A mean-field theory for predicting single polymer collapse induced by neutral crowders

Macromolecular crowding can induce the collapse of a single long polymer into a globular form due to depletion forces of entropic nature. This phenomenon has been shown to play a significant role in compacting the genome within the bacterium Escherichia coli into a well-defined region of the cell known as the nucleoid. Motivated by the biological significance of this process, numerous theoretical and computational studies have searched for the primary determinants of the behavior of polymer-crowder phases. However, our understanding of this process remains incomplete and there is debate on a quantitatively unified description. In particular, different simulation studies with explicit crowders have proposed different order parameters as potential predictors for the collapse transition. In this work, we present a comprehensive analysis of published simulation data obtained from different sources. Based on the common behavior we find in this data, we develop a unified phenomenological model that we show to be predictive. Finally, to further validate the accuracy of the model, we conduct new simulations on polymers of various sizes, and investigate the role of jamming of the crowders.

N2FXm, a method for joint nuclear and cytoplasmic volume measurements, unravels the osmo-mechanical regulation of nuclear volume in mammalian cells

In eukaryotes, cytoplasmic and nuclear volumes are tightly regulated to ensure proper cell homeostasis. However, current methods to measure cytoplasmic and nuclear volumes, including confocal 3D reconstruction, have limitations, such as relying on two-dimensional projections or poor vertical resolution. Here, to overcome these limitations, we describe a method, N2FXm, to jointly measure cytoplasmic and nuclear volumes in single cultured adhering human cells, in real time, and across cell cycles. We find that this method accurately provides joint size over dynamic measurements and at different time resolutions. Moreover, by combining several experimental perturbations and analyzing a mathematical model including osmotic effects and tension, we show that N2FXm can give relevant insights on how mechanical forces exerted by the cytoskeleton on the nuclear envelope can affect the growth of nucleus volume by biasing nuclear import. Our method, by allowing for accurate joint nuclear and cytoplasmic volume dynamic measurements at different time resolutions, highlights the non-constancy of the nucleus/cytoplasm ratio along the cell cycle.

Metacommunity structure preserves genome diversity in the presence of gene-specific selective sweeps under moderate rates of horizontal gene transfer

The horizontal transfer of genes is fundamental for the eco-evolutionary dynamics of microbial communities, such as oceanic plankton, soil, and the human microbiome. In the case of an acquired beneficial gene, classic population genetics would predict a genome-wide selective sweep, whereby the genome spreads clonally within the community and together with the beneficial gene, removing genome diversity. Instead, several sources of metagenomic data show the existence of "gene-specific sweeps", whereby a beneficial gene spreads across a bacterial community, maintaining genome diversity. Several hypotheses have been proposed to explain this process, including the decreasing gene flow between ecologically distant populations, frequency-dependent selection from linked deleterious allelles, and very high rates of horizontal gene transfer. Here, we propose an additional possible scenario grounded in eco-evolutionary principles. Specifically, we show by a mathematical model and simulations that a metacommunity where species can occupy multiple patches, acting together with a realistic (moderate) HGT rate, helps maintain genome diversity. Assuming a scenario of patches dominated by single species, our model predicts that diversity only decreases moderately upon the arrival of a new beneficial gene, and that losses in diversity can be quickly restored. We explore the generic behaviour of diversity as a function of three key parameters, frequency of insertion of new beneficial genes, migration rates and horizontal transfer rates.Our results provides a testable explanation for how diversity can be maintained by gene-specific sweeps even in the absence of high horizontal gene transfer rates.

Clonal cooperation through soluble metabolite exchange facilitates metastatic outgrowth by modulating Allee effect

Cancers feature substantial intratumoral heterogeneity of genetic and phenotypically distinct lineages. Although interactions between coexisting lineages are emerging as a potential contributor to tumor evolution, the extent and nature of these interactions remain largely unknown. We postulated that tumors develop ecological interactions that sustain diversity and facilitate metastasis. Using a combination of fluorescent barcoding, mathematical modeling, metabolic analysis, and in vivo models, we show that the Allee effect, i.e., growth dependency on population size, is a feature of tumor lineages and that cooperative ecological interactions between lineages alleviate the Allee barriers to growth in a model of triple-negative breast cancer. Soluble metabolite exchange formed the basis for these cooperative interactions and catalyzed the establishment of a polyclonal community that displayed enhanced metastatic dissemination and outgrowth in xenograft models. Our results highlight interclonal metabolite exchange as a key modulator of tumor ecology and a contributing factor to overcoming Allee effect-associated growth barriers to metastasis.

Centripetal nuclear shape fluctuations associate with chromatin condensation in early prophase

The nucleus plays a central role in several key cellular processes, including chromosome organisation, DNA replication and gene transcription. Recent work suggests an association between nuclear mechanics and cell-cycle progression, but many aspects of this connection remain unexplored. Here, by monitoring nuclear shape fluctuations at different cell cycle stages, we uncover increasing inward fluctuations in late G2 and in early prophase, which are initially transient, but develop into instabilities when approaching the nuclear-envelope breakdown. We demonstrate that such deformations correlate with chromatin condensation by perturbing both the chromatin and the cytoskeletal structures. We propose that the contrasting forces between an extensile stress and centripetal pulling from chromatin condensation could mechanically link chromosome condensation with nuclear-envelope breakdown, two main nuclear processes occurring during mitosis.

A fitness trade-off explains the early fate of yeast aneuploids with chromosome gains

The early development of aneuploidy from an accidental chromosome missegregation shows contrasting effects. On the one hand, it is associated with significant cellular stress and decreased fitness. On the other hand, it often carries a beneficial effect and provides a quick (but typically transient) solution to external stress. These apparently controversial trends emerge in several experimental contexts, particularly in the presence of duplicated chromosomes. However, we lack a mathematical evolutionary modeling framework that comprehensively captures these trends from the mutational dynamics and the trade-offs involved in the early stages of aneuploidy. Here, focusing on chromosome gains, we address this point by introducing a fitness model where a fitness cost of chromosome duplications is contrasted by a fitness advantage from the dosage of specific genes. The model successfully captures the experimentally measured probability of emergence of extra chromosomes in a laboratory evolution setup. Additionally, using phenotypic data collected in rich media, we explored the fitness landscape, finding evidence supporting the existence of a per-gene cost of extra chromosomes. Finally, we show that the substitution dynamics of our model, evaluated in the empirical fitness landscape, explains the relative abundance of duplicated chromosomes observed in yeast population genomics data. These findings lay a firm framework for the understanding of the establishment of newly duplicated chromosomes, providing testable quantitative predictions for future observations.

Abstract 2613: A modified Luria-Delbrück assay allows quantification of colorectal cancer persister cells’ mutation rate

When cancer cells are exposed to lethal doses of targeted therapies, the emergence of a subpopulation of drug-tolerant persister cells (DTPs) is often observed. We previously reported that colorectal cancer (CRC) cells exposed to targeted therapies activate an adaptive mutability stress response, involving DNA damage induction and a switch to low-fidelity DNA replication. Therefore, targeted treatment might lead to increased mutation rate in DTPs, but mutation rates of cancer cells during treatment have not been quantitatively assessed. Here, we combined biological experiments and mathematical modelling to characterize emergence and dynamics of DTPs. From this, we extrapolated parameters governing dynamics of cancer cells populations and designed a modified Luria-Delbrück assay on mammalian cells (MC-LD) to quantify mutations rates of CRC cells under standard growth conditions and during exposure to targeted therapy. We selected mismatch repair proficient CRC cell lines sensitive to different clinically used therapeutic agents, and derived clones to be used for experiments. By monitoring cell dynamics in drug-response growth assays, we found that CRC cells exposed to targeted therapy display a biphasic killing curve reaching a stable plateau, a pattern indicative of emergence of DTPs. By fitting model estimation to population growth assays, we predicted that, even if a subgroup of DTPs predated treatment, the majority of them emerged only upon exposure to targeted therapies. We also observed that DTPs slowly replicate under treatment, as shown by Carboxy fluorescein succinimidyl ester (CFSE) analysis and staining with 5-ethynyl-2’-deoxyuridine (EdU). We used these population dynamics parameters to design the MC-LD assay. CRC clones were plated in several 96-multiwell plates each, and after an expansion phase in standard culture conditions, treatment was added. After 3-4 weeks, a minority of wells showed growth of resistant colonies: based on the measured growth rates, we could predict that the resistant cells arose before treatment by spontaneous mutation. The remaining wells contained a homogenous population of DTPs. After several weeks of treatment, when pre-treatment resistant clones would have already emerged, late-emerging resistant colonies appeared in a subset of wells in which DTPs had previously been detected. Using the number of residual DTPs and resistant colonies to infer mutation rates, we found a 7- to 50-fold increase (depending on the cell line) in DTPs’ mutation rate compared to sensitive cells.In conclusion, we developed a new assay which allows quantitative comparisons of spontaneous and drug-induced mutation rates in cancer cells and showed that adaptive mutability in DTPs leads to increased mutation rates. This approach could be used to measure whether and how a wide range of environmental conditions affect DTP phenotype and mutation rates in mammalian cells.

Citation Format: Alberto Sogari, Mariangela Russo, Simone Pompei, Mattia Corigliano, Giovanni Crisafulli, Andrea Bertotti, Marco Gherardi, Federica Di Nicolantonio, Marco Cosentino Lagomarsino, Alberto Bardelli. A modified Luria-Delbrück assay allows quantification of colorectal cancer persister cells’ mutation rate [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2613.

Protein degradation sets the fraction of active ribosomes at vanishing growth

Growing cells adopt common basic strategies to achieve optimal resource allocation under limited resource availability. Our current understanding of such “growth laws” neglects degradation, assuming that it occurs slowly compared to the cell cycle duration. Here we argue that this assumption cannot hold at slow growth, leading to important consequences. We propose a simple framework showing that at slow growth protein degradation is balanced by a fraction of “maintenance” ribosomes. Consequently, active ribosomes do not drop to zero at vanishing growth, but as growth rate diminishes, an increasing fraction of active ribosomes performs maintenance. Through a detailed analysis of compiled data, we show that the predictions of this model agree with data from E. coli and S. cerevisiae. Intriguingly, we also find that protein degradation increases at slow growth, which we interpret as a consequence of active waste management and/or recycling. Our results highlight protein turnover as an underrated factor for our understanding of growth laws across kingdoms.

The idea that simple quantitative relationships relate cell physiology to cellular composition dates back to the 1950s, but the recent years saw a leap in our understanding of such “growth laws”, with relevant implications regarding the interdependence between growth, metabolism and biochemical networks. However, recent works on nutrient-limited growth mainly focused on laboratory conditions that are favourable to growth. Thus, our current mathematical understanding of the growth laws neglects protein degradation, under the argument that it occurs slowly compared to the timescale of the cell cycle. Instead, at slow growth the timescales of mass loss from protein degradation and dilution become comparable. In this work, we propose that protein degradation shapes the quantitative relationships between ribosome allocation and growth rate, and determines a fraction of ribosomes that do not contribute to growth and need to remain active to balance degradation.

Volume growth in animal cells is cell cycle dependent and shows additive fluctuations

The way proliferating animal cells coordinate the growth of their mass, volume, and other relevant size parameters is a long-standing question in biology. Studies focusing on cell mass have identified patterns of mass growth as a function of time and cell cycle phase, but little is known about volume growth. To address this question, we improved our fluorescence exclusion method of volume measurement (FXm) and obtained 1700 single-cell volume growth trajectories of HeLa cells. We find that, during most of the cell cycle, volume growth is close to exponential and proceeds at a higher rate in S-G2 than in G1. Comparing the data with a mathematical model, we establish that the cell-to-cell variability in volume growth arises from constant-amplitude fluctuations in volume steps rather than fluctuations of the underlying specific growth rate. We hypothesize that such 'additive noise' could emerge from the processes that regulate volume adaptation to biophysical cues, such as tension or osmotic pressure.

Dynamics of Bacterial Chromosomes by Locus Tracking in Fluorescence Microscopy

In the last two decades, it has been shown that bacterial chromosomes have remarkable spatial organization at various scales, and they display well-defined movements during the cell cycle, for example to reliably segregate daughter chromosomes. More recently, various labs have begun investigating also the short time dynamics (displacements during time intervals of 0.1 s-100 s), which should be related to the molecular structure. Probing these dynamics is analogous to "microrheology" approaches that have been applied successfully to study mechanical response of complex fluids. These studies of chromosome fluctuation dynamics have revealed differences of fluctuation amplitude across the chromosome, and different characters of motion depending on the time window of interest. Different fluctuation amplitudes have also been observed for the same chromosomal loci under antibiotic treatments, with magnitudes that are correlated to changes in intracellular density and thus crowding. We describe how to carry out tracking experiments of single loci and how to analyze locus motility. We point out the importance of considering in the analysis the number of GFP molecules per fluorescent locus, as well as the nature of the protein they are fused to, and also how to measure intracellular density.

ppGpp is a bacterial cell size regulator

Growth and division are central to cell size. Bacteria achieve size homeostasis by dividing when growth has added a constant size since birth, termed the adder principle, by unknown mechanisms.^1,2 Growth is well known to be regulated by guanosine tetraphosphate (ppGpp), which controls diverse processes from ribosome production to metabolic enzyme activity and replication initiation and whose absence or excess can induce stress, filamentation, and small growth-arrested cells.^3-6 These observations raise unresolved questions about the relation between ppGpp and size homeostasis mechanisms during normal exponential growth. Here, to untangle effects of ppGpp and nutrients, we gained control of cellular ppGpp by inducing the synthesis and hydrolysis enzymes RelA and Mesh1. We found that ppGpp not only exerts control over the growth rate but also over cell division and thus the steady state cell size. In response to changes in ppGpp level, the added size already establishes its new constant value while the growth rate still adjusts, aided by accelerated or delayed divisions. Moreover, the magnitude of the added size and resulting steady-state birth size correlate consistently with the ppGpp level, rather than with the growth rate, which results in cells of different size that grow equally fast. Our findings suggest that ppGpp serves as a key regulator that coordinates cell size and growth control.

Epistasis, aneuploidy, and functional mutations underlie evolution of resistance to induced microtubule depolymerization

Cells with blocked microtubule polymerization are delayed in mitosis, but eventually manage to proliferate despite substantial chromosome missegregation. While several studies have analyzed the first cell division after microtubule depolymerization, we have asked how cells cope long-term with microtubule impairment. We allowed 24 clonal populations of yeast cells with beta-tubulin mutations preventing proper microtubule polymerization, to evolve for ˜150 generations. At the end of the laboratory evolution experiment, cells had regained the ability to form microtubules and were less sensitive to microtubule-depolymerizing drugs. Whole-genome sequencing identified recurrently mutated genes, in particular for tubulins and kinesins, as well as pervasive duplication of chromosome VIII. Recreating these mutations and chromosome VIII disomy prior to evolution confirmed that they allow cells to compensate for the original mutation in beta-tubulin. Most of the identified mutations did not abolish function, but rather restored microtubule functionality. Analysis of the temporal order of resistance development in independent populations repeatedly revealed the same series of events: disomy of chromosome VIII followed by a single additional adaptive mutation in either tubulins or kinesins. Since tubulins are highly conserved among eukaryotes, our results have implications for understanding resistance to microtubule-targeting drugs widely used in cancer therapy.

Two different cell-cycle processes determine the timing of cell division in Escherichia coli

Cells must control the cell cycle to ensure that key processes are brought to completion. In Escherichia coli, it is controversial whether cell division is tied to chromosome replication or to a replication-independent inter-division process. A recent model suggests instead that both processes may limit cell division with comparable odds in single cells. Here, we tested this possibility experimentally by monitoring single-cell division and replication over multiple generations at slow growth. We then perturbed cell width, causing an increase of the time between replication termination and division. As a consequence, replication became decreasingly limiting for cell division, while correlations between birth and division and between subsequent replication-initiation events were maintained. Our experiments support the hypothesis that both chromosome replication and a replication-independent inter-division process can limit cell division: the two processes have balanced contributions in non-perturbed cells, while our width perturbations increase the odds of the replication-independent process being limiting.

An evolutionary model identifies the main evolutionary biases for the evolution of genome-replication profiles

Recent results comparing the temporal program of genome replication of yeast species belonging to the Lachancea clade support the scenario that the evolution of the replication timing program could be mainly driven by correlated acquisition and loss events of active replication origins. Using these results as a benchmark, we develop an evolutionary model defined as birth-death process for replication origins and use it to identify the evolutionary biases that shape the replication timing profiles. Comparing different evolutionary models with data, we find that replication origin birth and death events are mainly driven by two evolutionary pressures, the first imposes that events leading to higher double-stall probability of replication forks are penalized, while the second makes less efficient origins more prone to evolutionary loss. This analysis provides an empirically grounded predictive framework for quantitative evolutionary studies of the replication timing program.

Taxonomic classification method for metagenomics based on core protein families with Core-Kaiju

Characterizing species diversity and composition of bacteria hosted by biota is revolutionizing our understanding of the role of symbiotic interactions in ecosystems. Determining microbiomes diversity implies the assignment of individual reads to taxa by comparison to reference databases. Although computational methods aimed at identifying the microbe(s) taxa are available, it is well known that inferences using different methods can vary widely depending on various biases. In this study, we first apply and compare different bioinformatics methods based on 16S ribosomal RNA gene and shotgun sequencing to three mock communities of bacteria, of which the compositions are known. We show that none of these methods can infer both the true number of taxa and their abundances. We thus propose a novel approach, named Core-Kaiju, which combines the power of shotgun metagenomics data with a more focused marker gene classification method similar to 16S, but based on emergent statistics of core protein domain families. We thus test the proposed method on various mock communities and we show that Core-Kaiju reliably predicts both number of taxa and abundances. Finally, we apply our method on human gut samples, showing how Core-Kaiju may give more accurate ecological characterization and a fresh view on real microbiomes.

Cytosolic Crowding Drives the Dynamics of Both Genome and Cytosol in Escherichia coli Challenged with Sub-lethal Antibiotic Treatments

In contrast to their molecular mode of action, the system-level effect of antibiotics on cells is only beginning to be quantified. Molecular crowding is expected to be a relevant global regulator, which we explore here through the dynamic response phenotypes in Escherichia coli, at single-cell resolution, under sub-lethal regimes of different classes of clinically relevant antibiotics, acting at very different levels in the cell. We measure chromosomal mobility through tracking of fast (<15 s timescale) fluctuations of fluorescently tagged chromosomal loci, and we probe the fluidity of the cytoplasm by tracking cytosolic aggregates. Measuring cellular density, we show how the overall levels of macromolecular crowding affect both quantities, regardless of antibiotic-specific effects. The dominant trend is a strong correlation between the effects in different parts of the chromosome and between the chromosome and cytosol, supporting the concept of an overall global role of molecular crowding in cellular physiology.

Single rod-shaped cell fluctuations from stochastic surface and volume growth rates

Growing rod-shaped bacterial cells need to modulate the production rates of different surface and bulk components. Population data show that the balance between these rates is central for cell physiology and affects cell shape, but we still know little about these processes in single cells. We study a minimal stochastic model where single cells grow by two fluctuating volume-specific surface and volume growth rates, solving for the steady-state distributions and the correlation functions of the main geometric features. Our predictions allow us to address the detectability of different scenarios for the intrinsic coupling between the allocation of resources to surface and bulk growth.

Adaptive mutability of colorectal cancers in response to targeted therapies

The emergence of drug resistance limits the efficacy of targeted therapies in human tumors. The prevalent view is that resistance is a fait accompli: when treatment is initiated, cancers already contain drug-resistant mutant cells. Bacteria exposed to antibiotics transiently increase their mutation rates (adaptive mutability), thus improving the likelihood of survival. We investigated whether human colorectal cancer (CRC) cells likewise exploit adaptive mutability to evade therapeutic pressure. We found that epidermal growth factor receptor (EGFR)/BRAF inhibition down-regulates mismatch repair (MMR) and homologous recombination DNA-repair genes and concomitantly up-regulates error-prone polymerases in drug-tolerant (persister) cells. MMR proteins were also down-regulated in patient-derived xenografts and tumor specimens during therapy. EGFR/BRAF inhibition induced DNA damage, increased mutability, and triggered microsatellite instability. Thus, like unicellular organisms, tumor cells evade therapeutic pressures by enhancing mutability.

Cellular response upon proliferation in the presence of an active mitotic checkpoint

Cells that replicate with an active mitotic checkpoint remain capable to mount multiple times an efficient arrest, are bigger than unperturbed cells, rely more heavily on Cdh1, and have an altered protein expression profile.

Eukaryotic cells treated with microtubule-targeting agents activate the spindle assembly checkpoint to arrest in mitosis and prevent chromosome mis-segregation. A fraction of mitotically arrested cells overcomes the block and proliferates even under persistent checkpoint-activating conditions. Here, we asked what allows proliferation in such unfavourable conditions. We report that yeast cells are delayed in mitosis at each division, implying that their spindle assembly checkpoint remains responsive. The arrest causes their cell cycle to be elongated and results in a size increase. Growth saturates at mitosis and correlates with the repression of various factors involved in translation. Contrary to unperturbed cells, growth of cells with an active checkpoint requires Cdh1. This peculiar cell cycle correlates with global changes in protein expression whose signatures partly overlap with the environmental stress response. Hence, cells dividing with an active checkpoint develop recognisable specific traits that allow them to successfully complete cell division notwithstanding a constant mitotic checkpoint arrest. These properties distinguish them from unperturbed cells. Our observation may have implications for the identification of new therapeutic windows and targets in tumors.

Network model of conviction-driven social segregation

To measure, predict, and prevent social segregation, it is necessary to understand the factors that cause it. While in most available descriptions space plays an essential role, one outstanding question is whether and how this phenomenon is possible in a well-mixed social network. We define and solve a simple model of segregation on networks based on discrete convictions. In our model, space does not play a role, and individuals never change their conviction, but they may choose to connect socially to other individuals based on two criteria: sharing the same conviction and individual popularity (regardless of conviction). The tradeoff between these two moves defines a parameter, analogous to the "tolerance" parameter in classical models of spatial segregation. We show numerically and analytically that this parameter determines a true phase transition (somewhat reminiscent of phase separation in a binary mixture) between a well-mixed and a segregated state. Additionally, minority convictions segregate faster and inter-specific aversion alone may lead to a segregation threshold with similar properties. Together, our results highlight the general principle that a segregation transition is possible in absence of spatial degrees of freedom, provided that conviction-based rewiring occurs on the same time scale of popularity rewirings.

Concurrent processes set E. coli cell division

A cell can divide only upon completion of chromosome segregation; otherwise, its daughters would lose genetic material. However, we do not know whether the partitioning of chromosomes is the key event for the decision to divide. We show how key trends in single-cell data reject the classic idea of replication-segregation as the rate-limiting process for cell division. Instead, the data agree with a model where two concurrent processes (setting replication initiation and interdivision time) set cell division on competing time scales. During each cell cycle, division is set by the slowest process (an "AND" gate). The concept of transitions between cell cycle stages as decisional processes integrating multiple inputs instead of cascading from orchestrated steps can affect the way we think of the cell cycle in general.

Subdiffusion of loci and cytoplasmic particles are different in compressed Escherichia coli cells

The complex physical nature of the bacterial intracellular environment remains largely unknown, and has relevance for key biochemical and biological processes of the cell. Although recent work has addressed the role of non-equilibrium sources of activity and crowding, the consequences of mechanical perturbations are relatively less explored. Here we use a microfabricated valve system to track both fluorescently labeled chromosomal loci and cytoplasmic particles in Escherichia coli cells shortly after applying a compressive force, observing the response on time scales that are too sudden to allow for biochemical response from the cell. Cytoplasmic diffusion slows markedly on compression but the exponent governing the growth of the ensemble-averaged mean-squared displacement of cytoplasmic particles is unaffected. In contrast, the corresponding exponent for DNA loci changes significantly. These results suggest that DNA elasticity and nucleoid organization play a more important role in loci subdiffusion than cytoplasmic viscoelasticity under such short time scales.

The Empirical Fluctuation Pattern of E. coli Division Control

In physics, it is customary to represent the fluctuations of a stochastic system at steady state in terms of linear response to small random perturbations. Previous work has shown that the same framework describes effectively the trade-off between cell-to-cell variability and correction in the control of cell division of single E. coli cells. However, previous analyses were motivated by specific models and limited to a subset of the measured variables. For example, most analyses neglected the role of growth rate variability. Here, we take a comprehensive approach and consider several sets of available data from both microcolonies and microfluidic devices in different growth conditions. We evaluate all the coupling coefficients between the three main measured variables (interdivision times, cell sizes and individual-cell growth rates). The linear-response framework correctly predicts consistency relations between a priori independent experimental measurements, which confirms its validity. Additionally, the couplings between the cell-specific growth rate and the other variables are typically non zero. Finally, we use the framework to detect signatures of mechanisms in experimental data involving growth rate fluctuations, finding that (1) noise-generating coupling between size and growth rate is a consequence of inter-generation growth rate correlations and (2) the correlation patterns agree with a near-adder model where the added size has a dependence on the single-cell growth rate. Our findings define relevant constraints that any theoretical description should reproduce, and will help future studies aiming to falsify some of the competing models of the cell cycle existing today in the literature.

Spontaneous domain formation in disordered copolymers as a mechanism for chromosome structuring

Motivated by the problem of domain formation in chromosomes, we studied a co-polymer model where only a subset of the monomers feel attractive interactions. These monomers are displaced randomly from a regularly-spaced pattern, thus introducing some quenched disorder in the system. Previous work has shown that in the case of regularly-spaced interacting monomers this chain can fold into structures characterized by multiple distinct domains of consecutive segments. In each domain, attractive interactions are balanced by the entropy cost of forming loops. We show by advanced replica-exchange simulations that adding disorder in the position of the interacting monomers further stabilizes these domains. The model suggests that the partitioning of the chain into well-defined domains of consecutive monomers is a spontaneous property of heteropolymers. In the case of chromosomes, evolution could have acted on the spacing of interacting monomers to modulate in a simple way the underlying domains for functional reasons.

Zipf and Heaps laws from dependency structures in component systems

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sublinear, and saturating) that we characterize quantitatively.

Cells Escape an Operational Mitotic Checkpoint through a Stochastic Process

Improperly attached chromosomes activate the mitotic checkpoint that arrests cell division before anaphase. Cells can maintain an arrest for several hours but eventually will resume proliferation, a process we refer to as adaptation. Whether adapting cells bypass an active block or whether the block has to be removed to resume proliferation is not clear. Likewise, it is not known whether all cells of a genetically homogeneous population are equally capable to adapt. Here, we show that the mitotic checkpoint is operational when yeast cells adapt and that each cell has the same propensity to adapt. Our results are consistent with a model of the mitotic checkpoint where adaptation is driven by random fluctuations of APC/C^Cdc20, the molecular species inhibited by the checkpoint. Our data provide a quantitative framework for understanding how cells overcome a constant stimulus that halts cell cycle progression.

Current quantization and fractal hierarchy in a driven repulsive lattice gas

Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the nonequilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density.

Cell-to-cell variability and robustness in S-phase duration from genome replication kinetics

Genome replication, a key process for a cell, relies on stochastic initiation by replication origins, causing a variability of replication timing from cell to cell. While stochastic models of eukaryotic replication are widely available, the link between the key parameters and overall replication timing has not been addressed systematically. We use a combined analytical and computational approach to calculate how positions and strength of many origins lead to a given cell-to-cell variability of total duration of the replication of a large region, a chromosome or the entire genome. Specifically, the total replication timing can be framed as an extreme-value problem, since it is due to the last region that replicates in each cell. Our calculations identify two regimes based on the spread between characteristic completion times of all inter-origin regions of a genome. For widely different completion times, timing is set by the single specific region that is typically the last to replicate in all cells. Conversely, when the completion time of all regions are comparable, an extreme-value estimate shows that the cell-to-cell variability of genome replication timing has universal properties. Comparison with available data shows that the replication program of three yeast species falls in this extreme-value regime.

Stochastic timing in gene expression for simple regulatory strategies

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such ‘timing fluctuations’ and we ask how they can be controlled. Our analytical estimates and simulations show that, for an induced gene, timing variability is minimal if the threshold level of expression is approximately half of the steady-state level. Timing fluctuations can be reduced by increasing the transcription rate, while they are insensitive to the translation rate. In presence of self-regulatory strategies, we show that self-repression reduces timing noise for threshold levels that have to be reached quickly, while self-activation is optimal at long times. These results lay a framework for understanding stochasticity of endogenous systems such as the cell cycle, as well as for the design of synthetic trigger circuits.

Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport

The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.

Procedures for Model-Guided Data Analysis of Chromosomal Loci Dynamics at Short Time Scales

This chapter provides theoretical background and practical procedures for model-guided analysis of mobility of chromosomal loci from movies of many single trajectories. We guide the reader through existing physical models and measurable quantities, illustrating how this knowledge is useful for the interpretation of the measurements.

Role of growth rate on the orientational alignment of Escherichia coli in a slit

We present experimental data on the nematic alignment of Escherichia coli bacteria confined in a slit, with an emphasis on the effect of growth rate and corresponding changes in cell aspect ratio. Global alignment with the channel walls arises from the combination of local nematic ordering of nearby cells, induced by cell division and the elongated shape of the cells, and the preferential orientation of cells proximate to the side walls of the slit. Decreasing the growth rate leads to a decrease in alignment with the walls, which is attributed primarily to effects of changing cell aspect ratio rather than changes in the variance in cell area. Decreasing confinement also reduces the degree of alignment by a similar amount as a decrease in the growth rate, but the distribution of the degree of alignment differs. The onset of alignment with the channel walls is coincident with the slits reaching their steady-state occupancy and connected to the re-orientation of locally aligned regions with respect to the walls during density fluctuations.

Nutrient consumption and chain tuning in diatoms exposed to storm-like turbulence

Current information on the response of phytoplankton to turbulence is linked to cell size and nutrient availability. Diatoms are considered to be favored by mixing as dissolved nutrients are more easily accessible for non-motile cells. We investigated how diatoms exploit microscale turbulence under nutrient repletion and depletion conditions. Here, we show that the chain-forming diatom Chaetoceros decipiens, continues to take up phosphorus and carbon even when silicon is depleted during turbulence. Our findings indicate that upon silica depletion, during turbulence, chain spectra of C. decipiens remained unchanged. We show here that longer chains are maintained during turbulence upon silica depletion whereas under still conditions, shorter chains are enriched. We interpret this as a sign of good physiological state leading to a delay of culture senescence. Our results show that C. decipiens senses and responds to turbulence both in nutrient repletion and depletion. This response is noteworthy due to the small size of the species. The coupling between turbulence and biological response that we depict here may have significant ecological implications. Considering the predicted increase of storms in Northern latitudes this response might modify community structure and succession. Our results partly corroborate Margalef's mandala and provide additional explanations for that conceptualization.

Contrasting evolutionary genome dynamics between domesticated and wild yeasts

Structural rearrangements have long been recognized as an important source of genetic variation, with implications in phenotypic diversity and disease, yet their detailed evolutionary dynamics remain elusive. Here we use long-read sequencing to generate end-to-end genome assemblies for 12 strains representing major subpopulations of the partially domesticated yeast Saccharomyces cerevisiae and its wild relative Saccharomyces paradoxus. These population-level high-quality genomes with comprehensive annotation enable precise definition of chromosomal boundaries between cores and subtelomeres and a high-resolution view of evolutionary genome dynamics. In chromosomal cores, S. paradoxus shows faster accumulation of balanced rearrangements (inversions, reciprocal translocations and transpositions), whereas S. cerevisiae accumulates unbalanced rearrangements (novel insertions, deletions and duplications) more rapidly. In subtelomeres, both species show extensive interchromosomal reshuffling, with a higher tempo in S. cerevisiae. Such striking contrasts between wild and domesticated yeasts are likely to reflect the influence of human activities on structural genome evolution.

Relevant parameters in models of cell division control

A recent burst of dynamic single-cell data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different models were used to propose specific mechanisms, but the links between them are poorly explored. The lack of comparative studies makes it difficult to appreciate how well any particular mechanism is supported by the data. Here, we describe a simple and generic framework in which two common formalisms can be used interchangeably: (i) a continuous-time division process described by a hazard function and (ii) a discrete-time equation describing cell size across generations (where the unit of time is a cell cycle). In our framework, this second process is a discrete-time Langevin equation with simple physical analogues. By perturbative expansion around the mean initial size (or interdivision time), we show how this framework describes a wide range of division control mechanisms, including combinations of time and size control, as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria. As we show by analytical estimates and numerical simulations, the available data are described precisely by the first-order approximation of this expansion, i.e., by a "linear response" regime for the correction of size fluctuations. Hence, a single dimensionless parameter defines the strength and action of the division control against cell-to-cell variability (quantified by a single "noise" parameter). However, the same strength of linear response may emerge from several mechanisms, which are distinguished only by higher-order terms in the perturbative expansion. Our analytical estimate of the sample size needed to distinguish between second-order effects shows that this value is close to but larger than the values of the current datasets. These results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division.

Both genome and cytosol dynamics change in E. coli challenged with sublethal rifampicin

While the action of many antimicrobial drugs is well understood at the molecular level, a systems-level physiological response to antibiotics remains largely unexplored. This work considers fluctuation dynamics of both the chromosome and cytosol in Escherichia coli, and their response to sublethal treatments of a clinically important antibiotic, rifampicin. We precisely quantify the changes in dynamics of chromosomal loci and cytosolic aggregates (a rheovirus nonstructural protein known as μNS-GFP), measuring short time-scale displacements across several hours of drug exposure. To achieve this we develop an empirical method correcting for photo-bleaching and loci size effects. This procedure allows us to characterize the dynamic response to rifampicin in different growth conditions, including a customised microfluidic device. We find that sub-lethal doses of rifampicin cause a small but consistent increase in motility of both the chromosomal loci and cytosolic aggregates. Chromosomal and cytosolic responses are consistent with each other and between different growth conditions.

Regulation of chain length in two diatoms as a growth-fragmentation process

Chain formation in diatoms is relevant because of several aspects of their adaptation to the ecosystem. However, the tools to quantify the regulation of their assemblage and infer specific mechanisms in a laboratory setting are scarce. To address this problem, we define an approach based on a statistical physics model of chain growth and separation in combination with experimental evaluation of chain-length distributions. Applying this combined analysis to data from Chaetoceros decipiens and Phaeodactylum tricornutum, we find that cells of the first species control chain separation, likely through a cell-to-cell communication process, while the second species only modulates the separation rate. These results promote quantitative methods for characterizing chain formation in several chain-forming species and in diatoms in particular.

Law of corresponding states for open collaborations

We study the relation between number of contributors and product size in Wikipedia and GitHub. In contrast to traditional production, this is strongly probabilistic, but is characterized by two quantitative nonlinear laws: a power-law bound to product size for increasing number of contributors, and the universal collapse of rescaled distributions. A variant of the random-energy model shows that both laws are due to the heterogeneity of contributors, and displays an intriguing finite-size scaling property with no equivalent in standard systems. The analysis uncovers the right intensive densities, enabling the comparison of projects with different numbers of contributors on equal grounds. We use this property to expose the detrimental effects of conflicting interactions in Wikipedia.

Mapping Topoisomerase IV Binding and Activity Sites on the E. coli Genome

Catenation links between sister chromatids are formed progressively during DNA replication and are involved in the establishment of sister chromatid cohesion. Topo IV is a bacterial type II topoisomerase involved in the removal of catenation links both behind replication forks and after replication during the final separation of sister chromosomes. We have investigated the global DNA-binding and catalytic activity of Topo IV in E. coli using genomic and molecular biology approaches. ChIP-seq revealed that Topo IV interaction with the E. coli chromosome is controlled by DNA replication. During replication, Topo IV has access to most of the genome but only selects a few hundred specific sites for its activity. Local chromatin and gene expression context influence site selection. Moreover strong DNA-binding and catalytic activities are found at the chromosome dimer resolution site, dif, located opposite the origin of replication. We reveal a physical and functional interaction between Topo IV and the XerCD recombinases acting at the dif site. This interaction is modulated by MatP, a protein involved in the organization of the Ter macrodomain. These results show that Topo IV, XerCD/dif and MatP are part of a network dedicated to the final step of chromosome management during the cell cycle.

DNA topoisomerases are ubiquitous enzymes that solve the topological problems associated with replication, transcription and recombination. Type II Topoisomerases play a major role in the management of newly replicated DNA. They contribute to the condensation and segregation of chromosomes to the future daughter cells and are essential for the optimal transmission of genetic information. In most bacteria, including the model organism Escherichia coli, these tasks are performed by two enzymes, DNA gyrase and DNA Topoisomerase IV (Topo IV). The distribution of the roles between these enzymes during the cell cycle is not yet completely understood. In the present study we use genomic and molecular biology methods to decipher the regulation of Topo IV during the cell cycle. Here we present data that strongly suggest the interaction of Topo IV with the chromosome is controlled by DNA replication and chromatin factors responsible for its loading to specific regions of the chromosome. In addition, our observations reveal, that by sharing several key factors, the DNA management processes ensuring accuracy of the late steps of chromosome segregation are all interconnected.

Individuality and universality in the growth-division laws of single E. coli cells

The mean size of exponentially dividing Escherichia coli cells in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time, and individual growth rate are only starting to be characterized. Recent studies in bacteria reported a universal trend where the spread in both size and doubling times is a linear function of the population means of these variables. Here we combine experiments and theory and use scaling concepts to elucidate the constraints posed by the second observation on the division control mechanism and on the joint fluctuations of sizes and doubling times. We found that scaling relations based on the means collapse both size and doubling-time distributions across different conditions and explain how the shape of their joint fluctuations deviates from the means. Our data on these joint fluctuations highlight the importance of cell individuality: Single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time. Our calculations show that these results emerge from a broad class of division control mechanisms requiring a certain scaling form of the "division hazard rate function," which defines the probability rate of dividing as a function of measurable parameters. This "model free" approach gives a rationale for the universal body-size distributions observed in microbial ecosystems across many microbial species, presumably dividing with multiple mechanisms. Additionally, our experiments show a crossover between fast and slow growth in the relation between individual-cell growth rate and division time, which can be understood in terms of different regimes of genome replication control.

Bacterial Chromosome Dynamics by Locus Tracking in Fluorescence Microscopy

Bacterial chromosomes have been shown in the last two decades to have remarkable spatial organization at various scales, and also well-defined movements during the cell cycle, for example, to reliably segregate daughter chromosomes. More recently, various labs have begun investigating the short-time dynamics (displacements during time intervals of 0.1-100 s), which one hopes to link to structure, in analogy to "microrheology" approaches applied successfully to study mechanical response of complex fluids. These studies of chromosome fluctuation dynamics have revealed differences of fluctuation amplitude across the chromosome, and different characters of motion depending on the time window of interest. The highly nontrivial motion at the shortest experimentally accessible times is still not fully understood in terms of physical models of DNA and cytosol. We describe how to carry out tracking experiments of single locus and how to analyze locus motility. We point out the importance of considering in the analysis the number of GFP molecules per fluorescent locus.

Stochasticity and homeostasis in the E. coli replication and division cycle

How cells correct for stochasticity to coordinate the chromosome replication and cellular division cycle is poorly understood. We used time-lapse microscopy and fluorescently labelled SeqA to determine the timing of birth, initiation, termination, and division, as well as cell size throughout the cell cycle. We found that the time between birth and initiation (B-period) compensates for stochastic variability in birth size and growth rate. The time between termination and division (D-period) also compensates for size and growth variability, invalidating the notion that replication initiation is the principal trigger for cell division. In contrast, the time between initiation and termination (C-period) did not display such compensations. Interestingly, the C-period did show small but systematic decreases for cells that spontaneously grew faster, which suggests a coupling between metabolic fluctuations and replication. An auto-regressive theoretical framework was employed to compare different possible models of sub-period control.

From structure to function of bacterial chromosomes: Evolutionary perspectives and ideas for new experiments

The link between chromosome structure and function is a challenging open question because chromosomes in vivo are highly dynamic and arduous to manipulate. Here, we examine several promising approaches to tackle this question specifically in bacteria, by integrating knowledge from different sources. Toward this end, we first provide a brief overview of experimental tools that have provided insights into the description of the bacterial chromosome, including genetic, biochemical and fluorescence microscopy techniques. We then explore the possibility of using comparative genomics to isolate functionally important features of chromosome organization, exploiting the fact that features shared between phylogenetically distant bacterial species reflect functional significance. Finally, we discuss possible future perspectives from the field of experimental evolution. Specifically, we propose novel experiments in which bacteria could be screened and selected on the basis of the structural properties of their chromosomes.

Dicke simulators with emergent collective quantum computational abilities

Using an approach inspired from spin glasses, we show that the multimode disordered Dicke model is equivalent to a quantum Hopfield network. We propose variational ground states for the system at zero temperature, which we conjecture to be exact in the thermodynamic limit. These ground states contain the information on the disordered qubit-photon couplings. These results lead to two intriguing physical implications. First, once the qubit-photon couplings can be engineered, it should be possible to build scalable pattern-storing systems whose dynamics is governed by quantum laws. Second, we argue with an example of how such Dicke quantum simulators might be used as a solver of "hard" combinatorial optimization problems.

Combined collapse by bridging and self-adhesion in a prototypical polymer model inspired by the bacterial nucleoid

Recent experimental results suggest that the E. coli chromosome feels a self-attracting interaction of osmotic origin, and is condensed in foci by bridging interactions. Motivated by these findings, we explore a generic modeling framework combining solely these two ingredients, in order to characterize their joint effects. Specifically, we study a simple polymer physics computational model with weak ubiquitous short-ranged self attraction and stronger sparse bridging interactions. Combining theoretical arguments and simulations, we study the general phenomenology of polymer collapse induced by these dual contributions, in the case of regularly spaced bridging. Our results distinguish a regime of classical Flory-like coil-globule collapse dictated by the interplay of excluded volume and attractive energy and a switch-like collapse where bridging interactions compete with entropy loss terms from the looped arms of a star-like rosette. Additionally, we show that bridging can induce stable compartmentalized domains. In these configurations, different "cores" of bridging proteins are kept separated by star-like polymer loops in an entropically favorable multi-domain configuration, with a mechanism that parallels micellar polysoaps. Such compartmentalized domains are stable, and do not need any intra-specific interactions driving their segregation. Domains can be stable also in the presence of uniform attraction, as long as the uniform collapse is above its theta point.

The genome-scale interplay amongst xenogene silencing, stress response and chromosome architecture in Escherichia coli

The gene expression state of exponentially growing Escherichia coli cells is manifested by high expression of essential and growth-associated genes and low levels of stress-related and horizontally acquired genes. An important player in maintaining this homeostasis is the H-NS-StpA gene silencing system. A Δhns-stpA deletion mutant results in high expression of otherwise-silent horizontally acquired genes, many located in the terminus-half of the chromosome, and an indirect downregulation of many highly expressed genes. The Δhns-stpA double mutant displays slow growth. Using laboratory evolution we address the evolutionary strategies that E. coli would adopt to redress this gene expression imbalance. We show that two global gene regulatory mutations-(i) point mutations inactivating the stress-responsive sigma factor RpoS or σ38 and (ii) an amplification of ∼40% of the chromosome centred around the origin of replication-converge in partially reversing the global gene expression imbalance caused by Δhns-stpA. Transcriptome data of these mutants further show a three-way link amongst the global gene regulatory networks of H-NS and σ38, as well as chromosome architecture. Increasing gene expression around the terminus of replication results in a decrease in the expression of genes around the origin and vice versa; this appears to be a persistent phenomenon observed as an association across ∼300 publicly-available gene expression data sets for E. coli. These global suppressor effects are transient and rapidly give way to more specific mutations, whose roles in reversing the growth defect of H-NS mutations remain to be understood.

Large-scale dynamics of horizontal transfers

The widespread exchange of genes between bacteria must have consequences on the global architecture of their genomes, which are being found in the abundant genomic data available today. Most of the expansion of bacterial protein families can be attributed to transfer events, which are positively biased for smaller evolutionary distances between genomes, and more frequent for classes that are larger, when summed over all known bacteria. Moreover, “innovation” events where horizontal transfers carry exogenous evolutionary families appear to be less frequent for larger genomes. This dynamic expansion of evolutionary families is interconnected with the acquisition of new biological functions and thus with the size and distribution of the genes’ functional categories found on a genome. This commentary presents our recent contributions to this line of work and possible future directions.