A geometrical model for DNA organization in bacteria

Physical models of bacterial chromosomes

The interplay between bacterial chromosome organization and functions such as transcription and replication can be studied in increasing detail using novel experimental techniques. Interpreting the resulting quantitative data, however, can be theoretically challenging. In this minireview, we discuss how connecting experimental observations to biophysical theory and modeling can give rise to new insights on bacterial chromosome organization. We consider three flavors of models of increasing complexity: simple polymer models that explore how physical constraints, such as confinement or plectoneme branching, can affect bacterial chromosome organization; bottom-up mechanistic models that connect these constraints to their underlying causes, for instance, chromosome compaction to macromolecular crowding, or supercoiling to transcription; and finally, data-driven methods for inferring interpretable and quantitative models directly from complex experimental data. Using recent examples, we discuss how biophysical models can both deepen our understanding of how bacterial chromosomes are structured and give rise to novel predictions about bacterial chromosome organization.

Chromosome structure modeling tools and their evaluation in bacteria

The three-dimensional (3D) structure of bacterial chromosomes is crucial for understanding chromosome function. With the growing availability of high-throughput chromosome conformation capture (3C/Hi-C) data, the 3D structure reconstruction algorithms have become powerful tools to study bacterial chromosome structure and function. It is highly desired to have a recommendation on the chromosome structure reconstruction tools to facilitate the prokaryotic 3D genomics. In this work, we review existing chromosome 3D structure reconstruction algorithms and classify them based on their underlying computational models into two categories: constraint-based modeling and thermodynamics-based modeling. We briefly compare these algorithms utilizing 3C/Hi-C datasets and fluorescence microscopy data obtained from Escherichia coli and Caulobacter crescentus, as well as simulated datasets. We discuss current challenges in the 3D reconstruction algorithms for bacterial chromosomes, primarily focusing on software usability. Finally, we briefly prospect future research directions for bacterial chromosome structure reconstruction algorithms.

Dynamics of chromosome organization in a minimal bacterial cell

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication and inheritance of genetic material. By creating a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics, we investigate changes in chromosome organization during replication and extend the applicability of an existing whole-cell model (WCM) for a genetically minimal bacterium, JCVI-syn3A, to the entire cell-cycle. To achieve cell-scale chromosome structures that are realistic, we model the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. In addition, the conformations of the circular DNA must avoid overlapping with ribosomes identitied in cryo-electron tomograms. While Syn3A lacks the complex regulatory systems known to orchestrate chromosome segregation in other bacteria, its minimized genome retains essential loop-extruding structural maintenance of chromosomes (SMC) protein complexes (SMC-scpAB) and topoisomerases. Through implementing the effects of these proteins in our simulations of replicating chromosomes, we find that they alone are sufficient for simultaneous chromosome segregation across all generations within nested theta structures. This supports previous studies suggesting loop-extrusion serves as a near-universal mechanism for chromosome organization within bacterial and eukaryotic cells. Furthermore, we analyze ribosome diffusion under the influence of the chromosome and calculate in silico chromosome contact maps that capture inter-daughter interactions. Finally, we present a methodology to map the polymer model of the chromosome to a Martini coarse-grained representation to prepare molecular dynamics models of entire Syn3A cells, which serves as an ultimate means of validation for cell states predicted by the WCM.

Machine learning classification of trajectories from molecular dynamics simulations of chromosome segregation

In contrast to the well characterized mitotic machinery in eukaryotes it seems as if there is no universal mechanism organizing chromosome segregation in all bacteria. Apparently, some bacteria even use combinations of different segregation mechanisms such as protein machines or rely on physical forces. The identification of the relevant mechanisms is a difficult task. Here, we introduce a new machine learning approach to this problem. It is based on the analysis of trajectories of individual loci in the course of chromosomal segregation obtained by fluorescence microscopy. While machine learning approaches have already been applied successfully to trajectory classification in other areas, so far it has not been possible to use them to discriminate segregation mechanisms in bacteria. A main obstacle for this is the large number of trajectories required to train machine learning algorithms that we overcome here by using trajectories obtained from molecular dynamics simulations. We used these trajectories to train four different machine learning algorithms, two linear models and two tree-based classifiers, to discriminate segregation mechanisms and possible combinations of them. The classification was performed once using the complete trajectories as high-dimensional input vectors as well as on a set of features which were used to transform the trajectories into low-dimensional input vectors for the classifiers. Finally, we tested our classifiers on shorter trajectories with duration times comparable (or even shorter) than typical experimental trajectories and on trajectories measured with varying temporal resolutions. Our results demonstrate that machine learning algorithms are indeed capable of discriminating different segregation mechanisms in bacteria and to even resolve combinations of the mechanisms on rather short time scales.

Generating Chromosome Geometries in a Minimal Cell From Cryo-Electron Tomograms and Chromosome Conformation Capture Maps

JCVI-syn3A is a genetically minimal bacterial cell, consisting of 493 genes and only a single 543 kbp circular chromosome. Syn3A’s genome and physical size are approximately one-tenth those of the model bacterial organism Escherichia coli’s, and the corresponding reduction in complexity and scale provides a unique opportunity for whole-cell modeling. Previous work established genome-scale gene essentiality and proteomics data along with its essential metabolic network and a kinetic model of genetic information processing. In addition to that information, whole-cell, spatially-resolved kinetic models require cellular architecture, including spatial distributions of ribosomes and the circular chromosome’s configuration. We reconstruct cellular architectures of Syn3A cells at the single-cell level directly from cryo-electron tomograms, including the ribosome distributions. We present a method of generating self-avoiding circular chromosome configurations in a lattice model with a resolution of 11.8 bp per monomer on a 4 nm cubic lattice. Realizations of the chromosome configurations are constrained by the ribosomes and geometry reconstructed from the tomograms and include DNA loops suggested by experimental chromosome conformation capture (3C) maps. Using ensembles of simulated chromosome configurations we predict chromosome contact maps for Syn3A cells at resolutions of 250 bp and greater and compare them to the experimental maps. Additionally, the spatial distributions of ribosomes and the DNA-crowding resulting from the individual chromosome configurations can be used to identify macromolecular structures formed from ribosomes and DNA, such as polysomes and expressomes.

Conformational Dynamics of Poly(T) Single-Stranded DNA at the Single-Molecule Level

The conformational dynamics of single-stranded DNA (ss-DNA) are implicated in the mechanisms of several key biological processes such as DNA replication and damage repair and have been modeled with those of semiflexible or flexible polymer. The high flexibility and customizability of ss-DNA also make it an excellent polymeric material for materials engineering. Polythymidine (poly(T)) is an excellent model ss-DNA as a flexible polymer since it does not form any secondary structure. However, only limited experimental results have been reported of poly(T) conformational dynamics with a very short length that is not relevant to the aforementioned processes and applications. Here, we provide the first experimental results of the conformational dynamics of poly(T) with lengths in the range of 130-170 nucleotides at the single-molecule level. Our experiments are based on single-molecule FRET and a DNA hairpin structure of which the folding kinetics are governed by the conformational dynamics of poly(T). We found that the folding kinetics deviate far from those of a flexible polymer model with a harmonic bending potential. To this end, we derived a simple model for the kinetics of DNA hairpin folding from the self-avoiding-walk (SAW). Our model describes the conformational dynamics of poly(T) very well and enables estimation of the conformational dimensionality. The estimated dimensionalities suggest that ss-DNA is completely flexible at 100 mM or a higher NaCl concentration, but not at 50 mM. These results will help understand the conformational dynamics of ss-DNA implicated in several key biological processes and maximize the utility of ss-DNA for materials engineering. Also, our system and model provide an excellent platform to investigate the conformational dynamics of ss-DNA.

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.

Bacterial chromosome organization by collective dynamics of SMC condensins

A prominent organizational feature of bacterial chromosomes was revealed by Hi-C experiments, indicating anomalously high contacts between the left and right chromosomal arms. These long-range contacts have been attributed to various nucleoid-associated proteins, including the ATPase Structural Maintenance of Chromosomes (SMC) condensin. Although the molecular structure of these ATPases has been mapped in detail, it still remains unclear by which physical mechanisms they collectively generate long-range chromosomal contacts. Here, we develop a computational model that captures the subtle interplay between molecular-scale activity of slip-links and large-scale chromosome organization. We first consider a scenario in which the ATPase activity of slip-links regulates their DNA-recruitment near the origin of replication, while the slip-link dynamics is assumed to be diffusive. We find that such diffusive slip-links can collectively organize the entire chromosome into a state with aligned arms, but not within physiological constraints. However, slip-links that include motor activity are far more effective at organizing the entire chromosome over all length-scales. The persistence of motor slip-links at physiological densities can generate large, nested loops and drive them into the bulk of the DNA. Finally, our model with motor slip-links can quantitatively account for the rapid arm-arm alignment of chromosomal arms observed in vivo.

Thermal stability and conformation of DNA and proteins under the confined condition in the matrix of hydrogels

Spatially confined environments are seen in biological systems and in the fields of biotechnology and nanotechnology. The confinement restricts the conformational space of polymeric molecules and increasing the degree of molecular crowding. Here, we developed preparation methods for agarose and polyacrylamide gels applicable to UV spectroscopy that can evaluate the confinement effects on DNA and protein structures. Measurements of UV absorbance and CD spectra showed no significant effect of the confinement in the porous media of agarose gels on the base-pair stability of DNA polynucleotides [poly(dA)/poly(dT)] and oligonucleotides (hairpin, duplex, and triplex structures). On the other hand, a highly confined environment created by polyacrylamide gels at high concentrations increased the stability of polynucleotides while leaving that of oligonucleotides unaffected. The changes in the base-pair stability of the polynucleotides were accompanied by the perturbation of the helical conformation. The polyacrylamide gels prepared in this study were also used for the studies on proteins (lysozyme, bovine serum albumin, and myoglobin). The effects on the proteins were different from the effects on DNA structures, suggesting different nature of interactions within the gel. The experimental methods and results are useful to understand the physical properties of nucleic acids and proteins under confined conditions.

Lattice Models of Bacterial Nucleoids

Mesoscale molecular modeling is providing a new window into the inner workings of living cells. Modeling of genomes, however, remains a technical challenge, due to their large size and complexity. We describe a lattice method for rapid generation of bacterial nucleoid models that integrates experimental data from a variety of biophysical techniques and provides a starting point for simulation and hypothesis generation. The current method builds models of a circular bacterial genome with supercoiled plectonemes, packed within the small space of the bacterial cell. Lattice models are generated for Mycoplasma genitalium and Escherichia coli nucleoids, and used to simulate interaction data. The method is rapid enough to allow generation of multiple models when analyzing structure/function relationships, and we demonstrate use of the lattice models in creation of an all-atom representation of an entire cell.

Features of genomic organization in a nucleotide-resolution molecular model of the Escherichia coli chromosome

We describe structural models of the Escherichia coli chromosome in which the positions of all 4.6 million nucleotides of each DNA strand are resolved. Models consistent with two basic chromosomal orientations, differing in their positioning of the origin of replication, have been constructed. In both types of model, the chromosome is partitioned into plectoneme-abundant and plectoneme-free regions, with plectoneme lengths and branching patterns matching experimental distributions, and with spatial distributions of highly-transcribed chromosomal regions matching recent experimental measurements of the distribution of RNA polymerases. Physical analysis of the models indicates that the effective persistence length of the DNA and relative contributions of twist and writhe to the chromosome's negative supercoiling are in good correspondence with experimental estimates. The models exhibit characteristics similar to those of ‘fractal globules,’ and even the most genomically-distant parts of the chromosome can be physically connected, through paths combining linear diffusion and inter-segmental transfer, by an average of only ∼10 000 bp. Finally, macrodomain structures and the spatial distributions of co-expressed genes are analyzed: the latter are shown to depend strongly on the overall orientation of the chromosome. We anticipate that the models will prove useful in exploring other static and dynamic features of the bacterial chromosome.

Model studies of the effects of intracellular crowding on nucleic acid interactions

Molecular interactions and reactions in living cells occur with high concentrations of background molecules and ions. Many research studies have shown that intracellular molecules have characteristics different from those obtained using simple aqueous solutions. To better understand the behavior of biomolecules in intracellular environments, biophysical experiments were conducted under cell-mimicking conditions in a test tube. It has been shown that the molecular environments at the physiological level of macromolecular crowding, spatial confinement, water activity and dielectric constant, have significant effects on the interactions of DNA and RNA for hybridization, higher-order folding, and catalytic activity. The experimental approaches using in vitro model systems are useful to reveal the origin of the environmental effects and to bridge the gap between the behaviors of nucleic acids in vitro and in vivo. This paper highlights the model experiments used to evaluate the influences of intracellular environment on nucleic acid interactions.

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.

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.

Non-equilibrium polar localization of proteins in bacterial cells

Many proteins are observed to localize to the poles within bacterial cells. Some bacteria show unipolar localization, yet under different conditions bipolar patterns can emerge. One mechanism for spontaneous polar localization has been shown to involve the combination of protein aggregation and nucleoid occlusion. Whether the different observed patterns represent global energy minima for the cellular system remains to be determined. In this paper we show that for a model consisting only of protein aggregation along with an excluded volume effect due to the DNA polymer, that unipolar patterns are the global energy ground state regardless of protein concentration and DNA density. We extend the model to allow for proteins to be added to the cellular volume at a constant rate and show that bipolar (or multi-foci) patterns emerge as the result of the system being kinetically trapped in a local energy minimum. Lastly we also consider the situation of a growing cell that starts with a pre-existing aggregate at one of the poles and determine conditions under which either unipolar or bipolar patterns can exist at the point when it is ready to divide. This work sheds new interpretations on recently published experimental data and suggests experiments to test whether such a mechanism can drive patterning in bacteria.

In vivo facilitated diffusion model

Under dilute in vitro conditions transcription factors rapidly locate their target sequence on DNA by using the facilitated diffusion mechanism. However, whether this strategy of alternating between three-dimensional bulk diffusion and one-dimensional sliding along the DNA contour is still beneficial in the crowded interior of cells is highly disputed. Here we use a simple model for the bacterial genome inside the cell and present a semi-analytical model for the in vivo target search of transcription factors within the facilitated diffusion framework. Without having to resort to extensive simulations we determine the mean search time of a lac repressor in a living E. coli cell by including parameters deduced from experimental measurements. The results agree very well with experimental findings, and thus the facilitated diffusion picture emerges as a quantitative approach to gene regulation in living bacteria cells. Furthermore we see that the search time is not very sensitive to the parameters characterizing the DNA configuration and that the cell seems to operate very close to optimal conditions for target localization. Local searches as implied by the colocalization mechanism are only found to mildly accelerate the mean search time within our model.

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

Recent experimental and theoretical approaches have attempted to quantify the physical organization (compaction and geometry) of the bacterial chromosome with its complement of proteins (the nucleoid). The genomic DNA exists in a complex and dynamic protein-rich state, which is highly organized at various length scales. This has implications for modulating (when not directly enabling) the core biological processes of replication, transcription and segregation. We overview the progress in this area, driven in the last few years by new scientific ideas and new interdisciplinary experimental techniques, ranging from high space- and time-resolution microscopy to high-throughput genomics employing sequencing to map different aspects of the nucleoid-related interactome. The aim of this review is to present the wide spectrum of experimental and theoretical findings coherently, from a physics viewpoint. In particular, we highlight the role that statistical and soft condensed matter physics play in describing this system of fundamental biological importance, specifically reviewing classic and more modern tools from the theory of polymers. We also discuss some attempts toward unifying interpretations of the current results, pointing to possible directions for future investigation.

A model for Escherichia coli chromosome packaging supports transcription factor-induced DNA domain formation

What physical mechanism leads to organization of a highly condensed and confined circular chromosome? Computational modeling shows that confinement-induced organization is able to overcome the chromosome's propensity to mix by the formation of topological domains. The experimentally observed high precision of separate subcellular positioning of loci (located on different chromosomal domains) in Escherichia coli naturally emerges as a result of entropic demixing of such chromosomal loops. We propose one possible mechanism for organizing these domains: regulatory control defined by the underlying E. coli gene regulatory network requires the colocalization of transcription factor genes and target genes. Investigating this assumption, we find the DNA chain to self-organize into several topologically distinguishable domains where the interplay between the entropic repulsion of chromosomal loops and their compression due to the confining geometry induces an effective nucleoid filament-type of structure. Thus, we propose that the physical structure of the chromosome is a direct result of regulatory interactions. To reproduce the observed precise ordering of the chromosome, we estimate that the domain sizes are distributed between 10 and 700 kb, in agreement with the size of topological domains identified in the context of DNA supercoiling.

The three-dimensional architecture of a bacterial genome and its alteration by genetic perturbation

We have determined the three-dimensional (3D) architecture of the Caulobacter crescentus genome by combining genome-wide chromatin interaction detection, live-cell imaging, and computational modeling. Using chromosome conformation capture carbon copy (5C), we derive ~13 kb resolution 3D models of the Caulobacter genome. The resulting models illustrate that the genome is ellipsoidal with periodically arranged arms. The parS sites, a pair of short contiguous sequence elements known to be involved in chromosome segregation, are positioned at one pole, where they anchor the chromosome to the cell and contribute to the formation of a compact chromatin conformation. Repositioning these elements resulted in rotations of the chromosome that changed the subcellular positions of most genes. Such rotations did not lead to large-scale changes in gene expression, indicating that genome folding does not strongly affect gene regulation. Collectively, our data suggest that genome folding is globally dictated by the parS sites and chromosome segregation.

Geometrical ordering of DNA in bacteria

The bacterium Caulobacter crescentus shows a remarkable spatial ordering of its chromosome that leads to a strong linear correlation between the position of genes on the chromosomal map and their spatial position in the cellular volume. In a recent study we have shown that a robust and universal geometrical ordering mechanism can explain this correlation. We demonstrated that self-avoidance of DNA, specific positioning of one or few DNA loci (such as origin or terminus) together with the action of DNA compaction proteins (that organize the chromosome into topological domains) are sufficient to get a linear arrangement of the chromosome along the cell axis. This configuration, however, only represents the population average. Individual cells can have DNA arrangements that deviate significantly from the mean configuration and that break left-right symmetry. Symmetry breaking is stronger for longer chromosomes.