Physical descriptions of the bacterial nucleoid at large scales, and their biological implications

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.

Macromolecular Crowding and DNA: Bridging the Gap between In Vitro and In Vivo

The cellular environment is highly crowded, with up to 40% of the volume fraction of the cell occupied by various macromolecules. Most laboratory experiments take place in dilute buffer solutions; by adding various synthetic or organic macromolecules, researchers have begun to bridge the gap between in vitro and in vivo measurements. This is a review of the reported effects of macromolecular crowding on the compaction and extension of DNA, the effect of macromolecular crowding on DNA kinetics, and protein-DNA interactions. Theoretical models related to macromolecular crowding and DNA are briefly reviewed. Gaps in the literature, including the use of biologically relevant crowders, simultaneous use of multi-sized crowders, empirical connections between macromolecular crowding and liquid-liquid phase separation of nucleic materials are discussed.

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

Characterisation of the Novel Filamentous Phage PMBT54 Infecting the Milk Spoilage Bacteria Pseudomonas carnis and Pseudomonas lactis

Filamentous bacteriophages are lysogenic and pseudo-lysogenic viruses that do not lyse their host but are often continuously secreted from the infected cell. They belong to the order Tubulavirales, which encompasses three families, with the Inoviridae being the largest. While the number of identified inoviral sequences has greatly increased in recent years due to metagenomic studies, morphological and physiological characterisation is still restricted to only a few members of the filamentous phages. Here, we describe the novel filamentous phage PMBT54, which infects the spoilage-relevant Pseudomonas species P. carnis and P. lactis. Its genome is 7320 bp in size, has a mol% GC content of 48.37, and codes for 13 open-reading frames, two of which are located on the (-) strand. The virion exhibits a typical filamentous morphology and is secreted from the host cell at various lengths. The phage was shown to promote biofilm formation in both host strains and, therefore, has potential implications for milk spoilage, as biofilms are a major concern in the dairy industry.

Organization of the bacterial nucleoid by DNA-bridging proteins and globular crowders

The genomic DNA of bacteria occupies only a fraction of the cell called the nucleoid, although it is not bounded by any membrane and would occupy a volume hundreds of times larger than the cell in the absence of constraints. The two most important contributions to the compaction of the DNA coil are the cross-linking of the DNA by nucleoid proteins (like H-NS and StpA) and the demixing of DNA and other abundant globular macromolecules which do not bind to the DNA (like ribosomes). The present work deals with the interplay of DNA-bridging proteins and globular macromolecular crowders, with the goal of determining the extent to which they collaborate in organizing the nucleoid. In order to answer this question, a coarse-grained model was developed and its properties were investigated through Brownian dynamics simulations. These simulations reveal that the radius of gyration of the DNA coil decreases linearly with the effective volume ratio of globular crowders and the number of DNA bridges formed by nucleoid proteins in the whole range of physiological values. Moreover, simulations highlight the fact that the number of DNA bridges formed by nucleoid proteins depends crucially on their ability to self-associate (oligomerize). An explanation for this result is proposed in terms of the mean distance between DNA segments and the capacity of proteins to maintain DNA-bridging in spite of the thermal fluctuations of the DNA network. Finally, simulations indicate that non-associating proteins preserve a high mobility inside the nucleoid while contributing to its compaction, leading to a DNA/protein complex which looks like a liquid droplet. In contrast, self-associating proteins form a little deformable network which cross-links the DNA chain, with the consequence that the DNA/protein complex looks more like a gel.

Spatiotemporal Coupling of DNA Supercoiling and Genomic Sequence Organization-A Timing Chain for the Bacterial Growth Cycle?

In this article we describe the bacterial growth cycle as a closed, self-reproducing, or autopoietic circuit, reestablishing the physiological state of stationary cells initially inoculated in the growth medium. In batch culture, this process of self-reproduction is associated with the gradual decline in available metabolic energy and corresponding change in the physiological state of the population as a function of "travelled distance" along the autopoietic path. We argue that this directional alteration of cell physiology is both reflected in and supported by sequential gene expression along the chromosomal OriC-Ter axis. We propose that during the E. coli growth cycle, the spatiotemporal order of gene expression is established by coupling the temporal gradient of supercoiling energy to the spatial gradient of DNA thermodynamic stability along the chromosomal OriC-Ter axis.

Local rigidification and possible coacervation of the Escherichia coli DNA by cationic nylon-3 polymers

Synthetic, cationic random nylon-3 polymers (β-peptides) show promise as inexpensive antimicrobial agents less susceptible to proteolysis than normal peptides. We have used superresolution, single-cell, time-lapse fluorescence microscopy to compare the effects on live Escherichia coli cells of four such polymers and the natural antimicrobial peptides LL-37 and cecropin A. The longer, densely charged monomethyl-cyclohexyl (MM-CH) copolymer and MM homopolymer rapidly traverse the outer membrane and the cytoplasmic membrane. Over the next ∼5 min, they locally rigidify the chromosomal DNA and slow the diffusive motion of ribosomal species to a degree comparable to LL-37. The shorter dimethyl-dimethylcyclopentyl (DM-DMCP) and dimethyl-dimethylcyclohexyl (DM-DMCH) copolymers, and cecropin A are significantly less effective at rigidifying DNA. Diffusion of the DNA-binding protein HU and of ribosomal species is hindered as well. The results suggest that charge density and contour length are important parameters governing these antimicrobial effects. The data corroborate a model in which agents having sufficient cationic charge distributed across molecular contour lengths comparable to local DNA-DNA interstrand spacings (∼6 nm) form a dense network of multivalent, electrostatic "pseudo-cross-links" that cause the local rigidification. In addition, at times longer than ∼30 min, we observe that the MM-CH copolymer and the MM homopolymer (but not the other four agents) cause gradual coalescence of the two nucleoid lobes into a single dense lobe localized at one end of the cell. We speculate that this process involves coacervation of the DNA by the cationic polymer, and may be related to the liquid droplet coacervates observed in eukaryotic cells.

Mesoscale Simulation of Bacterial Chromosome and Cytoplasmic Nanoparticles in Confinement

In this study we investigated, using a simple polymer model of bacterial chromosome, the subdiffusive behaviors of both cytoplasmic particles and various loci in different cell wall confinements. Non-Gaussian subdiffusion of cytoplasmic particles as well as loci were obtained in our Langevin dynamic simulations, which agrees with fluorescence microscope observations. The effects of cytoplasmic particle size, locus position, confinement geometry, and density on motions of particles and loci were examined systematically. It is demonstrated that the cytoplasmic subdiffusion can largely be attributed to the mechanical properties of bacterial chromosomes rather than the viscoelasticity of cytoplasm. Due to the randomly positioned bacterial chromosome segments, the surrounding environment for both particle and loci is heterogeneous. Therefore, the exponent characterizing the subdiffusion of cytoplasmic particle/loci as well as Laplace displacement distributions of particle/loci can be reproduced by this simple model. Nevertheless, this bacterial chromosome model cannot explain the different responses of cytoplasmic particles and loci to external compression exerted on the bacterial cell wall, which suggests that the nonequilibrium activity, e.g., metabolic reactions, play an important role in cytoplasmic subdiffusion.

Free energy and segregation dynamics of two channel-confined polymers of different lengths

Polymers confined to a narrow channel are subject to strong entropic forces that tend to drive the molecules apart. In this study, we use Monte Carlo computer simulations to study the segregation behavior of two flexible hard-sphere polymers under confinement in a cylindrical channel. We focus on the effects of using polymers of different lengths. We measure the variation of the conformational free energy, F, with the center-of-mass separation distance, λ. The simulations reveal four different separation regimes, characterized by different scaling properties of the free energy with respect to the polymer lengths and the channel diameter, D. We propose a regime map in which the state of the system is determined by the values of the quantities N_{2}/N_{1} and λ/(N_{1}+N_{2})D^{-β}, where N_{1} and N_{2} are the polymer lengths, and where β≈0.64. The observed scaling behavior of F(λ) in each regime is in reasonable agreement with predictions using a simple theoretical model. In addition, we use MC dynamics simulations to study the segregation dynamics of initially overlapping polymers by measurement of the incremental mean first-passage time with respect to λ. For systems characterized by a wide range of λ in which a short polymer is nested within a longer one, the segregation dynamics are close to that expected for two noninteracting one-dimensional random walkers undergoing unbiased diffusion. When the free-energy gradient is large, segregation is rapid and characterized by out-of-equilibrium effects.

Mechanotransduction in Prokaryotes: A Possible Mechanism of Spaceflight Adaptation

Our understanding of the mechanisms of microgravity perception and response in prokaryotes (Bacteria and Archaea) lag behind those which have been elucidated in eukaryotic organisms. In this hypothesis paper, we: (i) review how eukaryotic cells sense and respond to microgravity using various pathways responsive to unloading of mechanical stress; (ii) we observe that prokaryotic cells possess many structures analogous to mechanosensitive structures in eukaryotes; (iii) we review current evidence indicating that prokaryotes also possess active mechanosensing and mechanotransduction mechanisms; and (iv) we propose a complete mechanotransduction model including mechanisms by which mechanical signals may be transduced to the gene expression apparatus through alterations in bacterial nucleoid architecture, DNA supercoiling, and epigenetic pathways.

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.

Cooperative effects on the compaction of DNA fragments by the nucleoid protein H-NS and the crowding agent PEG probed by Magnetic Tweezers

BACKGROUND

DNA bridging promoted by the H-NS protein, combined with the compaction induced by cellular crowding, plays a major role in the structuring of the E. coli genome. However, only few studies consider the effects of the physical interplay of these two factors in a controlled environment.

METHODS

We apply a single molecule technique (Magnetic Tweezers) to study the nanomechanics of compaction and folding kinetics of a 6 kb DNA fragment, induced by H-NS bridging and/or PEG crowding.

RESULTS

In the presence of H-NS alone, the DNA shows a step-wise collapse driven by the formation of multiple bridges, and little variations in the H-NS concentration-dependent unfolding force. Conversely, the DNA collapse force observed with PEG was highly dependent on the volume fraction of the crowding agent. The two limit cases were interpreted considering the models of loop formation in a pulled chain and pulling of an equilibrium globule respectively.

CONCLUSIONS

We observed an evident cooperative effect between H-NS activity and the depletion of forces induced by PEG.

GENERAL SIGNIFICANCE

Our data suggest a double role for H-NS in enhancing compaction while forming specific loops, which could be crucial in vivo for defining specific mesoscale domains in chromosomal regions in response to environmental changes.

Requirements for DNA-Bridging Proteins to Act as Topological Barriers of the Bacterial Genome

Bacterial genomes have been shown to be partitioned into several-kilobase-long chromosomal domains that are topologically independent from each other, meaning that change of DNA superhelicity in one domain does not propagate to neighbors. Both in vivo and in vitro experiments have been performed to question the nature of the topological barriers at play, leading to several predictions on possible molecular actors. Here, we address the question of topological barriers using polymer models of supercoiled DNA chains that are constrained such as to mimic the action of predicted molecular actors. More specifically, we determine under which conditions DNA-bridging proteins may act as topological barriers. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. As a result, we find that DNA-bridging proteins must exert rather strong constraints on their binding sites; they must block the diffusion of the excess of twist through the two binding sites on the DNA molecule and, simultaneously, prevent the rotation of one DNA segment relative to the other one. Importantly, not all DNA-bridging proteins satisfy this second condition. For example, single bridges formed by proteins that bind DNA nonspecifically, like H-NS dimers, are expected to fail with this respect. Our findings might also explain, in the case of specific DNA-bridging proteins like LacI, why multiple bridges are required to create stable independent topological domains. Strikingly, when the relative rotation of the DNA segments is not prevented, relaxation results in complex intrication of the two domains. Moreover, although the value of the torsional stress in each domain may vary, their differential is preserved. Our work also predicts that nucleoid-associated proteins known to wrap DNA must form higher protein-DNA complexes to efficiently work as topological barriers.

Biophysical Properties of Escherichia coli Cytoplasm in Stationary Phase by Superresolution Fluorescence Microscopy

In nature, bacteria must survive long periods of nutrient deprivation while maintaining the ability to recover and grow when conditions improve. This quiescent state is called stationary phase. The biochemistry of Escherichia coli in stationary phase is reasonably well understood. Much less is known about the biophysical state of the cytoplasm. Earlier studies of harvested nucleoids concluded that the stationary-phase nucleoid is "compacted" or "supercompacted," and there are suggestions that the cytoplasm is "glass-like." Nevertheless, stationary-phase bacteria support active transcription and translation. Here, we present results of a quantitative superresolution fluorescence study comparing the spatial distributions and diffusive properties of key components of the transcription-translation machinery in intact E. coli cells that were either maintained in 2-day stationary phase or undergoing moderately fast exponential growth. Stationary-phase cells are shorter and exhibit strong heterogeneity in cell length, nucleoid volume, and biopolymer diffusive properties. As in exponential growth, the nucleoid and ribosomes are strongly segregated. The chromosomal DNA is locally more rigid in stationary phase. The population-weighted average of diffusion coefficients estimated from mean-square displacement plots is 2-fold higher in stationary phase for both RNA polymerase (RNAP) and ribosomal species. The average DNA density is roughly twice as high as that in cells undergoing slow exponential growth. The data indicate that the stationary-phase nucleoid is permeable to RNAP and suggest that it is permeable to ribosomal subunits. There appears to be no need to postulate migration of actively transcribed genes to the nucleoid periphery.IMPORTANCE Bacteria in nature usually lack sufficient nutrients to enable growth and replication. Such starved bacteria adapt into a quiescent state known as the stationary phase. The chromosomal DNA is protected against oxidative damage, and ribosomes are stored in a dimeric structure impervious to digestion. Stationary-phase bacteria can recover and grow quickly when better nutrient conditions arise. The biochemistry of stationary-phase E. coli is reasonably well understood. Here, we present results from a study of the biophysical state of starved E. coli Superresolution fluorescence microscopy enables high-resolution location and tracking of a DNA locus and of single copies of RNA polymerase (the transcription machine) and ribosomes (the translation machine) in intact E. coli cells maintained in stationary phase. Evidently, the chromosomal DNA remains sufficiently permeable to enable transcription and translation to occur. This description contrasts with the usual picture of a rigid stationary-phase cytoplasm with highly condensed DNA.

Bacterial Nucleoid: Interplay of DNA Demixing and Supercoiling

This work addresses the question of the interplay of DNA demixing and supercoiling in bacterial cells. Demixing of DNA from other globular macromolecules results from the overall repulsion between all components of the system and leads to the formation of the nucleoid, which is the region of the cell that contains the genomic DNA in a rather compact form. Supercoiling describes the coiling of the axis of the DNA double helix to accommodate the torsional stress injected in the molecule by topoisomerases. Supercoiling is able to induce some compaction of the bacterial DNA, although to a lesser extent than demixing. In this work, we investigate the interplay of these two mechanisms with the goal of determining whether the total compaction ratio of the DNA is the mere sum or some more complex function of the compaction ratios due to each mechanism. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. This work reveals that there actually exist different regimes, depending on the crowder volume ratio and the DNA superhelical density. In particular, a regime in which the effects of DNA demixing and supercoiling on the compaction of the DNA coil simply add up is shown to exist up to moderate values of the superhelical density. In contrast, the mean radius of the DNA coil no longer decreases above this threshold and may even increase again for sufficiently large crowder concentrations. Finally, the model predicts that the DNA coil may depart from the spherical geometry very close to the jamming threshold as a trade-off between the need to minimize both the bending energy of the stiff plectonemes and the volume of the DNA coil to accommodate demixing.

Preferential Localization of the Bacterial Nucleoid

Prokaryotes do not make use of a nucleus membrane to segregate their genetic material from the cytoplasm, so that their nucleoid is potentially free to explore the whole volume of the cell. Nonetheless, high resolution images of bacteria with very compact nucleoids show that such spherical nucleoids are invariably positioned at the center of mononucleoid cells. The present work aims to determine whether such preferential localization results from generic (entropic) interactions between the nucleoid and the cell membrane or instead requires some specific mechanism, like the tethering of DNA at mid-cell or periodic fluctuations of the concentration gradient of given chemical species. To this end, we performed numerical simulations using a coarse-grained model based on the assumption that the formation of the nucleoid results from a segregative phase separation mechanism driven by the de-mixing of the DNA and non-binding globular macromolecules. These simulations show that the abrupt compaction of the DNA coil, which takes place at large crowder density, close to the jamming threshold, is accompanied by the re-localization of the DNA coil close to the regions of the bounding wall with the largest curvature, like the hemispherical caps of rod-like cells, as if the DNA coil were suddenly acquiring the localization properties of a solid sphere. This work therefore supports the hypothesis that the localization of compact nucleoids at regular cell positions involves either some anchoring of the DNA to the cell membrane or some dynamical localization mechanism.

Bacterial chromosome organization. I. Crucial role of release of topological constraints and molecular crowders

We showed in our previous studies that just 3% cross-links (CLs), at special points along the contour of the bacterial DNA, help the DNA-polymer to get organized at micron length scales [T. Agarwal et al., J. Phys.: Condens. Matter 30, 034003 (2018) and T. Agarwal et al., EPL (Europhys. Lett.) 121, 18004 (2018)]. In this work, we investigate how does the release of topological constraints help in the "organization" of the DNA-polymer. Furthermore, we show that the chain compaction induced by the crowded environment in the bacterial cytoplasm contributes to the organization of the DNA-polymer. We model the DNA chain as a flexible bead-spring ring polymer, where each bead represents 1000 base pairs. The specific positions of the CLs have been taken from the experimental contact maps of the bacteria Caulobacter crescentus and Escherichia coli. We introduce different extents of ease of release of topological constraints in our model by systematically changing the diameter of the monomer bead. It varies from the value where chain crossing can occur freely to the value where chain crossing is disallowed. We also study the role of compaction of the chain due to molecular crowders by introducing an "effective" weak Lennard-Jones attraction between the monomers. Using Monte Carlo simulations, we show that the release of topological constraints and the crowding environment play a crucial role to obtain a unique organization of the polymer.

Confinement induces helical organization of chromosome-like polymers

Helical organization is commonly observed for a variety of biopolymers. Here we study the helical organization of two types of biopolymers, i.e., DNA-like semiflexible and bottle-brush polymers, in a cell-like confined space. A bottle-brush polymer consists of a backbone and side chains emanating from the backbone, resembling a supercoiled bacterial chromosome. Using computer simulations, we calculate 'writhe' distributions of confined biopolymers for a wide range of parameters. Our effort clarifies the conditions under which biopolymers are helically organized. While helical organization is not easily realized for DNA-like biomolecules, cylindrical confinement can induce spiral patterns in a bottle brush, similarly to what was observed with bacterial chromosomes. They also suggest that ring-shape bottle brushes have a stronger tendency for helical organization. We discuss how our results can be used to interpret chromosome experiments. For instance, they suggest that experimental resolution has unexpected consequences on writhe measurements (e.g., narrowing of the writhe distribution and kinetic separation of opposite helical states).

Rigidification of the Escherichia coli cytoplasm by the human antimicrobial peptide LL-37 revealed by superresolution fluorescence microscopy

Natural antimicrobial peptides (AMPs) that exhibit broad-spectrum antibacterial activity are often highly positively charged. Fluorescence microscopy shows that after permeabilization of Escherichia coli membranes by the cationic AMP LL-37 a massive influx of peptide freezes the diffusive motion of the chromosomal DNA and a subset of ribosomes. Both are highly negatively charged. Cells cannot recover growth. We suggest that LL-37 forms noncovalent, electrostatic linkages between DNA strands and among polyribosomes, rigidifying the entire cytoplasm. While the preponderance of polyanionic biopolymers in the cytoplasm facilitates diffusion in normal growth, this same characteristic renders the bacterium highly susceptible to attack by polycationic AMPs. The results help explain why bacteria develop resistance to AMPs very slowly and may inform the design of new antibacterial agents.

Superresolution, single-particle tracking reveals effects of the cationic antimicrobial peptide LL-37 on the Escherichia coli cytoplasm. Seconds after LL-37 penetrates the cytoplasmic membrane, the chromosomal DNA becomes rigidified on a length scale of ∼30 nm, evidenced by the loss of jiggling motion of specific DNA markers. The diffusive motion of a subset of ribosomes is also frozen. The mean diffusion coefficients of the DNA-binding protein HU and the nonendogenous protein Kaede decrease twofold. Roughly 10⁸ LL-37 copies flood the cell (mean concentration ∼90 mM). Much of the LL-37 remains bound within the cell after extensive rinsing with fresh growth medium. Growth never recovers. The results suggest that the high concentration of adsorbed polycationic peptides forms a dense network of noncovalent, electrostatic linkages within the chromosomal DNA and among 70S-polysomes. The bacterial cytoplasm comprises a concentrated collection of biopolymers that are predominantly polyanionic (e.g., DNA, ribosomes, RNA, and most globular proteins). In normal cells, this provides a kind of electrostatic lubrication, enabling facile diffusion despite high biopolymer volume fraction. However, this same polyanionic nature renders the cytoplasm susceptible to massive adsorption of polycationic agents once penetration of the membranes occurs. If this phenomenon proves widespread across cationic agents and bacterial species, it will help explain why resistance to antimicrobial peptides develops only slowly. The results suggest two design criteria for polycationic peptides that efficiently kill gram-negative bacteria: facile penetration of the outer membrane and the ability to alter the cytoplasm by electrostatically linking double-stranded DNA and 70S-polysomes.

A segregative phase separation scenario of the formation of the bacterial nucleoid

The mechanism responsible for the compaction of the genomic DNA of bacteria inside a structure called the nucleoid is a longstanding but still lively debated question. Most puzzling is the fact that the nucleoid occupies only a small fraction of the cell, although it is not separated from the rest of the cytoplasm by any membrane and would occupy a volume about a thousand times larger outside the cell. Here, by performing numerical simulations using coarse-grained models, we elaborate on the conjecture that the formation of the nucleoid may result from a segregative phase separation mechanism driven by the demixing of the DNA coil and non-binding globular macromolecules present in the cytoplasm, presumably functional ribosomes. Simulations performed with crowders having a spherical, dumbbell or octahedral geometry highlight the sensitive dependence of the level of DNA compaction on the dissymmetry of DNA/DNA, DNA/crowder, and crowder/crowder repulsive interactions, thereby supporting the segregative phase separation scenario. Simulations also consistently predict a much stronger DNA compaction close to the jamming threshold. Moreover, simulations performed with crowders of different sizes suggest that the final density distribution of each species results from the competition between thermodynamic forces and steric hindrance, so that bigger crowders are expelled selectively from the nucleoid only at moderate total crowder concentrations. This work leads to several predictions, which may eventually be tested experimentally.

Segregation of polymers under cylindrical confinement: effects of polymer topology and crowding

Monte Carlo computer simulations are used to study the segregation behaviour of two polymers under cylindrical confinement. Using a multiple-histogram method, the conformational free energy, F, of the polymers was measured as a function of the centre-of-mass separation distance, λ. We examined the scaling of the free energy functions with the polymer length, the length and diameter of the confining cylinder, the polymer topology (i.e. linear vs. ring polymers), and the packing fraction and size of mobile crowding agents. In the absence of crowders, the observed scaling of F(λ) is similar to that predicted using a simple model employing the de Gennes blob model and the approximation that the free energy of overlapping chains in a tube is equal to that of two isolated chains each in a tube of half the cross-sectional area. Simulations were used to test the latter approximation and reveal that it yields poor quantitative predictions. This, along with generic finite-size effects, likely gives rise to the discrepancies between the predicted and measured values of scaling exponents for F(λ). For segregation in the presence of crowding agents, the free energy barrier generally decreases with increasing crowder packing fraction, thus reducing the entropic forces driving segregation. However, for fixed packing fraction, the barrier increases as the crowder/monomer size ratio decreases.

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.

Entropic elasticity and dynamics of the bacterial chromosome: A simulation study

We study the compression and extension dynamics of a DNA-like polymer interacting with non-DNA binding and DNA-binding proteins, by means of computer simulations. The geometry we consider is inspired by recent experiments probing the compressional elasticity of the bacterial nucleoid (DNA plus associated proteins), where DNA is confined into a cylindrical container and subjected to the action of a "piston"-a spherical bead to which an external force is applied. We quantify the effect of steric interactions (excluded volume) on the force-extension curves as the polymer is compressed. We find that non-DNA-binding proteins, even at low densities, exert an osmotic force which can be a lot larger than the entropic force exerted by the compressed DNA. The trends we observe are qualitatively robust with respect to changes in protein sizes and are similar for neutral and charged proteins (and DNA). We also quantify the dynamics of DNA expansion following removal of the "piston": while the expansion is well fitted by power laws, the apparent exponent depends on protein concentration and protein-DNA interaction in a significant way. We further highlight an interesting kinetic process which we observe during the expansion of DNA interacting with DNA-binding proteins when the interaction strength is intermediate: the proteins bind while the DNA is packaged by the compression force, but they "pop-off" one-by-one as the force is removed, leading to a slow unzipping kinetics. Finally, we quantify the importance of supercoiling, which is an important feature of bacterial DNA in vivo.

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.

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.

Particle-directed assembly of semiflexible polymer chains

We use Langevin dynamics simulations to study aggregation of semiflexible polymers driven by attractions between polymers and spherical particles. We consider a simple model with purely repulsive polymer/polymer and particle/particle interactions but attractive polymer/particle interactions. We find a rich "phase diagram" that contains several different types of globular and rod-like aggregates with either liquid-like or crystalline structure for the particle positions. Systems that exhibit rod-like aggregates with crystalline internal order exhibit a discontinuous rod-globule transition, while systems with liquid-like internal order exhibit a smooth crossover between isotropic and elongated aggregates with increasing chain stiffness. Polymers in elongated liquid-like aggregates often adopt helical configurations that wind around the axis of the aggregate.

The Escherichia coli Nucleoid in Stationary Phase

Compaction of DNA is an essential phenomenon that affects all facets of cellular biology. Surprisingly, given the abundance and apparent simplicity of bacteria, our understanding of chromosome organization in these ancient organisms is inadequate. In this chapter we will focus on arguably the best understood aspect of DNA folding in the model bacterium Escherichia coli: the supercondensation of the chromosome that occurs during periods of starvation and stress.

Thermodynamics of long supercoiled molecules: insights from highly efficient Monte Carlo simulations

Supercoiled DNA polymer models for which the torsional energy depends on the total twist of molecules (Tw) are a priori well suited for thermodynamic analysis of long molecules. So far, nevertheless, the exact determination of Tw in these models has been based on a computation of the writhe of the molecules (Wr) by exploiting the conservation of the linking number, Lk=Tw+Wr, which reflects topological constraints coming from the helical nature of DNA. Because Wr is equal to the number of times the main axis of a DNA molecule winds around itself, current Monte Carlo algorithms have a quadratic time complexity, O(L(2)), with respect to the contour length (L) of the molecules. Here, we present an efficient method to compute Tw exactly, leading in principle to algorithms with a linear complexity, which in practice is O(L(1.2)). Specifically, we use a discrete wormlike chain that includes the explicit double-helix structure of DNA and where the linking number is conserved by continuously preventing the generation of twist between any two consecutive cylinders of the discretized chain. As an application, we show that long (up to 21 kbp) linear molecules stretched by mechanical forces akin to magnetic tweezers contain, in the buckling regime, multiple and branched plectonemes that often coexist with curls and helices, and whose length and number are in good agreement with experiments. By attaching the ends of the molecules to a reservoir of twists with which these can exchange helix turns, we also show how to compute the torques in these models. As an example, we report values that are in good agreement with experiments and that concern the longest molecules that have been studied so far (16 kbp).

Chromosome-like organization of an asymmetrical ring polymer confined in a cylindrical space

To what extent does a confined polymer show chromosome-like organization? Using molecular dynamics simulations, we study a model Escherichia coli (E. coli) chromosome: an asymmetrical ring polymer, formed by small monomers on one side and big monomers on the other confined in a concentric-shell or simple cylinder with closed ends. The ring polymer is organized in the way observed for the E. coli chromosome: if the big monomers are assumed to be localized in the inner cylinder, the two "subchains" forming the ring are spontaneously partitioned in a parallel orientation with the "body" (big-monomer) chain linearly organized with a desired precision and the crossing (small-monomer) chain residing preferentially in the peripheral region. Furthermore, we show that the introduction of a "fluctuating boundary" between the two subchains leads to a double-peak distribution of ter-proximate loci, as seen in experiments, which would otherwise remain single-peaked. In a simple cylinder, however, a chromosome-like organization of the ring polymer typically requires an external mechanism such as cell-wall attachment. Finally, our results clarify to what degree the spatial organization of the chromosomes can be accomplished solely by ring asymmetry and anisotropic confinement.

Revisiting operons: an analysis of the landscape of transcriptional units in E. coli

Background

Bacterial operons are considerably more complex than what were thought. At least their components are dynamically rather than statically defined as previously assumed. Here we present a computational study of the landscape of the transcriptional units (TUs) of E. coli K12, revealed by the available genomic and transcriptomic data, providing new understanding about the complexity of TUs as a whole encoded in the genome of E. coli K12.

Results and conclusion

Our main findings include that (i) different TUs may overlap with each other by sharing common genes, giving rise to clusters of overlapped TUs (TUCs) along the genomic sequence; (ii) the intergenic regions in front of the first gene of each TU tend to have more conserved sequence motifs than those of the other genes inside the TU, suggesting that TUs each have their own promoters; (iii) the terminators associated with the 3’ ends of TUCs tend to be Rho-independent terminators, substantially more often than terminators of TUs that end inside a TUC; and (iv) the functional relatedness of adjacent gene pairs in individual TUs is higher than those in TUCs, suggesting that individual TUs are more basic functional units than TUCs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0805-8) contains supplementary material, which is available to authorized users.

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.

Concentration- and chromosome-organization-dependent regulator unbinding from DNA for transcription regulation in living cells

Binding and unbinding of transcription regulators at operator sites constitute a primary mechanism for gene regulation. While many cellular factors are known to regulate their binding, little is known on how cells can modulate their unbinding for regulation. Using nanometer-precision single-molecule tracking, we study the unbinding kinetics from DNA of two metal-sensing transcription regulators in living Escherichia coli cells. We find that they show unusual concentration-dependent unbinding kinetics from chromosomal recognition sites in both their apo and holo forms. Unexpectedly, their unbinding kinetics further varies with the extent of chromosome condensation, and more surprisingly, varies in opposite ways for their apo-repressor versus holo-activator forms. These findings suggest likely broadly relevant mechanisms for facile switching between transcription activation and deactivation in vivo and in coordinating transcription regulation of resistance genes with the cell cycle.

Binding and unbinding of transcription regulators at operator sites regulates gene expression. By single-molecule tracking of metal-sensing regulators, here the authors show that the unbinding kinetics depends on regulator concentration and chromosome condensation, and varies with their metal-binding states.

Polymers under confinement: single polymers, how they interact, and as model chromosomes

How confinement or a physical constraint modifies polymer chains is not only a classical problem in polymer physics but also relevant in a variety of contexts such as single-molecule manipulations, nanofabrication in narrow pores, and modelling of chromosome organization. Here, we review recent progress in our understanding of polymers in a confined (and crowded) space. To this end, we highlight converging views of these systems from computational, experimental, and theoretical approaches, and then clarify what remains to be clarified. In particular, we focus on exploring how cylindrical confinement reshapes individual chains and induces segregation forces between them - by pointing to the relationships between intra-chain organization and chain segregation. In the presence of crowders, chain molecules can be entropically phase-separated into a condensed state. We include a kernel of discussions on the nature of chain compaction by crowders, especially in a confined space. Finally, we discuss the relevance of confined polymers for the nucleoid, an intracellular space in which the bacterial chromosome is tightly packed, in part by cytoplasmic crowders.

A polymer in a crowded and confined space: effects of crowder size and poly-dispersity

DNA compaction in a bacterial cell is in part carried out by entropic (depletion) forces induced by "free" proteins or crowding particles in the cytoplasm. Indeed, recent in vitro experiments highlight these effects by showing that they alone can condense the E. coli chromosome to its in vivo size. Using molecular dynamics simulations and a theoretical approach, we study how a flexible chain molecule can be compacted by crowding particles with variable sizes in a (cell-like) cylindrical space. Our results show that with smaller crowding agents the compaction occurs at a lower volume fraction but at a larger concentration such that doubling their size is equivalent to increasing their concentration fourfold. Similarly, the effect of polydispersity can be correctly mimicked by adjusting the size of crowders in a homogeneous system. Under different conditions, however, crowding particles can induce chain adsorption onto the cylinder wall, stretching the chain, which would otherwise remain condensed.

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.

Life at the mesoscale: the self-organised cytoplasm and nucleoplasm

The cell contains highly dynamic structures exploiting physical principles of self-organisation at the mesoscale (100 nm to 10 μm). Examples include non-membrane bound cytoplasmic bodies, cytoskeleton-based motor networks and multi-scale chromatin organisation. The challenges of mesoscale self-organisation were discussed at a CECAM workshop in July 2014. Biologists need approaches to observe highly dynamic, low affinity, low specificity associations and to perturb single structures, while biological physicists and biomathematicians need to work closely with biologists to build and validate quantitative models. A table of terminology is included to facilitate multidisciplinary efforts to reveal the richness and diversity of mesoscale cell biology.

Simulating the entropic collapse of coarse-grained chromosomes

Depletion forces play a role in the compaction and decompaction of chromosomal material in simple cells, but it has remained debatable whether they are sufficient to account for chromosomal collapse. We present coarse-grained molecular dynamics simulations, which reveal that depletion-induced attraction is sufficient to cause the collapse of a flexible chain of large structural monomers immersed in a bath of smaller depletants. These simulations use an explicit coarse-grained computational model that treats both the supercoiled DNA structural monomers and the smaller protein crowding agents as combinatorial, truncated Lennard-Jones spheres. By presenting a simple theoretical model, we quantitatively cast the action of depletants on supercoiled bacterial DNA as an effective solvent quality. The rapid collapse of the simulated flexible chromosome at the predicted volume fraction of depletants is a continuous phase transition. Additional physical effects to such simple chromosome models, such as enthalpic interactions between structural monomers or chain rigidity, are required if the collapse is to be a first-order phase transition.

Diffusion within the cytoplasm: a mesoscale model of interacting macromolecules

Recent experiments carried out in the dense cytoplasm of living cells have highlighted the importance of proteome composition and nonspecific intermolecular interactions in regulating macromolecule diffusion and organization. Despite this, the dependence of diffusion-interaction on physicochemical properties such as the degree of poly-dispersity and the balance between steric repulsion and nonspecific attraction among macromolecules was not systematically addressed. In this work, we study the problem of diffusion-interaction in the bacterial cytoplasm, combining theory and experimental data to build a minimal coarse-grained representation of the cytoplasm, which also includes, for the first time to our knowledge, the nucleoid. With stochastic molecular-dynamics simulations of a virtual cytoplasm we are able to track the single biomolecule motion, sizing from 3 to 80 nm, on submillisecond-long trajectories. We demonstrate that the size dependence of diffusion coefficients, anomalous exponents, and the effective viscosity experienced by biomolecules in the cytoplasm is fine-tuned by the intermolecular interactions. Accounting only for excluded volume in these potentials gives a weaker size-dependence than that expected from experimental data. On the contrary, adding nonspecific attraction in the range of 1-10 thermal energy units produces a stronger variation of the transport properties at growing biopolymer sizes. Normal and anomalous diffusive regimes emerge straightforwardly from the combination of high macromolecular concentration, poly-dispersity, stochasticity, and weak nonspecific interactions. As a result, small biopolymers experience a viscous cytoplasm, while the motion of big ones is jammed because the entanglements produced by the network of interactions and the entropic effects caused by poly-dispersity are stronger.

Conserved patterns in bacterial genomes: a conundrum physically tailored by evolutionary tinkering

The proper functioning of bacteria is encoded in their genome at multiple levels or scales, each of which is constrained by specific physical forces. At the smallest spatial scales, interatomic forces dictate the folding and function of proteins and nucleic acids. On longer length scales, stochastic forces emerging from the thermal jiggling of proteins and RNAs impose strong constraints on the organization of genes along chromosomes, more particularly in the context of the building of nucleoprotein complexes and the operational mode of regulatory agents. At the cellular level, transcription, replication and cell division activities generate forces that act on both the internal structure and cellular location of chromosomes. The overall result is a complex multi-scale organization of genomes that reflects the evolutionary tinkering of bacteria. The goal of this review is to highlight avenues for deciphering this complexity by focusing on patterns that are conserved among evolutionarily distant bacteria. To this end, I discuss three different organizational scales: the protein structures, the chromosomal organization of genes and the global structure of chromosomes.

Bacterial nucleoid structure probed by active drag and resistive pulse sensing

We combine steerable optical trap and microcapillary Coulter counter experiments to detect global changes in bacterial nucleoid organization.

From a melt of rings to chromosome territories: the role of topological constraints in genome folding

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.

Integration of syntactic and semantic properties of the DNA code reveals chromosomes as thermodynamic machines converting energy into information

Understanding genetic regulation is a problem of fundamental importance. Recent studies have made it increasingly evident that, whereas the cellular genetic regulation system embodies multiple disparate elements engaged in numerous interactions, the central issue is the genuine function of the DNA molecule as information carrier. Compelling evidence suggests that the DNA, in addition to the digital information of the linear genetic code (the semantics), encodes equally important continuous, or analog, information that specifies the structural dynamics and configuration (the syntax) of the polymer. These two DNA information types are intrinsically coupled in the primary sequence organisation, and this coupling is directly relevant to regulation of the genetic function. In this review, we emphasise the critical need of holistic integration of the DNA information as a prerequisite for understanding the organisational complexity of the genetic regulation system.

Polymer modeling of the E. coli genome reveals the involvement of locus positioning and macrodomain structuring for the control of chromosome conformation and segregation

The mechanisms that control chromosome conformation and segregation in bacteria have not yet been elucidated. In Escherichia coli, the mere presence of an active process remains an open question. Here, we investigate the conformation and segregation pattern of the E. coli genome by performing numerical simulations on a polymer model of the chromosome. We analyze the roles of the intrinsic structuring of chromosomes and the forced localization of specific loci, which are observed in vivo. Specifically, we examine the segregation pattern of a chromosome that is divided into four structured macrodomains (MDs) and two non-structured regions. We find that strong osmotic-like organizational forces, which stem from the differential condensation levels of the chromosome regions, dictate the cellular disposition of the chromosome. Strikingly, the comparison of our in silico results with fluorescent imaging of the chromosome choreography in vivo reveals that in the presence of MDs the targeting of the origin and terminus regions to specific positions are sufficient to generate a segregation pattern that is indistinguishable from experimentally observed patterns.

Computational analyses of transcriptomic data reveal the dynamic organization of the Escherichia coli chromosome under different conditions

The circular chromosome of Escherichia coli has been suggested to fold into a collection of sequentially consecutive domains, genes in each of which tend to be co-expressed. It has also been suggested that such domains, forming a partition of the genome, are dynamic with respect to the physiological conditions. However, little is known about which DNA segments of the E. coli genome form these domains and what determines the boundaries of these domain segments. We present a computational model here to partition the circular genome into consecutive segments, theoretically suggestive of the physically folded supercoiled domains, along with a method for predicting such domains under specified conditions. Our model is based on a hypothesis that the genome of E. coli is partitioned into a set of folding domains so that the total number of unfoldings of these domains in the folded chromosome is minimized, where a domain is unfolded when a biological pathway, consisting of genes encoded in this DNA segment, is being activated transcriptionally. Based on this hypothesis, we have predicted seven distinct sets of such domains along the E. coli genome for seven physiological conditions, namely exponential growth, stationary growth, anaerobiosis, heat shock, oxidative stress, nitrogen limitation and SOS responses. These predicted folding domains are highly stable statistically and are generally consistent with the experimental data of DNA binding sites of the nucleoid-associated proteins that assist the folding of these domains, as well as genome-scale protein occupancy profiles, hence supporting our proposed model. Our study established for the first time a strong link between a folded E. coli chromosomal structure and the encoded biological pathways and their activation frequencies.