Genome replication in asynchronously growing microbial populations.

Biological cells replicate their genomes in a well-planned manner. The DNA replication program of an organism determines the timing at which different genomic regions are replicated, with fundamental consequences for cell homeostasis and genome stability. In a growing cell culture, genomic regions that are replicated early should be more abundant than regions that are replicated late. This abundance pattern can be experimentally measured using deep sequencing. However, a general quantitative theory linking this pattern to the replication program is still lacking. In this paper, we predict the abundance of DNA fragments in asynchronously growing cultures from any given stochastic model of the DNA replication program. As key examples, we present stochastic models of the DNA replication programs in budding yeast and Escherichia coli. In both cases, our model results are in excellent agreement with experimental data and permit to infer key information about the replication program. In particular, our method is able to infer the locations of known replication origins in budding yeast with high accuracy. These examples demonstrate that our method can provide insight into a broad range of organisms, from bacteria to eukaryotes.

Error-suppression mechanism of PCR by blocker strands.

The polymerase chain reaction (PCR) is a central technique in biotechnology. Its ability to amplify a specific target region of a DNA sequence has led to prominent applications, including virus tests, DNA sequencing, genotyping, and genome cloning. These applications rely on the specificity of the primer hybridization and therefore require effective suppression of hybridization errors. A simple and effective method to achieve that is to add blocker strands, also called clamps, to the PCR mixture. These strands bind to the unwanted target sequence, thereby blocking the primer mishybridization. Because of its simplicity, this method is applicable to a broad nucleic-acid-based biotechnology. However, the precise mechanism by which blocker strands suppress PCR errors remains to be understood, limiting the applicability of this technique. Here, we combine experiments and theoretical modeling to reveal this mechanism. We find that the blocker strands both energetically destabilize the mishybridized complex and sculpt a kinetic barrier to suppress mishybridization. This combination of energetic and kinetic biasing extends the viable range of annealing temperatures, which reduces design constraint of the primer sequence and extends the applicability of PCR.

Thermodynamic bounds on time-reversal asymmetry.

Quantifying irreversibility of a system using finite information constitutes a major challenge in stochastic thermodynamics. We introduce an observable that measures the time-reversal asymmetry between two states after a given time lag. Our central result is a bound on the time-reversal asymmetry in terms of the total cycle affinity driving the system out of equilibrium. This result leads to further thermodynamic bounds on the asymmetry of directed fluxes, on the asymmetry of finite-time cross-correlations, and on the cycle affinity of coarse-grained dynamics.

Coalescent dynamics of planktonic communities.

Planktonic communities are extremely diverse and include a vast number of rare species. The dynamics of these rare species is best described by individual-based models. However, individual-based approaches to planktonic diversity face substantial difficulties, due to the large number of individuals required to make realistic predictions. In this paper, we study the diversity of planktonic communities by means of a spatial coalescence model that incorporates transport by oceanic currents. As a main advantage, our approach requires simulating a number of individuals equal to the size of the sample one is interested in, rather than the size of the entire community. By theoretical analysis and simulations, we explore the conditions upon which our coalescence model is equivalent to individual-based dynamics. As an application, we use our model to predict the impact of chaotic advection by oceanic currents on biodiversity. We conclude that the coalescent approach permits one to simulate marine microbial communities much more efficiently than with individual-based models.

Speed variations of bacterial replisomes.

Replisomes are multi-protein complexes that replicate genomes with remarkable speed and accuracy. Despite their importance, their dynamics is poorly characterized, especially in vivo. In this paper, we present an approach to infer the replisome dynamics from the DNA abundance distribution measured in a growing bacterial population. Our method is sensitive enough to detect subtle variations of the replisome speed along the genome. As an application, we experimentally measured the DNA abundance distribution in Escherichia coli populations growing at different temperatures using deep sequencing. We find that the average replisome speed increases nearly fivefold between 17 °C and 37 °C. Further, we observe wave-like variations of the replisome speed along the genome. These variations correlate with previously observed variations of the mutation rate, suggesting a common dynamical origin. Our approach has the potential to elucidate replication dynamics in E. coli mutants and in other bacterial species.

Optimization and Fabrication of Multi-Level Microchannels for Long-Term Imaging of Bacterial Growth and Expansion.

Bacteria are unicellular organisms whose length is usually around a few micrometers. Advances in microfabrication techniques have enabled the design and implementation of microdevices to confine and observe bacterial colony growth. Microstructures hosting the bacteria and microchannels for nutrient perfusion usually require separate microfabrication procedures due to different feature size requirements. This fact increases the complexity of device integration and assembly process. Furthermore, long-term imaging of bacterial dynamics over tens of hours requires stability in the microscope focusing mechanism to ensure less than one-micron drift in the focal axis. In this work, we design and fabricate an integrated multi-level, hydrodynamically-optimized microfluidic chip to study long-term Escherichia coli population dynamics in confined microchannels. Reliable long-term microscopy imaging and analysis has been limited by focus drifting and ghost effect, probably caused by the shear viscosity changes of aging microscopy immersion oil. By selecting a microscopy immersion oil with the most stable viscosity, we demonstrate successful captures of focally stable time-lapse bacterial images for ≥72 h. Our fabrication and imaging methodology should be applicable to other single-cell studies requiring long-term imaging.

Population genetics in microchannels.

SignificanceMany microbial populations proliferate in small channels. In such environments, reproducing cells organize in parallel lanes. Reproducing cells shift these lanes, potentially expelling other cells from the channel. In this paper, we combine theory and experiments to understand how these dynamics affects the diversity of a microbial population. We theoretically predict that genetic diversity is quickly lost along lanes of cells. Our experiments confirm that a population of proliferating Escherichia coli in a microchannel organizes into lanes of genetically identical cells within a few generations. Our findings elucidate the effect of lane formation on populations evolution, with potential applications ranging from microbial ecology in soil to dynamics of epithelial tissues in higher organisms.

Search and Localization Dynamics of the CRISPR-Cas9 System.

The CRISPR-Cas9 system acts as the prokaryotic immune system and has important applications in gene editing. The protein Cas9 is one of its crucial components. The role of Cas9 is to search for specific target sequences on the DNA and cleave them. In this Letter, we introduce a model of facilitated diffusion for Cas9 and fit its parameters to single-molecule experiments. Our model confirms that Cas9 search for targets by sliding, but shows that its sliding length is rather short. We then investigate how Cas9 explores a long stretch of DNA containing randomly placed targets. We solve this problem by mapping it into the theory of Anderson localization in condensed matter physics. Our theoretical approach rationalizes experimental evidence on the distribution of Cas9 molecules along the DNA.

Enhanced Mutation Rate, Relaxed Selection, and the "Domino Effect" are associated with Gene Loss in Blattabacterium, A Cockroach Endosymbiont.

Intracellular endosymbionts have reduced genomes that progressively lose genes at a timescale of tens of million years. We previously reported that gene loss rate is linked to mutation rate in Blattabacterium, however, the mechanisms causing gene loss are not yet fully understood. Here, we carried out comparative genomic analyses on the complete genome sequences of a representative set of 67 Blattabacterium strains, with sizes ranging between 511 and 645 kb. We found that 200 of the 566 analyzed protein-coding genes were lost in at least one lineage of Blattabacterium, with the most extreme case being one gene that was lost independently in 24 lineages. We found evidence for three mechanisms influencing gene loss in Blattabacterium. First, gene loss rates were found to increase exponentially with the accumulation of substitutions. Second, genes involved in vitamin and amino acid metabolism experienced relaxed selection in Cryptocercus and Mastotermes, possibly triggered by their vertically inherited gut symbionts. Third, we found evidence of epistatic interactions among genes leading to a "domino effect" of gene loss within pathways. Our results highlight the complexity of the process of genome erosion in an endosymbiont.

Generalized Euler-Lotka equation for correlated cell divisions.

Cell division times in microbial populations display significant fluctuations that impact the population growth rate in a nontrivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical biology. However, cell division times can be significantly correlated, due to physical properties of cells that are passed through generations. In this Letter, we derive an equation remarkably similar to the Euler-Lotka equation which is valid in the presence of correlations. Our exact result is based on large deviation theory and does not require particularly strong assumptions on the underlying dynamics. We apply our theory to a phenomenological model of bacterial cell division in E. coli and to experimental data. We find that the discrepancy between the growth rate predicted by the Euler-Lotka equation and our generalized version is relatively small, but large enough to be measurable by our approach.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells.

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

Increased Mutation Rate Is Linked to Genome Reduction in Prokaryotes.

The evolutionary processes that drive variation in genome size across the tree of life remain unresolved. Effective population size (Ne) is thought to play an important role in shaping genome size [1-3]-a key example being the reduced genomes of insect endosymbionts, which undergo population bottlenecks during transmission [4]. However, the existence of reduced genomes in marine and terrestrial prokaryote species with large Ne indicate that genome reduction is influenced by multiple processes [3]. One candidate process is enhanced mutation rate, which can increase adaptive capacity but can also promote gene loss. To investigate evolutionary forces associated with prokaryotic genome reduction, we performed molecular evolutionary and phylogenomic analyses of nine lineages from five bacterial and archaeal phyla. We found that gene-loss rate strongly correlated with synonymous substitution rate (a proxy for mutation rate) in seven of the nine lineages. However, gene-loss rate showed weak or no correlation with the ratio of nonsynonymous/synonymous substitution rate (dN/dS). These results indicate that genome reduction is largely associated with increased mutation rate, while the association between gene loss and changes in Ne is less well defined. Lineages with relatively high dS and dN, as well as smaller genomes, lacked multiple DNA repair genes, providing a proximate cause for increased mutation rates. Our findings suggest that similar mechanisms drive genome reduction in both intracellular and free-living prokaryotes, with implications for developing a comprehensive theory of prokaryote genome size evolution.

Ocean currents promote rare species diversity in protists.

Oceans host communities of plankton composed of relatively few abundant species and many rare species. The number of rare protist species in these communities, as estimated in metagenomic studies, decays as a steep power law of their abundance. The ecological factors at the origin of this pattern remain elusive. We propose that chaotic advection by oceanic currents affects biodiversity patterns of rare species. To test this hypothesis, we introduce a spatially explicit coalescence model that reconstructs the species diversity of a sample of water. Our model predicts, in the presence of chaotic advection, a steeper power law decay of the species abundance distribution and a steeper increase of the number of observed species with sample size. A comparison of metagenomic studies of planktonic protist communities in oceans and in lakes quantitatively confirms our prediction. Our results support that oceanic currents positively affect the diversity of rare aquatic microbes.

Error-Speed Correlations in Biopolymer Synthesis.

Synthesis of biopolymers such as DNA, RNA, and proteins are biophysical processes aided by enzymes. The performance of these enzymes is usually characterized in terms of their average error rate and speed. However, because of thermal fluctuations in these single-molecule processes, both error and speed are inherently stochastic quantities. In this Letter, we study fluctuations of error and speed in biopolymer synthesis and show that they are in general correlated. This means that, under equal conditions, polymers that are synthesized faster due to a fluctuation tend to have either better or worse errors than the average. The error-correction mechanism implemented by the enzyme determines which of the two cases holds. For example, discrimination in the forward reaction rates tends to grant smaller errors to polymers with faster synthesis. The opposite occurs for discrimination in monomer rejection rates. Our results provide an experimentally feasible way to identify error-correction mechanisms by measuring the error-speed correlations.

Bet-hedging strategies in expanding populations.

In ecology, species can mitigate their extinction risks in uncertain environments by diversifying individual phenotypes. This observation is quantified by the theory of bet-hedging, which provides a reason for the degree of phenotypic diversity observed even in clonal populations. Bet-hedging in well-mixed populations is rather well understood. However, many species underwent range expansions during their evolutionary history, and the importance of phenotypic diversity in such scenarios still needs to be understood. In this paper, we develop a theory of bet-hedging for populations colonizing new, unknown environments that fluctuate either in space or time. In this case, we find that bet-hedging is a more favorable strategy than in well-mixed populations. For slow rates of variation, temporal and spatial fluctuations lead to different outcomes. In spatially fluctuating environments, bet-hedging is favored compared to temporally fluctuating environments. In the limit of frequent environmental variation, no opportunity for bet-hedging exists, regardless of the nature of the environmental fluctuations. For the same model, bet-hedging is never an advantageous strategy in the well-mixed case, supporting the view that range expansions strongly promote diversification. These conclusions are robust against stochasticity induced by finite population sizes. Our findings shed light on the importance of phenotypic heterogeneity in range expansions, paving the way to novel approaches to understand how biodiversity emerges and is maintained.

Assembly of heteropolymers via a network of reaction coordinates.

In biochemistry, heteropolymers encoding biological information are assembled out of equilibrium by sequentially incorporating available monomers found in the environment. Current models of polymerization treat monomer incorporation as a sequence of discrete chemical reactions between intermediate metastable states. In this paper, we use ideas from reaction rate theory and describe nonequilibrium assembly of a heteropolymer via a continuous reaction coordinate. Our approach allows for estimating the copy error and incorporation speed from the Gibbs free energy landscape of the process. We apply our theory to several examples from a simple reaction characterized by a free energy barrier to more complex cases incorporating error correction mechanisms, such as kinetic proofreading.

Hyperaccurate currents in stochastic thermodynamics.

Thermodynamic observables of mesoscopic systems can be expressed as integrated empirical currents. Their fluctuations are bound by thermodynamic uncertainty relations. We introduce the hyperaccurate current as the integrated empirical current with the least fluctuations in a given nonequilibrium system. For steady-state systems described by overdamped Langevin equations, we derive an equation for the hyperaccurate current by means of a variational principle. We show that the hyperaccurate current coincides with the entropy production if and only if the latter saturates the thermodynamic uncertainty relation, and it can be substantially more precise otherwise. The hyperaccurate current can be used to improve estimates of entropy production from experimental data.

Arcsine Laws in Stochastic Thermodynamics.

We show that the fraction of time that a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by Lévy for Brownian motion. Stochastic currents with long streaks above or below their average are much more likely than those that spend similar fractions of time above and below their average. Our result is confirmed with experimental data from a Brownian Carnot engine. We also conjecture that two other random times associated with currents obey the arcsine law: the time a current reaches its maximum value and the last time a current crosses its average value. These results apply to, inter alia, molecular motors, quantum dots, and colloidal systems.

Evolution of Complex Asexual Reproductive Strategies in Jellyfish.

Many living organisms in terrestrial and aquatic ecosystems rely on multiple reproductive strategies to reduce the risk of extinction in variable environments. Examples are provided by the polyp stage of several bloom-forming jellyfish species, which can reproduce asexually using different budding strategies. These strategies broadly fall into three categories: (1) fast localized reproduction, (2) dormant cysts, or (3) motile and dispersing buds. Similar functional strategies are also present in other groups of species. However, mechanisms leading to the evolution of this rich reproductive diversity are yet to be clarified. Here we model how risk of local population extinction and differential fitness of alternative modes of asexual reproduction could drive the evolution of multiple reproductive modes as seen in jellyfish polyps. Depending on environmental parameters, we find that evolution leads to a unique evolutionarily stable strategy, wherein multiple reproductive strategies generally coexist. As the extinction risk increases, this strategy shifts from a pure budding mode to a dual strategy and finally to one characterized by allocation into all three modes. We identify relative fitness-dependent thresholds in extinction risk where these transitions can occur and discuss our predictions in light of observations on polyp reproduction in laboratory and natural systems.