobacterium. We also demonstrate that CO₂ retention in the carboxysome is necessary, whereas selective uptake of 3- into the carboxysome would not appreciably enhance energetic efficiency. Altogether, integration of pH produces a model that is quantitatively consistent with cyanobacterial physiology, emphasizing that pH cannot be neglected when describing biological systems interacting with inorganic carbon pools.

Data of gene expression levels across individuals, cell types, and disease states is expanding, yet our understanding of how expression levels impact phenotype is limited. Here, we present a massively parallel system for assaying the effect of gene expression levels on fitness in Saccharomyces cerevisiae by systematically altering the expression level of 100 genes at 100 distinct levels spanning a 500-fold range at high resolution. We show that the relationship between expression levels and growth is gene and environment specific and provides information on the function, stoichiometry, and interactions of genes. Wild-type expression levels in some conditions are not optimal for growth, and genes whose fitness is greatly affected by small changes in expression level tend to exhibit lower cell-to-cell variability in expression. Our study addresses a fundamental gap in understanding the functional significance of gene expression regulation and offers a framework for evaluating the phenotypic effects of expression variation.

Livestock farming incurs large and varied environmental burdens, dominated by beef. Replacing beef with resource efficient alternatives is thus potentially beneficial, but may conflict with nutritional considerations. Here we show that protein-equivalent plant based alternatives to the beef portion of the mean American diet are readily devisible, and offer mostly improved nutritional profile considering the full lipid profile, key vitamins, minerals, and micronutrients. We then show that replacement diets require on average only 10% of land, 4% of greenhouse gas (GHG) emissions, and 6% of reactive nitrogen (Nr) compared to what the replaced beef diet requires. Applied to 320 million Americans, the beef-to-plant shift can save 91 million cropland acres (and 770 million rangeland acres), 278 million metric ton CO_2e, and 3.7 million metric ton Nr annually. These nationwide savings are 27%, 4%, and 32% of the respective national environmental burdens.

Reported values in the literature on the number of cells in the body differ by orders of magnitude and are very seldom supported by any measurements or calculations. Here, we integrate the most up-to-date information on the number of human and bacterial cells in the body. We estimate the total number of bacteria in the 70 kg "reference man" to be 3.8·10¹³. For human cells, we identify the dominant role of the hematopoietic lineage to the total count (≈90%) and revise past estimates to 3.0·10¹³ human cells. Our analysis also updates the widely-cited 10:1 ratio, showing that the number of bacteria in the body is actually of the same order as the number of human cells, and their total mass is about 0.2 kg.

Can a heterotrophic organism be evolved to synthesize biomass from CO₂ directly? So far, non-native carbon fixation in which biomass precursors are synthesized solely from CO₂ has remained an elusive grand challenge. Here, we demonstrate how a combination of rational metabolic rewiring, recombinant expression, and laboratory evolution has led to the biosynthesis of sugars and other major biomass constituents by a fully functional Calvin-Benson-Bassham (CBB) cycle in E. coli. In the evolved bacteria, carbon fixation is performed via a non-native CBB cycle, while reducing power and energy are obtained by oxidizing a supplied organic compound (e.g., pyruvate). Genome sequencing reveals that mutations in flux branchpoints, connecting the non-native CBB cycle to biosynthetic pathways, are essential for this phenotype. The successful evolution of a non-native carbon fixation pathway, though not yet resulting in net carbon gain, strikingly demonstrates the capacity for rapid trophic-mode evolution of metabolism applicable to biotechnology.

Pyruvate formate-lyase (PFL) is a ubiquitous enzyme that supports increased ATP yield during sugar fermentation. While the PFL reaction is known to be reversible in vitro, the ability of PFL to support microbial growth by condensing acetyl-CoA and formate in vivo has never been directly tested. Here, we employ Escherichia coli mutant strains that cannot assimilate acetate via the glyoxylate shunt and use carbon labeling experiments to unequivocally demonstrate PFL-dependent co-assimilation of acetate and formate. Moreover, PFL-dependent growth is faster than growth on acetate using the glyoxylate shunt. Hence, growth via the reverse activity of PFL could have substantial ecological and biotechnological significance.

Most proteins show changes in level across growth conditions. Many of these changes seem to be coordinated with the specific growth rate rather than the growth environment or the protein function. Although cellular growth rates, gene expression levels and gene regulation have been at the center of biological research for decades, there are only a few models giving a base line prediction of the dependence of the proteome fraction occupied by a gene with the specific growth rate. We present a simple model that predicts a widely coordinated increase in the fraction of many proteins out of the proteome, proportionally with the growth rate. The model reveals how passive redistribution of resources, due to active regulation of only a few proteins, can have proteome wide effects that are quantitatively predictable. Our model provides a potential explanation for why and how such a coordinated response of a large fraction of the proteome to the specific growth rate arises under different environmental conditions. The simplicity of our model can also be useful by serving as a baseline null hypothesis in the search for active regulation. We exemplify the usage of the model by analyzing the relationship between growth rate and proteome composition for the model microorganism E.coli as reflected in recent proteomics data sets spanning various growth conditions. We find that the fraction out of the proteome of a large number of proteins, and from different cellular processes, increases proportionally with the growth rate. Notably, ribosomal proteins, which have been previously reported to increase in fraction with growth rate, are only a small part of this group of proteins. We suggest that, although the fractions of many proteins change with the growth rate, such changes may be partially driven by a global effect, not necessarily requiring specific cellular control mechanisms.

Turnover numbers, also known as kcat values, are fundamental properties of enzymes. However, kcat data are scarce and measured in vitro, thus may not faithfully represent the in vivo situation. A basic question that awaits elucidation is: how representative are kcat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate kvivomax, the observed maximal catalytic rate of an enzyme inside cells. Comparison with kcat values from Escherichia coli, yields a correlation of r2= 0.62 in log scale (p < 10−10), with a root mean square difference of 0.54 (3.5-fold in linear scale), indicating that in vivo and in vitro maximal rates generally concur. By accounting for the degree of saturation of enzymes and the backward flux dictated by thermodynamics, we further refine the correspondence between kvivomax and kcat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a high-throughput method for extracting enzyme kinetic constants from omics data.

Knowing key timescales enables us to quickly gain intuition, perform sanity checks and serves as a sixth sense in understanding how cells grow and communicate. This SnapShot briefly communicates some of the insights we collected about rates and durations of these processes from thinking about cell biology by the numbers.

It is often presented as common knowledge that, in the human body, bacteria outnumber human cells by a ratio of at least 10:1. Revisiting the question, we find that the ratio is much closer to 1:1.

Genetically identical cells exposed to the same environment display variability in gene expression (noise), with important consequences for the fidelity of cellular regulation and biological function. Although population average gene expression is tightly coupled to growth rate, the effects of changes in environmental conditions on expression variability are not known. Here, we measure the single-cell expression distributions of approximately 900 Saccharomyces cerevisiæ promoters across four environmental conditions using flow cytometry, and find that gene expression noise is tightly coupled to the environment and is generally higher at lower growth rates. Nutrient-poor conditions, which support lower growth rates, display elevated levels of noise for most promoters, regardless of their specific expression values. We present a simple model of noise in expression that results from having an asynchronous population, with cells at different cell-cycle stages, and with different partitioning of the cells between the stages at different growth rates. This model predicts non-monotonic global changes in noise at different growth rates as well as overall higher variability in expression for cell-cycle-regulated genes in all conditions. The consistency between this model and our data, as well as with noise measurements of cells growing in a chemostat at well-defined growth rates, suggests that cell-cycle heterogeneity is a major contributor to gene expression noise. Finally, we identify gene and promoter features that play a role in gene expression noise across conditions. Our results show the existence of growth-related global changes in gene expression noise and suggest their potential phenotypic implications.

The pioneering model of Henri, Michaelis, and Menten was based on the fast equilibrium assumption: the substrate binds its enzyme reversibly, and substrate dissociation is much faster than product formation. Here, we examine this assumption from a somewhat different point of view, asking what fraction of enzymesubstrate complexes are futile, i.e., result in dissociation rather than product formation. In Knowles notion of a \u201cperfect\u201d enzyme, all encounters of the enzyme with its substrate result in conversion to product. Thus, the perfect enzymes catalytic efficiency, kcat/KM, is constrained by only the diffusion on-rate, and the fraction of futile encounters (defined as φ) approaches zero. The available data on >1000 different enzymes suggest that for ≥90% of enzymes φ > 0.99 and for the \u201caverage enzyme\u201d φ ≥ 0.9999; namely,

The high environmental costs of raising livestock are now widely appreciated, yet consumption of animal-based food items continues and is expanding throughout the world. Consumers' ability to distinguish among, and rank, various interchangeable animal-based items is crucial to reducing environmental costs of diets. However, the individual environmental burdens exerted by the five dominant livestock categories - beef, dairy, poultry, pork and eggs - are not fully known. Quantifying those burdens requires splitting livestock's relatively well-known total environmental costs (e.g. land and fertilizer use for feed production) into partial categorical costs. Because such partitioning quantifies the relative environmental desirability of various animal-based food items, it is essential for environmental impact minimization efforts to be made. Yet to date, no such partitioning method exists. The present paper presents such a partitioning method for feed production-related environmental burdens. This approach treated each of the main feed classes individually - concentrates (grain, soy, by-products; supporting production of all livestock), processed roughage (mostly hay and silage) and pasture - which is key given these classes' widely disparate environmental costs. It was found that for the current US food system and national diet, concentrates are partitioned as follows: beef 0·21±0·112, poultry 0·27±0·046, dairy 0·24±0·041, pork 0·23±0·093 and eggs 0·04±0·018. Pasture and processed roughage, consumed only by cattle, are 0·92±0·034 and 0·87±0·031 due to beef, with the remainder due to dairy. In a follow-up paper, the devised methodology will be employed to partition total land, irrigated water, greenhouse gases and reactive nitrogen burdens incurred by feed production among the five edible livestock categories.

Apart from addressing humanity's growing demand for fuels, pharmaceuticals, plastics and other value added chemicals, metabolic engineering of microbes can serve as a powerful tool to address questions concerning the characteristics of cellular metabolism. Along these lines, we developed an in vivo metabolic strategy that conclusively identifies the product specificity of glycerate kinase. By deleting E. coli's phosphoglycerate mutases, we divide its central metabolism into an 'upper' and 'lower' metabolism, each requiring its own carbon source for the bacterium to grow. Glycerate can serve to replace the upper or lower carbon source depending on the product of glycerate kinase. Using this strategy we show that while glycerate kinase from Arabidopsis thaliana produces 3-phosphoglycerate, both E. coli' s enzymes generate 2-phosphoglycerate. This strategy represents a general approach to decipher enzyme specificity under physiological conditions.

The microscopic world of a cell can be as alien to our human-centered intuition as the confinement of quarks within protons or the event horizon of a black hole. We are prone to thinking by analogy - Golgi cisternae stack like pancakes, red blood cells look like donuts - but very little in our human experience is truly comparable to the immensely crowded, membrane-subdivided interior of a eukaryotic cell or the intricately layered structures of a mammalian tissue.

Livestock production impacts air and water quality, ocean health, and greenhouse gas (GHG) emissions on regional to global scales and it is the largest use of land globally. Quantifying the environmental impacts of the various livestock categories, mostly arising from feed production, is thus a grand challenge of sustainability science. Here, we quantify land, irrigation water, and reactive nitrogen (Nr) impacts due to feed production, and recast published full life cycle GHG emission estimates, for each of the major animal-based categories in the US diet. Our calculations reveal that the environmental costs per consumed calorie of dairy, poultry, pork, and eggs are mutually comparable (to within a factor of 2), but strikingly lower than the impacts of beef. Beef production requires 28, 11, 5, and 6 times more land, irrigation water, GHG, and Nr, respectively, than the average of the other livestock categories. Preliminary analysis of three staple plant foods shows two- to sixfold lower land, GHG, and Nr requirements than those of the nonbeef animal-derived calories, whereas irrigation requirements are comparable. Our analysis is based on the best data currently available, but follow-up studies are necessary to improve parameter estimates and fill remaining knowledge gaps. Data imperfections notwithstanding, the key conclusion - that beef production demands about 1 order of magnitude more resources than alternative livestock categories - is robust under existing uncertainties. The study thus elucidates the multiple environmental benefits of potential, easy-toimplement dietary changes, and highlights the uniquely high resource demands of beef.

Proteomics techniques generate an avalanche of data and promise to satisfy biologists' long-held desire to measure absolute protein abundances on a genome-wide scale. However, can this knowledge be translated into a clearer picture of how cells invest their protein resources? This article aims to give a broad perspective on the composition of proteomes as gleaned from recent quantitative proteomics studies. We describe proteomaps, an approach for visualizing the composition of proteomes with a focus on protein abundances and functions. In proteomaps, each protein is shown as a polygon-shaped tile, with an area representing protein abundance. Functionally related proteins appear in adjacent regions. General trends in proteomes, such as the dominance of metabolism and protein production, become easily visible. We make interactive visualizations of published proteome datasets accessible at www.proteomaps.net. We suggest that evaluating the way protein resources are allocated by various organisms and cell types in different conditions will sharpen our understanding of how and why cells regulate the composition of their proteomes.

To understand gene function, genetic analysis uses large perturbations such as gene deletion, knockdown or over-expression. Large perturbations have drawbacks: they move the cell far from its normal working point, and can thus be masked by off-target effects or compensation by other genes. Here, we offer a complementary approach, called noise genetics. We use natural cell-cell variations in protein level and localization, and correlate them to the natural variations of the phenotype of the same cells. Observing these variations is made possible by recent advances in dynamic proteomics that allow measuring proteins over time in individual living cells. Using motility of human cancer cells as a model system, and time-lapse microscopy on 566 fluorescently tagged proteins, we found 74 candidate motility genes whose level or localization strongly correlate with motility in individual cells. We recovered 30 known motility genes, and validated several novel ones by mild knockdown experiments. Noise genetics can complement standard genetics for a variety of phenotypes.

In metabolism research, thermodynamics is usually used to determine the directionality of a reaction or the feasibility of a pathway. However, the relationship between thermodynamic potentials and fluxes is not limited to questions of directionality: thermodynamics also affects the kinetics of reactions through the flux-force relationship, which states that the logarithm of the ratio between the forward and reverse fluxes is directly proportional to the change in Gibbs energy due to a reaction (Δ_rG). Accordingly, if an enzyme catalyzes a reaction with a Δ_rG of -5.7 kJ/mol then the forward flux will be roughly ten times the reverse flux. As Δ_rG approaches equilibrium (Δ_rG = 0 kJ/mol), exponentially more enzyme counterproductively catalyzes the reverse reaction, reducing the net rate at which the reaction proceeds. Thus, the enzyme level required to achieve a given flux increases dramatically near equilibrium. Here, we develop a framework for quantifying the degree to which pathways suffer these thermodynamic limitations on flux. For each pathway, we calculate a single thermodynamically-derived metric (the Max-min Driving Force, MDF), which enables objective ranking of pathways by the degree to which their flux is constrained by low thermodynamic driving force. Our framework accounts for the effect of pH, ionic strength and metabolite concentration ranges and allows us to quantify how alterations to the pathway structure affect the pathway's thermodynamics. Applying this methodology to pathways of central metabolism sheds light on some of their features, including metabolic bypasses (e.g., fermentation pathways bypassing substrate-level phosphorylation), substrate channeling (e.g., of oxaloacetate from malate dehydrogenase to citrate synthase), and use of alternative cofactors (e.g., quinone as an electron acceptor instead of NAD). The methods presented here place another arrow in metabolic engineers' quiver, providing a simple means of evaluating the thermodynamic and kinetic quality of different pathway chemistries that produce the same molecules.

Novel methods such as mass-spectrometry enable a view of the proteomes of cells in unprecedented detail. Recently, these efforts have culminated in quantitative measurements of the number of copies per cell for most expressed proteins in organisms ranging from bacteria to mammalian cells. Here, we estimate the expected total number of proteins per unit of cell volume using known parameters related to the composition of cells such as the fraction of cell mass that is protein, and the average protein length. Using simple arguments, we estimate a range of 2-4 million proteins per cubic micron (i.e. 1fL) in bacteria, yeast, and mammalian cells. Interestingly, we find that measured values that are reported for fission yeast and mammalian cells are often about 3-10 times lower. We discuss this apparent discrepancy and how to use the estimate as benchmark to recalibrate proteome-wide quantitative censuses or to revisit assumptions about cell composition.

Most genes change expression levels across conditions, but it is unclear which of these changes represents specific regulation and what determines their quantitative degree. Here, we accurately measured activities of ∼900 S. cerevisiae and ∼1800 E. coli promoters using fluorescent reporters. We show that in both organisms 60-90% of promoters change their expression between conditions by a constant global scaling factor that depends only on the conditions and not on the promoter's identity. Quantifying such global effects allows precise characterization of specific regulation - promoters deviating from the global scale line. These are organized into few functionally related groups that also adhere to scale lines and preserve their relative activities across conditions. Thus, only several scaling factors suffice to accurately describe genome-wide expression profiles across conditions. We present a parameter-free passive resource allocation model that quantitatively accounts for the global scaling factors. It suggests that many changes in expression across conditions result from global effects and not specific regulation, and provides means for quantitative interpretation of expression profiles.

Steady-state metabolite concentrations in a microorganism typically span several orders of magnitude. The underlying principles governing these concentrations remain poorly understood. Here, we hypothesize that observed variation can be explained in terms of a compromise between factors that favor minimizing metabolite pool sizes (e.g. limited solvent capacity) and the need to effectively utilize existing enzymes. The latter requires adequate thermodynamic driving force in metabolic reactions so that forward flux substantially exceeds reverse flux. To test this hypothesis, we developed a method, metabolic tug-of-war (mTOW), which computes steady-state metabolite concentrations in microorganisms on a genome-scale. mTOW is shown to explain up to 55% of the observed variation in measured metabolite concentrations in E. coli and C. acetobutylicum across various growth media. Our approach, based strictly on first thermodynamic principles, is the first method that successfully predicts high-throughput metabolite concentration data in bacteria across conditions.

Michaelis and Menten's mechanism for enzymatic catalysis is remarkable both in its simplicity and its wide applicability. The extension for reversible processes, as done by Haldane, makes it even more relevant as most enzymes catalyze reactions that are reversible in nature and carry in vivo flux in both directions. Here, we decompose the reversible Michaelis-Menten equation into three terms, each with a clear physical meaning: catalytic capacity, substrate saturation and thermodynamic driving force. This decomposition facilitates a better understanding of enzyme kinetics and highlights the relationship between thermodynamics and kinetics, a relationship which is often neglected. We further demonstrate how our separable rate law can be understood from different points of view, shedding light on factors shaping enzyme catalysis.

Standard Gibbs energies of reactions are increasingly being used in metabolic modeling for applying thermodynamic constraints on reaction rates, metabolite concentrations and kinetic parameters. The increasing scope and diversity of metabolic models has led scientists to look for genome-scale solutions that can estimate the standard Gibbs energy of all the reactions in metabolism. Group contribution methods greatly increase coverage, albeit at the price of decreased precision. We present here a way to combine the estimations of group contribution with the more accurate reactant contributions by decomposing each reaction into two parts and applying one of the methods on each of them. This method gives priority to the reactant contributions over group contributions while guaranteeing that all estimations will be consistent, i.e. will not violate the first law of thermodynamics. We show that there is a significant increase in the accuracy of our estimations compared to standard group contribution. Specifically, our cross-validation results show an 80% reduction in the median absolute residual for reactions that can be derived by reactant contributions only. We provide the full framework and source code for deriving estimates of standard reaction Gibbs energy, as well as confidence intervals, and believe this will facilitate the wide use of thermodynamic data for a better understanding of metabolism.

Translational coupling is the interdependence of translation efficiency of neighboring genes encoded within an operon. The degree of coupling may be quantified by measuring how the translation rate of a gene is modulated by the translation rate of its upstream gene. Translational coupling was observed in prokaryotic operons several decades ago, but the quantitative range of modulation translational coupling leads to and the factors governing this modulation were only partially characterized. In this study, we systematically quantify and characterize translational coupling in E. coli synthetic operons using a library of plasmids carrying fluorescent reporter genes that are controlled by a set of different ribosome binding site (RBS) sequences. The downstream gene expression level is found to be enhanced by the upstream gene expression via translational coupling with the enhancement level varying from almost no coupling to over 10-fold depending on the upstream gene's sequence. Additionally, we find that the level of translational coupling in our system is similar between the second and third locations in the operon. The coupling depends on the distance between the stop codon of the upstream gene and the start codon of the downstream gene. This study is the first to systematically and quantitatively characterize translational coupling in a synthetic E. coli operon. Our analysis will be useful in accurate manipulation of gene expression in synthetic biology and serves as a step toward understanding the mechanisms involved in translational expression modulation.

Contrary to the textbook portrayal of glycolysis as a single pathway conserved across all domains of life, not all sugar-consuming organisms use the canonical Embden - Meyerhoff - Parnass (EMP) glycolytic pathway. Prokaryotic glucose metabolism is particularly diverse, including several alternative glycolytic pathways, the most common of which is the Entner-Doudoroff (ED) pathway. The prevalence of the ED pathway is puzzling as it produces only one ATP per glucose - half as much as the EMP pathway. We argue that the diversity of prokaryotic glucose metabolism may reflect a tradeoff between a pathway's energy (ATP) yield and the amount of enzymatic protein required to catalyze pathway flux. We introduce methods for analyzing pathways in terms of thermodynamics and kinetics and show that the ED pathway is expected to require several-fold less enzymatic protein to achieve the same glucose conversion rate as the EMP pathway. Through genomic analysis, we further show that prokaryotes use different glycolytic pathways depending on their energy supply. Specifically, energy-deprived anaerobes over-whelmingly rely upon the higher ATP yield of the EMP pathway, whereas the ED pathway is common among facultative anaerobes and even more common among aerobes. In addition to demonstrating how protein costs can explain the use of alternative metabolic strategies, this study illustrates a direct connection between an organism's environment and the thermodynamic and biochemical properties of the metabolic pathways it employs.

Protein levels are a dominant factor shaping natural and synthetic biological systems. Although proper functioning of metabolic pathways relies on precise control of enzyme levels, the experimental ability to balance the levels of many genes in parallel is a major outstanding challenge. Here, we introduce a rapid and modular method to span the expression space of several proteins in parallel. By combinatorially pairing genes with a compact set of ribosome-binding sites, we modulate protein abundance by several orders of magnitude. We demonstrate our strategy by using a synthetic operon containing fluorescent proteins to span a 3D color space. Using the same approach, we modulate a recombinant carotenoid biosynthesis pathway in Escherichia coli to reveal a diversity of phenotypes, each characterized by a distinct carotenoid accumulation profile. In a single combinatorial assembly, we achieve a yield of the industrially valuable compound astaxanthin 4-fold higher than previously reported. The methodology presented here provides an efficient tool for exploring a high-dimensional expression space to locate desirable phenotypes.

Sustainability indicators strive to convey the impacts of human activities on natural resource utilization, yet many fail to express these impacts in a simple relatable manner. We introduce a new sustainability indicator, EcoTime, which recasts an environmental burden of a process or item (e.g.; the emission of 10 kg CO ₂ associated with a car trip) in time units (seconds, days, etc.). The EcoTime units represent the burden's share of a benchmark quota calculated according to location or context. For example, a developed country's average yearly CO ₂ emissions of 11 ton per capita would translate to 365 EcoTime days in which case the 10 kg CO ₂ mentioned above would equal ≈8 EcoTime hours. Since time units are commonly used the EcoTime indicator is easy to communicate to a varying audience alleviating challenges often associated with existing sustainability indicators. It leverages our innate ability to easily grasp contrasting time units over several orders of magnitude, ranging from seconds to years. Another key advantage of EcoTime is that its value shifts attention from the absolute environmental impact, which may not be meaningful to most people, to impact magnitude relative to world resource availability or usage, thus giving the burden an intuitive, intrinsic context. In addition, EcoTimes of different impact types can be conveniently and succinctly grouped as a vector (e.g.; GHG emissions, water, or land footprints), or, because of the similar units, as a composite scalar. We provide several case study examples of the methodology.

Electrosynthesis is a promising approach that enables the biological production of commodities, like fuels and fine chemicals, using renewably produced electricity. Several techniques have been proposed to mediate the transfer of electrons fromthe cathode to living cells. Of these, the electroproduction of formate as amediator seems especially promising: formate is readily soluble, of lowtoxicity and can be produced at relatively high efficiency and at reasonable current density. While organisms that are capable of formatotrophic growth, i.e. growth on formate, exist naturally, they are generally less suitable for bulk cultivation and industrial needs.Hence, it may be helpful to engineer a model organismof industrial relevance, such as E. coli, for growth on formate. There are numerousmetabolic pathways that can potentially support formatotrophic growth. Here we analyze these diverse pathways according to various criteria including biomass yield, thermodynamic favorability, chemical motive force, kinetics and the practical challenges posed by their expression.We find that the reductive glycine pathway, composed of the tetrahydrofolate system, the glycine cleavage system, serine hydroxymethyltransferase and serine deaminase, is a promising candidate to support electrosynthesis in E. coli. The approach presented here exemplifies how combining different computational approaches into a systematic analysis methodology provides assistance in redesigning metabolism. This article is part of a Special Issue entitled: Metals in Bioenergetics and Biomimetics Systems.

Regulation of proteins across the cell cycle is a basic process in cell biology. It has been difficult to study this globally in human cells due to lack of methods to accurately follow protein levels and localizations over time. Estimates based on global mRNA measurements suggest that only a few percent of human genes have cell-cycle dependent mRNA levels. Here, we used dynamic proteomics to study the cell-cycle dependence of proteins. We used 495 clones of a human cell line, each with a different protein tagged fluorescently at its endogenous locus. Protein level and localization was quantified in individual cells over 24h of growth using time-lapse microscopy. Instead of standard chemical or mechanical methods for cell synchronization, we employed in-silico synchronization to place protein levels and localization on a time axis between two cell divisions. This non-perturbative synchronization approach, together with the high accuracy of the measurements, allowed a sensitive assay of cell-cycle dependence. We further developed a computational approach that uses texture features to evaluate changes in protein localizations. We find that 40% of the proteins showed cell cycle dependence, of which 11% showed changes in protein level and 35% in localization. This suggests that a broader range of cell-cycle dependent proteins exists in human cells than was previously appreciated. Most of the cell-cycle dependent proteins exhibit changes in cellular localization. Such changes can be a useful tool in the regulation of the cell-cycle being fast and efficient.

Background: Constraint-based modeling is increasingly employed for metabolic network analysis. Its underlying assumption is that natural metabolic phenotypes can be predicted by adding physicochemical constraints to remove unrealistic metabolic flux solutions. The loopless-COBRA approach provides an additional constraint that eliminates thermodynamically infeasible internal cycles (or loops) from the space of solutions. This allows the prediction of flux solutions that are more consistent with experimental data. However, it is not clear if this approach over-constrains the models by removing non-loop solutions as well.Results: Here we apply Gordan's theorem from linear algebra to prove for the first time that the constraints added in loopless-COBRA do not over-constrain the problem beyond the elimination of the loops themselves.Conclusions: The loopless-COBRA constraints can be reliably applied. Furthermore, this proof may be adapted to evaluate the theoretical soundness for other methods in constraint-based modeling.

Thermodynamics impose a major constraint on the structure of metabolic pathways. Here, we use carbon fixation pathways to demonstrate how thermodynamics shape the structure of pathways and determine the cellular resources they consume. We analyze the energetic profile of prototypical reactions and show that each reaction type displays a characteristic change in Gibbs energy. Specifically, although carbon fixation pathways display a considerable structural variability, they are all energetically constrained by two types of reactions: carboxylation and carboxyl reduction. In fact, all adenosine triphosphate (ATP) molecules consumed by carbon fixation pathways - with a single exception - are used, directly or indirectly, to power one of these unfavorable reactions. When an indirect coupling is employed, the energy released by ATP hydrolysis is used to establish another chemical bond with high energy of hydrolysis, e.g. a thioester. This bond is cleaved by a downstream enzyme to energize an unfavorable reaction. Notably, many pathways exhibit reduced ATP requirement as they couple unfavorable carboxylation or carboxyl reduction reactions to exergonic reactions other than ATP hydrolysis. In the most extreme example, the reductive acetyl coenzyme A (acetyl-CoA) pathway bypasses almost all ATP-consuming reactions. On the other hand, the reductive pentose phosphate pathway appears to be the least ATP-efficient because it is the only carbon fixation pathway that invests ATP in metabolic aims other than carboxylation and carboxyl reduction. Altogether, our analysis indicates that basic thermodynamic considerations accurately predict the resource investment required to support a metabolic pathway and further identifies biochemical mechanisms that can decrease this requirement.

Motivation: The laws of thermodynamics describe a direct, quantitative relationship between metabolite concentrations and reaction directionality. Despite great efforts, thermodynamic data suffer from limited coverage, scattered accessibility and nonstandard annotations. We present a framework for unifying thermodynamic data from multiple sources and demonstrate two new techniques for extrapolating the Gibbs energies of unmeasured reactions and conditions. Results: Both methods account for changes in cellular conditions (pH, ionic strength, etc.) by using linear regression over the ΔG° of pseudoisomers and reactions. The Pseudoisomeric Reactant Contribution method systematically infers compound formation energies using measured K' and pK _a data. The Pseudoisomeric Group Contribution method extends the group contribution method and achieves a high coverage of unmeasured reactions. We define a continuous index that predicts the reversibility of a reaction under a given physiological concentration range. In the characteristic physiological range 3μM-3mM, we find that roughly half of the reactions in Escherichia coli's metabolism are reversible. These new tools can increase the accuracy of thermodynamic-based models, especially in non-standard pH and ionic strengths. The reversibility index can help modelers decide which reactions are reversible in physiological conditions.

Identifying the factors that determine microbial growth rate under various environmental and genetic conditions is a major challenge of systems biology. While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, including maximal biomass yield, the prediction of actual growth rate is a long standing goal. This gap stems from strictly relying on data regarding reaction stoichiometry and directionality, without accounting for enzyme kinetic considerations. Here we present a novel metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts metabolic flux rate and growth rate by utilizing prior data on enzyme turnover rates and enzyme molecular weights, without requiring measurements of nutrient uptake rates. The method is based on an identified design principle of metabolism in which enzymes catalyzing high flux reactions across different media tend to be more efficient in terms of having higher turnover numbers. Extending upon previous attempts to utilize kinetic data in genome-scale metabolic modeling, our approach takes into account the requirement for specific enzyme concentrations for catalyzing predicted metabolic flux rates, considering isozymes, protein complexes, and multi-functional enzymes. MOMENT is shown to significantly improve the prediction accuracy of various metabolic phenotypes in E. coli, including intracellular flux rates and changes in gene expression levels under different growth rates. Most importantly, MOMENT is shown to predict growth rates of E. coli under a diverse set of media that are correlated with experimental measurements, markedly improving upon existing state-of-the art stoichiometric modeling approaches. These results support the view that a physiological bound on cellular enzyme concentrations is a key factor that determines microbial growth rate.

Metabolic engineering of plants can reduce the cost and environmental impact of agriculture while providing for the needs of a growing population. Although our understanding of plant metabolism continues to increase at a rapid pace, relatively few plant metabolic engineering projects with commercial potential have emerged, in part because of a lack of principles for the rational manipulation of plant phenotype. One underexplored approach to identifying such design principles derives from analysis of the dominant constraints on plant fitness, and the evolutionary innovations in response to those constraints, that gave rise to the enormous diversity of natural plant metabolic pathways.

A key concept in economics and engineering is used to deduce which traits and which tasks that an organism performs are important for fitness.

Metabolic pathways may seem arbitrary and unnecessarily complex. In many cases, a chemist might devise a simpler route for the biochemical transformation, so why has nature chosen such complex solutions? In this review, we distill lessons from a century of metabolic research and introduce new observations suggesting that the intricate structure of metabolic pathways can be explained by a small set of biochemical principles. Using glycolysis as an example, we demonstrate how three key biochemical constraints-thermodynamic favorability, availability of enzymatic mechanisms and the physicochemical properties of pathway intermediates-eliminate otherwise plausible metabolic strategies. Considering these constraints, glycolysis contains no unnecessary steps and represents one of the very few pathway structures that meet cellular demands. The analysis presented here can be applied to metabolic engineering efforts for the rational design of pathways that produce a desired product while satisfying biochemical constraints.

While the reductive pentose phosphate cycle is responsible for the fixation of most of the carbon in the biosphere, it has several natural substitutes. In fact, due to the characterization of three new carbon fixation pathways in the last decade, the diversity of known metabolic solutions for autotrophic growth has doubled. In this review, the different pathways are analysed and compared according to various criteria, trying to connect each of the different metabolic alternatives to suitable environments or metabolic goals. The different roles of carbon fixation are discussed; in addition to sustaining autotrophic growth it can also be used for energy conservation and as an electron sink for the recycling of reduced electron carriers. Our main focus in this review is on thermodynamic and kinetic aspects, including thermodynamically challenging reactions, the ATP requirement of each pathway, energetic constraints on carbon fixation, and factors that are expected to limit the rate of the pathways. Finally, possible metabolic structures of yet unknown carbon fixation pathways are suggested and discussed.

The laws of thermodynamics constrain the action of biochemical systems. However, thermodynamic data on biochemical compounds can be difficult to find and is cumbersome to perform calculations with manually. Even simple thermodynamic questions like 'how much Gibbs energy is released by ATP hydrolysis at pH 5?' are complicated excessively by the search for accurate data. To address this problem, eQuilibrator couples a comprehensive and accurate database of thermodynamic properties of biochemical compounds and reactions with a simple and powerful online search and calculation interface. The web interface to eQuilibrator (http:// equilibrator.weizmann.ac.il) enables easy calculation of Gibbs energies of compounds and reactions given arbitrary pH, ionic strength and metabolite concentrations. The eQuilibrator code is open-source and all thermodynamic source data are freely downloadable in standard formats. Here we describe the database characteristics and implementation and demonstrate its use.

Background: C ₄ plants such as corn and sugarcane assimilate atmospheric CO ₂ into biomass by means of the C ₄ carbon fixation pathway. We asked how PEP formation rate, a key step in the carbon fixation pathway, might work at a precise rate, regulated by light, despite fluctuations in substrate and enzyme levels constituting and regulating this process.Results: We present a putative mechanism for robustness in C ₄ carbon fixation, involving a key enzyme in the pathway, pyruvate orthophosphate dikinase (PPDK), which is regulated by a bifunctional enzyme, Regulatory Protein (RP). The robust mechanism is based on avidity of the bifunctional enzyme RP to its multimeric substrate PPDK, and on a product-inhibition feedback loop that couples the system output to the activity of the bifunctional regulator. The model provides an explanation for several unusual biochemical characteristics of the system and predicts that the system's output, phosphoenolpyruvate (PEP) formation rate, is insensitive to fluctuations in enzyme levels (PPDK and RP), substrate levels (ATP and pyruvate) and the catalytic rate of PPDK, while remaining sensitive to the system's input (light levels).Conclusions: The presented PPDK mechanism is a new way to achieve robustness using product inhibition as a feedback loop on a bifunctional regulatory enzyme. This mechanism exhibits robustness to protein and metabolite levels as well as to catalytic rate changes. At the same time, the output of the system remains tuned to input levels.

What governs the concentrations of metabolites within living cells? Beyond specific metabolic and enzymatic considerations, are there global trends that affect their values? We hypothesize that the physico-chemical properties of metabolites considerably affect their in-vivo concentrations. The recently achieved experimental capability to measure the concentrations of many metabolites simultaneously has made the testing of this hypothesis possible. Here, we analyze such recently available data sets of metabolite concentrations within E. coli, S. cerevisiae, B. subtilis and human. Overall, these data sets encompass more than twenty conditions, each containing dozens (28-108) of simultaneously measured metabolites. We test for correlations with various physico-chemical properties and find that the number of charged atoms, non-polar surface area, lipophilicity and solubility consistently correlate with concentration. In most data sets, a change in one of these properties elicits a ~100 fold increase in metabolite concentrations. We find that the non-polar surface area and number of charged atoms account for almost half of the variation in concentrations in the most reliable and comprehensive data set. Analyzing specific groups of metabolites, such as amino-acids or phosphorylated nucleotides, reveals even a higher dependence of concentration on hydrophobicity. We suggest that these findings can be explained by evolutionary constraints imposed on metabolite concentrations and discuss possible selective pressures that can account for them. These include the reduction of solute leakage through the lipid membrane, avoidance of deleterious aggregates and reduction of non-specific hydrophobic binding. By highlighting the global constraints imposed on metabolic pathways, future research could shed light onto aspects of biochemical evolution and the chemical constraints that bound metabolic engineering efforts.

Latency and ongoing replication have both been proposed to explain the drug-insensitive human immunodeficiency virus (HIV) reservoir maintained during antiretroviral therapy. Here we explore a novel mechanism for ongoing HIV replication in the face of antiretroviral drugs. We propose a model whereby multiple infections per cell lead to reduced sensitivity to drugs without requiring drug-resistant mutations, and experimentally validate the model using multiple infections per cell by cell-free HIV in the presence of the drug tenofovir. We then examine the drug sensitivity of cell-to-cell spread of HIV, a mode of HIV transmission that can lead to multiple infection events per target cell. Infections originating from cell-free virus decrease strongly in the presence of antiretrovirals tenofovir and efavirenz whereas infections involving cell-to-cell spread are markedly less sensitive to the drugs. The reduction in sensitivity is sufficient to keep multiple rounds of infection from terminating in the presence of drugs. We examine replication from cell-to-cell spread in the presence of clinical drug concentrations using a stochastic infection model and find that replication is intermittent, without substantial accumulation of mutations. If cell-to-cell spread has the same properties in vivo, it may have adverse consequences for the immune system, lead to therapy failure in individuals with risk factors, and potentially contribute to viral persistence and hence be a barrier to curing HIV infection.

The kinetic parameters of enzymes are key to understanding the rate and specificity of most biological processes. Although specific trends are frequently studied for individual enzymes, global trends are rarely addressed. We performed an analysis of k_cat and K_M values of several thousand enzymes collected from the literature. We found that the "average enzyme" exhibits a k_cat of ̃10 s^-1 and a k _cat/ K_M of ̃105 s^-1 M^-1, much below the diffusion limit and the characteristic textbook portrayal of kinetically superior enzymes. Why do most enzymes exhibit moderate catalytic efficiencies? Maximal rates may not evolve in cases where weaker selection pressures are expected. We find, for example, that enzymes operating in secondary metabolism are, on average, ̃30-fold slower than those of central metabolism. We also find indications that the physicochemical properties of substrates affect the kinetic parameters. Specifically, low molecular mass and hydrophobicity appear to limit KM optimization. In accordance, substitution with phosphate, CoA, or other large modifiers considerably lowers the K_M values of enzymes utilizing the substituted substrates. It therefore appears that both evolutionary selection pressures and physicochemical constraints shape the kinetic parameters of enzymes. It also seems likely that the catalytic efficiency of some enzymes toward their natural substrates could be increased in many cases by natural or laboratory evolution.

Cyanobacteria play a key role in marine photosynthesis, which contributes to the global carbon cycle and to the world oxygen supply. Genes encoding the photosystem-II (PSII) reaction centre are found in many cyanophage genomes, and it was suggested that the horizontal transfer of these genes might be involved in increasing phage fitness. Recently, evidence for the existence of phages carrying Photosystem-I (PSI) genes was also reported. Here, using a combination of different marine metagenomic datasets and a unique crossing of the datasets, we now describe the finding of phages that, as in plants and cyanobacteria, contain both PSII and PSI genes. In addition, these phages also contain NADH dehydrogenase genes. The presence of modified PSII and PSI genes in the same viral entities in combination with electron transfer proteins like NAD(P)H dehydrogenase (NDH-1) strongly points to a role in perturbation of the cyanobacterial host photosynthetic electron flow. We therefore suggest that, depending on the physiological condition of the infected cyanobacterial host, the viruses may use different options to maximize survival. The modified PSI may alternate between functioning with PSII in linear electron transfer and contributing to the production of both NADPH and ATP or functioning independently of PSII in cyclic mode via the NDH-1 complex and thus producing only ATP.

Central carbon metabolism uses a complex series of enzymatic steps to convert sugars into metabolic precursors. These precursors are then used to generate the entire biomass of the cell. Are there simplifying principles that can explain the structure of such metabolic networks? Here we address this question by studying central carbon metabolism in E. coli. We use all known classes of enzymes that work on carbohydrates to generate rules for converting compounds and for generating possible paths between compounds. We find that central carbon metabolism is built as a minimal walk between the 12 precursor metabolites that form the basis for biomass and one precursor essential for the positive net ATP balance in glycolysis: every pair of consecutive precursors in the network is connected by the minimal number of enzymatic steps. Similarly, input sugars are converted into precursors by the shortest possible enzymatic paths. This suggests an optimality principle for the structure of central carbon metabolism. The present approach may be used to study other metabolic networks and to design new minimal pathways.

Carbon fixation is the process by which CO₂ is incorporated into organic compounds. In modern agriculture in which water, light, and nutrients can be abundant, carbon fixation could become a significant growth-limiting factor. Hence, increasing thefixation rate is of major importance in the road toward sustainability in food and energy production. There have been recent attempts to improve the rate and specificity of Rubisco, the carboxylating enzyme operating in the Calvin-Benson cycle; however, they have achieved only limited success. Nature employs several alternative carbon fixation pathways, which prompted us to ask whether more efficient novel synthetic cycles could be devised. Using the entire repertoire of approximately 5,000 metabolic enzymes known to occur in nature, we computationally identified alternative carbon fixation pathways that combine existing metabolic building blocks from various organisms.Wecompared the natural and synthetic pathways based on physicochemical criteria that include kinetics, energetics, and topology. Our study suggests that some of the proposed synthetic pathways could have significant quantitative advantages over their natural counterparts, such as the overall kinetic rate. One such cycle, which is predicted to be two to three times faster than the Calvin-Benson cycle, employs the most effective carboxylating enzyme, phosphoenolpyruvate carboxylase, using the core of the naturally evolved C4 cycle. Although implementing such alternative cycles presents daunting challenges related to expression levels, activity, stability, localization, and regulation, we believe our findings suggest exciting avenues of exploration in the grand challenge of enhancing food and renewable fuel production via metabolic engineering and synthetic biology.

Rubisco (D-ribulose 1,5-bisphosphate carboxylase/oxygenase), probably the most abundant protein in the biosphere, performs an essential part in the process of carbon fixation through photosynthesis, thus facilitating life on earth. Despite the significant effect that Rubisco has on the fitness of plants and other photosynthetic organisms, this enzyme is known to have a low catalytic rate and a tendency to confuse its substrate, carbon dioxide, with oxygen. This apparent inefficiency is puzzling and raises questions regarding the roles of evolution versus biochemical constraints in shaping Rubisco. Herewe examine these questions by analyzing themeasured kinetic parameters of Rubisco from various organisms living in various environments. The analysis presented here suggests that the evolution of Rubisco is confined to an effectively one-dimensional landscape, which ismanifested in simple power lawcorrelations between its kinetic parameters.Within this one-dimensional landscape,which may represent biochemical and structural constraints, Rubisco appears to be tuned to the intracellular environment in which it resides such that the net photosynthesis rate is nearly optimal. Our analysis indicates that the specificity of Rubisco is not the main determinant of its efficiency but rather the trade-off between the carboxylation velocity and CO₂ affinity. As a result, the presence of oxygen has only a moderate effect on the optimal performance of Rubisco, which is determined mostly by the local CO₂ concentration. Rubisco appears as an experimentally testable example for the evolution of proteins subject both to strong selection pressure and to biochemical constraints that strongly confine the evolutionary plasticity to a low-dimensional landscape.

The academic path is a challenging journey full of hurdles and without a clear roadmap. As young faculty, we searched for support in steering through the complexities of our new roles. Here we describe our experience in forming a peer support group and share the lessons learnt along the way.

Although the quantitative description of biological systems has been going on for centuries, recent advances in the measurement of phenomena ranging from metabolism to gene expression to signal transduction have resulted in a new emphasis on biological numeracy. This article describes the confluence of two different approaches to biological numbers. First, an impressive array of quantitative measurements make it possible to develop intuition about biological numbers ranging from how many gigatons of atmospheric carbon are fixed every year in the process of photosynthesis to the number of membrane transporters needed to provide sugars to rapidly dividing Escherichia coli cells. As a result of the vast array of such quantitative data, the BioNumbers web site has recently been developed as a repository for biology by the numbers. Second, a complementary and powerful tradition of numerical estimates familiar from the physical sciences and canonized in the so-called "Fermi problems" calls for efforts to estimate key biological quantities on the basis of a few foundational facts and simple ideas from physics and chemistry. In this article, we describe these two approaches and illustrate their synergism in several particularly appealing case studies. These case studies reveal the impact that an emphasis on numbers can have on important biological questions.

BioNumbers (http://www.bionumbers.hms.harvard.edu) is a database of key numbers in molecular and cell biology-the quantitative properties of biological systems of interest to computational, systems and molecular cell biologists. Contents of the database range from cell sizes to metabolite concentrations, from reaction rates to generation times, from genome sizes to the number of mitochondria in a cell. While always of importance to biologists, having numbers in hand is becoming increasingly critical for experimenting, modeling, and analyzing biological systems. BioNumbers was motivated by an appreciation of how long it can take to find even the simplest number in the vast biological literature. All numbers are taken directly from a literature source and that reference is provided with the number. BioNumbers is designed to be highly searchable and queries can be performed by keywords or browsed by menus. BioNumbers is a collaborative community platform where registered users can add content and make comments on existing data. All new entries and commentary are curated to maintain high quality. Here we describe the database characteristics and implementation, demonstrate its use, and discuss future directions for its development.

A current challenge in biology is to understand the dynamics of protein circuits in living human cells. Can one define and test equations for the dynamics and variability of a protein over time? Here, we address this experimentally and theoretically, by means of accurate time-resolved measurements of endogenously tagged proteins in individual human cells. As a model system, we choose three stable proteins displaying cell-cycle-dependant dynamics. We find that protein accumulation with time per cell is quadratic for proteins with long mRNA life times and approximately linear for a protein with short mRNA lifetime. Both behaviors correspond to a classical model of transcription and translation. A stochastic model, in which genes slowly switch between ON and OFF states, captures measured cell-cell variability. The data suggests, in accordance with the model, that switching to the gene ON state is exponentially distributed and that the cell-cell distribution of protein levels can be approximated by a Gamma distribution throughout the cell cycle. These results suggest that relatively simple models may describe protein dynamics in individual human cells.

The sun's spectrum harvested through photosynthesis is the primary source of energy for life on earth. Plants, green algae, and cyanobacteria-the major primary producers on earth-utilize reaction centers that operate at wavelengths of 680 and 700 nm. Why were these wavelengths "chosen" in evolution? This study analyzes the efficiency of light conversion into chemical energy as a function of hypothetical reaction center absorption wavelengths given the sun's spectrum and the overpotential cost associated with charge separation. Surprisingly, it is found here that when taking into account the empirical charge separation cost the range 680-720 nm maximizes the conversion efficiency. This suggests the possibility that the wavelengths of photosystem I and II were optimized at some point in their evolution for the maximal utilization of the sun's spectrum.

Why do seemingly identical cells respond differently to a drug? To address this, we studied the dynamics and variability of the protein response of human cancer cells to a chemotherapy drug, camptothecin. We present a dynamic-proteomics approach that measures the levels and locations of nearly 1000 different endogenously tagged proteins in individual living cells at high temporal resolution. All cells show rapid translocation of proteins specific to the drug mechanism, including the drug target (topoisomerase-1), and slower, wide-ranging temporal waves of protein degradation and accumulation. However, the cells differ in the behavior of a subset of proteins. We identify proteins whose dynamics differ widely between cells, in a way that corresponds to the outcomes - cell death or survival. This opens the way to understanding molecular responses to drugs in individual cells.

Modulation of the activity of the molecular chaperone HSP90 has been extensively discussed as a means to alter phenotype in many traits and organisms. Such changes can be due to the exposure of cryptic genetic variation, which in some instances may also be accomplished by mild environmental alteration. Should such polymorphisms be widespread, natural selection may be more effective at producing phenotypic change in suboptimal environments. However, the frequency and identity of buffered polymorphisms in natural populations are unknown. Here, we employ quantitative genetic dissection of an Arabidopsis thaliana developmental response, hypocotyl elongation in the dark, to detail the underpinnings of genetic variation responsive to HSP90 modulation. We demonstrate that HSP90-dependent alleles occur in continuously distributed, environmentally responsive traits and are amenable to quantitative genetic mapping techniques. Furthermore, such alleles are frequent in natural populations and can have significant effects on natural phenotypic variation. We also find that HSP90 modulation has both general and allele-specific effects on developmental stability; that is, developmental stability is a phenotypic trait that can be affected by natural variation. However, effects of revealed variation on trait means outweigh effects of decreased developmental stability, and the HSP90-dependent trait alterations could be acted on by natural selection. Thus, HSP90 may centrally influence canalization, assimilation, and the rapid evolutionary alteration of phenotype through the concealment and exposure of cryptic genetic variation.

Biological signaling systems produce an output, such as the level of a phosphorylated protein, in response to defined input signals. The output level as a function of the input level is called the system's input-output relation. One may ask whether this input-output relation is sensitive to changes in the concentrations of the system's components, such as proteins and ATP. Because component concentrations often vary from cell to cell, it might be expected that the input-output relation will likewise vary. If this is the case, different cells exposed to the same input signal will display different outputs. Such variability can be deleterious in systems where survival depends on accurate match of output to input. Here we suggest a mechanism that can provide input-output robustness, that is, an input-output relation that does not depend on variations in the concentrations of any of the system's components. The mechanism is based on certain bacterial signaling systems. It explains how specific molecular details can work together to provide robustness. Moreover, it suggests an approach that can help identify a wide family of nonequilibrium mechanisms that potentially have robust input-output relations.

Physiological and evolutionary adaptations operate at very different time scales. Nevertheless, there are reasons to believe there should be a strong relationship between the two, as together they modify the phenotype. Physiological adaptations change phenotype by altering certain microscopic parameters; evolutionary adaptation can either alter genetically these same parameters or others to achieve distinct or similar ends. Although qualitative discussions of this relationship abound, there has been very little quantitative analysis. Here, we use the hemoglobin molecule as a model system to quantify the relationship between physiological and evolutionary adaptations. We compare measurements of oxygen saturation curves of 25 mammals with those of human hemoglobin under a wide range of physiological conditions. We fit the data sets to the Monod-Wyman-Changeux model to extract microscopic parameters. Our analysis demonstrates that physiological and evolutionary change act on different parameters. The main parameter that changes in the physiology of hemoglobin is relatively constant in evolution, whereas the main parameter that changes in the evolution of hemoglobin is relatively constant in physiology. This orthogonality suggests continued selection for physiological adaptability and hints at a role for this adaptability in evolutionary change.

Myelination in the peripheral nervous system requires close contact between Schwann cells and the axon, but the underlying molecular basis remains largely unknown. Here we show that cell adhesion molecules (CAMs) of the nectin-like (Necl, also known as SynCAM or Cadm) family mediate Schwann cell-axon interaction during myelination. Necl4 is the main Necl expressed by myelinating Schwann cells and is located along the internodes in direct apposition to Necl1, which is localized on axons. Necl4 serves as the glial binding partner for axonal Necl1, and the interaction between these two CAMs mediates Schwann cell adhesion. The disruption of the interaction between Necl1 and Necl4 by their soluble extracellular domains, or the expression of a dominant-negative Necl4 in Schwann cells, inhibits myelination. These results suggest that Necl proteins are important for mediating axon-glia contact during myelination in peripheral nerves.

We present a protocol to tag proteins expressed from their endogenous chromosomal locations in individual mammalian cells using central dogma tagging. The protocol can be used to build libraries of cell clones, each expressing one endogenous protein tagged with a fluorophore such as the yellow fluorescent protein. Each round of library generation produces 100-200 cell clones and takes about 1 month. The protocol integrates procedures for high-throughput single-cell cloning using flow cytometry, high-throughput cDNA generation and 3 rapid amplification of cDNA ends, semi-automatic protein localization screening using fluorescent microscopy and freezing cells in 96-well format.

Diverse cellular processes are carried out by distinct integrin-mediated adhesions. Cell spreading and migration are driven by focal complexes; robust adhesion to the extracellular matrix by focal adhesions; and matrix remodeling by fibrillar adhesions. The mechanism(s) regulating the spatio-temporal distribution and dynamics of the three types of adhesion are unknown. Here, we combine live-cell imaging, labeling with phosphospecific-antibodies and overexpression of a novel tyrosine phosphomimetic mutant of paxillin, to demonstrate that the modulation of tyrosine phosphorylation of paxillin regulates both the assembly and turnover of adhesion sites. Moreover, phosphorylated paxillin enhanced lamellipodial protrusions, whereas non-phosphorylated paxillin was essential for fibrillar adhesion formation and for fibronectin fibrillogenesis. We further show that focal adhesion kinase preferentially interacted with the tyrosine phosphomimetic paxillin and its recruitment is implicated in high turnover of focal complexes and translocation of focal adhesions. We created a mathematical model that recapitulates the salient features of the measured dynamics, and conclude that tyrosine phosphorylation of the adaptor protein paxillin functions as a major switch, regulating the adhesive phenotype of cells.

A long term goal for molecular biologists is to visualize and quantify the levels and localizations of all proteins at the single cell level under endogenous regulation throughout time. Recent advances in protein tagging, microscopy, and image analysis have brought this goal much closer. But how to integrate these techniques to arrive at proteome scale results? Here I review one approach, incorporating random endogenous gene tagging, high-throughput incubated time- lapse microscopy, and automated image analysis, that can provide information on, for example, the accumulation rates of proteins throughout the cell cycle and the variability of protein level expression. Dynamic proteomics has the potential to shed light on many long standing questions and could contribute to challenging undertakings such as following signal transduction in a mammalian cell from input to output.

We examined cell cycle-dependent changes in the proteome of human cells by systematically measuring protein dynamics in individual living cells. We used time-lapse microscopy to measure the dynamics of a random subset of 20 nuclear proteins, each tagged with yellow fluorescent protein (YFP) at its endogenous chromosomal location. We synchronized the cells in silico by aligning protein dynamics in each cell between consecutive divisions. We observed widespread (40%) cell-cycle dependence of nuclear protein levels and detected previously unknown cell cycle-dependent localization changes. This approach to dynamic proteomics can aid in discovery and accurate quantification of the extensive regulation of protein concentration and localization in individual living cells.

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time.

Western harmony is comprised of sequences of chords, which obey grammatical rules. It is of interest to develop a compact representation of the harmonic movement of chord sequences. Here, we apply an approach from analysis of complex networks, known as "network motifs" to define repeating dynamical patterns in musical harmony. We describe each piece as a graph, where the nodes are chords and the directed edges connect chords which occur consecutively in the piece. We detect several patterns, each of which is a walk on this graph, which recur in diverse musical pieces from the Baroque to modern-day popular music. These patterns include cycles of three or four nodes, with up to two mutual edges (edges that point in both directions). Cliques and patterns with more than two mutual edges are rare. Some of these universal patterns of harmony are well known and correspond to basic principles of music theory such as hierarchy and directionality. This approach can be extended to search for recurring patterns in other musical components and to study other dynamical systems that can be represented as walks on graphs.

Protein expression is a stochastic process that leads to phenotypic variation among cells. The cell-cell distribution of protein levels in microorganisms has been well characterized but little is known about such variability in human cells. Here, we studied the variability of protein levels in human cells, as well as the temporal dynamics of this variability, and addressed whether cells with higher than average protein levels eventually have lower than average levels, and if so, over what timescale does this mixing occur. We measured fluctuations over time in the levels of 20 endogenous proteins in living human cells, tagged by the gene for yellow fluorescent protein at their chromosomal loci. We found variability with a standard deviation that ranged, for different proteins, from about 15% to 30% of the mean. Mixing between high and low levels occurred for all proteins, but the mixing time was longer than two cell generations (more than 40 h) for many proteins. We also tagged pairs of proteins with two colours, and found that the levels of proteins in the same biological pathway were far more correlated than those of proteins in different pathways. The persistent memory for protein levels that we found might underlie individuality in cell behaviour and could set a timescale needed for signals to affect fully every member of a cell population.

Can complex engineered and biological networks be coarse-grained into smaller and more understandable versions in which each node represents an entire pattern in the original network? To address this, we define coarse-graining units as connectivity patterns which can serve as the nodes of a coarse-grained network and present algorithms to detect them. We use this approach to systematically reverse-engineer electronic circuits, forming understandable high-level maps from incomprehensible transistor wiring: first, a coarse-grained version in which each node is a gate made of several transistors is established. Then the coarse-grained network is itself coarse-grained, resulting in a high-level blueprint in which each node is a circuit module made of many gates. We apply our approach also to a mammalian protein signal-transduction network, to find a simplified coarse-grained network with three main signaling channels that resemble multi-layered perceptrons made of cross-interacting MAP-kinase cascades. We find that both biological and electronic networks are "self-dissimilar," with different network motifs at each level. The present approach may be used to simplify a variety of directed and nondirected, natural and designed networks.

Summary: Biological and engineered networks have recently been shown to display network motifs: a small set of characteristic patterns that occur much more frequently than in randomized networks with the same degree sequence. Network motifs were demonstrated to play key information processing roles in biological regulation networks. Existing algorithms for detecting network motifs act by exhaustively enumerating all subgraphs with a given number of nodes in the network. The runtime of such algorithms increases strongly with network size. Here, we present a novel algorithm that allows estimation of subgraph concentrations and detection of network motifs at a runtime that is asymptotically independent of the network size. This algorithm is based on random sampling of subgraphs. Network motifs are detected with a surprisingly small number of samples in a wide variety of networks. Our method can be applied to estimate the concentrations of larger subgraphs in larger networks than was previously possible with exhaustive enumeration algorithms. We present results for high-order motifs in several biological networks.

Genes and proteins generate molecular circuitry that enables the cell to process information and respond to stimuli. A major challenge is to identify characteristic patterns in this network of interactions that may shed light on basic cellular mechanisms. Previous studies have analyzed aspects of this network, concentrating on either transcription-regulation or protein-protein interactions. Here we search for composite network motifs: characteristic network patterns consisting of both transcription-regulation and protein-protein interactions that recur significantly more often than in random networks. To this end we developed algorithms for detecting motifs in networks with two or more types of interactions and applied them to an integrated data set of protein-protein interactions and transcription regulation in Saccharomyces cerevisiae. We found a two-protein mixed-feedback loop motif, five types of three-protein motifs exhibiting coregulation and complex formation, and many motifs involving four proteins. Virtually all four-protein motifs consisted of combinations of smaller motifs. This study presents a basic framework for detecting the building blocks of networks with multiple types of interactions.

Complex biological, technological, and sociological networks can be of very different sizes and connectivities, making it difficult to compare their structures. Here we present an approach to systematically study similarity in the local structure of networks, based on the significance profile (SP) of small subgraphs in the network compared to randomized networks. We find several superfamilies of previously unrelated networks with very similar SPs. One superfamily, including transcription networks of microorganisms, represents "rate-limited" information-processing networks strongly constrained by the response time of their components. A distinct superfamily includes protein signaling, developmental genetic networks, and neuronal wiring. Additional superfamilies include power grids, protein-structure networks and geometric networks, World Wide Web links and social networks, and word-adjacency networks from different languages.

Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the network. It is of interest to understand how network motifs combine to form larger structures. To address this, we present a systematic approach to define \u201cmotif generalizations\u201d: families of motifs of different sizes that share a common architectural theme. To define motif generalizations, we first define \u201croles\u201d in a subgraph according to structural equivalence. For example, the feedforward loop triada motif in transcription, neuronal, and some electronic networkshas three roles: an input node, an output node, and an internal node. The roles are used to define possible generalizations of the motif. The feedforward loop can have three simple generalizations, based on replicating each of the three roles and their connections. We present algorithms for efficiently detecting motif generalizations. We find that the transcription networks of bacteria and yeast display only one of the three generalizations, the multi-output feedforward generalization. In contrast, the neuronal network of C. elegans mainly displays the multi-input generalization. Forward-logic electronic circuits display a multi-input, multi-output hybrid. Thus, networks which share a common motif can have very different generalizations of that motif. Using mathematical modeling, we describe the information processing functions of the different motif generalizations in transcription, neuronal, and electronic networks.

King [preceding Comment, Phys. Rev. E 70, 058101 (2004)] points out biases in one of the two common algorithms for generating simple random graphsthe matching, or stub-pairing, algorithm. We clarify that in our simulations of simple graphs we used a different algorithm, the Markov-chain Monte Carlo switching algorithm, which is more uniform. As for multigraphs, the stub-pairing algorithm indeed samples uniformly configurations rather than multigraphs, as King points out, and thus is relevant for our model, which pertains to configurations. Finally, we demonstrate that the algorithm we used to generate families of random networks with scale-free out-degree and compact in-degree does not result in noticeable biases.

Understanding the subgraph distribution in random networks is important for modeling complex systems. In classic Erdős networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as [Formula presented] However, many natural networks have a non-Poissonian degree distribution. Here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks, characterized by an arbitrary degree sequence. We find scaling rules for the commonly occurring case of directed scale-free networks, in which the outgoing degree distribution scales as [Formula presented] Considering the power exponent of the degree distribution, [Formula presented] as a control parameter, we show that random networks exhibit transitions between three regimes. In each regime, the subgraph number of appearances follows a different scaling law, [Formula presented], where [Formula presented] for [Formula presented] [Formula presented] for [Formula presented] and [Formula presented] for [Formula presented] where s is the maximal outdegree in the subgraph, and [Formula presented] We find that certain subgraphs appear much more frequently than in Erdős networks. These results are in very good agreement with numerical simulations. This has implications for detecting network motifs, subgraphs that occur in natural networks significantly more than in their randomized counterparts.

Complex networks are studied across many fields of science. To uncover their structural design principles, we defined "network motifs," patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks. We found such motifs in networks from biochemistry, neurobiology, ecology, and engineering. The motifs shared by ecological food webs were distinct from the motifs shared by the genetic networks of Escherichia coli and Saccharomyces cerevisiae or from those found in the World Wide Web. Similar motifs were found in networks that perform information processing, even though they describe elements as different as biomolecules within a cell and synaptic connections between neurons in Caenorhabditis elegans. Motifs may thus define universal classes of networks. This approach may uncover the basic building blocks of most networks.

Little is known about the design principles of transcriptional regulation networks that control gene expression in cells. Recent advances in data collection and analysis, however, are generating unprecedented amounts of information about gene regulation networks. To understand these complex wiring diagrams, we sought to break down such networks into basic building blocks. We generalize the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks. We applied new algorithms for systematically detecting network motifs to one of the best-characterized regulation networks, that of direct transcriptional interactions in Escherichia coli. We find that much of the network is composed of repeated appearances of three highly significant motifs. Each network motif has a specific function in determining gene expression, such as generating temporal expression programs and governing the responses to fluctuating external signals. The motif structure also allows an easily interpretable view of the entire known transcriptional network of the organism. This approach may help define the basic computational elements of other biological networks.

The innovative concept of complex fuzzy sets is introduced. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0,1] but extended to the unit circle in the complex plane. Thus, the complex fuzzy set provides a mathematical framework for describing membership in a set in terms of a complex number. A study of this original concept is presented, including examples of possible applications, which demonstrate the new theory.

Although T cell responses to the quantitatively major myelin proteins, myelin basic protein (MBP) and proteolipid protein (PLP), are likely to be of importance in the course of multiple sclerosis (MS), cell-mediated autoimmune responses to other myelin antigens, in particular quantitatively minor myelin antigens, such as myelin-associated glycoprotein (MAG) and the central nervous system-specific myelin oligodendrocyte glycoprotein (MOG), could also play a prevalent role in disease initiation or progression. Highly purified myelin antigens were used in this study to assess cell-mediated immune response to MOG in MS patients, in the context of the reactivity to other myelin antigens, MBP, PLP, and MAG. The greatest incidence of proliferative response by MS peripheral blood lymphocytes was to MOG, as 12 of 24 patients tested reacted and, of these, 8 reacted to MOG exclusively. In contrast, only 1 control individual of 16 tested reacted positively to MOG. The incidence of responses to MBP, PLP, and MAG did not differ greatly between MS patients and control individuals. A predominant T cell reactivity to MOG in MS suggests an important role for cell-mediated immune response to this antigen in the pathogenesis of MS.