Simulating the entropic collapse of coarse-grained chromosomes

In Silico View of Crowding: Biomolecular Processes to Nanomaterial Design

It is widely accepted that deciphering biomolecular structure and function requires going beyond the single-molecule or single-complex paradigm. The densely packed macromolecules, cosolutes, and metabolites in the living cell impose crowding effects on the biomolecular structure and dynamics that need to be accounted for. Molecular simulations have proven to be a powerful tool to advance the current molecular-level understanding of such a highly concentrated, complex milieu. This Mini-Review focuses on summarizing the understanding achieved so far for the effects of crowding on biomolecular processes using computational methods, along with highlighting a new direction in employing crowding as a tool for tunable nanomaterial design. The two schools of thought that form the pillars of the current understanding of crowding effects are discussed. The investigation of crowded solutions using physics-based models that encompass different time and length scales to mimic the intracellular environment are described. The limitations and challenges faced by the current models and simulation methods are addressed, highlighting the gaps to be filled for better agreement with experiments. Crowding can also act as an effective tool to modulate the structure-property-function relationships of nanomaterials, leading to the development of novel functional materials. A few recent studies, mostly experimental, have been summarized in this direction. The Mini-Review concludes with an outlook for future developments in this field in order to enable accurate mimicking of the intracellular environment using simulations and to bridge the gap between biological processes and nanomaterial design.

Differentiating the roles of proteins and polysomes in nucleoid size homeostasis in Escherichia coli

A defining feature of the bacterial cytosolic interior is a distinct membrane-less organelle, the nucleoid, that contains the chromosomal DNA. Although increasing experimental evidence indicates that macromolecular crowding is the dominant mechanism for nucleoid formation, it has remained unclear which crowders control nucleoid volume. It is commonly assumed that polyribosomes play a dominant role, yet the volume fraction of soluble proteins in the cytosol is comparable with that of polyribosomes. Here, we develop a free energy-based model for the cytosolic interior of a bacterial cell to distinguish contributions arising from polyribosomes and cytosolic proteins in nucleoid volume control. The parameters of the model are determined from the existing experimental data. We show that, while the polysomes establish the existence of the nucleoid as a distinct phase, the proteins control the nucleoid volume in physiologically relevant conditions. Our model explains experimental findings in Escherichia coli that the nucleoid compaction curves in osmotic shock measurements do not depend on cell growth rate and that dissociation of polysomes in slow growth rates does not lead to significant nucleoid expansion, while the nucleoid phase disappears in fastest growth rates. Furthermore, the model predicts a cross-over in the exclusion of crowders by their linear dimensions from the nucleoid phase: below the cross-over of 30-50 nm, the concentration of crowders in the nucleoid phase decreases linearly as a function of the crowder diameter, while decreasing exponentially above the cross-over size. Our work points to the possibility that bacterial cells maintain nucleoid size and protein concentration homeostasis via feedback in which protein concentration controls nucleoid dimensions and the nucleoid dimensions control protein synthesis rate.

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.

Steric repulsion introduced by loop constraints modulates the microphase separation of chromatins

Within the confines of a densely populated cell nucleus, chromatin undergoes intricate folding, forming loops, domains, and compartments under the governance of topological constraints and phase separation. This coordinated process inevitably introduces interference between different folding strategies. In this study, we model interphase chromatins as block copolymers with hetero-hierarchical loops within a confined system. Employing dissipative particle dynamics simulations and scaling analysis, we aim to explain how the structure and distribution of loop domains modulate the microphase separation of chromatins. Our results highlight the correlation between the microphase separation of the copolymer and the length, heterogeneity, and hierarchically nested levels of the loop domains. This correlation arises from steric repulsion intrinsic to loop domains. The steric repulsion induces variations in chain stiffness (including local orientation correlations and the persistence length), thereby influencing the degree of phase separation. Through simulations of block copolymers with distinct groups of hetero-hierarchical loop anchors, we successfully reproduce changes in phase separation across diverse cell lines, under fixed interaction parameters. These findings, in qualitative alignment with Hi-C data, suggest that the variations of loop constraints alone possess the capacity to regulate higher-order structures and the gene expressions of interphase chromatins.

Adsorption of semiflexible polymers in crowded environments

Macromolecular crowding is a feature of cellular and cell-free systems that, through depletion effects, can impact the interactions of semiflexible biopolymers with surfaces. In this work, we use computer simulations to study crowding-induced adsorption of semiflexible polymers on otherwise repulsive surfaces. Crowding particles are modeled explicitly, and we investigate the interplay between the bending stiffness of the polymer and the volume fraction and size of crowding particles. Adsorption to flat surfaces is promoted by stiffer polymers, smaller crowding particles, and larger volume fractions of crowders. We characterize transitions from non-adsorbed to partially and strongly adsorbed states as a function of bending stiffness. The crowding-induced transitions occur at smaller values of the bending stiffness as the volume fraction of crowders increases. Concomitant effects on the size and shape of the polymer are reflected by crowding- and stiffness-dependent changes to the radius of gyration. For various polymer lengths, we identify a critical crowding fraction for adsorption and analyze its scaling behavior in terms of polymer stiffness. We also consider crowding-induced adsorption in spherical confinement and identify a regime in which increasing the bending stiffness induces desorption. The results of our simulations shed light on the interplay of crowding and bending stiffness on the spatial organization of biopolymers in encapsulated cellular and cell-free systems.

Collapse transition of a heterogeneous polymer in a crowded medium

Long chain molecules can be entropically compacted in a crowded medium. We study the compaction transition of a heterogeneous polymer with ring topology by crowding effects in a free or confined space. For this, we use molecular dynamics simulations in which the effects of crowders are taken into account through effective interactions between chain segments. Our parameter choices are inspired by the Escherichia coli chromosome. The polymer consists of small and big monomers; the big monomers dispersed along the backbone are to mimic the binding of RNA polymerases. Our results show that the compaction transition is a two-step process: initial compaction induced by the association (clustering) of big monomers followed by a gradual overall compaction. They also indicate that cylindrical confinement makes the initial transition more effective; for representative parameter choices, the initial compaction accounts for about 60% reduction in the chain size. Our simulation results support the view that crowding promotes clustering of active transcription units into transcription factories.

Multiscale Dynamic Structuring of Bacterial Chromosomes

Since the nucleoid was isolated from bacteria in the 1970s, two fundamental questions emerged and are still in the spotlight: how bacteria organize their chromosomes to fit inside the cell and how nucleoid organization enables essential biological processes. During the last decades, knowledge of bacterial chromosome organization has advanced considerably, and today, such chromosomes are considered to be highly organized and dynamic structures that are shaped by multiple factors in a multiscale manner. Here we review not only the classical well-known factors involved in chromosome organization but also novel components that have recently been shown to dynamically shape the 3D structuring of the bacterial genome. We focus on the different functional elements that control short-range organization and describe how they collaborate in the establishment of the higher-order folding and disposition of the chromosome. Recent advances have opened new avenues for a deeper understanding of the principles and mechanisms of chromosome organization in bacteria. Expected final online publication date for the Annual Review of Microbiology, Volume 75 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Interconnecting solvent quality, transcription, and chromosome folding in Escherichia coli

All cells fold their genomes, including bacterial cells, where the chromosome is compacted into a domain-organized meshwork called the nucleoid. How compaction and domain organization arise is not fully understood. Here, we describe a method to estimate the average mesh size of the nucleoid in Escherichia coli. Using nucleoid mesh size and DNA concentration estimates, we find that the cytoplasm behaves as a poor solvent for the chromosome when the cell is considered as a simple semidilute polymer solution. Monte Carlo simulations suggest that a poor solvent leads to chromosome compaction and DNA density heterogeneity (i.e., domain formation) at physiological DNA concentration. Fluorescence microscopy reveals that the heterogeneous DNA density negatively correlates with ribosome density within the nucleoid, consistent with cryoelectron tomography data. Drug experiments, together with past observations, suggest the hypothesis that RNAs contribute to the poor solvent effects, connecting chromosome compaction and domain formation to transcription and intracellular organization.

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.

Crowding-induced interactions of ring polymers

Macromolecular crowding and the presence of surfaces can significantly impact the spatial organization of biopolymers. While the importance of crowding-induced depletion interactions in biology has been recognized, much remains to be understood about the effect of crowding on biopolymers such as DNA plasmids. A fundamental problem highlighted by recent experiments is to characterize the impact of crowding on polymer-polymer and polymer-surface interactions. Motivated by the need for quantitative insight, we studied flexible ring polymers in crowded environments using Langevin dynamics simulations. The simulations demonstrated that crowding can lead to compaction of isolated ring polymers and enhanced interactions between two otherwise repulsive polymers. Using umbrella sampling, we determined the potential of mean force (PMF) between two ring polymers as a function of their separation distance at different volume fractions of crowding particles, φ. An effective attraction emerged at φ≈ 0.4, which is similar to the degree of crowding in cells. Analogous simulations showed that crowding can lead to strong adsorption of a ring polymer to a wall, with an effective attraction to the wall emerging at a smaller volume fraction of crowders (φ≈ 0.2). Our results reveal the magnitude of depletion interactions in a biologically-inspired model and highlight how crowding can be used to tune interactions in both cellular and cell-free systems.

Chromosome Segregation in Bacillus subtilis Follows an Overall Pattern of Linear Movement and Is Highly Robust against Cell Cycle Perturbations

We have followed the segregation of origin regions on the Bacillus subtilis chromosome in the fastest practically achievable temporal manner, for a large fraction of the cell cycle. We show that segregation occurred in highly variable patterns but overall in an almost linear manner throughout the cell cycle. Segregation was slowed down, but not arrested, by treatment of cells that led to transient blocks in DNA replication, showing that segregation is highly robust against cell cycle perturbation. Computer simulations based on entropy-driven separation of newly synthesized DNA polymers can recapitulate sudden bursts of movement and segregation patterns compatible with the observed in vivo patterns, indicating that for Bacillus, segregation patterns may include entropic forces helping to separate chromosomes during the cell cycle.

Although several proteins have been identified that facilitate chromosome segregation in bacteria, no clear analogue of the mitotic machinery in eukaryotic cells has been identified. In order to investigate if recognizable patterns of segregation exist during the cell cycle, we tracked the segregation of duplicated origin regions in Bacillus subtilis for 60 min in the fastest practically achievable resolution, achieving 10-s intervals. We found that while separation occurred in random patterns, often including backwards movement, overall, segregation of loci near the origins of replication was linear for the entire cell cycle. Thus, the process of partitioning can be best described as directed motion. Simulations with entropy-driven separation of polymers synthesized by two polymerases show sudden bursts of movement and segregation patterns compatible with the observed in vivo patterns, showing that for Bacillus, segregation patterns can be modeled based on entropic forces. To test if obstacles for replication forks lead to an alteration of the partitioning pattern, we challenged cells with chemicals inducing DNA damage or blocking of topoisomerase activity. Both treatments led to a moderate slowing down of separation, but linear segregation was retained, showing that chromosome segregation is highly robust against cell cycle perturbation.

IMPORTANCE We have followed the segregation of origin regions on the Bacillus subtilis chromosome in the fastest practically achievable temporal manner, for a large fraction of the cell cycle. We show that segregation occurred in highly variable patterns but overall in an almost linear manner throughout the cell cycle. Segregation was slowed down, but not arrested, by treatment of cells that led to transient blocks in DNA replication, showing that segregation is highly robust against cell cycle perturbation. Computer simulations based on entropy-driven separation of newly synthesized DNA polymers can recapitulate sudden bursts of movement and segregation patterns compatible with the observed in vivo patterns, indicating that for Bacillus, segregation patterns may include entropic forces helping to separate chromosomes during the cell cycle.

The effects of polydisperse crowders on the compaction of the Escherichia coli nucleoid

DNA binding proteins, supercoiling, macromolecular crowders, and transient DNA attachments to the cell membrane have all been implicated in the organization of the bacterial chromosome. However, it is unclear what role these factors play in compacting the bacterial DNA into a distinct organelle-like entity, the nucleoid. By analyzing the effects of osmotic shock and mechanical squeezing on Escherichia coli, we show that macromolecular crowders play a dominant role in the compaction of the DNA into the nucleoid. We find that a 30% increase in the crowder concentration from physiological levels leads to a three-fold decrease in the nucleoid's volume. The compaction is anisotropic, being higher along the long axes of the cell at low crowding levels. At higher crowding levels, the nucleoid becomes spherical, and its compressibility decreases significantly. Furthermore, we find that the compressibility of the nucleoid is not significantly affected by cell growth rates and by prior treatment with rifampicin. The latter results point out that in addition to poly ribosomes, soluble cytoplasmic proteins have a significant contribution in determining the size of the nucleoid. The contribution of poly ribosomes dominates at faster and soluble proteins at slower growth rates.

Depletion force between disordered linear macromolecules

When two macromolecules come very near in a fluid, the surrounding molecules, having finite volume, are less likely to get in between. This leads to a pressure difference manifesting as an entropic attraction, called depletion force. Here we calculate the density profile of liquid molecules surrounding a disordered rigid macromolecules modeled as a random arrangement of hard spheres on a linear backbone. We analytically determine the position dependence of the depletion force between two such disordered molecules by calculating the free energy of the system. We then use molecular dynamics simulations to obtain the depletion force between stiff disordered polymers as well as flexible ones and compare the two against each other. We also show how the disorder averaging can be handled starting from the inhomogenous reference interaction site model equations.

Confined crowded polymers near attractive surfaces

We present results from molecular dynamics simulations of a spherically confined neutral polymer in the presence of crowding particles, studying polymer shapes and conformations as a function of the strength of the attraction to the confining wall, solvent quality, and the density of crowders. The conformations of the polymer under good solvent conditions are weakly dependent on crowder particle density, even when the polymer is strongly confined. In contrast, under poor solvent conditions, when the polymer assumes a collapsed conformation when unconfined, it can exhibit transitions to two different adsorbed phases, when either the interaction with the wall or the density of crowder particles is changed. One such transition involves a desorbed collapsed phase change to an adsorbed extended phase as the attraction of the polymer towards the confining wall is increased. Such an adsorbed extended phase can exhibit a second transition to an ordered adsorbed collapsed phase as the crowder particle density is increased. The ordered adsorbed collapsed phase of the polymer differs significantly in its structure from the desorbed collapsed phase. We revisit the earlier understanding of the adsorption of confined polymers on attractive surfaces in light of our results.

Cell morphology and nucleoid dynamics in dividing Deinococcus radiodurans

Our knowledge of bacterial nucleoids originates mostly from studies of rod- or crescent-shaped bacteria. Here we reveal that Deinococcus radiodurans, a relatively large spherical bacterium with a multipartite genome, constitutes a valuable system for the study of the nucleoid in cocci. Using advanced microscopy, we show that D. radiodurans undergoes coordinated morphological changes at both the cellular and nucleoid level as it progresses through its cell cycle. The nucleoid is highly condensed, but also surprisingly dynamic, adopting multiple configurations and presenting an unusual arrangement in which oriC loci are radially distributed around clustered ter sites maintained at the cell centre. Single-particle tracking and fluorescence recovery after photobleaching studies of the histone-like HU protein suggest that its loose binding to DNA may contribute to this remarkable plasticity. These findings demonstrate that nucleoid organization is complex and tightly coupled to cell cycle progression in this organism.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

Comparative study of the crowding-induced collapse effect in hard-sphere, flexible polymer and rod-like polymer systems

A systematic Langevin simulation is performed to study the crowding-induced collapse effect on a probed chain in three typical systems: hard sphere (HS), flexible polymer and rod-like polymer.

Morphology of depletant-induced erythrocyte aggregates

Red blood cells suspended in quiescent plasma tend to aggregate into multicellular assemblages, including linearly stacked columnar rouleaux, which can reversibly form more complex clusters or branching networks. While these aggregates play an essential role in establishing hemorheological and pathological properties, the biophysics behind their self-assembly into dynamic mesoscopic structures remains under-explored. We employ coarse-grained molecular simulations to model low-hematocrit erythrocytes subject to short-range implicit depletion forces, and demonstrate not only that depletion interactions are sufficient to account for a sudden dispersion-aggregate transition, but also that the volume fraction of depletant macromolecules controls small aggregate morphology. We observe a sudden transition from a dispersion to a linear column rouleau, followed by a slow emergence of disorderly amorphous clusters of many short rouleaux at larger volume fractions. This work demonstrates how discocyte topology and short-range, non-specific, physical interactions are sufficient to self-assemble erythrocytes into various aggregate structures, with markedly different morphologies and biomedical consequences.

Interfering With DNA Decondensation as a Strategy Against Mycobacteria

Tuberculosis is once again a major global threat, leading to more than 1 million deaths each year. Treatment options for tuberculosis patients are limited, expensive and characterized by severe side effects, especially in the case of multidrug-resistant forms. Uncovering novel vulnerabilities of the pathogen is crucial to generate new therapeutic strategies. Using high resolution microscopy techniques, we discovered one such vulnerability of Mycobacterium tuberculosis. We demonstrate that the DNA of M. tuberculosis can condense under stressful conditions such as starvation and antibiotic treatment. The DNA condensation is reversible and specific for viable bacteria. Based on these observations, we hypothesized that blocking the recovery from the condensed state could weaken the bacteria. We showed that after inducing DNA condensation, and subsequent blocking of acetylation of DNA binding proteins, the DNA localization in the bacteria is altered. Importantly under these conditions, Mycobacterium smegmatis did not replicate and its survival was significantly reduced. Our work demonstrates that agents that block recovery from the condensed state of the nucleoid can be exploited as antibiotic. The combination of fusidic acid and inhibition of acetylation of DNA binding proteins, via the Eis enzyme, potentiate the efficacy of fusidic acid by 10 and the Eis inhibitor to 1,000-fold. Hence, we propose that successive treatment with antibiotics and drugs interfering with recovery from DNA condensation constitutes a novel approach for treatment of tuberculosis and related bacterial infections.

Force-extension behavior of DNA in the presence of DNA-bending nucleoid associated proteins

Interactions between nucleoid associated proteins (NAPs) and DNA affect DNA polymer conformation, leading to phenomena such as concentration dependent force-extension behavior. These effects, in turn, also impact the local binding behavior of the protein, such as high forces causing proteins to unbind, or proteins binding favorably to locally bent DNA. We develop a coarse-grained NAP-DNA simulation model that incorporates both force- and concentration-dependent behaviors, in order to study the interplay between NAP binding and DNA conformation. This model system includes multi-state protein binding and unbinding, motivated by prior work, but is now dependent on the local structure of the DNA, which is related to external forces acting on the DNA strand. We observe the expected qualitative binding behavior, where more proteins are bound at lower forces than at higher forces. Our model also includes NAP-induced DNA bending, which affects DNA elasticity. We see semi-quantitative matching of our simulated force-extension behavior to the reported experimental data. By using a coarse-grained simulation, we are also able to look at non-equilibrium behaviors, such as dynamic extension of a DNA strand. We stretch a DNA strand at different rates and at different NAP concentrations to observe how the time scales of the system (such as pulling time and unbinding time) work in concert. When these time scales are similar, we observe measurable rate-dependent changes in the system, which include the number of proteins bound and the force required to extend the DNA molecule. This suggests that the relative time scales of different dynamic processes play an important role in the behavior of NAP-DNA systems.

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.

Formation of Chromatin Subcompartments by Phase Separation

Chromatin is partitioned on multiple length scales into subcompartments that differ from each other with respect to their molecular composition and biological function. It is a key question how these compartments can form even though diffusion constantly mixes the nuclear interior and rapidly balances concentration gradients of soluble nuclear components. Different biophysical concepts are currently used to explain the formation of "chromatin bodies" in a self-organizing manner and without consuming energy. They rationalize how soluble protein factors that are dissolved in the liquid nuclear phase, the nucleoplasm, bind and organize transcriptionally active or silenced chromatin domains. In addition to cooperative binding of proteins to a preformed chromatin structure, two different mechanisms for the formation of phase-separated chromatin subcompartments have been proposed. One is based on bridging proteins that cross-link polymer segments with particular properties. Bridging can induce a collapse of the nucleosome chain and associated factors into an ordered globular phase. The other mechanism is based on multivalent interactions among soluble molecules that bind to chromatin. These interactions can induce liquid-liquid phase separation, which drives the assembly of liquid-like nuclear bodies around the respective binding sites on chromatin. Both phase separation mechanisms can explain that chromatin bodies are dynamic spherical structures, which can coalesce and are in constant and rapid exchange with the surrounding nucleoplasm. However, they make distinct predictions about how the size, density, and stability of chromatin bodies depends on the concentration and interaction behavior of the molecules involved. Here, we compare the different biophysical mechanisms for the assembly of chromatin bodies and discuss experimental strategies to distinguish them from each other. Furthermore, we outline the implications for the establishment and memory of functional chromatin state patterns.

Entropic effect of macromolecular crowding enhances binding between nucleosome clutches in heterochromatin, but not in euchromatin

Sharp increase in macromolecular crowding induces abnormal chromatin compaction in the cell nucleus, suggesting its non-negligible impact on chromatin structure and function. However, the details of the crowding-induced chromatin compaction remain poorly understood. In this work, we present a computer simulation study on the entropic effect of macromolecular crowding on the interaction between chromatin structural units called nucleosome clutches. Nucleosome clutches were modeled by a chain of nucleosomes collapsed by harmonic restraints implicitly mimicking the nucleosome association mediated by histone tails and linker histones. The nucleosome density of the clutches was set close to either that of high-density heterochromatin or that of low-density euchromatin. The effective interactions between these nucleosome clutches were calculated in various crowding conditions, and it was found that the increase in the degree of macromolecular crowding induced attractive interaction between two clutches with high nucleosome density. Interestingly, the increased degree of macromolecular crowding did not induce any attraction between two clutches with low nucleosome density. Our results suggest that the entropic effect of macromolecular crowding can enhance binding between nucleosome clutches in heterochromatin, but not in euchromatin, as a result of the difference in nucleosome packing degrees.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

A ring-polymer model shows how macromolecular crowding controls chromosome-arm organization in Escherichia coli

Macromolecular crowding influences various cellular processes such as macromolecular association and transcription, and is a key determinant of chromosome organization in bacteria. The entropy of crowders favors compaction of long chain molecules such as chromosomes. To what extent is the circular bacterial chromosome, often viewed as consisting of “two arms”, organized entropically by crowding? Using computer simulations, we examine how a ring polymer is organized in a crowded and cylindrically-confined space, as a coarse-grained bacterial chromosome. Our results suggest that in a wide parameter range of biological relevance crowding is essential for separating the two arms in the way observed with Escherichia coli chromosomes at fast-growth rates, in addition to maintaining the chromosome in an organized collapsed state. Under different conditions, however, the ring polymer is centrally condensed or adsorbed onto the cylindrical wall with the two arms laterally collapsed onto each other. We discuss the relevance of our results to chromosome-membrane interactions.

How are molecular crowding and the spatial organization of a biopolymer interrelated

In a crowded cellular interior, dissolved biomolecules or crowders exert excluded volume effects on other biomolecules, which in turn control various processes including protein aggregation and chromosome organization. As a result of these effects, a long chain molecule can be phase-separated into a condensed state, redistributing the surrounding crowders. Using computer simulations and a theoretical approach, we study the interrelationship between molecular crowding and chain organization. In a parameter space of biological relevance, the distributions of monomers and crowders follow a simple relationship: the sum of their volume fractions rescaled by their size remains constant. Beyond a physical picture of molecular crowding it offers, this finding explains a few key features of what has been known about chromosome organization in an E. coli cell.

Effects of molecular crowding and confinement on the spatial organization of a biopolymer

A chain molecule can be entropically collapsed in a crowded medium in a free or confined space. Here, we present a unified view of how molecular crowding collapses a flexible polymer in three distinct spaces: free, cylindrical, and (two-dimensional) slit-like. Despite their seeming disparities, a few general features characterize all these cases, even though the ϕ_c-dependence of chain compaction differs between the two cases: a > a_c and a < a_c, where ϕ_c is the volume fraction of crowders, a is the monomer size, and a_c is the crowder size. For a > a_c (applicable to a coarse-grained model of bacterial chromosomes), chain size depends on the ratio aϕ_c/a_c, and "full" compaction occurs universally at aϕ_c/a_c ≈ 1; for a_c > a (relevant for protein folding), it is controlled by ϕ_c alone and crowding has a modest effect on chain size in a cellular environment (ϕ_c ≈ 0.3). Also for a typical parameter range of biological relevance, molecular crowding can be viewed as effectively reducing the solvent quality, independent of confinement.

Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains, which for definiteness we model on 10 kb long DNA filaments, is shown to have a non-monotonic, unimodal dependence on the colloid diameter, dc. The maximum incidence of knots occurs when dc is about equal to half of the gyration radius of the isolated chain. The degree of enhancement of knots grows rapidly with the solution density and can be very conspicuous relative to the case of isolated chains with no crowders. For instance, at 30% volume fraction the relative increase is more than fourfold. This dramatic enhancement is shown to originate from the depletion-induced chain compaction over multiple and concurring length scales. The same effect accounts for the variations of the knot length that accompany the changes in knotting probability. The findings suggest that crowded media could be viably used as a passive physical means for controlling and modulating the incidence and length of knots in DNA and other types of semiflexible polymers.

Compaction of isolated Escherichia coli nucleoids: Polymer and H-NS protein synergetics

Escherichia coli nucleoids were compacted by the inert polymer polyethylene glycol (PEG) in the presence of the H-NS protein. The protein by itself appears to have little impact on the size of the nucleoids as determined by fluorescent microscopy. However, it has a significant impact on the nucleoidal collapse by PEG. This is quantitatively explained by assuming the H-NS protein enhances the effective diameter of the DNA helix leading to an increase in the depletion forces induced by the PEG. Ultimately, however, the free energy of the nucleoid itself turns out to be independent of the H-NS concentration. This is because the enhancement of the supercoil excluded volume is negligible. The experiments on the nucleoids are corroborated by dynamic light scattering and EMSA analyses performed on DNA plasmids in the presence of PEG and H-NS.

Unexpected Swelling of Stiff DNA in a Polydisperse Crowded Environment

We investigate the conformations of DNA-like stiff chains, characterized by contour length (L) and persistence length (lp), in a variety of crowded environments containing monodisperse soft spherical (SS) and spherocylindrical (SC) particles, a mixture of SS and SC, and a milieu mimicking the composition of proteins in the Escherichia coli cytoplasm. The stiff chain, whose size modestly increases in SS crowders up to ϕ ≈ 0.1, is considerably more compact at low volume fractions (ϕ ≤ 0.2) in monodisperse SC particles than in a medium containing SS particles. A 1:1 mixture of SS and SC crowders induces greater chain compaction than the pure SS or SC crowders at the same ϕ, with the effect being highly nonadditive. We also discover a counterintuitive result that the polydisperse crowding environment, mimicking the composition of a cell lysate, swells the DNA-like polymer, which is in stark contrast to the size reduction of flexible polymers in the same milieu. Trapping of the stiff chain in a fluctuating tube-like environment created by large-sized crowders explains the dramatic increase in size and persistence length of the stiff chain. In the polydisperse medium, mimicking the cellular environment, the size of the DNA (or related RNA) is determined by L/lp. At low L/lp, the size of the polymer is unaffected, whereas there is a dramatic swelling at an intermediate value of L/lp. We use these results to provide insights into recent experiments on crowding effects on RNA and also make testable predictions.

The spatial biology of transcription and translation in rapidly growing Escherichia coli

Single-molecule fluorescence provides high resolution spatial distributions of ribosomes and RNA polymerase (RNAP) in live, rapidly growing Escherichia coli. Ribosomes are more strongly segregated from the nucleoids (chromosomal DNA) than previous widefield fluorescence studies suggested. While most transcription may be co-translational, the evidence indicates that most translation occurs on free mRNA copies that have diffused from the nucleoids to a ribosome-rich region. Analysis of time-resolved images of the nucleoid spatial distribution after treatment with the transcription-halting drug rifampicin and the translation-halting drug chloramphenicol shows that both drugs cause nucleoid contraction on the 0–3 min timescale. This is consistent with the transertion hypothesis. We suggest that the longer-term (20–30 min) nucleoid expansion after Rif treatment arises from conversion of 70S-polysomes to 30S and 50S subunits, which readily penetrate the nucleoids. Monte Carlo simulations of a polymer bead model built to mimic the chromosomal DNA and ribosomes (either 70S-polysomes or 30S and 50S subunits) explain spatial segregation or mixing of ribosomes and nucleoids in terms of excluded volume and entropic effects alone. A comprehensive model of the transcription-translation-transertion system incorporates this new information about the spatial organization of the E. coli cytoplasm. We propose that transertion, which radially expands the nucleoids, is essential for recycling of 30S and 50S subunits from ribosome-rich regions back into the nucleoids. There they initiate co-transcriptional translation, which is an important mechanism for maintaining RNAP forward progress and protecting the nascent mRNA chain. Segregation of 70S-polysomes from the nucleoid may facilitate rapid growth by shortening the search time for ribosomes to find free mRNA concentrated outside the nucleoid and the search time for RNAP concentrated within the nucleoid to find transcription initiation sites.

Force-Extension for DNA in a Nanoslit: Mapping between the 3D and 2D Limits

The force-extension relation for a semiflexible polymer confined in a nanoslit is investigated. Both the effective correlation length and force-extension relation change as the chain goes from 3D (large slit heights) to 2D (tight confinement). At low forces, correlations along the polymer give an effective dimensionality. The strong force limit can be interpolated with the weak force limit for two regimes: when confinement dominates over extensile force and vice versa. These interpolations give good agreement with simulations for all slit heights and forces. We thus generalize the Marko-Siggia force-extension relation for DNA and other semiflexible biopolymers in nanoconfinement.