Publications

Patterns in time and space spanning a wide range of scales abound in nature, from the circadian oscillations in cyanobacteria to epidemic cycles, from the exquisite skins in zebras to the spatial structure of ecological habitats. For many of these systems, deterministic descriptions may necessitate fine tuning of parameters in order for patterns to form, in a way that is incompatible with their observed natural robustness. Furthermore, endogenous stochasticity such as that coming from fluctuations in small copy numbers of the interacting basic variables may be significant for these systems, in addition to external sources of noise that act as a macroscopic bias to deterministic, reproducible dynamics. Here we survey natural systems for which demographic noise has been shown to be important, and for which an individual-based description that is intrinsically stochastic is needed. This amounts to characterizing their microscopic dynamics via master equations, which return the probability for observing a system in a given state, at a given time. The application of perturbative expansions to obtain approximate analytical and numerical solutions of the master equations describing these specific systems, shows how the effects of demographic noise emerge in a perturbative fashion, and how endogenous stochasticity can be self-consistently amplified, yielding almost regular oscillations, termed quasi-cycles. These quasi-cycles appear for parameter values that lie outside the regions in parameter space where deterministic oscillations are predicted, thereby enhancing robustness. Thus, counter intuitively, noise can organize in regular quasi-periodic orbits, thereby building macroscopic order from microscopic disorder. This intriguing concept, introduced for the temporal domain, can be extended to the realm of spatial systems: demographic noise can seed the emergence of stochastic Turing patterns, which have been observed in systems ranging from developmental patterns, hallucinations to microbial biofilms. We illustrate the analytical approach by making reference to simple toy models and highlight the constructive role that demographic noise can play in seeding stochastic self-organized patterns in specific systems, both in time and space.

Chromosomal sites in rod-like bacteria move sub-diffusely, driven by the out-of-equilibrium nature of the viscoelastic, crowded intracellular environment. Furthermore, it has been shown that there is a pronounced dynamical asymmetry between longitudinal (long-axis) and transverse (radial) motions, manifested in different exponents in the mean-square displacements MSDt~tα, αl and αr respectively. Here, using polymer simulations and experimental observations of a locus in Bacillus subtilis, we substantiate the notion that asymmetric dynamics are a result of the asymmetric structure of the bacterial chromosome modeled as a bottlebrush polymer in a poor solvent. Our simulations recapitulate the observed asymmetry as well as the range of the observed exponent values that are related to scaling models of polymer dynamics, lending support to the notion that asymmetric dynamics is a consequence of the bottlebrush structure of the bacterial chromosome.

Active matter, from motile bacteria to animals, can exhibit striking collective and coherent behavior. Despite significant advances in understanding the behavior of homogeneous systems, little is known about the self-organization and dynamics of heterogeneous active matter, such as complex and diverse bacterial communities. Under oxygen gradients, many bacterial species swim towards air-liquid interfaces in auto-organized, directional bioconvective flows, whose spatial scales exceed the cell size by orders of magnitude. Here we show that multispecies bacterial suspensions undergoing oxytactic-driven bioconvection exhibit dynamically driven spatial segregation, despite the enhanced mixing of bioconvective flows, and the fact that these species coexist in their natural habitat. Segregation is observed as patterns of spatially interlocked domains, with local dominance of one of the constituent species in the suspension. Our findings suggest that segregation mechanisms are driven by species-specific motile behaviors under conditions of hydrodynamic flow, rather than biochemical repulsion. Thus, species with different motile characteristics in the same ecological context can enhance their access to limiting resources. This work provides novel insights on the role of heterogeneity in active matter, as well as on the dynamics of complex microbial communities, their spatial organization and their collective behavior.

Temperate phage-mediated horizontal gene transfer is a potent driver of genetic diversity in the evolution of bacteria. Most lambdoid prophages in Escherichia coli are integrated into the chromosome with the same orientation with respect to the direction of chromosomal replication, and their location on the chromosome is far from homogeneous. To better understand these features, we studied the interplay between lysogenic and lytic states of phage lambda in both native and inverted integration orientations at the wild-type integration site as well as at other sites on the bacterial chromosome. Measurements of free phage released by spontaneous induction showed that the stability of lysogenic states is affected by location and orientation along the chromosome, with stronger effects near the origin of replication. Competition experiments and range expansions between lysogenic strains with opposite orientations and insertion loci indicated that there are no major differences in growth. Moreover, measurements of the level of transcriptional bursts of the cI gene coding for the lambda phage repressor using single-molecule fluorescence in situ hybridization resulted in similar levels of transcription for both orientations and prophage location. We postulate that the preference for a given orientation and location is a result of a balance between the maintenance of lysogeny and the ability to lyse.

In the absence of sex as in higher organisms such as mammals and plants, bacteria engage in horizontal gene transfer processes in order to acquire new ben-eficial traits and drive their genetic diversity in one stroke. Often, exogenous DNA integrates into the genome of a host at unique sites that are found within physi-ologically relevant times, among millions of possible sites on the hosts genome. Here we address the question of what are the search mechanisms that allow these unique sites to be found efficiently, within the complex interior of a bacterial cell. We review recent advances in the field, enabled by the ability to follow in real time search processes at the level of individual molecules within single cells.

Circadian clock arrays in multicellular filaments of the heterocyst-forming cyanobacterium Anabaena sp. strain PCC 7120 display remarkable spatio-temporal coherence under nitrogen-replete conditions. To shed light on the interplay between circadian clocks and the formation of developmental patterns, we followed the expression of a clock-controlled gene under nitrogen deprivation, at the level of individual cells. Our experiments showed that differentiation into heterocysts took place preferentially within a limited interval of the circadian clock cycle, that gene expression in different vegetative intervals along a developed filament was discoordinated, and that the circadian clock was active in individual heterocysts. Furthermore, Anabaena mutants lacking the kaiABC genes encoding the circadian clock core components produced heterocysts but failed in diazotrophy. Therefore, genes related to some aspect of nitrogen fixation, rather than early or mid-heterocyst differentiation genes, are likely affected by the absence of the clock. A bioinformatics analysis supports the notion that RpaA may play a role as master regulator of clock outputs in Anabaena, the temporal control of differentiation by the circadian clock and the involvement of the clock in proper diazotrophic growth. Together, these results suggest that under nitrogen-deficient conditions, the clock coherent unit in Anabaena is reduced from a full filament under nitrogen-rich conditions to the vegetative cell interval between heterocysts. IMPORTANCE Circadian clocks, from unicellular organisms to animals, temporally align biological processes to day and night cycles. We study the dynamics of a circadian clock-controlled gene at the individual cell level in the multicellular filamentous cyanobacterium Anabaena, under nitrogen-stress conditions. Under these conditions, some cells along filaments differentiate to carry out atmospheric nitrogen fixation and lose their capability for oxygenic photosynthesis. We found that clock synchronization is limited to organismic units of contiguous photosynthetic cells, contrary to nitrogen-replete conditions in which clocks are synchronized over a whole filament. We provided evidence that the circadian clock regulates the process of differentiation, allowing it to occur preferentially within a limited time window during the circadian clock period. Lastly, we present evidence that the signal from the core clock to clock-regulated genes is conveyed in Anabaena as in unicellular cyanobacteria.

Integrative and conjugative elements (ICEs) are mobile genetic elements that can transfer by conjugation to recipient cells. Some ICEs integrate into a unique site in the genome of their hosts. We studied quantitatively the process by which an ICE searches for its unique integration site in the Bacillus subtilis chromosome. We followed the motion of both ICEBs1 and the chromosomal integration site in real time within individual cells. ICEBs1 exhibited a wide spectrum of dynamical behaviors, ranging from rapid sub-diffusive displacements crisscrossing the cell, to kinetically trapped states. The chromosomal integration site moved sub-diffusively and exhibited pronounced dynamical asymmetry between longitudinal and transversal motions, highlighting the role of chromosomal structure and the heterogeneity of the bacterial interior in the search. The successful search for and subsequent recombination into the integration site is a key step in the acquisition of integrating mobile genetic elements. Our findings provide new insights into intracellular transport processes involving large DNA molecules.

Biological patterns that emerge during the morphogenesis of multicellular organisms can display high precision at large scales, while at cellular scales, cells exhibit large fluctuations stemming from cell-cell differences in molecular copy numbers also called demographic noise. We study the conflicting interplay between high precision and demographic noise in trichome patterns on the epidermis of wild-type Arabidopsis thaliana leaves, as a two-dimensional model system. We carry out a statistical characterization of these patterns and show that their power spectra display fat tails - a signature compatible with noise-driven stochastic Turing patterns - which are absent in power spectra of patterns driven by deterministic instabilities. We then present a theoretical model that includes demographic noise stemming from birth- death processes of genetic regulators which we study analytically and by stochastic simulations. The model captures the observed experimental features of trichome patterns.

Circadian clocks display remarkable reliability despite significant stochasticity in biomolecular reac-tions. We study the dynamics of a circadian clock-controlled geneattheindividualcelllevelinAnabaena sp. PCC 7120, a multicellular filamentous cyanobacterium. Wefoundsignificantsynchronizationandspa-tial coherence along filaments, clock coupling due to cell-cell communication, and gating of the cell cycle. Furthermore, we observed low-amplitude circadian oscillatory transcription of kai genes comprising the post-transcriptional core oscillatory circuit, and high-amplitude oscillations of rpaA coding for the master regulator transducing the core clock output. Transcriptional oscillations of rpaA suggest an additional level of regulation. A stochastic, one-dimensional toy model of coupled clock cores and their phosphorylation states shows that demographic noise can seed stochastic oscillations outside the region where deterministic limit cycles with circadian periods occur. The model reproduces the observed spatio-temporal coherence along filaments, and provides a robust description of coupled circadianclocksinamulticellularorganism. NTRODUCTION.

Cell-cell communication is an essential attribute of multicellular organisms. The effects of perturbed communication were studied in septal protein mutants of the heterocyst-forming filamentous cyanobacterium Anabaena sp. PCC 7120 model organism. Strains bearing sepJ and sepJ/fraC/fraD deletions showed differences in growth, pigment absorption spectra, and spatial patterns of expression of the hetR gene encoding a heterocyst differentiation master regulator. Global changes in gene expression resulting from deletion of those genes were mapped by RNA sequencing analysis of wild-type and mutant strains, both under nitrogen-replete and nitrogen-poor conditions. The effects of sepJ and fraC/fraD deletions were non-additive, and perturbed cell-cell communication led to significant changes in global gene expression. Most significant effects, related to carbon metabolism, included increased expression of genes encoding carbon uptake systems and components of the photosynthetic apparatus, as well as decreased expression of genes encoding cell wall components related to heterocyst differentiation and to polysaccharide export.

Under nitrogen-poor conditions, multicellular cyanobacteria such as Anabaena sp. PCC 7120 undergo a process of differentiation, forming nearly regular, developmental patterns of individual nitrogen-fixing cells, called heterocysts, interspersed between intervals of vegetative cells that carry out photosynthesis. Developmental pattern formation is mediated by morphogen species that can act as activators and inhibitors, some of which can diffuse along filaments. We survey the limitations of the classical, deterministic Turing mechanism that has been often invoked to explain pattern formation in these systems, and then, focusing on a simpler system governed by birth-death processes, we illustrate pedagogically a recently proposed paradigm that provides a much more robust description of pattern formation: stochastic Turing patterns. We emphasize the essential role that cell-to-cell differences in molecular numberscaused by inevitable fluctuations in gene expressionplay, the so called demographic noise, in seeding the formation of stochastic Turing patterns over a much larger region of parameter space, compared to their deterministic counterparts.

Brouwer's fixed point theorem, a fundamental theorem in algebraic topology proved more than a hundred years ago, states that given any continuous map from a closed, simply connected set into itself, there is a point that is mapped unto itself. Here we point out the connection between a one-dimensional application of Brouwer's fixed point theorem and a mechanism proposed to explain how extension of single-stranded DNA substrates by recombinases of the RecA superfamily facilitates significantly the search for homologous sequences on long chromosomes.

Under nitrogen deprivation, the one-dimensional cyanobacterial organism Anabaena sp. PCC 7120 develops patterns of single, nitrogen-fixing cells separated by nearly regular intervals of photosynthetic vegetative cells. We study a minimal, stochastic model of developmental patterns in Anabaena that includes a nondiffusing activator, two diffusing inhibitor morphogens, demographic fluctuations in the number of morphogen molecules, and filament growth. By tracking developing filaments, we provide experimental evidence for different spatiotemporal roles of the two inhibitors during pattern maintenance and for small molecular copy numbers, justifying a stochastic approach. In the deterministic limit, the model yields Turing patterns within a region of parameter space that shrinks markedly as the inhibitor diffusivities become equal. Transient, noise-driven, stochastic Turing patterns are produced outside this region, which can then be fixed by downstream genetic commitment pathways, dramatically enhancing the robustness of pattern formation, also in the biologically relevant situation in which the inhibitors' diffusivities may be comparable.

A method is described for labeling individual messenger RNA (mRNA) transcripts in fixed bacteria for use in single-molecule fluorescence in situ hybridization (smFISH) experiments in E. coli. smFISH allows the measurement of cell-to-cell variability in mRNA copy number of genes of interest, as well as the subcellular location of the transcripts. The main steps involved are fixation of the bacterial cell culture, permeabilization of cell membranes, and hybridization of the target transcripts with sets of commercially available short fluorescently-labeled oligonucleotide probes. smFISH can allow the imaging of the transcripts of multiple genes in the same cell, with limitations imposed by the spectral overlap between different fluorescent markers. Following completion of the protocol illustrated below, cells can be readily imaged using a microscope coupled with a camera suitable for low-intensity fluorescence. These images, together with cell contours obtained from segmentation of phase contrast frames, or from cell membrane staining, allow the calculation of the mRNA copy number distribution of a sample of cells using open-source or custom-written software. The labeling method described here can also be applied to image transcripts with stochastic optical reconstruction microscopy (STORM).

Small non-coding RNAs can exert significant regulatory activity on gene expression in bacteria. In recent years, substantial progress has been made in understanding bacterial gene expression by sRNAs. However, recent findings that demonstrate that families of mRNAs show non-trivial sub-cellular distributions raise the question of how localization may affect the regulatory activity of sRNAs. Here we address this question within a simple mathematical model. We show that the non-uniform spatial distributions of mRNA can alter the threshold-linear response that characterizes sRNAs that act stoichiometrically, and modulate the hierarchy among targets co-regulated by the same sRNA. We also identify conditions where the sub-cellular organization of cofactors in the sRNA pathway can induce spatial heterogeneity on sRNA targets. Our results suggest that under certain conditions, interpretation and modeling of natural and synthetic gene regulatory circuits need to take into account the spatial organization of the transcripts of participating genes.

Cyanobacteria carry out oxygenic photosynthesis, play a key role in the cycling of carbon and nitrogen in the biosphere, and have had a large impact on the evolution of life and the Earth itself. Many cyanobacterial strains exhibit a multicellular lifestyle, growing as filaments that can be hundreds of cells long and endowed with intercellular communication. Furthermore, under depletion of combined nitrogen, filament growth requires the activity of two interdependent cell types: vegetative cells that fix CO2 and heterocysts that fix N2. Intercellular molecular transfer is essential for signaling involved in the regulation of heterocyst differentiation and for reciprocal nutrition of heterocysts and vegetative cells. Here we review various aspects of multicellularity in cyanobacterial filaments and their differentiation, including filament architecture with emphasis on the structures used for intercellular communication; we survey theoretical models that have been put forward to understand heterocyst patterning and discuss the factors that need to be considered for these models to reflect the biological entity; and finally, since cell division in filamentous cyanobacteria has the peculiarity of producing linked instead of independent cells, we review distinct aspects of cell division in these organisms.

Post-transcriptional regulatory processes may change transcript levels and affect cell-to-cell variability or noise. We study small-RNA downregulation to elucidate its effects on noise in the iron homeostasis network of Escherichia coli. In this network, the small-RNA RyhB undergoes stoichiometric degradation with the transcripts of target genes in response to iron stress. Using single-molecule fluorescence in situ hybridization, we measured transcript numbers of the RyhB-regulated genes sodB and fumA in individual cells as a function of iron deprivation. We observed a monotonic increase of noise with iron stress but no evidence of theoretically predicted, enhanced stoichiometric fluctuations in transcript numbers, nor of bistable behavior in transcript distributions. Direct detection of RyhB in individual cells shows that its noise is much smaller than that of these two targets, when RyhB production is significant. A generalized two-state model of bursty transcription that neglects RyhB fluctuations describes quantitatively the dependence of noise and transcript distributions on iron deprivation, enabling extraction of in vivo RyhB-mediated transcript degradation rates. The transcripts' threshold-linear behavior indicates that the effective in vivo interaction strength between RyhB and its two target transcripts is comparable. Strikingly, the bacterial cell response exhibits Fur-dependent, switch-like activation instead of a graded response to iron deprivation.

Under nitrogen deprivation, filaments of the cyanobacterium Anabaena undergo a process of development, resulting in a one-dimensional pattern of nitrogen-fixing heterocysts separated by about ten photosynthetic vegetative cells. Many aspects of gene expression before nitrogen deprivation and during the developmental process remain to be elucidated. Furthermore, the coupling of gene expression fluctuations between cells along a multicellular filament is unknown. We studied the statistics of fluctuations of gene expression of HetR, a transcription factor essential for heterocyst differentiation, both under steady-state growth in nitrogen-rich conditions and at different times following nitrogen deprivation, using a chromosomally-encoded translational hetR-gfp fusion. Statistical analysis of fluorescence at the individual cell level in wild-type and mutant filaments demonstrates that expression fluctuations of hetR in nearby cells are coupled, with a characteristic spatial range of circa two to three cells, setting the scale for cellular interactions along a filament. Correlations between cells predominantly arise from intercellular molecular transfer and less from cell division. Fluctuations after nitrogen step-down can build up on those under nitrogen-replete conditions. We found that under nitrogen-rich conditions, basal, steady-state expression of the HetR inhibitor PatS, cell-cell communication influenced by the septal protein SepJ and positive HetR auto-regulation are essential determinants of fluctuations in hetR expression and its distribution along filaments. A comparison between the expression of hetR-gfp under nitrogen-rich and nitrogen-poor conditions highlights the differences between the two HetR inhibitors PatS and HetN, as well as the differences in specificity between the septal proteins SepJ and FraC/FraD. Activation, inhibition and cell-cell communication lie at the heart of developmental processes. Our results show that proteins involved in these basic ingredients combine together in the presence of inevitable stochasticity in gene expression, to control the coupled fluctuations of gene expression that give rise to a one-dimensional developmental pattern in this organism.

The search for specific sequences on long genomes is a key process in many biological contexts. How can specific target sequences be located with high efficiency, within physiologically relevant times? We addressed this question for viral integration, a fundamental mechanism of horizontal gene transfer driving prokaryotic evolution, using the infection of Escherichia coli bacteria with bacteriophage λ and following the establishment of a lysogenic state. Following the targeting process in individual live E. coli cells in real time revealed that λ DNA remains confined near the entry point of a cell following infection. The encounter between the 15-bp-long target sequence on the chromosome and the recombination site on the viral genome is facilitated by the directed motion of bacterial DNA generated during chromosome replication, in conjunction with constrained diffusion of phage DNA. Moving the native bacterial integration site to different locations on the genome and measuring the integration frequency in these strains reveals that the frequencies of the native site and a site symmetric to it relative to the origin are similar, whereas both are significantly higher than when the integration site is moved near the terminus, consistent with the replication-driven mechanism we propose. This novel search mechanism is yet another example of the exquisite coevolution of λ with its host.

The inherently stochastic nature of biomolecular processes is one of the main sources giving rise to cell-to-cell variations in protein and mRNA abundance, termed noise. Noise in isogenic populations can enhance survival under adverse conditions and stress, and has therefore played a fundamental role in evolution. On the other hand, noise may have detrimental effects and therefore cells must also display robustness to fluctuations and possess mechanisms of control in order to function properly. Noise can be introduced at every step in the cascade of intermediate events resulting in the production of functional proteins. While initial studies of noise focused on stochasticity introduced at the transcriptional level, recent years have witnessed a gradual shift of emphasis into the effects that post-transcriptional processes have on phenotypic noise. Here, we survey the insights that have been gained on the effects of processes that modify RNA transcript populations on phenotypic noise, including regulation by noncoding RNAs in prokaryotes and eukaryotes, alternative splicing and transcriptional interference.

Cell-to-cell variations in protein abundance, called noise, give rise to phenotypic variability between isogenic cells. Studies of noise have focused on stochasticity introduced at transcription, yet the effects of post-transcriptional regulatory processes on noise remain unknown. We study the effects of RyhB, a small-RNA of Escherichia coli produced on iron stress, on the phenotypic variability of two of its downregulated target proteins, using dual chromosomal fusions to fluorescent reporters and measurements in live individual cells. The total noise of each of the target proteins is remarkably constant over a wide range of RyhB production rates despite cells being in stress. In fact, coordinate downregulation of the two target proteins by RyhB reduces the correlation between their levels. Hence, an increase in phenotypic variability under stress is achieved by decoupling the expression of different target proteins in the same cell, rather than by an increase in the total noise of each. Extrinsic noise provides the dominant contribution to the total protein noise over the total range of RyhB production rates. Stochastic simulations reproduce qualitatively key features of our observations and show that a feed-forward loop formed by transcriptional extrinsic noise, an sRNA and its target genes exhibits strong noise filtration capabilities.

Living organisms often have to adapt to sudden environmental changes and reach homeostasis. To achieve adaptation, cells deploy motifs such as feedback in their genetic networks, endowing the cellular response with desirable properties. We studied the iron homeostasis network of E. coli, which employs feedback loops to regulate iron usage and uptake, while maintaining intracellular iron at non-toxic levels. Using fluorescence reporters for iron-dependent promoters in bulk and microfluidics-based, single-cell experiments, we show that E. coli cells exhibit damped oscillations in gene expression, following sudden reductions in external iron levels. The oscillations, lasting for several generations, are independent of position along the cell cycle. Experiments with mutants in network components demonstrate the involvement of iron uptake in the oscillations. Our findings suggest that the response is driven by intracellular iron oscillations large enough to induce nearly full network activation/deactivation. We propose a mathematical model based on a negative feedback loop closed by rapid iron uptake, and including iron usage and storage, which captures the main features of the observed behaviour. Taken together, our results shed light on the control of iron metabolism in bacteria and suggest that the oscillations represent a compromise between the requirements of stability and speed of response.

Homologous recombination plays pivotal roles in DNA repair and in the generation of genetic diversity. To locate homologous target sequences at which strand exchange can occur within a timescale that a cell's biology demands, a single-stranded DNA-recombinase complex must search among a large number of sequences on a genome by forming synapses with chromosomal segments of DNA. A key element in the search is the time it takes for the two sequences of DNA to be compared, i.e. the synapse lifetime. Here, we visualize for the first time fluorescently tagged individual synapses formed by RecA, a prokaryotic recombinase, and measure their lifetime as a function of synapse length and differences in sequence between the participating DNAs. Surprisingly, lifetimes can be ~10 s long when the DNAs are fully heterologous, and much longer for partial homology, consistently with ensemble FRET measurements. Synapse lifetime increases rapidly as the length of a region of full homology at either the 3-or5-ends of the invading single-stranded DNA increases above 30 bases. A few mismatches can reduce dramatically the lifetime of synapses formed with nearly homologous DNAs. These results suggest the need for facilitated homology search mechanisms to locate homology successfully within the timescales observed in vivo.

We measured persistence exponents θ(φ) of Ostwald ripening in two dimensions, as a function of the area fraction φ occupied by coarsening domains. The values of θ(φ) in two systems, succinonitrile and brine, quenched to their liquid-solid coexistence region, compare well with one another, providing compelling evidence for the universality of the one-parameter family of exponents. For small φ, θ (φ) □ 0.39 φ, as predicted by a model that assumes no correlations between evolving domains. These constitute the first measurements of persistence exponents in the case of phase transitions with a conserved order parameter.

The tumor suppressor BRCA2 protein plays a major role in the regulation of Rad51-catalyzed homologous recombination. BRCA2 interacts with monomeric Rad51 primarily via conserved BRC domains and coordinates the formation of Rad51 filaments at double-stranded DNA (dsDNA) breaks. A number of cancer-associated mutations in BRC4 and BRC2 domains have been reported. To elucidate their effects on homologous recombination, we studied Rad51 filament formation on single-stranded DNA and dsDNA substrates and Rad51-catalyzed strand exchange, in the presence of wild-type and mutated peptides of either BRC4 or BRC2. While the wild-type BRC2 and BRC4 peptides inhibited filament formation and, thus, strand exchange, the mutated forms decreased significantly these inhibitory effects. These results are consistent with a three-dimensional model for the interface between individual BRC repeats and Rad51. We suggest that mutations at sites crucial for the association between Rad51 and BRC domains impair the ability of BRCA2 to recruit Rad51 to dsDNA breaks, hampering recombinational repair.

Inactivation of bacteriophage lambda CI repressor leads almost exclusively to lytic development. Prophage induction can be initiated either by DNA damage or by heat treatment of a temperature-sensitive repressor. These two treatments also cause a concurrent activation of either the host SOS or heat-shock stress responses respectively. We studied the effects of these two methods of induction on the lytic pathway by monitoring the activation of different lambda promoters, and found that the lambda genetic network co-ordinates information from the host stress response networks. Our results show that the function of the CII transcriptional activator, which facilitates the lysogenic developmental pathway, is not observed following either method of induction. Mutations in the cro gene restore the CII function irrespective of the induction method. Deletion of the heat-shock protease gene ftsH can also restore CII function following heat induction but not following SOS induction. Our findings highlight the importance of the elimination of CII function during induction as a way to ensure an efficient lytic outcome. We also show that, despite the common inhibitory effect on CII function, there are significant differences in the heat- and SOS-induced pathways leading to the lytic cascade.

Recombination is arguably one of the most fundamental mechanisms driving genetic diversity during evolution. Recombination takes place in one way or another from viruses such as HIV and polio, to bacteria, and finally to man. In both prokaryotes and eukaryotes, homologous recombination is assisted by enzymes, recombinases, that promote the exchange of strands between two segments of DNA, thereby creating new genetic combinations. In bacteria, homologous recombination takes place as a pathway for the repair of DNA lesions and also during horizontal or lateral gene transfer processes, in which cells take in exogenous pieces of DNA. This allows bacteria to evolve rapidly by acquiring large sequences of DNA, a process which would take too long by gene duplications and single mutations. I will survey recent results on the fidelity of homologous recombination as catalyzed by the bacterial recombinase RecA. These results show discrimination up to the level of single base mismatches, during the initial stages of the recombination process. A cascaded kinetic proofreading process is proposed to explain this high discrimination. Kinetic proofreading ideas are also reviewed.

Biological developmental pathways require proper timing of gene expression. We investigated timing variations of defined steps along the lytic cascade of bacteriophage λ. Gene expression was followed in individual lysogenic cells, after induction with a pulse of UV irradiation. At low UV doses, some cells undergo partial induction and eventually divide, whereas others follow the lytic pathway. The timing of events in cells committed to lysis is independent of the level of activation of the SOS response, suggesting that the lambda network proceeds autonomously after induction. An increased loss of temporal coherence of specific events from prophage induction to lysis is observed, even though the coefficient of variation of timing fluctuations decreases. The observed temporal variations are not due to cell factors uniformly dilating the timing of execution of the cascade. This behavior is reproduced by a simple model composed of independent stages, which for a given mean duration predicts higher temporal precision, when a cascade consists of a large number of steps. Evidence for the independence of regulatory modules in the network is presented.

Bacteria, like eukaryotic organisms, must compact the DNA molecule comprising their genome and form a functional chromosome. Yet, bacteria do it differently. A number of factors contribute to genome compaction and organization in bacteria, including entropic effects, supercoiling and DNA-protein interactions. A gamut of new experimental techniques have allowed new advances in the investigation of these factors, and spurred much interest in the dynamic response of the chromosome to environmental cues, segregation, and architecture, during both exponential and stationary phases. We review these recent developments with emphasis on the multifaceted roles that DNA-protein interactions play.

Homologous recombination plays a key role in generating genetic diversity, while maintaining protein functionality. The mechanisms by which RecA enables a single-stranded segment of DNA to recognize a homologous tract within a whole genome are poorly understood. The scale by which homology recognition takes place is of a few tens of base pairs, after which the quest for homology is over. To study the mechanism of homology recognition, RecA-promoted homologous recombination between short DNA oligomers with different degrees of heterology was studied in vitro, using fluorescence resonant energy transfer. RecA can detect single mismatches at the initial stages of recombination, and the efficiency of recombination is strongly dependent on the location and distribution of mismatches. Mismatches near the 5 end of the incoming strand have a minute effect, whereas mismatches near the 3 end hinder strand exchange dramatically. There is a characteristic DNA length above which the sensitivity to heterology decreases sharply. Experiments with competitor sequences with varying degrees of homology yield information about the process of homology search and synapse lifetime. The exquisite sensitivity to mismatches and the directionality in the exchange process support a mechanism for homology recognition that can be modeled as a kinetic proofreading cascade.

Genomic DNA in bacteria is concentrated in a distinct structure, the bacterial chromosome or nucleoid [Pettijohn, D.E. (1996) The Nucleoid. In Neidhardt, F.C., Curtis 111, R., Ingraham, J.L., Lin, E.C.C., Low, K.B., Magasanik, B., Reznikoff, W.S., Riley, M., Schaechter, M. and Umbarger, H.E. (eds.), Escherichia coli and Salmonella. ASM Press, Washington D.C., pp. 158-166; Trun, N.J. and Marko, J.F. (1998) Architecture of a bacterial chromosome. Am. Soc. Microbial. Rev., 64, 276-283]. Stripped of all bound proteins and RNA being produced during transcription and then stretched, the length of the DNA is circa 1.5 mm, a factor of about a thousandfold larger than typical bacterial dimensions. Thus, bacteria, like all living organisms, face the daunting challenge of compacting their genome to fit inside the cell in such a way that the information encoded in the DNA will be accessible for gene expression and replication of the genome. In the case of bacteria, members of the prokaryote world (cells without a nucleus), natural selection resulted in three mechanisms that act together to compact the genome and produce a functional, dynamic architecture: supercoiling, macromolecular crowding, and the association of the DNA with a class of nucleoid-associated or histone-like proteins. I will now describe briefly these mechanisms.

A variety of sources such as radiation, chemical mutagens and products of metabolism induce damage to the genomes of organisms very often, from bacteria to man. Damage can be fatal for the organism since it can prevent DNA replication, and thus cell division. Evolution has given rise to elaborate mechanisms to either repair or bypass this damage. Upon encountering damage to their genomes, bacteria such as E coli respond by activating the SOS network, consisting of about forty genes whose task is to repair/bypass the DNA damage, in order to enable DNA replication. The SOS genetic network deploys a variety of specific functions such as detecting damage, repairing it correctly by nucleotide excision (the NER mechanism) or by recombination, and if these functions do not succeed, bypassing damage by mutagenesis. The activation of all these functions requires a high degree of coordination and regulation, whose understanding is poor in spite of decades of study. I will survey recent findings in which the execution of the response was followed at the level of individual cells. These findings illuminate certain aspects of the concerted response, which are inacccessible to techniques in which large cell ensembles are interrogated. In particular, the findings show that the response exhibits highly precise modulations in the activation of a number of gene promoters, modulations which posess a digital character. Importantly, the precise timing mechanism responsible for the modulations is independent of the cell cycle, the main built-in clock of the cell. Genes responsible for the precision are identified. I will also highlight the importance of this network as one of the main forces driving the evolution of bacterial genomes.

The SOS genetic network is responsible for the repair/bypass of DNA damage in bacterial cells. While the initial stages of the response have been well characterized, less is known about the dynamics of the response after induction and its shutoff. To address this, we followed the response of the SOS network in living individual Escherichia coli cells. The promoter activity (PA) of SOS genes was monitored using fluorescent protein-promoter fusions, with high temporal resolution, after ultraviolet irradiation activation. We find a temporal pattern of discrete activity peaks masked in studies of cell populations. The number of peaks increases, while their amplitude reaches saturation, as the damage level is increased. Peak timing is highly precise from cell to cell and is independent of the stage in the cell cycle at the time of damage. Evidence is presented for the involvement of the umuDC operon in maintaining the pattern of PA and its temporal precision, providing further evidence for the role UmuD cleavage plays in effecting a timed pause during the SOS response, as previously proposed. The modulations in PA we observe share many features in common with the oscillatory behavior recently observed in a mammalian DNA damage response. Our results, which reveal a hitherto unknown modulation of the SOS response, underscore the importance of carrying out dynamic measurements at the level of individual living cells in order to unravel how a natural genetic network operates at the systems level.

The lysis-lysogeny decision of bacteriophage λ has been a paradigm for a developmental genetic network, which is composed of interlocked positive and negative feedback loops. This genetic network is capable of responding to environmental signals and to the number of infecting phages. An interplay between CI and Cro functions suggested a bistable switch model for the lysis-lysogeny decision. Here, we present a real-time picture of the execution of lytic and lysogenic pathways with unprecedented temporal resolution. We monitor, in vivo, both the level and function of the CII and Q gene regulators. These activators are cotranscribed yet control opposite developmental pathways. Conditions that favor the lysogenic response show severe delay and down-regulation of Q activity, in both CII-dependent and CII-independent ways. Whereas CII activity correlates with its protein level, Q shows a pronounced threshold before its function is observed. Our quantitative analyses suggest that by regulating CII and CIII, Cro plays a key role in the ability of the λ genetic network to sense the difference between one and more than one phage particles infecting a cell. Thus, our results provide an improved framework to explain the longstanding puzzle of the decision process.

The lysis-lysogeny decision of bacteriophage lambda (lambda) is a paradigm for developmental genetic networks. There are three key features, which characterize the network. First, after infection of the host bacterium, a decision between lytic or lysogenic development is made that is dependent upon environmental signals and the number of infecting phages per cell. Second, the lysogenic prophage state is very stable. Third, the prophage enters lytic development in response to DNA-damaging agents. The CI and Cro regulators define the lysogenic and lytic states, respectively, as a bistable genetic switch. Whereas CI maintains a stable lysogenic state, recent studies indicate that Cro sets the lytic course not by directly blocking CI expression but indirectly by lowering levels of CII which activates d transcription. We discuss how a relatively, simple phage like lambda employs a complex genetic network in decision-making processes, providing a challenge for theoretical modeling.

HU is an abundant, highly conserved protein associated with the bacterial chromosome. It belongs to a small class of proteins that includes the eukaryotic proteins TBP, SRY, HMG-I and LEF-I, which bind to DNA non-specifically at the minor groove. HU plays important roles as an accessory architectural factor in a variety of bacterial cellular processes such as DNA compaction, replication, transposition, recombination and gene regulation. In an attempt to unravel the role this protein plays in shaping nucleoid structure, we have carried out fluorescence resonance energy transfer measurements of HU-DNA oligonucleotide complexes, both at the ensemble and single-pair levels. Our results provide direct experimental evidence for concerted DNA bending by HU, and the abrogation of this effect at HU to DNA ratios above about one HU dimer per 10-12 bp. These findings support a model in which a number of HU molecules form an ordered helical scaffold with DNA lying in the periphery. The abrogation of these nucleosome-like structures for high HU to DNA ratios suggests a unique role for HU in the dynamic modulation of bacterial nucleoid structure.

Holliday junctions form during DNA repair and homologous recombination processes. These processes entail branch migration, whereby the length of two arms of a cruciform increases at the expense of the two others. Branch migration is carried out in prokaryotic cells by the RuvAB motor complex. We study RuvAB-catalyzed branch migration by following the motion of a small paramagnetic bead tethered to a surface by two opposing arms of a single cruciform. The bead, pulled under the action of magnetic tweezers, exerts tension on the cruciform, which in turn transmits the force to a single RuvAB complex bound at the crossover point. This setup provides a unique means of measuring several kinetic parameters of interest such as the translocation rate, the processivity, and the force on the substrate against which the RuvAB complex cannot effect translocation. RuvAB-catalyzed branch migration proceeds with a small, discrete number of rates, supporting the view that the monomers comprising the RuvB hexameric rings are not functionally homogeneous and that dimers or trimers constitute the active subunits. The most frequently encountered rate, 98 ± 3 bp/sec, is approximately five times faster than previously estimated. The apparent processivity of branch migration between pauses of inactivity is ≈7,000 bp. Branch migration persists against opposing forces up to 23 pN.

Histonelike nucleoid structuring protein (H-NS) is an abundant prokaryotic protein participating in nucleoid structure, gene regulation, and silencing. It plays a key role in cell response to changes in temperature and osmolarity. Force-extension measurements of single, twist-relaxed λ-DNA-H-NS complexes show that these adopt more extended configurations compared to the naked DNA substrates. Crosslinking indicates that H-NS can decorate DNA molecules at one H-NS dimer per 15-20 bp. These results suggest that H-NS polymerizes along DNA, forming a complex of higher bending rigidity. These effects are not observed above 32°C or at high osmolarity, supporting the hypothesis that a direct H-NS-DNA interaction plays a key role in gene silencing. Thus, we propose that H-NS plays a unique structural role, different from that of HU and IHF, and functions as one of the environmental sensors of the cell.

We studied local budding and tubulation induced in highly oblate lipid vesicles by the anchoring of either polymers having a hydrophilic backbone and grafted hydrophobic anchor groups, or by oleoyl-coenzyme A, an amphiphilic molecule important in lipid metabolism. The dynamics of bud formation, shrinkage, and readsorption is consistent with an induced spontaneous curvature coupled with local amphiphile diffusion on the membrane. We report a novel metastable state prior to bud readsorption.

I review the results of an experimental and theoretical study of the effects of polymers having a number of hydrophobic anchors grafted along a hydrophilic backbone on phospholipid vesicles of different geometries. Pearling of tubular vesicles, tubulation at the rim of highly oblate vesicles, and finally a coiling instability in highly multilamellar tubes have been observed, above threshold polymer concentrations. These instabilities can be accounted for within a single framework in which the local polymer concentration is coupled to local membrane curvature, and in which polymers effect these changes by inducing curvature in the bilayers on which they anchor. Curvature is induced by two mechanisms: a local deformation due to anchoring, and an increase in the area of one leaflet of a bilayer with respect to the other.

We introduce a method for detecting and tracking small particles in a solution near a surface. The method is based on blocking the backreflected illumination beam in an objective-type total internal reflection microscope, leaving unhindered the light scattered by the particles and resulting in dark-field illumination. Using this method, we tracked the motion of 60-nm polystyrene beads with a signal-tonoise ratio of 6 and detected 20-nm gold particles with a signal-to-noise ratio of 5. We illustrate the methods use by following the Brownian motion of small beads attached by short DNA tethers to a substrate.

We studied the interaction between the integration host factor (IHF), a major nucleoid-associated protein in bacteria, and single DNA molecules. Force-extension measurements of λ DNA and an analysis of the Brownian motion of small beads tethered to a surface by single short DNA molecules, in equilibrium with an IHF solution, indicate that: (i) the DNA-IHF complex retains a random, although more compact, coiled configuration for zero or small values of the tension, (ii) IHF induces DNA compaction by binding to multiple DNA sites with low specificity, and (iii) with increasing tension on the DNA, the elastic properties of bare DNA are recovered. This behavior is consistent with the predictions of a statistical mechanical model describing how proteins bending DNA are driven off by an applied tension on the DNA molecule. Estimates of the amount of bound IHF in DNA-IHF complexes obtained from the model agree very well with independent measurements of this quantity obtained from the analysis of DNA-IHF crosslinking. Our findings support the long-held view that IHF other histone-like proteins play an important role in shaping the long-scale structure of the bacterial nucleoid.

The mechanism responsible for the pearling instability on hollow tubular lipid vesicles was examined via nonequilibrium experiment. It was found that two mechanisms are responsible for this effect: spontaneous curvature and area difference.

We study experimentally a coiling instability of cylindrical multilamellar stacks of phospholipid membranes, induced by polymers with hydrophobic anchors grafted along their hydrophilic backbone. Our system is unique in that coils form in the absence of both twist and adhesion. We interpret our experimental results in terms of a model in which local membrane curvature and polymer concentration are coupled. The model predicts the occurrence of maximally tight coils above a threshold polymer occupancy. A proper comparison between the model and experiment involved imaging of projections from simulated coiled tubes with maximal curvature and complicated torsions.

Using rheometry and light scattering, we have studied the viscoelasticity of gels formed by the kinetically arrested phase separation in an emulsion-polymer mixture; to prevent the gels from collapsing under their own weight, we have used an isopycnic solvent. At constant osmotic pressure (set by the polymer concentration) and droplet volume fractions φ well above the gelation transition, we find the elastic modulus to increase roughly linearly with φ, indicating an entropic elasticity based on the cluster packing.

We study experimentally a coiling instability of cylindrical multilamellar stacks of phospholipid membranes, induced by polymers with hydrophobic anchors grafted along their hydrophilic backbone. We interpret our experimental results in terms of a model in which local membrane curvature and polymer concentration are coupled. The model predicts the occurrence of maximally tight coils above a threshold polymer concentration. Indeed, only maximally tight coils are observed experimentally. Our system is unique in that coils form in the absence of twist and adhesion.

Powder mixtures partially filling horizontal, slowly rotating tubes segregate under certain conditions into bands of different composition along the tube axis. The one-dimensional patterns of bands evolve in time through coarsening. Recent work on the origin and dynamics of axial segregation of powder mixtures is reviewed.

We present a new approach to probing single-particle dynamics that uses dynamic light scattering from a localized region. By scattering a focused laser beam from a micron-size particle, we measure its spatial fluctuations via the temporal autocorrelation of the scattered intensity. We demonstrate the applicability of this approach by measuring the three-dimensional force constants of a single bead and a pair of beads trapped by laser tweezers. The scattering equations that relate the scattered intensity autocorrelation to the particle position correlation function are derived. This technique has potential applications for measurement of biomolecular force constants and probing viscoelastic properties of complex media.

We report an experimental measurement of the temporal dependence of the area A_us in a two-dimensional soap froth which has not been swept by the passage of soap films up to time t, as the froth coarsens from an initial time t₀ within the scaling regime. We find A_us scales with the mean cell area ⟨A⟩ as A_us ∝ ⟨A⟩^−θ, with a first-passage exponent θ = 1.16 ± 0.02; and for the average perimeter ⟨P⟩: ⟨P⟩ ∝ ⟨A⟩^ψ and A_us ∝ ⟨P⟩^φ with values of the scaling exponents ψ = 0.49 ± 0.01 and φ = 2.38 ± 0.02. We also find a scaling function in A_us(t)/A_us(t₀) versus ⟨A(t)⟩/⟨A(t₀)⟩.

We developed an experimental technique which probes the dynamics of a single colloidal particle over many decades in time, with spatial resolution of a few nanometers. By scattering a focused laser beam from a particle observed in an optical microscope, we measure its fluctuations via the temporal autocorrelation function of the scattered intensity g\(t\). This technique is demonstrated by applying it to a single Brownian particle in an optical trap of force constant k. The decay times of g\(t\), which are related to the particle position autocorrelation function, scale as k⁻¹, as expected from theory.

A binary mixture of granular materials in a horizontal, rotating tube segregates under certain circumstances into an alternating pattern of bands of two types along the tube axis, each type being rich in one of the components. The pattern coarsens with time through band shrinking and merging, until a steady state characterized by some average bandwidth is reached. We have studied experimentally the long-term evolution of segregation patterns in sand-glass bead mixtures. We observe that during coarsening, the two types of band evolve differently, indicating that another transport mechanism is at work besides diffusion. We propose that glass beads are transported axially due to \u201cavalanche waves\u201d, a hallmark of the discontinuous flow characterizing sand-rich bands.

We study by light scattering methods the behavior of soap films drawn from solutions of different surfactant concentration. For concentrations just above the critical micelle concentration, micelles induce a depletion attraction and thus a reduction in equilibrium film thickness. For larger surfactant concentrations we observe stepwise thinning, due to the organization of micelles in layers parallel to the film plane. Our results show that the behavior of the micelles in the confining geometry of the film is analogous to that of ordinary fluids confined between walls. The ability to go from a gaslike to a liquidlike configuration of micelles by changing surfactant concentration allows us to test model predictions of density oscillations in confined liquids.

We present an experimental study of the effects of hydrophilic, nonadsorbing polymers on the stability of monodisperse oil-in-water emulsions. Above some threshold polymer concentration, the chains induce droplet segregation into fluid and solid phases due to the depletion effect. At higher polymer concentrations, polymers induce the formation of gel-like structures of droplets. Phase diagrams of droplet volume fraction versus polymer concentration are presented. At large droplet volume fractions where droplets are deformed, the polymers enhance considerably the stability of the emulsion against droplet coalescence. We compare our results with recent experiments and models of colloid-polymer mixtures.

We have studied experimentally phase separation in binary mixtures comprised of nearly monodisperse emulsion droplets of two different sizes. For three values of ξ, where ξ

Thin soap films drawn from concentrated surfactant solutions show stepwise thinning due to micellar organization into layers. We study by light scattering methods the extent of order as a function of surfactant concentration and show that the behavior of the micelles in the confining geometry of the film is analogous to that of ordinary fluids confined between walls. Our results compare very well with predictions of a recent model for density oscillations in liquids, supplemented by a calculation of bulk properties based on the rescaled mean spherical approximation.

We report results from an experimental study of coarsening in thin layers of succinonitrile in the presence of impurities. By quenching the latter from the liquid phase to different temperatures within the liquid-solid coexistence region, different solid area fractions φ are obtained. As φ is incresed from 0.13 to 0.40, liquidlike order develops among the coarsening crystals due to diffusional interactions. The latter give rise to local correlations between the size and rate of growth of crystals within a neighborhood of size ξ(φ). We study these and compare our findings with recent theoretical models of coarsening.

We present results of an experimental study of surfactant-polymer interactions in free-standing soap films. The relaxation of thermally induced corrugations of the surfactant monolayers comprising a film is studied by reflectivity and light-scattering methods. Our data show that polymers influence the thickness of the equilibrium state of a soap film and lead to the creation of new metastable states of larger thickness. The overall behavior is consistent with a picture in which chains form depletion layers near the surfactant walls, inducing an attractive interaction between the monolayers at large polymer concentrations.

Time-dependent correlations in the scaling state of an evolving two-dimensional soap froth are studied. In particular, we consider the topological distribution function of those cells that are destined to survive for long times. Experimental results are compared with mean-field based dynamic equations and with topological simulations.

We have studied segregation in binary mixtures of different granular media subjected to rotation in horizontal tubes. Mixtures separate into bands of different relative concentrations arranged along the axis of the tubes. Axial modulations of the tube radius lock bands in space and induce segregation in otherwise nonsegregating mixtures of glass beads. The segregation results from an instability analogous to spinodal decomposition, and we present a model which describes this instability.

We present a preliminary account of an experimental study of the influence of nonionic polymers on the draining process and thickness of freely suspended vertical soap films. We studied films of both cationic and anionic surfactants. While the presence of a polymer leads to a monotonous reduction in thickness with concentration in the former case, the behavior in the latter is very different: an increase in polymer concentration leads to an increase in thickness of black films and to their eventual loss of stability through disruption of micellar stratification.

Soap froths are paradigms of a class of evolving systems known as cellular structures. The evolution of mature structures is characterized by system-independent or universal statistical distributions which have scaling properties. Recent experimental work on two-dimensional soap froths will be presented to illustrate the latter. A theoretical model that accounts for these universal distributions by a mechanism of marginal stability will be presented.

A large class of evolving nonequilibrium systems, known collectively as cellular structures, are composed of nearly-uniform domains of polygonal-like or polyhedral-like shape (in two- or three-dimensional systems respectively) separated by thin boundaries endowed with line or surface energy. Work done mainly during the last decade has shown that the evolution of mature structures is characterized by universal or system-independent statistical distributions which possess scaling properties. The author presents an introduction to cellular structures, discusses the fundamental role played by geometry in the evolution of these systems and surveys the recent experimental and theoretical developments in the field.

We report results from an experimental study of coarsening in thin layers of succinonitrile in the presence of impurities. We quench the latter from the liquid phase to different temperatures within the liquid-solid coexistence region thus controling the solid area fraction . As is increased from 0.13 to 0.40, liquidlike order develops among the coarsening crystals due to diffusional interactions. The latter give rise to local correlations between the size and rate of growth of crystals within a neighborhood of size (). We study these and compare our findings with recent theoretical models of coarsening.

Evolving random cellular structures are observed to reach a universal scaling regime. A mean-field approach to finding fixed-point distributions in cell-side number is extended to distributions for the average area of cells with a given number of sides. This approach leads to simplified equations that can be analyzed analytically and numerically. The theorys results are compared to experimental results on dynamics and distributions in soap froths and good agreement is achieved.

We report the results of the first measurements of the mobility/friction coefficients of a sphere dragged horizontally through a vertically vibrated granular medium. The friction coefficient depends on the state of excitation of the medium and drops rapidly when the acceleration of the vibrated cell exceeds that of gravity. We propose a simple model involving fluidization/solidification events during a period of vibration of the cell. We argue that the observed mobility is proportional to the fraction of the time spent in the «fluid» state and discuss the origin of the observed dependence on the various parameters.

We used diffusing wave spectroscopy to determine the phase diagrams of binary mixtures of charge-stabilized colloidal particles of different dimensions in the low-screening limit. As the ratio of radii r=r1/r2 was increased progressively towards 1, the structure of the diagrams evolved from eutecticlike to azeotropiclike and finally to a diagram where complete solubility was found, much like in atomic systems. We present for the first time evidence for liquid-galss transitions in these strongly interacting systems as the relative composition of both species is varied.

We have studied experimentally the coarsening of two-dimensional soap froths in the presence of pinning centers. When the average bubble size is smaller than the average interpin distance, the growth is unaffected. When both dimensions become comparable the froth enters a crossover regime followed by a pinned state where growth stops. The nature of the long-time configurations depends strongly on the size of the pins relative to the size of the plateau borders. For thick pins, the final configurations consist of combinations of Steiner trees of small numbers of points with pins located at vertices of the film network. For thin pins the final average bubble size is larger than in the case of thick pins and the final configurations are much more varied. Qualitatively similar behavior is observed in grain growth in metals with impurities.

The time evolution of a wide variety of physical systems exhibiting two-dimensional cellular structures has recently been studied and found to lead to a universal distribution xi of the number of sides, l, of the cells. A simple model for the evolution of these structures is presented and analysed. The model exhibits a one-parameter family of fixed-point distributions X^*₁(σ) Within this model, universality is maintained by a mechanism in which a particular marginally stable fixed point is selected. The predictions of the model compare well with experimental observations in soap froths.

Quasielastic light scattering measurements are performed on a suspension of spherical particles possessing an intrinsic optical anisotropy. The particles are prepared by emulsion polymerization of a polytetrafluoroethylene copolymer, and have a radius of 85 nm. A theoretical treatment is developed which shows that the correlation function of depolarized scattered intensity contains both the translational and rotational self-diffusion coefficients D_s and D_r. The measurements allow the derivation of the dependence of D_s and D_r on the volume fraction. The experimental data demonstrate that the rotational diffusion of a sphere is influenced by hydrodynamic interactions, in qualitative agreement with recent calculations by Jones.

An experimental study of the temporal evolution of two-dimensional drained soap froths is presented. The long-time behavior of the froth shows a linear dependence of the average bubble area on time. By keeping nearly constant and thin plateau borders at all times, deviations from 120° in the angle between adjacent films at a vertex are not observed. In addition, evidence of dynamical scaling of area distributions is presented.

We study an experimental orbit on a two-torus with a golden-mean winding number obtained from a forced Rayleigh-Bénard system at the onset of chaos. This experimental orbit is compared with the orbit generated by a simple theoretical model, the circle map, at its golden-mean winding number at the onset of chaos. The "spectrum of singularities" of the two orbits are compared. Within error, these are identical. Since the spectrum characterizes the metric properties of the entire orbit, this result confirms theoretical speculations that these orbits, taken as a whole, enjoy a kind of universality. PACS numbers: 47.20. + m, 05.45. + b, 47.25. -c.

We study an experimental orbit on a two-torus with a golden-mean winding number obtained from a forced Rayleigh-Bénard system at the onset of chaos. This experimental orbit is compared with the orbit generated by a simple theoretical model, the circle map, at its golden-mean winding number at the onset of chaos. The "spectrum of singularities" of the two orbits are compared. Within error, these are identical. Since the spectrum characterizes the metric properties of the entire orbit, this result confirms theoretical speculations that these orbits, taken as a whole, enjoy a kind of universality.