Large-Scale Conformational Transitions in Supercoiled DNA Revealed by Coarse-Grained Simulation

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.

Circular Polycatenanes: Supramolecular Structures with Topologically Tunable Properties

Polycatenanes, macrochains of topologically interlocked rings with unique physical properties have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Most of the work has been, so far, focused on linear chains and on their variety of conformational properties compared to standard polymers. Here we go beyond the linear case and show that, by circularizing such macrochains, one can exploit the topology of the local interlockings to store twist in the system, significantly altering its metric and local properties. Moreover, by properly defining the twist (Tw) and writhe (Wr) of these macrorings we show the validity of a relation equivalent to the Călugăreanu-White-Fuller theorem Tw+Wr=const, originally proved for ribbonlike structures such as double stranded DNA. Our results suggest that circular polycatenanes with storable and tunable twist can form a new category of highly designable multiscale structures with potential applications in supramolecular chemistry and material science.

Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model's ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.

Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids

Ring polymers in dense solutions are among the most intriguing problems in polymer physics. Because of its natural occurrence in circular form, DNA has been extensively used as a proxy to study the fundamental physics of ring polymers in different topological states. Yet, torsionally constrained-such as supercoiled-topologies have been largely neglected so far. The applicability of existing theoretical models to dense supercoiled DNA is thus unknown. Here, we address this gap by coupling large-scale molecular dynamics simulations with differential dynamic microscopy of entangled supercoiled DNA plasmids. We find that, unexpectedly, larger supercoiling increases the size of entangled plasmids and concomitantly induces an enhancement in DNA mobility. These findings are reconciled as due to supercoiling-driven asymmetric and double-folded plasmid conformations that reduce interplasmid entanglements and threadings. Our results suggest a way to topologically tune DNA mobility via supercoiling, thus enabling topological control over the (micro)rheology of DNA-based complex fluids.

Supercoiled DNA and non-equilibrium formation of protein complexes: A quantitative model of the nucleoprotein ParBS partition complex

ParABS, the most widespread bacterial DNA segregation system, is composed of a centromeric sequence, parS, and two proteins, the ParA ATPase and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS-anchored complexes that serve as substrates for ParA molecules to catalyze positioning and segregation events. The exact nature of this ParBS complex has remained elusive, what we address here by revisiting the Stochastic Binding model (SBM) introduced to explain the non-specific binding profile of ParB in the vicinity of parS. In the SBM, DNA loops stochastically bring loci inside a sharp cluster of ParB. However, previous SBM versions did not include the negative supercoiling of bacterial DNA, leading to use unphysically small DNA persistences to explain the ParB binding profiles. In addition, recent super-resolution microscopy experiments have revealed a ParB cluster that is significantly smaller than previous estimations and suggest that it results from a liquid-liquid like phase separation. Here, by simulating the folding of long (≥ 30 kb) supercoiled DNA molecules calibrated with realistic DNA parameters and by considering different possibilities for the physics of the ParB cluster assembly, we show that the SBM can quantitatively explain the ChIP-seq ParB binding profiles without any fitting parameter, aside from the supercoiling density of DNA, which, remarkably, is in accord with independent measurements. We also predict that ParB assembly results from a non-equilibrium, stationary balance between an influx of produced proteins and an outflux of excess proteins, i.e., ParB clusters behave like liquid-like protein condensates with unconventional “leaky” boundaries.

In bacteria, faithful genome inheritance requires the two replicated DNA molecules to be segregated at the opposite halves of the cell. ParABS, the most widespread bacterial DNA segregation system, is composed of a centromere sequence, parS, and two proteins, the ParA ATPase and the ParB DNA binding protein. Hundreds of ParB assemble dynamically to form clusters around parS, which then serve as substrates for ParA molecules to catalyze the positioning and segregation events. The nature of these clusters and their interaction with DNA have remained elusive. Here, we propose a realistic minimal model that captures quantitatively the peculiar DNA binding profile of ParB in the vicinity of parS in Escherichia coli. From the viewpoint of DNA, the only fitting parameter is the in vivo supercoiling density resulting from the removal of DNA helices by toposiomerases, which is in accord with previous independent estimations. From the viewpoint of ParB clusters, we predict that they behave like liquid-like protein condensates with unconventional boundaries. Namely, we predict boundaries to be leaky (i.e. not sharp) as a result of the non-equilibrium protein production, diffusion and dilution. Altogether, our work provides novel insights into bacterial DNA organization and intracellular liquid-liquid phase separation.

Moltemplate: A Tool for Coarse-Grained Modeling of Complex Biological Matter and Soft Condensed Matter Physics

Coarse-grained models have long been considered indispensable tools in the investigation of biomolecular dynamics and assembly. However, the process of simulating such models is arduous because unconventional force fields and particle attributes are often needed, and some systems are not in thermal equilibrium. Although modern molecular dynamics programs are highly adaptable, software designed for preparing all-atom simulations typically makes restrictive assumptions about the nature of the particles and the forces acting on them. Consequently, the use of coarse-grained models has remained challenging. Moltemplate is a file format for storing coarse-grained molecular models and the forces that act on them, as well as a program that converts moltemplate files into input files for LAMMPS, a popular molecular dynamics engine. Moltemplate has broad scope and an emphasis on generality. It accommodates new kinds of forces as they are developed for LAMMPS, making moltemplate a popular tool with thousands of users in computational chemistry, materials science, and structural biology. To demonstrate its wide functionality, we provide examples of using moltemplate to prepare simulations of fluids using many-body forces, coarse-grained organic semiconductors, and the motor-driven supercoiling and condensation of an entire bacterial chromosome.

Coarse-grained modelling of DNA plectoneme pinning in the presence of base-pair mismatches

Damaged or mismatched DNA bases result in the formation of physical defects in double-stranded DNA. In vivo, defects in DNA must be rapidly and efficiently repaired to maintain cellular function and integrity. Defects can also alter the mechanical response of DNA to bending and twisting constraints, both of which are important in defining the mechanics of DNA supercoiling. Here, we use coarse-grained molecular dynamics (MD) simulation and supporting statistical-mechanical theory to study the effect of mismatched base pairs on DNA supercoiling. Our simulations show that plectoneme pinning at the mismatch site is deterministic under conditions of relatively high force (>2 pN) and high salt concentration (>0.5 M NaCl). Under physiologically relevant conditions of lower force (0.3 pN) and lower salt concentration (0.2 M NaCl), we find that plectoneme pinning becomes probabilistic and the pinning probability increases with the mismatch size. These findings are in line with experimental observations. The simulation framework, validated with experimental results and supported by the theoretical predictions, provides a way to study the effect of defects on DNA supercoiling and the dynamics of supercoiling in molecular detail.

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.

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.

Influence of Nucleoid-Associated Proteins on DNA Supercoiling

DNA supercoiling, where the DNA strand forms a writhe to relieve torsional stress, plays a vital role in packaging the genetic material in cells. Experiment, simulation, and theory have all demonstrated how supercoiling emerges due to the over- or underwinding of the DNA strand. Nucleoid-associated proteins (NAPs) help structure DNA in prokaryotes, yet the role that they play in the supercoiling process has not been as thoroughly investigated. We develop a coarse-grained simulation to model DNA supercoiling in the presence of proteins, providing a rigorous physical understanding of how NAPs affect supercoiling behavior. Specifically, we demonstrate how the force and torque necessary to form supercoils are affected by the presence of NAPs. NAPs that bend DNA stabilize the supercoil, thus shifting the transition between extended and supercoiled DNAs. We develop a theory to explain how NAP binding affects DNA supercoiling. This provides insight into how NAPs modulate DNA compaction via a combination of supercoiling and local protein-dependent deformations.

Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.

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.