Publications
2024

(2024) Developmental Cell. Abstract
Neutrophils exhibit selfamplified swarming to sites of injury and infection. How swarming is controlled to ensure the proper level of neutrophil recruitment is unknown. Using an ex vivo model of infection, we find that human neutrophils use active relay to generate multiple pulsatile waves of swarming signals. Unlike classic active relay systems such as action potentials, neutrophil swarming relay waves are selfextinguishing, limiting the spatial range of cell recruitment. We identify an NADPHoxidasebased negative feedback loop that is needed for this selfextinguishing behavior. Through this circuit, neutrophils adjust the number and size of swarming waves for homeostatic levels of cell recruitment over a wide range of initial cell densities. We link a broken homeostat to neutrophil overrecruitment in the context of human chronic granulomatous disease.Competing Interest StatementThe authors have declared no competing interest.

(2024) Proceedings of the National Academy of Sciences. 121, 25, e232300912. Abstract
Error correction is central to many biological systems and is critical for protein function and cell health. During mitosis, error correction is required for the faithful inheritance of genetic material. When functioning properly, the mitotic spindle segregates an equal number of chromosomes to daughter cells with high fidelity. Over the course of spindle assembly, many initially erroneous attachments between kinetochores and microtubules are fixed through the process of error correction. Despite the importance of chromosome segregation errors in cancer and other diseases, there is a lack of methods to characterize the dynamics of error correction and how it can go wrong. Here, we present an experimental method and analysis framework to quantify chromosome segregation error correction in human tissue culture cells with live cell confocal imaging, timed premature anaphase, and automated counting of kinetochores after cell division. We find that errors decrease exponentially over time during spindle assembly. A coarsegrained model, in which errors are corrected in a chromosomeautonomous manner at a constant rate, can quantitatively explain both the measured error correction dynamics and the distribution of anaphase onset times. We further validated our model using perturbations that destabilized microtubules and changed the initial configuration of chromosomal attachments. Taken together, this work provides a quantitative framework for understanding the dynamics of mitotic error correction.

(2024) BioRxiv. Abstract
Mechanical energy, specifically in the form of ultrasound, can induce pressure variations and temperature fluctuations when applied to an aqueous media. These conditions can both positively and negatively affect protein complexes, consequently altering their stability, folding patterns, and selfassembling behavior. Despite much scientific progress, our current understanding of the effects of ultrasound on the selfassembly of amyloidogenic proteins remains limited. In the present study, we demonstrate that when the amplitude of the delivered ultrasonic energy is sufficiently low, it can induce refolding of specific motifs in protein monomers, which is sufficient for primary nucleation; this has been revealed by MD. These ultrasoundinduced structural changes are initiated by pressure perturbations and are accelerated by a temperature factor. Furthermore, the prolonged action of lowamplitude ultrasound enables the elongation of amyloid protein nanofibrils directly from natively folded monomeric lysozyme protein, in a controlled manner, until it reaches a critical length. Using solution Xray scattering, we determined that nanofibrillar assemblies, formed either under the action of sound or from natively fibrillated lysozyme, share identical structural characteristics. Thus, these results provide insights into the effects of ultrasound on fibrillar protein selfassembly and lay the foundation for the potential use of sound energy in protein chemistry.Significance Statement Understanding how and why proteins form amyloid fibrils is crucial for research into various diseases, including neurodegeneration. Ultrasound is routinely used in research settings as a tool for generating amyloid seeds (nucleation sites) from mature fibrils, which accelerate the rate of fibril growth. However, ultrasound can have various effects on aqueous media including temperature, extreme shear, and free radicals. Here we show that when the ultrasound parameters are precisely adjusted, they can be utilized as a tool for amyloid growth directly from the natively folded monomers. Thus, it is possible to induce minor changes in the folding of proteins, which trigger nucleation and accelerate amyloid growth. This knowledge lays the foundation for the potential use of sound in protein chemistry.Competing Interest StatementThe authors have declared no competing interest.

(2024) BioRxiv. Abstract
A critical cell cycle checkpoint for most bacteria is the onset of constriction when the septal peptidoglycan synthesis starts. According to the current understanding, the arrival of FtsN to midcell triggers this checkpoint in Escherichia coli. Recent structural and in vitro data suggests that recruitment of FtsN to the Zring leads to a conformational switch in actinlike FtsA, which links FtsZ protofilaments to the cell membrane and acts as a hub for the late divisome proteins. Here, we investigate this putative pathway using in vivo measurements and stochastic cell cycle modeling. Quantitatively upregulating protein concentrations and determining the resulting division timings shows that FtsN and FtsA numbers are not ratelimiting for the division in E. coli. However, at higher overexpression levels, they affect divisions: FtsN by accelerating and FtsA by inhibiting them. At the same time, we find that the numbers of FtsZ in the cell are ratelimiting for cell divisions in addition to other processes. Altogether, these findings suggest that instead of FtsN, FtsZ protofilaments drive the conformational switch of FtsA and lead to the onset of constriction. Our data is also suggestive that FtsA minirings are not present at any significant numbers in wildtype cells.Competing Interest StatementThe authors have declared no competing interest.

(2024) eLife. 12, RP87895. Abstract
The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population’s mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with powerlaw fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/ nmboffi/spin_glass_evodyn.

(2024) arXiv.org. Abstract
Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effect, is inherent to thinwalled cylindrical shells, which are particularly ubiquitous in living systems, such as rodshaped bacteria. However, tubular biological structures are often pressurized, and the knowledge of the mechanical response upon bending in this scenario is limited. In this work, we use a computational model to study the mechanical response and the deformations as a result of bending pressurized tubes. In addition, we employ tensionfield theory to describe the mechanical behaviour before and after the wrinkling transition. Furthermore, we investigate the development and evolution of wrinkle patterns beyond the instability, showing different wrinkled configurations. We discover the existence of a multiwavelength mode following the purely sinusoidal wrinkles and anticipating the kinked configuration of the tube.

(2024) arXiv.org. Abstract
The LuriaDelbrück model is a classic model of population dynamics with random mutations, that has been used historically to prove that random mutations drive evolution. In typical scenarios, the relevant mutation rate is exceedingly small, and mutants are counted only at the final time point. Here, inspired by recent experiments on DNA repair, we study a mathematical model that is formally equivalent to the LuriaDelbrück setup, with the repair rate p playing the role of mutation rate, albeit taking on large values, of order unity per cell division. We find that although at large times the fraction of repaired cells approaches one, the variance of the number of repaired cells undergoes a phase transition: when p>1/2 the variance decreases with time, but, intriguingly, for p
2023

(2023) arXiv.org. Abstract
Cell growth and gene expression, essential elements of all living systems, have long been the focus of biophysical interrogation. Advances in singlecell methods have invigorated theoretical studies into these processes. However, until recently, there was little dialog between the two areas of study. Most theoretical models for gene regulation assumed gene activity to be oblivious to the progression of the cell cycle between birth and division. But there are numerous ways in which the periodic character of all cellular observables can modulate gene expression. The molecular factors required for transcription and translation increase in number during the cell cycle, but are also diluted due to the continuous increase in cell volume. The replication of the genome changes the dosage of those same cellular players but also provides competing targets for regulatory binding. Finally, cell division reduces their number again, and so forth. Stochasticity is inherent to all these biological processes, manifested in fluctuations in the synthesis and degradation of new cellular components as well as the random partitioning of molecules at each cell division. The notion of gene expression as stationary is thus hard to justify. In this review, we survey the emerging paradigm of cellcycle regulated gene expression, with an emphasis on the global expression patterns rather than genespecific regulation. We discuss recent experimental reports where cell growth and gene expression were simultaneously measured in individual cells, providing first glimpses into the coupling between the two. While the experimental findings, not surprisingly, differ among genes and organisms, several theoretical models have emerged that attempt to reconcile these differences and form a unifying framework for understanding gene expression in growing cells.

(2023) Current Biology. 33, 22, p. 48804892.e14 Abstract
Bacteria undergo cycles of growth and starvation to which they must adapt swiftly. One important strategy for adjusting growth rates relies on ribosomal levels. Although high ribosomal levels are required for fast growth, their dynamics during starvation remain unclear. Here, we analyzed ribosomal RNA (rRNA) content of individual Salmonella cells by using fluorescence in situ hybridization (rRNAFISH) and measured a dramatic decrease in rRNA numbers only in a subpopulation during nutrient limitation, resulting in a bimodal distribution of cells with high and low rRNA content. During nutritional upshifts, the two subpopulations were associated with distinct phenotypes. Using a transposon screen coupled with rRNAFISH, we identified two mutants, DksA and RNase I, acting on rRNA transcription shutdown and degradation, which abolished the formation of the subpopulation with low rRNA content. Our work identifies a bacterial mechanism for regulation of ribosomal bimodality that may be beneficial for population survival during starvation.

(2023) PRX Life. 1, 2, 023001. Abstract
Some ant species are known as efficient transporters that can cooperatively carry food items which would be too large for a single ant. Previous studies of cooperative transport focused on the role of individual ants and their behavioral rules that allow for efficient coordination. However, the resulting detailed microscopic description requires a numerical treatment in order to extract macroscopic features of the object's trajectory. Here, we instead treat the carried object as a single active swimmer whose movement is characterized by two variables: velocity amplitude and direction. We experimentally observe Paratrechina longicornis ants cooperatively transporting loads of varying sizes. By analyzing the statistical features of the load's movement, we show how the salient properties of the cooperative transport are encoded in its deterministic and random accelerations. We find that while the autocorrelation time of the velocity direction increases with group size, the autocorrelation time of the speed has a maximum at an intermediate group size, corresponding to the critical slow down close to the previously identified phase transition. Our statistical model for cooperative ant transport demonstrates that an active swimmer model can be employed to describe a system of interacting individuals.

(2023) Physical Review E. 108, 3, 034402. Abstract
In the past decade, great strides have been made to quantify the dynamics of singlecell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of singlecell growth and division influence evolutionary dynamics. This requires us to connect processes on the singlecell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the singlecell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarsegrained so that the forces of natural selection and genetic drift can be expressed in terms of the longterm fitness We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the singlecell dynamics affect the fate of a new mutant independently from how they affect the longterm growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the EulerLotka equation.

(2023) American Journal of Physics. 91, 8, p. 653658 Abstract
Search processes are ubiquitous in physical and biological phenomena, often involving the random motion of molecules. In particular, transcription factors (TFs) are proteins that regulate gene expression and need to find their DNA targets quickly—which is difficult to achieve with random motion alone. Nature came up with a remarkable solution known as facilitated diffusion, combining 1D diffusion along the DNA and “excursions” of diffusion in 3D that help the TF to quickly arrive at distant parts of the DNA. In this paper, we show that this process can be analyzed naturally using the concept of conditional probability, providing an alternative intuition to the effectiveness of this mechanism.

(2023) BioRxiv. Abstract
The surge in interest in individual differences has coincided with the latest replication crisis centered around brainwide association studies of brainbehavior correlations. Yet the reliability of the measures we use in cognitive neuroscience, a crucial component of this brainbehavior relationship, is often assumed but not directly tested. Here, we evaluate the reliability of different cognitive tasks on a large dataset of over 250 participants, who each completed a multiday task battery. We show how reliability improves as a function of number of trials, and describe the convergence of the reliability curves for the different tasks, allowing us to score tasks according to their suitability for studies of individual differences. To improve the accessibility of these findings, we designed a simple webbased tool that implements this function to calculate the convergence factor and predict the expected reliability for any given number of trials and participants, even based on limited pilot data.Competing Interest StatementThe authors have declared no competing interest.

(2023) arXiv.org. Abstract
Transcription Factors (TFs) are proteins crucial for regulating gene expression. Effective regulation requires the TFs to rapidly bind to the correct target, enabling the cell to respond timely to various stimuli such as nutrient availability or toxin presence. At the same time, the search process is limited by slow diffusive movement and 'false' targets in DNA  segments of DNA sequences that are similar to the true target. In eukaryotic cells most TFs have an Intrinsically Disordered Region (IDR), which is a long, flexible polymeric tail comprised of hundreds of amino acids. Recent experimental findings indicate that the IDR of certain TFs plays a crucial role in the search process. However, the principles underlying the IDR's role remain unclear. Here, we reveal key design principles of the IDR related to TF binding affinity and search time. Our results indicate a significant enhancement in both of these aspects attributed to the presence of the IDR. Additionally, we propose experiments to verify these theoretical predictions.

(2023) Physical Review Letters. 130, 25, 258201. Abstract
The statistics of noise emitted by ultrathin crumpled sheets is measured while they exhibit logarithmic relaxations under load. We find that the logarithmic relaxation advanced via a series of discrete, audible, micromechanical events that are logPoisson distributed (i.e., the process becomes a Poisson process when time stamps are replaced by their logarithms). The analysis places constraints on the possible mechanisms underlying the glasslike slow relaxation and memory retention in these systems.

Mycobacterium tuberculosis grows linearly at the singlecell level with larger variability than model organisms(2023) BioRxiv. Abstract
The ability of bacterial pathogens to regulate growth is crucial to control homeostasis, virulence, and drug response. Yet, we do not understand the growth and cell cycle behaviors of Mycobacterium tuberculosis (Mtb), a slowgrowing pathogen, at the singlecell level. Here, we use timelapse imaging and mathematical modeling to characterize these fundamental properties of Mtb. Whereas most organisms grow exponentially at the singlecell level, we find that Mtb exhibits a unique linear growth mode. Mtb growth characteristics are highly variable from celltocell, notably in their growth speeds, cell cycle timing, and cell sizes. Together, our study demonstrates that growth behavior of Mtb diverges from what we have learned from model bacteria. Instead, Mtb generates a heterogeneous population while growing slowly and linearly. Our study provides a new level of detail into how Mtb grows and creates heterogeneity, and motivates more studies of growth behaviors in bacterial pathogens.

(2023) Soft Matter. 19, 12, p. 22242230 Abstract
Many bacterial species are helical in shape, including the widespread pathogen H. pylori. Motivated by recent experiments on H. pylori showing that cell wall synthesis is not uniform [J. A. Taylor, et al., eLife, 2020, 9, e52482], we investigate the possible formation of helical cell shape induced by elastic heterogeneity. We show, experimentally and theoretically, that helical morphogenesis can be produced by pressurizing an elastic cylindrical vessel with helical reinforced lines. The properties of the pressurized helix are highly dependent on the initial helical angle of the reinforced region. We find that steep angles result in crooked helices with, surprisingly, a reduced endtoend distance upon pressurization. This work helps explain the possible mechanisms for the generation of helical cell morphologies and may inspire the design of novel pressurecontrolled helical actuators.

(2023) Proceedings of the National Academy of Sciences  PNAS. 120, 11, e221479612. Abstract
How cells regulate their cell cycles is a central question for cell biology. Models of cell size homeostasis have been proposed for bacteria, archaea, yeast, plant, and mammalian cells. New experiments bring forth high volumes of data suitable for testing existing models of cell size regulation and proposing new mechanisms. In this paper, we use conditional independence tests in conjunction with data of cell size at key cell cycle events (birth, initiation of DNA replication, and constriction) in the model bacterium Escherichia coli to select between the competing cell cycle models. We find that in all growth conditions that we study, the division event is controlled by the onset of constriction at midcell. In slow growth, we corroborate a model where replicationrelated processes control the onset of constriction at midcell. In faster growth, we find that the onset of constriction is affected by additional cues beyond DNA replication. Finally, we also find evidence for the presence of additional cues triggering initiations of DNA replication apart from the conventional notion where the mother cells solely determine the initiation event in the daughter cells via an adder per origin model. The use of conditional independence tests is a different approach in the context of understanding cell cycle regulation and it can be used in future studies to further explore the causal links between cell events.

(2023) Mathematics Going Forward. Teissier B. & Morel JM.(eds.). Vol. 2313. p. 8184 Abstract
A derivation, natural for people who think physically, is offered of Galperin’s result on a collision experiment that replicates the digits of π. We thereby hope to liven up a teatime for Catriona Byrne who is retiring in 2022 after 4 decades as godmother of mathematics at Springer.
2022

(2022) Physical Review E. 105, 5, 064502. Abstract
Dynamic instability  the growth, catastrophe, and shrinkage of quasionedimensional filaments  has been observed in multiple biopolymers. Scientists have long understood the catastrophic cessation of growth and subsequent depolymerization as arising from the interplay of hydrolysis and polymerization at the tip of the polymer. Here we show that for a broad class of catastrophe models, the expected catastrophe time distribution is exponential. We show that the distribution shape is insensitive to noise, but that depletion of monomers from a finite pool can dramatically change the distribution shape by reducing the polymerization rate. We derive a form for this finitepool catastrophe time distribution and show that finitepool effects can be important even when the depletion of monomers does not greatly alter the polymerization rate.

(2022) Physical review letters. 128, 23, 234501. Abstract
We study the dynamics of flow networks in porous media using two and three dimensional porenetwork models. We consider a class of erosion dynamics for a single phase flow with no deposition, chemical reactions, or topology changes assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.

(2022) Genetics (Austin). 220, 4, iyac028. Abstract
Adaptation dynamics on fitness landscapes is often studied theoretically in the strongselection, weakmutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strongselection, weakmutation model with the same parameters), how it affects the shape of longterm fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitnessparameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).

Singlecell microfluidic analysis unravels individual cellular fates during DoubleStrand Break Repair(2022) BioRxiv. Abstract
Trinucleotide repeat expansions are responsible for two dozen human disorders. Contracting expanded repeats by DoubleStrand Break Repair (DSBR) might be a therapeutic approach. Given the complexity of manipulating human cells, recent assays were made to quantify DSBR efficacy in yeast, using a fluorescent reporter. In this study DSBR is characterized with an interdisciplinary approach, linking large population dynamics and individual cells. Timeresolved molecular measurements of changes in the population are first confronted to a coupled differential equation model to obtain repair processes rates. Comparisons with measurements in microfluidic devices, where the progeny of 80150 individual cells are followed, show good agreement between individual trajectories and mathematical and molecular results. Further analysis of individual progenies shows the heterogeneity of individual cell contributions to global repair efficacy. Three different categories of repair are identified: highefficacy errorfree, lowefficacy errorfree and lowefficacy errorprone. These categories depend on the type of endonuclease used and on the target sequence.

(2022) Cell reports (Cambridge). 38, 12, 110539. Abstract
Escherichia coli cell cycle features two critical cellcycle checkpoints: initiation of replication and the onset of constriction. While the initiation of DNA replication has been extensively studied, it is less clear what triggers the onset of constriction and when exactly it occurs during the cell cycle. Here, using highthroughput fluorescence microscopy in microfluidic devices, we determine the timing for the onset of constriction relative to the replication cycle in different growth rates. Our singlecell data and modeling indicate that the initiation of constriction is coupled to replicationrelated processes in slow growth conditions. Furthermore, our data suggest that this coupling involves the midcell chromosome blocking the onset of constriction via some form of nucleoid occlusion occurring independently of SlmA and the Ter linkage proteins. This work highlights the coupling between replication and division cycles and brings up a new nucleoid mediated control mechanism in E. coli.

(2022) Physical review letters. 128, 5, 058101. Abstract
A thinwalled tube, e.g., a drinking straw, manifests an instability when bent by localizing the curvature change in a small region. This instability has been extensively studied since the seminal work of Brazier nearly a century ago. However, the scenario of pressurized tubes has received much less attention. Motivated by rodshaped bacteria such as E. coli, whose cell walls are much thinner than their radius and are subject to a substantial internal pressure, we study, theoretically, how this instability is affected by this internal pressure. In the parameter range relevant to the bacteria, we find that the internal pressure significantly postpones the onset of the instability, while the bending stiffness of the cell wall has almost no influence. This study suggests a new method to infer turgor pressure in rodshaped bacteria from bending experiments.
2021

(2021) eLife. 10, e72565. Abstract
Collection of highthroughput data has become prevalent in biology. Large datasets allow the use of statistical constructs such as binning and linear regression to quantify relationships between variables and hypothesize underlying biological mechanisms based on it. We discuss several such examples in relation to singlecell data and cellular growth. In particular, we show instances where what appears to be ordinary use of these statistical methods leads to incorrect conclusions such as growth being nonexponential as opposed to exponential and vice versa. We propose that the data analysis and its interpretation should be done in the context of a generative model, if possible. In this way, the statistical methods can be validated either analytically or against synthetic data generated via the use of the model, leading to a consistent method for inferring biological mechanisms from data. On applying the validated methods of data analysis to infer cellular growth on our experimental data, we find the growth of length in
to be nonexponential. Our analysis shows that in the later stages of the cell cycle the growth rate is faster than exponential. 
(2021) Reports on Progress in Physics. 84, 11, 116601. Abstract
The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context of antibiotic treatments or exponential growth in constant environments, nongenetic variability has significant effects on population dynamics. Here, we review research that elucidates the relationship between celltocell variability and population dynamics. After summarizing the relevant experimental observations, we discuss models of bethedging and phenotypic switching. In the context of these models, we discuss how switching between phenotypes at the singlecell level can help populations survive in uncertain environments. Next, we review more finegrained models of phenotypic variability where the relationship between singlecell growth rates, generation times and cell sizes is explicitly considered. Variability in these traits can have significant effects on the population dynamics, even in a constant environment. We show how these effects can be highly sensitive to the underlying model assumptions. We close by discussing a number of open questions, such as how environmental and intrinsic variability interact and what the role of nongenetic variability in evolutionary dynamics is.

(2021) Physical Review Fluids. 6, 8, L082302. Abstract
Polymer retention from the flow of a polymer solution through porous media results in substantial decrease of the permeability; however, the underlying physics of this effect is unknown. While the polymer retention leads to a decrease in pore volume, here we show that this cannot cause the full reduction in permeability. Instead, to determine the origin of this anomalous decrease in permeability, we use confocal microscopy to measure the porelevel velocities in an indexmatched model porous medium. We show that they exhibit an exponential distribution and, upon polymer retention, this distribution is broadened yet retains the same exponential form. Surprisingly, the velocity distributions are scaled by the inverse square root of the permeabilities. We combine experiment and simulation to show these changes result from diversion of flow in the random porousmedium network rather than reduction in pore volume upon polymer retention.

(2021) Journal of statistical mechanics. 2021, 7, 073503. Abstract
Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key proteins enhances the population fitness, extrapolating the solution at two limits where the segregation is perfectly asymmetric (asymmetry a = 1) and when the asymmetry is small (0

(2021) Frontiers in Microbiology. 12, 712007. Abstract
Mechanical rupture, or lysis, of the cytoplasmic membrane is a common cell death pathway in bacteria occurring in response to βlactam antibiotics. A better understanding of the cellular design principles governing the susceptibility and response of individual cells to lysis could indicate methods of potentiating βlactam antibiotics and clarify relevant aspects of cellular physiology. Here, we take a singlecell approach to bacterial cell lysis to examine three cellular features—turgor pressure, mechanosensitive channels, and cell shape changes—that are expected to modulate lysis. We develop a mechanical model of bacterial cell lysis and experimentally analyze the dynamics of lysis in hundreds of single Escherichia coli cells. We find that turgor pressure is the only factor, of these three cellular features, which robustly modulates lysis. We show that mechanosensitive channels do not modulate lysis due to insufficiently fast solute outflow, and that cell shape changes result in more severe cellular lesions but do not influence the dynamics of lysis. These results inform a singlecell view of bacterial cell lysis and underscore approaches of combatting antibiotic tolerance to βlactams aimed at targeting cellular turgor.

(2021) Physical Review E. 104, 1, 014406. Abstract
Scientists have observed and studied diffusive waves in contexts as disparate as population genetics and cell signaling. Often, these waves are propagated by discrete entities or agents, such as individual cells in the case of cell signaling. For a broad class of diffusive waves, we characterize the transition between the collective propagation of diffusive waves, in which the wave speed is well described by continuum theory, and the propagation of diffusive waves by individual agents. We show that this transition depends heavily on the dimensionality of the system in which the wave propagates and that disordered systems yield dynamics largely consistent with lattice systems. In some system dimensionalities, the intuition that closely packed sources more accurately mimic a continuum can be grossly violated.

(2021) PLoS Computational Biology. 17, 6, e1009080. Abstract
Microbial populations show striking diversity in cell growth morphology and lifecycle; however, our understanding of how these factors influence the growth rate of cell populations remains limited. We use theory and simulations to predict the impact of asymmetric cell division, cell size regulation and singlecell stochasticity on the population growth rate. Our model predicts that coarsegrained noise in the singlecell growth rate lambda decreases the population growth rate, as previously seen for symmetrically dividing cells. However, for a given noise in lambda we find that dividing asymmetrically can enhance the population growth rate for cells with strong size control (between a "sizer" and an "adder"). To reconcile this finding with the abundance of symmetrically dividing organisms in nature, we propose that additional constraints on cell growth and division must be present which are not included in our model, and we explore the effects of selected extensions thereof. Further, we find that within our model, epigenetically inherited generation times may arise due to size control in asymmetrically dividing cells, providing a possible explanation for recent experimental observations in budding yeast. Taken together, our findings provide insight into the complex effects generated by noncanonical growth morphologies.

(2021) Physical review letters. 126, 7, 078101. Abstract
Gene expression is a stochastic process. Despite the increase of protein numbers in growing cells, the protein concentrations are often found to be confined within small ranges throughout the cell cycle. Generally, the noise in protein concentration can be decomposed into an intrinsic and an extrinsic component, where the former vanishes for high expression levels. Considering the time trajectory of protein concentration as a random walker in the concentration space, an effective restoring force (with a corresponding "spring constant") must exist to prevent the divergence of concentration due to random fluctuations. In this work, we prove that the magnitude of the effective spring constant is directly related to the fraction of intrinsic noise in the total protein concentration noise. We show that one can infer the magnitude of intrinsic, extrinsic, and measurement noises of gene expression solely based on timeresolved data of protein concentration, without any a priori knowledge of the underlying gene expression dynamics. We apply this method to experimental data of singlecell bacterial gene expression. The results allow us to estimate the average copy numbers and the translation burst parameters of the studied proteins.

(2021) Physical Review Letters. 126, 7, 079901. Abstract
In our Letter, we presented an approach to linking the statistics of independent lineages to a population’s fitness. Here we correct two minor errors and point out an inconsistency with the algorithm used to generate some of the figures and the one described in the Letter. These errors have no implications on the main conclusions of our work. (Formula Presented).

(2021) Nature Communications. 12, 1, 130. Abstract
Homeostasis of protein concentrations in cells is crucial for their proper functioning, requiring steadystate concentrations to be stable to fluctuations. Since gene expression is regulated by proteins such as transcription factors (TFs), the full set of proteins within the cell constitutes a large system of interacting components, which can become unstable. We explore factors affecting stability by coupling the dynamics of mRNAs and proteins in a growing cell. We find that mRNA degradation rate does not affect stability, contrary to previous claims. However, global structural features of the network can dramatically enhance stability. Importantly, a network resembling a bipartite graph with a lower fraction of interactions that target TFs has a higher chance of being stable. Scrambling the E. coli transcription network, we find that the biological network is significantly more stable than its randomized counterpart, suggesting that stability constraints may have shaped network structure during the course of evolution.
2020

(2020) eLife. 9, p. 148 e61771. Abstract
In biological contexts as diverse as development, apoptosis, and synthetic microbial consortia, collections of cells or subcellular components have been shown to overcome the slow signaling speed of simple diffusion by utilizing diffusive relays, in which the presence of one type of diffusible signaling molecule triggers participation in the emission of the same type of molecule. This collective effect gives rise to fasttraveling diffusive waves. Here, in the context of cell signaling, we show that system dimensionality – the shape of the extracellular medium and the distribution of cells within it – can dramatically affect the wave dynamics, but that these dynamics are insensitive to details of cellular activation. As an example, we show that neutrophil swarming experiments exhibit dynamical signatures consistent with the proposed signaling motif. We further show that cell signaling relays generate much steeper concentration profiles than does simple diffusion, which may facilitate neutrophil chemotaxis.

(2020) Abstract
Probability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random processes, using examples from all these disciplines and more. The reader learns via case studies and begins to recognize the sort of problems that are best tackled probabilistically. The emphasis is on conceptual understanding, the development of intuition and gaining insight, keeping technicalities to a minimum. Nevertheless, a glimpse into the depth of the topics is provided, preparing students for more specialized texts while assuming only an undergraduatelevel background in mathematics. The wide range of areas covered  never before discussed together in a unified fashion – includes Markov processes and random walks, Langevin and Fokker–Planck equations, noise, generalized central limit theorem and extreme values statistics, random matrix theory and percolation theory.

(2020) Physical review letters. 125, 4, 048102. Abstract
In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a singlecell due to variability at the singlecell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a nonmonotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.

(2020) Genetics (Austin). 215, 3, p. 767777 Abstract
Selection of mutants in a microbial population depends on multiple cellular traits. In serialdilution evolution experiments, three key traits are the lag time when transitioning from starvation to growth, the exponential growth rate, and the yield (number of cells per unit resource). Here, we investigate how these traits evolve in laboratory evolution experiments using a minimal model of population dynamics, where the only interaction between cells is competition for a single limiting resource. We find that the fixation probability of a beneficial mutation depends on a linear combination of its growth rate and lag time relative to its immediate ancestor, even under clonal interference. The relative selective pressure on growth rate and lag time is set by the dilution factor; a larger dilution factor favors the adaptation of growth rate over the adaptation of lag time. The model shows that yield, however, is under no direct selection. We also show how the adaptation speeds of growth and lag depend on experimental parameters and the underlying supply of mutations. Finally, we investigate the evolution of covariation between these traits across populations, which reveals that the population growth rate and lag time can evolve a nonzero correlation even if mutations have uncorrelated effects on the two traits. Altogether these results provide useful guidance to future experiments on microbial evolution.

(2020) Proceedings of the National Academy of Sciences  PNAS. 117, 25, p. 1424314250 Abstract
Cells must couple cellcycle progress to their growth rate to restrict the spread of cell sizes present throughout a population. Linear, rather than exponential, accumulation of Whi5, was proposed to provide this coordination by causing a higher Whi5 concentration in cells born at a smaller size. We tested this model using the inducible GAL7 promoter to make the Whi5 concentration independent of cell size. At an expression level that equalizes the mean cell size with that of wildtype cells, the size distributions of cells with galactoseinduced Whi5 expression and wildtype cells are indistinguishable. Fluorescence microscopy confirms that the endogenous and GAL7 promoters produce different relationships between Whi5 concentration and cell volume without diminishing size control in the G1 phase. We also expressed Cln3 from the GAL1 promoter, finding that the spread in cell sizes for an asynchronous population is unaffected by this perturbation. Our findings indicate that size control in budding yeast does not fundamentally originate from the linear accumulation of Whi5, contradicting a previous claim and demonstrating the need for further models of cellcycle regulation to explain how cell size controls passage through Start.

(2020) Biophysical Journal. 118, 12, p. 29052913 Abstract
The cyanobacterium Synechococcus elongatus possesses a circadian clock in the form of a group of proteins whose concentrations and phosphorylation states oscillate with daily periodicity under constant conditions. The circadian clock regulates the cell cycle such that the timing of the cell divisions is biased toward certain times during the circadian period, but the mechanism underlying this phenomenon remains unclear. Here, we propose a mechanism in which a protein limiting for division accumulates at a rate proportional to the cell volume growth and is modulated by the clock. This “modulated rate” model, in which the clock signal is integrated over time to affect division timing, differs fundamentally from the previously proposed “gating” concept, in which the clock is assumed to suppress divisions during a specific time window. We found that although both models can capture the singlecell statistics of division timing in S. elongatus, only the modulated rate model robustly places divisions away from darkness during changes in the environment. Moreover, within the framework of the modulated rate model, existing experiments on S. elongatus are consistent with the simple mechanism that division timing is regulated by the accumulation of a division limiting protein in a phase with genes whose activity peaks at dusk.

(2020) Journal of the Royal Society Interface. 17, 166, 20190827. Abstract
In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the wellknown EulerLotka equation, which relates the steadystate distribution of phenotypes to the population growth rate. We derive a generalization of the EulerLotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.

(2020) Physical Review B. 101, 12, 121403. Abstract
We study heat conduction mediated by longitudinal phonons in onedimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find nontrivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that, suprisingly, the thermal conductance of a system with strong disorder, characterized by a "heavytailed" probability distribution, and with large impedance mismatch between the bath and the system, scales normally with the system size, i.e., in a manner consistent with Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.

(2020) Journal of statistical mechanics. 2020, 1, 013214. Abstract
The generalized central limit theorem is a remarkable generalization of the central limit theorem, showing that the sum of a large number of independent, identicallydistributed (i.i.d) random variables with infinite variance may converge under appropriate scaling to a distribution belonging to a special family known as Levy stable distributions. Similarly, the maximum of i.i.d. variables may converge to a distribution belonging to one of three universality classes (Gumbel, Weibull and Frechet). Here, we rederive these known results following a mathematically nonrigorous yet highly transparent renormalizationgroupinspired approach that captures both of these universal results following a nearly identical procedure.

(2020) Physical Review. E. 101, 1, 012401. Abstract
Singlecell experiments have revealed celltocell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate are usually based on the assumption that the generation times of mother and daughter cells are uncorrelated. This assumption, however, is inconsistent with the exponential growth of cell volume in time observed for many cell types. Here we develop a more general and biologically relevant model in which cells grow exponentially and generation times are correlated in a manner which controls cell size. In addition to the fluctuating generation times, we also allow the singlecell growth rates to fluctuate and account for their correlations across the lineage tree. Surprisingly, we find that the population growth rate only depends on the distribution of singlecell growth rates and their correlations.
2019

(2019) eLife. 8, e42599. Abstract
The singlecelled green algae Chlamydomonas reinhardtii with its two flagella—microtubulebased structures of equal and constant lengths—is the canonical model organism for studying size control of organelles. Experiments have identified motordriven transport of tubulin to the flagella tips as a key component of their length control. Here we consider a class of models whose key assumption is that proteins responsible for the intraflagellar transport (IFT) of tubulin are present in limiting amounts. We show that the limitingpool assumption is insufficient to describe the results of severing experiments, in which a flagellum is regenerated after it has been severed. Next, we consider an extension of the limitingpool model that incorporates proteins that depolymerize microtubules. We show that this ‘active disassembly’ model of flagellar length control explains in quantitative detail the results of severing experiments and use it to make predictions that can be tested in experiments.

(2019) Science advances. 5, 7, eaav3842. Abstract
Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hillclimbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect longterm fitness evolution. By using a spinglass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.

(2019) Physical review. B. 100, 2, p. 1 024110. Abstract
We study the spread of a quantummechanical wave packet in a noisy environment, modeled using a tightbinding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations between different levelcrossing events can be neglected, we use the solution of the LandauZener problem to find how the diffusion constant depends on the noise. We also show that when an electric field or external disordered potential is applied to the system, the diffusion constant is suppressed with no drift term arising. The results are relevant to various quantum systems, including exciton diffusion in photosynthesis and electronic transport in solidstate physics.

(2019) Biophysical Journal. 116, 12, p. 23782389 Abstract
Membrane lysis, or rupture, is a cell death pathway in bacteria frequently caused by cell walltargeting antibiotics. Although previous studies have clarified the biochemical mechanisms of antibiotic action, a physical understanding of the processes leading to lysis remains lacking. Here, we analyze the dynamics of membrane bulging and lysis in Escherichia coli, in which the formation of an initial, partially subtended spherical bulge (“bulging”) after cell wall digestion occurs on a characteristic timescale of 1 s and the growth of the bulge (“swelling”) occurs on a slower characteristic timescale of 100 s. We show that bulging can be energetically favorable due to the relaxation of the entropic and stretching energies of the inner membrane, cell wall, and outer membrane and that the experimentally observed timescales are consistent with model predictions. We then show that swelling is mediated by the enlargement of wall defects, after which cell lysis is consistent with both the inner and outer membranes exceeding characteristic estimates of the yield areal strains of biological membranes. These results contrast biological membrane physics and the physics of thin, rigid shells. They also have implications for cellular morphogenesis and antibiotic discovery across different species of bacteria.

(2019) Physical review letters. 122, 6, 068101. Abstract
Asymmetric segregation of key proteins at cell division  be it a beneficial or deleterious protein  is ubiquitous in unicellular organisms and often considered as an evolved trait to increase fitness in a stressed environment. Here, we provide a general framework to describe the evolutionary origin of this asymmetric segregation. We compute the population fitness as a function of the protein segregation asymmetry a, and show that the value of a which optimizes the population growth manifests a phase transition between symmetric and asymmetric partitioning phases. Surprisingly, the nature of phase transition is different for the case of beneficial proteins as opposed to deleterious proteins: a smooth (second order) transition from purely symmetric to asymmetric segregation is found in the former, while a sharp transition occurs in the latter. Our study elucidates the optimization problem faced by evolution in the context of protein segregation, and motivates further investigation of asymmetric protein segregation in biological systems.

(2019) eLife. 8, e40472. Abstract
MreB is an actin homolog that is essential for coordinating the cell wall synthesis required for the rod shape of many bacteria. Previously we have shown that filaments of MreB bind to the curved membranes of bacteria and translocate in directions determined by principal membrane curvatures to create and reinforce the rod shape (Hussain et al., 2018). Here, in order to understand how MreB filament dynamics affects their cellular distribution, we model how MreB filaments bind and translocate on membranes with different geometries. We find that it is both energetically favorable and robust for filaments to bind and orient along directions of largest membrane curvature. Furthermore, significant localization to different membrane regions results from processive MreB motion in various geometries. These results demonstrate that the in vivo localization of MreB observed in many different experiments, including those examining negative Gaussian curvature, can arise from translocation dynamics alone.
2018

(2018) Europhysics Letters. 124, 1, 16001. Abstract
It is well known that the contribution of harmonic phonons to the thermal conductivity of 1D systems diverges with the harmonic chain length L. Within various onedimensional models containing disorder it was shown that the thermal conductivity scales as under certain boundary conditions. Here we show that when the chain is weakly coupled to the heat reservoirs and there is strong disorder this scaling can be violated. We find a weaker powerlaw dependence on L, and show that for sufficiently strong disorder the thermal conductivity ceases to be anomalous  it does not depend on L and hence obeys Fourier's law. This is despite both density of states and the diverging localization length scaling anomalously. Surprisingly, in this strong disorder regime two anomalously scaling quantities cancel each other to recover Fourier's law of heat transport.

(2018) Nature Communications. 9, 1, 4496. Abstract
Many experiments show that the numbers of mRNA and protein are proportional to the cell volume in growing cells. However, models of stochastic gene expression often assume constant transcription rate per gene and constant translation rate per mRNA, which are incompatible with these experiments. Here, we construct a minimal gene expression model to fill this gap. Assuming ribosomes and RNA polymerases are limiting in gene expression, we show that the numbers of proteins and mRNAs both grow exponentially during the cell cycle and that the concentrations of all mRNAs and proteins achieve cellular homeostasis; the competition between genes for the RNA polymerases makes the transcription rate independent of the genome number. Furthermore, by extending the model to situations in which DNA (mRNA) can be saturated by RNA polymerases (ribosomes) and becomes limiting, we predict a transition from exponential to linear growth of cell volume as the proteintoDNA ratio increases.

(2018) Physical Review Materials. 2, 7, 075201. Abstract
We study localization of waves in a onedimensional disordered metamaterial of bilayers composed of thin fixed length scatterers placed randomly along a homogenous medium. As an interplay between order and disorder, we identify a new regime of strong disorder where the localization length becomes independent of the amount of disorder but depends on the frequency of the wave excitation and on the properties of the fixed length scatterer. As an example of a naturally occurring nearly onedimensional disordered bilayer, we calculate the wavelengthdependent reflection spectrum for Koi fish using the experimentally measured parameters and find that the main mechanisms for the emergence of their silver structural coloration can be explained through the phenomenon of localization of light in the regime of strong disorder discussed above. Finally, we show that, by tuning the thickness of the fixed length scatterer, the above design principles could be used to engineer disordered metamaterials which selectively allow harmonics of a fundamental frequency to be transmitted in an effect which is similar to the insertion of a halfwave cavity in a quarterwavelength stack. However, in contrast to the Lorentzian resonant peak of a halfwave cavity, we find that our disordered layer has a Gaussian line shape whose width becomes narrower as the number of disordered layers is increased.

(2018) Physical Review E. 98, 1, 012420. Abstract
Discriminating between correct and incorrect substrates is a core process in biology, but how is energy apportioned between the conflicting demands of accuracy (μ), speed (σ), and total entropy production rate (P)? Previous studies have focused on biochemical networks with simple structure or relied on simplifying kinetic assumptions. Here, we use the linear framework for timescale separation to analytically examine steadystate probabilities away from thermodynamic equilibrium for networks of arbitrary complexity. We also introduce a method of scaling parameters that is inspired by Hopfield's treatment of kinetic proofreading. Scaling allows asymptotic exploration of highdimensional parameter spaces. We identify in this way a broad class of complex networks and scalings for which the quantity σln(μ)/P remains asymptotically finite whenever accuracy improves from equilibrium, so that μeq/μ→0. Scalings exist, however, even for Hopfield's original network, for which σln(μ)/P is asymptotically infinite, illustrating the parametric complexity. Outside the asymptotic regime, numerical calculations suggest that, under more restrictive parametric assumptions, networks satisfy the bound, σln(μ/μeq)/P

(2018) Annual Review of Biophysics. 47, 1, p. 251271 Abstract
Most microorganisms regulate their cell size. In this article, we review some of the mathematical formulations of the problem of cell size regulation. We focus on coarsegrained stochastic models and the statistics that they generate. We review the biologically relevant insights obtained from these models. We then describe cell cycle regulation and its molecular implementations, protein number regulation, and population growth, all in relation to size regulation. Finally, we discuss several future directions for developing understanding beyond phenomenological models of cell size regulation.

(2018) Trends in microbiology (Regular ed.). 26, 4, p. 376385 Abstract
For many decades, the wedding of quantitative data with mathematical modeling has been fruitful, leading to important biological insights. Here, we review some of the ongoing efforts to gain insights into problems in microbiology – and, in particular, cellcycle progression and its regulation – through observation and quantitative analysis of the natural fluctuations in the system. We first illustrate this idea by reviewing a classic example in microbiology – the Luria–Delbrück experiment – and discussing how, in that case, useful information was obtained by looking beyond the mean outcome of the experiment, but instead paying attention to the variability between replicates of the experiment. We then switch gears to the contemporary problem of cell cycle progression and discuss in more detail how insights into cell size regulation and, when relevant, coupling between the cell cycle and the circadian clock, can be gained by studying the natural fluctuations in the system and their statistical properties. We end with a more general discussion of how (in this context) the correct level of phenomenological model should be chosen, as well as some of the pitfalls associated with this type of analysis. Throughout this review the emphasis is not on providing details of the experimental setups or technical details of the models used, but rather, in fleshing out the conceptual structure of this particular approach to the problem. For this reason, we choose to illustrate the framework on a rather broad range of problems, and on organisms from all domains of life, to emphasize the commonality of the ideas and analysis used (as well as their differences).

(2018) Nature Microbiology. 3, 2, p. 148154 Abstract
In nature, microorganisms exhibit different volumes spanning six orders of magnitude ^{1} . Despite their capability to create different sizes, a clonal population in a given environment maintains a uniform size across individual cells. Recent studies in eukaryotic and bacterial organisms showed that this homogeneity in cell size can be accomplished by growing a constant size between two cell cycle events (that is, the adder model ^{26} ). Demonstration of the adder model led to the hypothesis that this phenomenon is a consequence of convergent evolution. Given that archaeal cells share characteristics with both bacteria and eukaryotes, we investigated whether and how archaeal cells exhibit control over cell size. To this end, we developed a softlithography method of growing the archaeal cells to enable quantitative timelapse imaging and singlecell analysis, which would be useful for other microorganisms. Using this method, we demonstrated that Halobacterium salinarum, a hypersalineadapted archaeal organism, grows exponentially at the singlecell level and maintains a narrowsize distribution by adding a constant length between cell division events. Interestingly, the archaeal cells exhibited greater variability in cell division placement and exponential growth rate across individual cells in a population relative to those observed in Escherichia coli ^{69} . Here, we present a theoretical framework that explains how these larger fluctuations in archaeal cell cycle events contribute to cell size variability and control.

(2018) eLife. 7, e32471. Abstract
MreB is essential for rod shape in many bacteria. Membraneassociated MreB filaments move around the rod circumference, helping to insert cell wall in the radial direction to reinforce rod shape. To understand how oriented MreB motion arises, we altered the shape of Bacillus subtilis. MreB motion is isotropic in round cells, and orientation is restored when rod shape is externally imposed. Stationary filaments orient within protoplasts, and purified MreB tubulates liposomes in vitro, orienting within tubes. Together, this demonstrates MreB orients along the greatest principal membrane curvature, a conclusion supported with biophysical modeling. We observed that spherical cells regenerate into rods in a local, selfreinforcing manner: rapidly propagating rods emerge from small bulges, exhibiting oriented MreB motion. We propose that the coupling of MreB filament alignment to shapereinforcing peptidoglycan synthesis creates a locallyacting, selforganizing mechanism allowing the rapid establishment and stable maintenance of emergent rod shape.
2017

(2017) Current Biology. 27, 21, p. 33673374.e7 Abstract
In model bacteria, such as E. coli and B. subtilis, regulation of cellcycle progression and cellular organization achieves consistency in cell size, replication dynamics, and chromosome positioning [1–3]. Mycobacteria elongate and divide asymmetrically, giving rise to significant variation in cell size and elongation rate among closely related cells [4, 5]. Given the physical asymmetry of mycobacteria, the models that describe coordination of cellular organization and cellcycle progression in model bacteria are not directly translatable [1, 2, 6–8]. Here, we used timelapse microscopy and fluorescent reporters of DNA replication and chromosome positioning to examine the coordination of growth, division, and chromosome dynamics at a singlecell level in Mycobacterium smegmatis (M. smegmatis) and Mycobacterium bovis Bacillus CalmetteGuérin (BCG). By analyzing chromosome and replisome localization, we demonstrated that chromosome positioning is asymmetric and proportional to cell size. Furthermore, we found that cellular asymmetry is maintained throughout the cell cycle and is not established at division. Using measurements and stochastic modeling of mycobacterial cell size and cellcycle timing in both slow and fast growth conditions, we found that wellstudied models of cellsize control are insufficient to explain the mycobacterial cell cycle. Instead, we showed that mycobacterial cellcycle progression is regulated by an unprecedented mechanism involving parallel adders (i.e., constant growth increments) that start at replication initiation. Together, these adders enable mycobacterial populations to regulate cell size, growth, and heterogeneity in the face of varying environments. Logsdon et al. study cellcycle dynamics of asymmetrically growing mycobacteria and show how cell cycle, chromosome organization, and division are coordinated in single cells. A parallel adder model, where cells add a constant length between initiations and initiation to division, describes cellsize control in M. smegmatis and BCG.

(2017) Frontiers in Cell and Developmental Biology. 5, 92. Abstract
Organisms across all domains of life regulate the size of their cells. However, the means by which this is done is poorly understood. We study two abstracted "molecular" models for size regulation: inhibitor dilution and initiator accumulation. We apply the models to two settings: bacteria like Escherichia coli, that grow fully before they set a division plane and divide into two equally sized cells, and cells that form a bud early in the cell division cycle, confine new growth to that bud, and divide at the connection between that bud and the mother cell, like the budding yeast Saccharomyces cerevisiae. In budding cells, delaying cell division until buds reach the same size as their mother leads to very weak size control, with average cell size and standard deviation of cell size increasing over time and saturating up to 100fold higher than those values for cells that divide when the bud is still substantially smaller than its mother. In budding yeast, both inhibitor dilution or initiator accumulation models are consistent with the observation that the daughters of diploid cells add a constant volume before they divide. This "adder" behavior has also been observed in bacteria. We find that in bacteria an inhibitor dilution model produces adder correlations that are not robust to noise in the timing of DNA replication initiation or in the timing from initiation of DNA replication to cell division (the C+D period). In contrast, in bacteria an initiator accumulation model yields robust adder correlations in the regime where noise in the timing of DNA replication initiation is much greater than noise in the C + D period, as reported previously (Ho and Amir, 2015). In bacteria, division into two equally sized cells does not broaden the size distribution.

The Effects of Stochasticity at the SingleCell Level and Cell Size Control on the Population Growth(2017) Cell Systems. 5, 4, p. 358367.e4 Abstract
Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the experimentally observed correlations between motherdaughter generation times that are unavoidable when cell size is controlled for, which is essentially always the case. Here, we study populationlevel growth in the presence of cell size control and corroborate our theory using experimental measurements of singlecell growth rates. We derive a closed formula for the population growth rate and demonstrate that it only depends on the singlecell growth rate variability, not other sources of stochasticity. Our work provides an evolutionary rationale for the narrow growth rate distributions often observed in nature: when singlecell growth rates are less variable but have a fixed mean, the population will exhibit an enhanced population growth rate as long as the correlations between the mother and daughter cells’ growth rates are not too strong. The effects of singlecell variability on the population growth are studied, and it is found that the only stochastic term of consequence is the growth rate variability, which typically decreases the population growth rate.

(2017) Nature Microbiology. 2, 9, 17115. Abstract
The shapes of most bacteria are imparted by the structures of their peptidoglycan cell walls, which are determined by many dynamic processes that can be described on various length scales ranging from shortrange glycan insertions to cellularscale elasticity. Understanding the mechanisms that maintain stable, rodlike morphologies in certain bacteria has proved to be challenging due to an incomplete understanding of the feedback between growth and the elastic and geometric properties of the cell wall. Here, we probe the effects of mechanical strain on cell shape by modelling the mechanical strains caused by bending and differential growth of the cell wall. We show that the spatial coupling of growth to regions of high mechanical strain can explain the plastic response of cells to bending and quantitatively predict the rate at which bent cells straighten. By growing filamentous Escherichia coli cells in doughnutshaped microchambers, we find that the cells recovered their straight, native rodshaped morphologies when released from captivity at a rate consistent with the theoretical prediction. We then measure the localization of MreB, an actin homologue crucial to cell wall synthesis, inside confinement and during the straightening process, and find that it cannot explain the plastic response to bending or the observed straightening rate. Our results implicate mechanical strain sensing, implemented by components of the elongasome yet to be fully characterized, as an important component of robust shape regulation in E. coli.

(2017) Physical Review B. 95, 14, 144207. Abstract
At low temperatures the dynamical degrees of freedom in amorphous solids are tunneling twolevel systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLSTLS interactions, we obtain a "TLS glass," described by the randomfield Ising model with random 1/r3 interactions. In this paper we perform a selfconsistent meanfield calculation, previously used to study the electronglass (EG) model [A. Amir, Phys. Rev. B 77, 165207 (2008)PRBMDO1098012110.1103/PhysRevB.77.165207]. Similarly to the electron glass, we find a 1λ distribution of relaxation rates λ, leading to logarithmic slow relaxation. However, with increased interactions the EG model shows slower dynamics whereas the TLSglass model shows faster dynamics. This suggests that given systemspecific properties, glass dynamics can be slowed down or sped up by the interactions.

(2017) Physical review letters. 118, 8, 085501. Abstract
We observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain longlasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior.

(2017) eLife. 6, e22186. Abstract
All organisms control the size of their cells. We focus here on the question of size regulation in bacteria, and suggest that the quantitative laws governing cell size and its dependence on growth rate may arise as byproducts of a regulatory mechanism which evolved to support multiple DNA replication forks. In particular, we show that the increase of bacterial cell size during Lenski’s longterm evolution experiments is a natural outcome of this proposal. This suggests that, in the context of evolution, cell size may be a ‘spandrel’.
2016

(2016) Proceedings of the National Academy of Sciences of the United States of America. 113, 52, p. 1500015005 Abstract
Bacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter's growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ. We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed "adderperorigin" model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation.

(2016) Optica. 3, 12, p. 14361439 Abstract
Photonic crystals with slowly varying lattice period are responsible for broadband light reflectance in many biological contexts, ranging from the coatings of shiny beetles to the eye shine of butterflies. We utilize a quantum scattering analogy to obtain an approximate but closedform expression for the reflectance of these adiabatically chirped photonic crystals (ACPCs). This expression allows us to devise a method for designing ACPCs with tailored reflectance spectra and obtain an estimate for the minimal number of layers required to exceed a given reflectance threshold. Comparison against the number of layers found in ACPCs throughout nature gives a quantitative measure of the optimality of chirped biological reflectors. Together, these results elucidate the design of chirped reflectors in nature and their possible application to future optical technologies.

(2016) Physical review letters. 117, 11, 116601. Abstract
Memory is one of the unique qualities of a glassy system. The relaxation of a glass to equilibrium contains information on the sample's excitation history, an effect often refer to as "aging." We demonstrate that under the right conditions a glass can also possess a different type of memory. We study the conductance relaxation of electron glasses that are fabricated at low temperatures. Remarkably, the dynamics are found to depend not only on the ambient measurement temperature but also on the maximum temperature to which the system was exposed. Hence the system "remembers" its highest temperature. This effect may be qualitatively understood in terms of energy barriers and local minima in configuration space and therefore may be a general property of the glass state.

(2016) Physical Review E. 94, 1, 012405. Abstract
We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a powerlaw tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

(2016) Physical Review E. 93, 4, 042310. Abstract
We explore the spectra and localization properties of the Nsite banded onedimensional nonHermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90 rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the densityofstates in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The biasdependent shape of this hole tracks the biasindependent contours of constant localization length. We treat the largeN limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

(2016) Current Biology. 26, 3, p. 356361 Abstract
To maintain a constant cell size, dividing cells have to coordinate cellcycle events with cell growth. This coordination has long been supposed to rely on the existence of size thresholds determining cellcycle progression [1]. In budding yeast, size is controlled at the G1/S transition [2]. In agreement with this hypothesis, the size at birth influences the time spent in G1: smaller cells have a longer G1 period [3]. Nevertheless, even though cells born smaller have a longer G1, the compensation is imperfect and they still bud at smaller cell sizes. In bacteria, several recent studies have shown that the incremental model of size control, in which size is controlled by addition of a constant volume (in contrast to a size threshold), is able to quantitatively explain the experimental data on four different bacterial species [47]. Here, we report on experimental results for the budding yeast Saccharomyces cerevisiae, finding, surprisingly, that cell size control in this organism is very well described by the incremental model, suggesting a common strategy for cell size control with bacteria. Additionally, we argue that for S. cerevisiae the "volume increment" is not added from birth to division, but rather between two budding events.

(2016) American Journal of Physics. 84, 1, p. 5760 Abstract
Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the firstreturntime distribution of a onedimensional random walker, which is a heavytailed distribution with infinite mean. Using the same method, we find the lastreturntime distribution, which follows the arcsine law. Both results have a broad range of applications in physics and other disciplines. The derivation presented here is readily accessible to physics undergraduates and provides an elementary introduction into random walks and their intriguing properties.

(2016) The American mathematical monthly. 123, 6, p. 609612 Abstract
In science, as in life, "surprises" can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like π or e. The inverse problem also arises, whereby the measured value of a physical constant admits a "surprisingly" simple approximation in terms of wellknown mathematical constants. Can we estimate the probability for this to be a mere coincidence, rather than an inkling of some theory? We answer the question in the most naive form.
2015

(2015) Frontiers in Microbiology. 6, JUL, 662. Abstract
Bacteria are able to maintain a narrow distribution of cell sizes by regulating the timing of cell divisions. In rich nutrient conditions, cells divide much faster than their chromosomes replicate. This implies that cells maintain multiple rounds of chromosome replication per cell division by regulating the timing of chromosome replications. Here, we show that both cell size and chromosome replication may be simultaneously regulated by the longstanding initiator accumulation strategy. The strategy proposes that initiators are produced in proportion to the volume increase and is accumulated at each origin of replication, and chromosome replication is initiated when a critical amount per origin has accumulated. We show that this model maps to the incremental model of size control, which was previously shown to reproduce experimentally observed correlations between various events in the cell cycle and explains the exponential dependence of cell size on the growth rate of the cell. Furthermore, we show that this model also leads to the efficient regulation of the timing of initiation and the number of origins consistent with existing experimental results.
2014

(2014) Systems and Synthetic Biology. 8, 3, p. 227235 Abstract
Rodlike bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements. Despite being one of the simplest morphologies, we are still far from a full understanding of how shape is robustly regulated, and how bacteria obtain their nearperfect cylindrical shapes with excellent precision. However, recent experimental and theoretical findings suggest that cellwall geometry and mechanical stress play important roles in regulating cell shape in rodlike bacteria. We review our current understanding of the cell wall architecture and the growth dynamics, and discuss possible candidates for regulatory cues of shape regulation in the absence or presence of external constraints. Finally, we suggest further future experimental and theoretical directions which may help to shed light on this fundamental problem.

(2014) EPL. 107, 4, 47011. Abstract
Characterizing the frequencydependent response of amorphous systems and glasses can provide important insights into their physics. Here, we study the response of an electron glass, where Coulomb interactions are important and have previously been shown to significantly modify the conductance and lead to memory effects and aging. We propose a model which allows us to take the interactions into account in a selfconsistent way, and explore the frequencydependent conduction at all frequencies. At low frequencies conduction occurs on the percolation backbone, and the model captures the variablerangehopping behavior. At high frequencies conduction is dominated by localized clusters. Despite the difference in physical mechanisms at low and high frequency, we are able to approximately scale all numerical data onto a single curve, using two parameters: the DC conduction and the DC dielectric constant. The behavior follows the universal scaling that is experimentally observed for a large class of amorphous solids.

(2014) Physical review letters. 112, 20, 208102. Abstract
Various bacteria such as the canonical gram negative Escherichia coli or the wellstudied gram positive Bacillus subtilis divide symmetrically after they approximately double their volume. Their size at division is not constant, but is typically distributed over a narrow range. Here, we propose an analytically tractable model for cell size control, and calculate the cell size and interdivision time distributions, as well as the correlations between these variables. We suggest ways of extracting the model parameters from experimental data, and show that existing data for E. coli supports partial size control, and a particular explanation: a cell attempts to add a constant volume from the time of initiation of DNA replication to the next initiation event. This hypothesis accounts for the experimentally observed correlations between mother and daughter cells as well as the exponential dependence of size on growth rate.

(2014) Proceedings of the National Academy of Sciences of the United States of America. 111, 16, p. 57785783 Abstract
Cell walls define a cell's shape in bacteria. The walls are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this paper, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell wall growth. By applying a precisely controllable hydrodynamic force to growing rodshaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreementwith the predictions of the theory of dislocationmediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell's responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments.

(2014) Physical Review A. 89, 3, 033807. Abstract
The electromagnetically induced transparency (EIT) spectrum of atoms diffusing in and out of a narrow beam is measured and shown to manifest the twodimensional δfunction anomaly in a classical setting. In the limit of smallarea beams, the EIT line shape is independent of power, and equal to the renormalized local density of states of a free particle Hamiltonian. The measured spectra for different powers and beam sizes collapses to a single universal curve with a characteristic logarithmic Van Hove singularity close to resonance.
2013

(2013) Physical Review E  Statistical, Nonlinear, and Soft Matter Physics. 87, 4, 042314. Abstract
We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rodshaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are created by a PeachKoehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind. The thermal nucleation rate of dislocation unbinding is calculated, for an arbitrary mobility tensor and external stress, including the case of a twistinduced PeachKoehler force along the cylinder axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite their vanishing Gaussian curvature.

(2013) American Journal of Physics. 81, 4, p. 253257 012303AJP. Abstract
Interference is the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics: specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer structure and solve it using recursion relations. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursion. We compare to experimental data for various beetles, whose optical structure resembles the proposed model. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concept of band structure in the context of the experimentally observed high reflectance and iridescent appearance of structurally colored beetles.

(2013) Physical Review X. 3, 2, 021017. Abstract
We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency, and spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localizationdelocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach, we calculate the speed of sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density and find good agreement of these predictions with numerical results using a recursive Greenfunction method that was adapted for this problem. The connection of our results to recent experiments on amorphous solids is discussed.
2012

(2012) Proceedings of the National Academy of Sciences of the United States of America. 109, 25, p. 98339838 Abstract
Recent experiments have illuminated a remarkable growth mechanism of rodshaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference [Garner EC, et al., (2011) Science 333:222–225], [DomínguezEscobar J, et al. (2011) Science 333:225–228], [van Teeffelen S, et al. (2011) PNAS 108:15822–15827]. We view these as dislocations in the partially ordered peptidoglycan structure, activated by glycan strand extension machinery, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Generation and motion of these interacting defects lead to surprising effects arising from the cylindrical geometry, with important implications for growth. We also discuss how long range elastic interactions and turgor pressure affect the dynamics of the fraction of actively moving dislocations in the bacterial cell wall.

Defects on cylinders: superfluid helium films and bacterial cell walls(2012) arxiv.org. Abstract
There is a deep analogy between the physics of crystalline solids and the behavior of superfluids, dating back to pioneering work of Phillip Anderson, Paul Martin and others. The stiffness to shear deformations in a periodic crystal resembles the superfluid density that controls the behavior of supercurrents in neutral superfluids such as He^4. Dislocations in solids have a close analogy with quantized vortices in superfluids. Remarkable recent experiments on the way rodshaped bacteria elongate their cell walls have focused attention on the dynamics and interactions of pointlike dislocation defects in partially ordered cylindrical crystalline monolayers. In these lectures, we review the physics of superfluid helium films on cylinders and discuss how confinement in one direction affects vortex interactions with supercurrents. Although there are similarities with the way dislocations respond to strains on cylinders, important differences emerge, due to the vector nature of the topological charges characterizing the dislocations.

(2012) Proceedings of the National Academy of Sciences of the United States of America. 109, 6, p. 18501855 Abstract
Slow relaxation occurs in many physical and biological systems. "Creep" is an example from everyday life. When stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: The relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the "waiting time." This ubiquitous phenomenon is called aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, which predicts logarithmic relaxations, and a particular aging dependence on the waiting time. We demonstrate the generality of the approach by comparing our predictions to experimental data on a diverse range of physical phenomena, from conductance in granular metals to disordered insulators and dirty semiconductors, to the low temperature dielectric properties of glasses.

Logarithmically diverging twophoton spectrum: Anomalous scale symmetry breaking in two dimensions(2012) Quantum Electronics and Laser Science Conference, QELS 2012. Abstract
For small area beams, the twophoton spectra of atoms diffusing in hot buffer gas approaches a universal, logarithmicallydiverging shape, connected to anomalous scale symmetry breaking of a twodimensional Hamiltonian.
2011

(2011) Physical review letters. 107, 18, 186407. Abstract
Experiments performed in the last years demonstrated slow relaxations and aging in the conductance of a large variety of materials. Here, we present experimental and theoretical results for conductance relaxation and aging for the casestudy example of porous silicon. The relaxations are experimentally observed even at room temperature over time scales of hours, and when a strong electric field is applied for a time t_{w}, the ensuing relaxation depends on t_{w}. We derive a theoretical curve and show that all experimental data collapse onto it with a single time scale as a fitting parameter. This time scale is found to be of the order of thousands of seconds at room temperature. The generic theory suggested is not finetuned to porous silicon, and thus we believe the results should be universal, and the presented method should be applicable for many other systems manifesting memory and other glassy effects.

(2011) Annual Review of Condensed Matter Physics. 2, p. 235262 Abstract
Examples of glasses are abundant, yet it remains one of the phases of matter whose understanding is very elusive. In recent years, remarkable experiments have been performed on the dynamical aspects of glasses. Electron glasses offer a particularly good example of the trademarks of glassy behavior, such as aging and slow relaxations. In this work we review the experimental literature on electron glasses, as well as the local meanfield theoretical framework put forward in recent years to understand some of these results. We also present novel theoretical results explaining the periodic aging experiment.
2010

(2010) Annalen der Physik. 18, 12, p. 836843 Abstract
Recently we have shown that slow relaxations in the electron glass system, can be understood in terms of the spectrum of a matrix describing the relaxation of the system close to a metastable state. The model focused on the electron glass system, but its generality was demonstrated on various other examples. Here, we study the noise spectrum in the same framework. We obtain a remarkable relation between the spectrum of relaxation rates A described by the distribution function P(λ)∼ 1/λ and the 1/f noise in the fluctuating occupancies of the localized electronic sites. This noise can be observed using local capacitance measurements. We confirm our analytic results using numerics, and also show how the Onsager symmetry is fulfilled in the system.

(2010) Physical review letters. 105, 7, 070601. Abstract
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum), for low densities, and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.

(2010) International Journal of Modern Physics B. 24, 1213, p. 17891810 Abstract
The Anderson localization transition is considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.

(2010) 50 Years of Anderson Localization. p. 191212 Abstract
The Anderson localization transition is considered at nite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.
2009

(2009) Physical Review B. 80, 24, 245214. Abstract
We use a local meanfield (Hartreelike) approach to study the conductance of a strongly localized electron system in two dimensions. We find a crossover between a regime where Coulomb interactions modify the conductance significantly to a regime where they are negligible. We show that under rather general conditions the conduction obeys a scaling relation which we verify using numerical simulations. The use of a local meanfield approach gives a clear physical picture, and removes the ambiguity of the use of singleparticle tunneling density of states (DOS) in the calculation of the conductance. Furthermore, the theory contains interactioninduced correlations between the on site energy of the localized states and distances, as well as finite temperature corrections of the DOS.

(2009) Physical review letters. 103, 12, 126403. Abstract
Glassy systems are ubiquitous in nature. They are characterized by slow relaxations to equilibrium without a typical time scale, aging, and memory effects. Understanding this has been a longstanding problem in physics. We study the aging of the electron glass, a system showing remarkable slow relaxations of the conductance. We find that the appropriate broad distribution of relaxation rates leads to a universal relaxation of the form log(1+tw/t) for the common aging protocol, where tw is the length of time the perturbation driving the system out of equilibrium was on, and t the time of measurement. These results agree well with several experiments performed on different glassy systems, and examining different physical observables, for times ranging from seconds to several hours. The suggested theoretical framework appears to offer a paradigm for aging in a broad class of glassy materials.

(2009) Physical Review E. 79, 5, 050105. Abstract
We study the spreading of a quantummechanical wave packet in a tightbinding model with a noisy potential and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite correlation time of the noisy environment and treat the system by utilizing the separation of fast (dephasing) and slow (diffusion) processes. We show that classical diffusive behavior emerges at long times and we calculate analytically the dependence of the classical diffusion coefficient on the noise magnitude and correlation time. This method provides a general solution to this problem for arbitrary conditions of the noisy environment. The calculation can be done in any dimension, but we demonstrate it in one dimension for clarity of representation. The results are relevant to a large variety of physical systems, from electronic transport in solidstate physics to light transmission in optical devices, diffusion of excitons, and quantum computation.
2008

(2008) Physical Review A. 77, 5, 050101. Abstract
We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudocontinuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudocontinuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random, several cases are identified. For a pseudocontinuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudocontinuum space. They last for a long time compared to the nonrandom case.

(2008) Physical Review B. 77, 16, 165207. Abstract
We study a microscopic meanfield model for the dynamics of the electron glass near a local equilibrium state. Phononinduced tunneling processes are responsible for generating transitions between localized electronic sites, which eventually lead to the thermalization of the system. We find that the decay of an excited state to a locally stable state is far from being exponential in time and does not have a characteristic time scale. Working in a meanfield approximation, we write rate equations for the average occupation numbers ni and describe the return to the locally stable state by using the eigenvalues of a rate matrix A describing the linearized time evolution of the occupation numbers. By analyzing the probability distribution P (λ) of the eigenvalues of A, we find that, under certain physically reasonable assumptions, it takes the form P (λ) ∼ 1 λ, leading naturally to a logarithmic decay in time. While our derivation of the matrix A is specific for the chosen model, we expect that other glassy systems, with different microscopic characteristics, will be described by random rate matrices belonging to the same universality class of A. Namely, the rate matrix has elements with a very broad distribution, as in the case of exponentials of a variable with nearly uniform distribution.