Lattice Models of Bacterial Nucleoids

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.

Replicating Chromosomes in Whole-Cell Models of Bacteria

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication of genetic material. In a recent study, we presented a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics. This approach was used to 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 modeled the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. Additionally, the polymer interacts with ribosomes distributed according to cryo-electron tomograms of Syn3A. The polymer model was further augmented by computational models of loop extrusion by structural maintenance of chromosomes (SMC) protein complexes and topoisomerase action, and the modeling and analysis of multi-fork replication states.

Integrative modeling of JCVI-Syn3A nucleoids with a modular approach

A lattice-based method is presented for creating 3D models of entire bacterial nucleoids integrating ultrastructural information cryoelectron tomography, genomic and proteomic data, and experimental atomic structures of biomolecules and assemblies. The method is used to generate models of the minimal genome bacterium JCVI-Syn3A, producing a series of models that test hypotheses about transcription, condensation, and overall distribution of the genome. Lattice models are also used to generate atomic models of an entire JCVI-Syn3A cell.

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.

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.

Integrative illustration of a JCVI-syn3A minimal cell

Data from genomics, proteomics, structural biology and cryo-electron microscopy are integrated into a structural illustration of a cross section through an entire JCVI-syn3.0 minimal cell. The illustration is designed with several goals: to inspire excitement in science, to depict the underlying scientific results accurately, and to be feasible in traditional media. Design choices to achieve these goals include reduction of visual complexity with simplified representations, use of orthographic projection to retain scale relationships, and an approach to color that highlights functional compartments of the cell. Given that this simple cell provides an attractive laboratory for exploring the central processes needed for life, several functional narratives are included in the illustration, including division of the cell and the first depiction of an entire cellular proteome. The illustration lays the foundation for 3D molecular modeling of this cell.

Building Structural Models of a Whole Mycoplasma Cell

Building structural models of entire cells has been a long-standing cross-discipline challenge for the research community, as it requires an unprecedented level of integration between multiple sources of biological data and enhanced methods for computational modeling and visualization. Here, we present the first 3D structural models of an entire Mycoplasma genitalium (MG) cell, built using the CellPACK suite of computational modeling tools. Our model recapitulates the data described in recent whole-cell system biology simulations and provides a structural representation for all MG proteins, DNA and RNA molecules, obtained by combining experimental and homology-modeled structures and lattice-based models of the genome. We establish a framework for gathering, curating and evaluating these structures, exposing current weaknesses of modeling methods and the boundaries of MG structural knowledge, and visualization methods to explore functional characteristics of the genome and proteome. We compare two approaches for data gathering, a manually-curated workflow and an automated workflow that uses homologous structures, both of which are appropriate for the analysis of mesoscale properties such as crowding and volume occupancy. Analysis of model quality provides estimates of the regularization that will be required when these models are used as starting points for atomic molecular dynamics simulations.

Direct visualization of the effect of DNA structure and ionic conditions on HU-DNA interactions

Architectural DNA–binding proteins are involved in many important DNA transactions by virtue of their ability to change DNA conformation. Histone-like protein from E. coli strain U93, HU, is one of the most studied bacterial architectural DNA–binding proteins. Nevertheless, there is still a limited understanding of how the interactions between HU and DNA are affected by ionic conditions and the structure of DNA. Here, using optical tweezers in combination with fluorescent confocal imaging, we investigated how ionic conditions affect the interaction between HU and DNA. We directly visualized the binding and the diffusion of fluorescently labelled HU dimers on DNA. HU binds with high affinity and exhibits low mobility on the DNA in the absence of Mg²⁺; it moves 30-times faster and stays shorter on the DNA with 8 mM Mg²⁺ in solution. Additionally, we investigated the effect of DNA tension on HU–DNA complexes. On the one hand, our studies show that binding of HU enhances DNA helix stability. On the other hand, we note that the binding affinity of HU for DNA in the presence of Mg²⁺ increases at tensions above 50 pN, which we attribute to force-induced structural changes in the DNA. The observation that HU diffuses faster along DNA in presence of Mg²⁺ compared to without Mg²⁺ suggests that the free energy barrier for rotational diffusion along DNA is reduced, which can be interpreted in terms of reduced electrostatic interaction between HU and DNA, possibly coinciding with reduced DNA bending.

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.

A Hi-C data-integrated model elucidates E. coli chromosome's multiscale organization at various replication stages

The chromosome of Escherichia coli is riddled with multi-faceted complexity. The emergence of chromosome conformation capture techniques are providing newer ways to explore chromosome organization. Here we combine a beads-on-a-spring polymer-based framework with recently reported Hi-C data for E. coli chromosome, in rich growth condition, to develop a comprehensive model of its chromosome at 5 kb resolution. The investigation focuses on a range of diverse chromosome architectures of E. coli at various replication states corresponding to a collection of cells, individually present in different stages of cell cycle. The Hi-C data-integrated model captures the self-organization of E. coli chromosome into multiple macrodomains within a ring-like architecture. The model demonstrates that the position of oriC is dependent on architecture and replication state of chromosomes. The distance profiles extracted from the model reconcile fluorescence microscopy and DNA-recombination assay experiments. Investigations into writhe of the chromosome model reveal that it adopts helix-like conformation with no net chirality, earlier hypothesized in experiments. A genome-wide radius of gyration map captures multiple chromosomal interaction domains and identifies the precise locations of rrn operons in the chromosome. We show that a model devoid of Hi-C encoded information would fail to recapitulate most genomic features unique to E. coli.

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.

Challenges in protein docking

Current developments in protein docking aim at improvement of applicability, accuracy and utility of modeling macromolecular complexes. The challenges include the need for greater emphasis on protein docking to molecules of different types, proper accounting for conformational flexibility upon binding, new promising methodologies based on residue co-evolution and deep learning, affinity prediction, and further development of fully automated docking servers. Importantly, new developments increasingly focus on realistic modeling of protein interactions in vivo, including crowded environment inside a cell, which involves multiple transient encounters, and propagating the system in time. This opinion paper offers the author's perspective on these challenges in structural modeling of protein interactions and the future of protein docking.

Art and Science of the Cellular Mesoscale

Experimental information from microscopy, structural biology, and bioinformatics may be integrated to build structural models of entire cells with molecular detail. This integrative modeling is challenging in several ways: the intrinsic complexity of biology results in models with many closely packed and heterogeneous components; the wealth of available experimental data is scattered among multiple resources and must be gathered, reconciled, and curated; and computational infrastructure is only now gaining the capability of modeling and visualizing systems of this complexity. We present recent efforts to address these challenges, both with artistic approaches to depicting the cellular mesoscale, and development and application of methods to build quantitative models.

Mesoscope: A Web-based Tool for Mesoscale Data Integration and Curation

Interest is growing for 3D models of the biological mesoscale, the intermediate scale between the nanometer scale of molecular structure and micrometer scale of cellular biology. However, it is currently difficult to gather, curate and integrate all the data required to define such models. To address this challenge we developed Mesoscope (mesoscope.scripps.edu/beta), a web-based data integration and curation tool. Mesoscope allows users to begin with a listing of molecules (such as data from proteomics), and to use resources at UniProt and the PDB to identify, prepare and validate appropriate structures and representations for each molecule, ultimately producing a portable output file used by CellPACK and other modeling tools for generation of 3D models of the biological mesoscale. The availability of this tool has proven essential in several exploratory applications, given the high complexity of mesoscale models and the heterogeneity of the available data sources.

Integrative Modeling and Visualization of Exosomes

Information from proteomics, microscopy, and structural biology are integrated to create structural models of exosomes, small vesicles released from cells. Three visualization methods are employed and compared: 2D painting of a cross section using traditional media, manual creation of a cross section using the mesoscale 2.5D digital painting software cellPAINT, and generation of a 3D atomic model using the mesoscale modeling program cellPACK.

EVR: reconstruction of bacterial chromosome 3D structure models using error-vector resultant algorithm

BACKGROUND

More and more 3C/Hi-C experiments on prokaryotes have been published. However, most of the published modeling tools for chromosome 3D structures are targeting at eukaryotes. How to transform prokaryotic experimental chromosome interaction data into spatial structure models is an important task and in great need.

RESULTS

We have developed a new reconstruction program for bacterial chromosome 3D structure models called EVR that exploits a simple Error-Vector Resultant (EVR) algorithm. This software tool is particularly optimized for the closed-loop structural features of prokaryotic chromosomes. The parallel implementation of the program can utilize the computing power of both multi-core CPUs and GPUs.

CONCLUSIONS

EVR can be used to reconstruct the bacterial 3D chromosome structure based on the contact frequency matrix derived from 3C/Hi-C experimental data quickly and precisely.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

Integrative modeling of the HIV-1 ribonucleoprotein complex

A coarse-grain computational method integrates biophysical and structural data to generate models of HIV-1 genomic RNA, nucleocapsid and integrase condensed into a mature ribonucleoprotein complex. Several hypotheses for the initial structure of the genomic RNA and oligomeric state of integrase are tested. In these models, integrase interaction captures features of the relative distribution of gRNA in the immature virion and increases the size of the RNP globule, and exclusion of nucleocapsid from regions with RNA secondary structure drives an asymmetric placement of the dimerized 5’UTR at the surface of the RNP globule.

The genome of HIV-1 is composed of two strands of RNA that are packaged in the mature virion as a condensed ribonucleoprotein complex with nucleocapsid, integrase, and other proteins. We have generated models of the HIV-1 ribonucleoprotein that integrate experimental results from multiple structural and biophysical experiments, exploring several hypotheses about the state of the RNA before condensation, and the role of crosslinking by integrase. The models suggest that the 5’UTR, which shows extensive secondary structure, has a propensity to be placed on the surface of the condensed globule, due to reduced binding of nucleocapsid to double-stranded regions within the 5’UTR. This unexpected localization of the 5’UTR may have consequences for the subsequent structural transitions that occur during the process of reverse transcription.

Computational approaches to macromolecular interactions in the cell

Structural modeling of a cell is an evolving strategic direction in computational structural biology. It takes advantage of new powerful modeling techniques, deeper understanding of fundamental principles of molecular structure and assembly, and rapid growth of the amount of structural data generated by experimental techniques. Key modeling approaches to principal types of macromolecular assemblies in a cell already exist. The main challenge, along with the further development of these modeling approaches, is putting them together in a consistent, unified whole cell model. This opinion piece addresses the fundamental aspects of modeling macromolecular assemblies in a cell, and the state-of-the-art in modeling of the principal types of such assemblies.

From Atoms to Cells: Using Mesoscale Landscapes to Construct Visual Narratives

Modeling and visualization of the cellular mesoscale, bridging the nanometer scale of molecules to the micrometer scale of cells, is being studied by an integrative approach. Data from structural biology, proteomics, and microscopy are combined to simulate the molecular structure of living cells. These cellular landscapes are used as research tools for hypothesis generation and testing, and to present visual narratives of the cellular context of molecular biology for dissemination, education, and outreach.

Perspectives on Structural Molecular Biology Visualization: From Past to Present

Visualization has been a key technology in the progress of structural molecular biology for as long as the field has existed. This perspective describes the nature of the visualization process in structural studies, how it has evolved over the years, and its relationship to the changes in technology that have supported and driven it. It focuses on how technical advances have changed the way we look at and interact with molecular structure, and how structural biology has fostered and challenged that technology.