Surfing on Protein Waves: Proteophoresis as a Mechanism for Bacterial Genome Partitioning

Loop-extruders alter bacterial chromosome topology to direct entropic forces for segregation

Entropic forces have been argued to drive bacterial chromosome segregation during replication. In many bacterial species, however, specifically evolved mechanisms, such as loop-extruding SMC complexes and the ParABS origin segregation system, contribute to or are even required for chromosome segregation, suggesting that entropic forces alone may be insufficient. The interplay between and the relative contributions of these segregation mechanisms remain unclear. Here, we develop a biophysical model showing that purely entropic forces actually inhibit bacterial chromosome segregation until late replication stages. By contrast, our model reveals that loop-extruders loaded at the origins of replication, as observed in many bacterial species, alter the effective topology of the chromosome, thereby redirecting and enhancing entropic forces to enable accurate chromosome segregation during replication. We confirm our model predictions with polymer simulations: purely entropic forces do not allow for concurrent replication and segregation, whereas entropic forces steered by specifically loaded loop-extruders lead to robust, global chromosome segregation during replication. Finally, we show how loop-extruders can complement locally acting origin separation mechanisms, such as the ParABS system. Together, our results illustrate how changes in the geometry and topology of the polymer, induced by DNA-replication and loop-extrusion, impact the organization and segregation of bacterial chromosomes.

Plasmid partitioning driven by collective migration of ParA between nucleoid lobes

The ParABS system is crucial for the faithful segregation and inheritance of many bacterial chromosomes and low-copy-number plasmids. However, despite extensive research, the spatiotemporal dynamics of the ATPase ParA and its connection to the dynamics and positioning of the ParB-coated cargo have remained unclear. In this study, we utilize high-throughput imaging, quantitative data analysis, and computational modeling to explore the in vivo dynamics of ParA and its interaction with ParB-coated plasmids and the nucleoid. As previously observed, we find that F-plasmid ParA undergoes collective migrations ("flips") between cell halves multiple times per cell cycle. We reveal that a constricting nucleoid is required for these migrations and that they are triggered by a plasmid crossing into the cell half with greater ParA. Using simulations, we show that these dynamics can be explained by the combination of nucleoid constriction and cooperative ParA binding to the DNA, in line with the behavior of other ParA proteins. We further show that these ParA flips act to equally partition plasmids between the two lobes of the constricted nucleoid and are therefore important for plasmid stability, especially in fast growth conditions for which the nucleoid constricts early in the cell cycle. Overall, our work identifies a second mode of action of the ParABS system and deepens our understanding of how this important segregation system functions.

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.

DNA Segregation in Enterobacteria

DNA segregation ensures that cell offspring receive at least one copy of each DNA molecule, or replicon, after their replication. This important cellular process includes different phases leading to the physical separation of the replicons and their movement toward the future daughter cells. Here, we review these phases and processes in enterobacteria with emphasis on the molecular mechanisms at play and their controls.

Organization and replicon interactions within the highly segmented genome of Borrelia burgdorferi

Borrelia burgdorferi, a causative agent of Lyme disease, contains the most segmented bacterial genome known to date, with one linear chromosome and over twenty plasmids. How this unusually complex genome is organized, and whether and how the different replicons interact are unclear. We recently demonstrated that B. burgdorferi is polyploid and that the copies of the chromosome and plasmids are regularly spaced in each cell, which is critical for faithful segregation of the genome to daughter cells. Regular spacing of the chromosome is controlled by two separate partitioning systems that involve the protein pairs ParA/ParZ and ParB/Smc. Here, using chromosome conformation capture (Hi-C), we characterized the organization of the B. burgdorferi genome and the interactions between the replicons. We uncovered that although the linear chromosome lacks contacts between the two replication arms, the two telomeres are in frequent contact. Moreover, several plasmids specifically interact with the chromosome oriC region, and a subset of plasmids interact with each other more than with others. We found that Smc and the Smc-like MksB protein mediate long-range interactions on the chromosome, but they minimally affect plasmid-chromosome or plasmid-plasmid interactions. Finally, we found that disruption of the two partition systems leads to chromosome restructuring, correlating with the mis-positioning of chromosome oriC. Altogether, this study revealed the conformation of a complex genome and analyzed the contribution of the partition systems and SMC family proteins to this organization. This work expands the understanding of the organization and maintenance of multipartite bacterial genomes.

Organization and replicon interactions within the highly segmented genome of Borrelia burgdorferi

Borrelia burgdorferi , a causative agent of Lyme disease, contains the most segmented bacterial genome known to date, with one linear chromosome and over twenty plasmids. How this unusually complex genome is organized, and whether and how the different replicons interact are unclear. We recently demonstrated that B. burgdorferi is polyploid and that the copies of the chromosome and plasmids are regularly spaced in each cell, which is critical for faithful segregation of the genome to daughter cells. Regular spacing of the chromosome is controlled by two separate partitioning systems that involve the protein pairs ParA/ParZ and ParB/SMC. Here, using chromosome conformation capture (Hi-C), we characterized the organization of the B. burgdorferi genome and the interactions between the replicons. We uncovered that although the linear chromosome lacks contacts between the two replication arms, the two telomeres are in frequent contact. Moreover, several plasmids specifically interact with the chromosome oriC region, and a subset of plasmids interact with each other more than with others. We found that SMC and the SMC-like MksB protein mediate long-range interactions on the chromosome, but they minimally affect plasmid-chromosome or plasmid-plasmid interactions. Finally, we found that disruption of the two partition systems leads to chromosome restructuring, correlating with the mis-positioning of chromosome oriC . Altogether, this study revealed the conformation of a complex genome and analyzed the contribution of the partition systems and SMC family proteins to this organization. This work expands the understanding of the organization and maintenance of multipartite bacterial genomes.

Polyploidy, regular patterning of genome copies, and unusual control of DNA partitioning in the Lyme disease spirochete

Borrelia burgdorferi, the tick-transmitted spirochete agent of Lyme disease, has a highly segmented genome with a linear chromosome and various linear or circular plasmids. Here, by imaging several chromosomal loci and 16 distinct plasmids, we show that B. burgdorferi is polyploid during growth in culture and that the number of genome copies decreases during stationary phase. B. burgdorferi is also polyploid inside fed ticks and chromosome copies are regularly spaced along the spirochete's length in both growing cultures and ticks. This patterning involves the conserved DNA partitioning protein ParA whose localization is controlled by a potentially phage-derived protein, ParZ, instead of its usual partner ParB. ParZ binds its own coding region and acts as a centromere-binding protein. While ParA works with ParZ, ParB controls the localization of the condensin, SMC. Together, the ParA/ParZ and ParB/SMC pairs ensure faithful chromosome inheritance. Our findings underscore the plasticity of cellular functions, even those as fundamental as chromosome segregation.

High-throughput imaging and quantitative analysis uncovers the nature of plasmid positioning by ParABS

The faithful segregation and inheritance of bacterial chromosomes and low-copy number plasmids requires dedicated partitioning systems. The most common of these, ParABS, consists of ParA, a DNA-binding ATPase and ParB, a protein that binds to centromeric-like parS sequences on the DNA cargo. The resulting nucleoprotein complexes are believed to move up a self-generated gradient of nucleoid-associated ParA. However, it remains unclear how this leads to the observed cargo positioning and dynamics. In particular, the evaluation of models of plasmid positioning has been hindered by the lack of quantitative measurements of plasmid dynamics. Here, we use high-throughput imaging, analysis and modelling to determine the dynamical nature of these systems. We find that F plasmid is actively brought to specific subcellular home positions within the cell with dynamics akin to an over-damped spring. We develop a unified stochastic model that quantitatively explains this behaviour and predicts that cells with the lowest plasmid concentration transition to oscillatory dynamics. We confirm this prediction for F plasmid as well as a distantly-related ParABS system. Our results indicate that ParABS regularly positions plasmids across the nucleoid but operates just below the threshold of an oscillatory instability, which according to our model, minimises ATP consumption. Our work also clarifies how various plasmid dynamics are achievable in a single unified stochastic model. Overall, this work uncovers the dynamical nature of plasmid positioning by ParABS and provides insights relevant for chromosome-based systems.

Chemophoresis engine: A general mechanism of ATPase-driven cargo transport

Cell polarity regulates the orientation of the cytoskeleton members that directs intracellular transport for cargo-like organelles, using chemical gradients sustained by ATP or GTP hydrolysis. However, how cargo transports are directly mediated by chemical gradients remains unknown. We previously proposed a physical mechanism that enables directed movement of cargos, referred to as chemophoresis. According to the mechanism, a cargo with reaction sites is subjected to a chemophoresis force in the direction of the increased concentration. Based on this, we introduce an extended model, the chemophoresis engine, as a general mechanism of cargo motion, which transforms chemical free energy into directed motion through the catalytic ATP hydrolysis. We applied the engine to plasmid motion in a ParABS system to demonstrate the self-organization system for directed plasmid movement and pattern dynamics of ParA-ATP concentration, thereby explaining plasmid equi-positioning and pole-to-pole oscillation observed in bacterial cells and in vitro experiments. We mathematically show the existence and stability of the plasmid-surfing pattern, which allows the cargo-directed motion through the symmetry-breaking transition of the ParA-ATP spatiotemporal pattern. We also quantitatively demonstrate that the chemophoresis engine can work even under in vivo conditions. Finally, we discuss the chemophoresis engine as one of the general mechanisms of hydrolysis-driven intracellular transport.

The formation of organelle/macromolecule patterns depending on chemical concentration under non-equilibrium conditions, first observed during macroscopic morphogenesis, has recently been observed at the intracellular level as well, and its relevance as intracellular morphogen has been demonstrated in the case of bacterial cell division. These studies have discussed how cargos maintain positional information provided by chemical concentration gradients/localization. However, how cargo transports are directly mediated by chemical gradients remains unknown. Based on the previously proposed mechanism of chemotaxis-like behavior of cargos (referred to as chemophoresis), we introduce a chemophoresis engine as a physicochemical mechanism of cargo motion, which transforms chemical free energy to directed motion. The engine is based on the chemophoresis force to make cargoes move in the direction of the increasing ATPase(-ATP) concentration and an enhanced catalytic ATPase hydrolysis at the positions of the cargoes. Applying the engine to ATPase-driven movement of plasmid-DNAs in bacterial cells, we constructed a mathematical model to demonstrate the self-organization for directed plasmid motion and pattern dynamics of ATPase concentration, as is consistent with in vitro and in vivo experiments. We propose that this chemophoresis engine works as a general mechanism of hydrolysis-driven intracellular transport.

Theory of Active Intracellular Transport by DNA Relaying

The spatiotemporal organization of bacterial cells is crucial for the active segregation of replicating chromosomes. In several species, including Caulobacter crescentus, the ATPase ParA binds to DNA and forms a gradient along the long cell axis. The ParB partition complex on the newly replicated chromosome translocates up this ParA gradient, thereby contributing to chromosome segregation. A DNA-relay mechanism-deriving from the elasticity of the fluctuating chromosome-has been proposed as the driving force for this cargo translocation, but a mechanistic theoretical description remains elusive. Here, we propose a minimal model to describe force generation by the DNA-relay mechanism over a broad range of operational conditions. Conceptually, we identify four distinct force-generation regimes characterized by their dependence on chromosome fluctuations. These relay force regimes arise from an interplay of the imposed ParA gradient, chromosome fluctuations, and an emergent friction force due to chromosome-cargo interactions.

Spatial control over near-critical-point operation ensures fidelity of ParABS-mediated DNA partition

In bacteria, most low-copy-number plasmid and chromosomally encoded partition systems belong to the tripartite ParABS partition machinery. Despite the importance in genetic inheritance, the mechanisms of ParABS-mediated genome partition are not well understood. Combining theory and experiment, we provided evidence that the ParABS system-DNA partitioning in vivo via the ParA-gradient-based Brownian ratcheting-operates near a transition point in parameter space (i.e., a critical point), across which the system displays qualitatively different motile behaviors. This near-critical-point operation adapts the segregation distance of replicated plasmids to the half length of the elongating nucleoid, ensuring both cell halves to inherit one copy of the plasmids. Further, we demonstrated that the plasmid localizes the cytoplasmic ParA to buffer the partition fidelity against the large cell-to-cell fluctuations in ParA level. The spatial control over the near-critical-point operation not only ensures both sensitive adaptation and robust execution of partitioning but also sheds light on the fundamental question in cell biology: how do cells faithfully measure cellular-scale distance by only using molecular-scale interactions?

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.

Pattern selection in reaction diffusion systems

Turing's theory of pattern formation has been used to describe the formation of self-organized periodic patterns in many biological, chemical, and physical systems. However, the use of such models is hindered by our inability to predict, in general, which pattern is obtained from a given set of model parameters. While much is known near the onset of the spatial instability, the mechanisms underlying pattern selection and dynamics away from onset are much less understood. Here, we provide physical insight into the dynamics of these systems. We find that peaks in a Turing pattern behave as point sinks, the dynamics of which is determined by the diffusive fluxes into them. As a result, peaks move toward a periodic steady-state configuration that minimizes the mass of the diffusive species. We also show that the preferred number of peaks at the final steady state is such that this mass is minimized. Our work presents mass minimization as a potential general principle for understanding pattern formation in reaction diffusion systems far from onset.

Engineering spatiotemporal organization and dynamics in synthetic cells

Constructing synthetic cells has recently become an appealing area of research. Decades of research in biochemistry and cell biology have amassed detailed part lists of components involved in various cellular processes. Nevertheless, recreating any cellular process in vitro in cell-sized compartments remains ambitious and challenging. Two broad features or principles are key to the development of synthetic cells-compartmentalization and self-organization/spatiotemporal dynamics. In this review article, we discuss the current state of the art and research trends in the engineering of synthetic cell membranes, development of internal compartmentalization, reconstitution of self-organizing dynamics, and integration of activities across scales of space and time. We also identify some research areas that could play a major role in advancing the impact and utility of engineered synthetic cells. This article is categorized under: Biology-Inspired Nanomaterials > Lipid-Based Structures Biology-Inspired Nanomaterials > Protein and Virus-Based Structures.

Multidomain ribosomal protein trees and the planctobacterial origin of neomura (eukaryotes, archaebacteria)

Palaeontologically, eubacteria are > 3× older than neomura (eukaryotes, archaebacteria). Cell biology contrasts ancestral eubacterial murein peptidoglycan walls and derived neomuran N-linked glycoprotein coats/walls. Misinterpreting long stems connecting clade neomura to eubacteria on ribosomal sequence trees (plus misinterpreted protein paralogue trees) obscured this historical pattern. Universal multiprotein ribosomal protein (RP) trees, more accurate than rRNA trees, are taxonomically undersampled. To reduce contradictions with genically richer eukaryote trees and improve eubacterial phylogeny, we constructed site-heterogeneous and maximum-likelihood universal three-domain, two-domain, and single-domain trees for 143 eukaryotes (branching now congruent with 187-protein trees), 60 archaebacteria, and 151 taxonomically representative eubacteria, using 51 and 26 RPs. Site-heterogeneous trees greatly improve eubacterial phylogeny and higher classification, e.g. showing gracilicute monophyly, that many 'rDNA-phyla' belong in Proteobacteria, and reveal robust new phyla Synthermota and Aquithermota. Monoderm Posibacteria and Mollicutes (two separate wall losses) are both polyphyletic: multiple outer membrane losses in Endobacteria occurred separately from Actinobacteria; neither phylum is related to Chloroflexi, the most divergent prokaryotes, which originated photosynthesis (new model proposed). RP trees support an eozoan root for eukaryotes and are consistent with archaebacteria being their sisters and rooted between Filarchaeota (=Proteoarchaeota, including 'Asgardia') and Euryarchaeota sensu-lato (including ultrasimplified 'DPANN' whose long branches often distort trees). Two-domain trees group eukaryotes within Planctobacteria, and archaebacteria with Planctobacteria/Sphingobacteria. Integrated molecular/palaeontological evidence favours negibacterial ancestors for neomura and all life. Unique presence of key pre-neomuran characters favours Planctobacteria only as ancestral to neomura, which apparently arose by coevolutionary repercussions (explained here in detail, including RP replacement) of simultaneous outer membrane and murein loss. Planctobacterial C-1 methanotrophic enzymes are likely ancestral to archaebacterial methanogenesis and β-propeller-α-solenoid proteins to eukaryotic vesicle coats, nuclear-pore-complexes, and intraciliary transport. Planctobacterial chaperone-independent 4/5-protofilament microtubules and MamK actin-ancestors prepared for eukaryote intracellular motility, mitosis, cytokinesis, and phagocytosis. We refute numerous wrong ideas about the universal tree.

Multidomain ribosomal protein trees and the planctobacterial origin of neomura (eukaryotes, archaebacteria)

Palaeontologically, eubacteria are > 3× older than neomura (eukaryotes, archaebacteria). Cell biology contrasts ancestral eubacterial murein peptidoglycan walls and derived neomuran N-linked glycoprotein coats/walls. Misinterpreting long stems connecting clade neomura to eubacteria on ribosomal sequence trees (plus misinterpreted protein paralogue trees) obscured this historical pattern. Universal multiprotein ribosomal protein (RP) trees, more accurate than rRNA trees, are taxonomically undersampled. To reduce contradictions with genically richer eukaryote trees and improve eubacterial phylogeny, we constructed site-heterogeneous and maximum-likelihood universal three-domain, two-domain, and single-domain trees for 143 eukaryotes (branching now congruent with 187-protein trees), 60 archaebacteria, and 151 taxonomically representative eubacteria, using 51 and 26 RPs. Site-heterogeneous trees greatly improve eubacterial phylogeny and higher classification, e.g. showing gracilicute monophyly, that many 'rDNA-phyla' belong in Proteobacteria, and reveal robust new phyla Synthermota and Aquithermota. Monoderm Posibacteria and Mollicutes (two separate wall losses) are both polyphyletic: multiple outer membrane losses in Endobacteria occurred separately from Actinobacteria; neither phylum is related to Chloroflexi, the most divergent prokaryotes, which originated photosynthesis (new model proposed). RP trees support an eozoan root for eukaryotes and are consistent with archaebacteria being their sisters and rooted between Filarchaeota (=Proteoarchaeota, including 'Asgardia') and Euryarchaeota sensu-lato (including ultrasimplified 'DPANN' whose long branches often distort trees). Two-domain trees group eukaryotes within Planctobacteria, and archaebacteria with Planctobacteria/Sphingobacteria. Integrated molecular/palaeontological evidence favours negibacterial ancestors for neomura and all life. Unique presence of key pre-neomuran characters favours Planctobacteria only as ancestral to neomura, which apparently arose by coevolutionary repercussions (explained here in detail, including RP replacement) of simultaneous outer membrane and murein loss. Planctobacterial C-1 methanotrophic enzymes are likely ancestral to archaebacterial methanogenesis and β-propeller-α-solenoid proteins to eukaryotic vesicle coats, nuclear-pore-complexes, and intraciliary transport. Planctobacterial chaperone-independent 4/5-protofilament microtubules and MamK actin-ancestors prepared for eukaryote intracellular motility, mitosis, cytokinesis, and phagocytosis. We refute numerous wrong ideas about the universal tree.

Plasmid Localization and Partition in Enterobacteriaceae

Plasmids are ubiquitous in the microbial world and have been identified in almost all species of bacteria that have been examined. Their localization inside the bacterial cell has been examined for about two decades; typically, they are not randomly distributed, and their positioning depends on copy number and their mode of segregation. Low-copy-number plasmids promote their own stable inheritance in their bacterial hosts by encoding active partition systems, which ensure that copies are positioned in both halves of a dividing cell. High-copy plasmids rely on passive diffusion of some copies, but many remain clustered together in the nucleoid-free regions of the cell. Here we review plasmid localization and partition (Par) systems, with particular emphasis on plasmids from Enterobacteriaceae and on recent results describing the in vivo localization properties and molecular mechanisms of each system. Partition systems also cause plasmid incompatibility such that distinct plasmids (with different replicons) with the same Par system cannot be stably maintained in the same cells. We discuss how partition-mediated incompatibility is a consequence of the partition mechanism.

Intracellular Positioning Systems Limit the Entropic Eviction of Secondary Replicons Toward the Nucleoid Edges in Bacterial Cells

Bacterial genomes, organized intracellularly as nucleoids, are composed of the main chromosome coexisting with different types of secondary replicons. Secondary replicons are major drivers of bacterial adaptation by gene exchange. They are highly diverse in type and size, ranging from less than 2 to more than 1000 kb, and must integrate with bacterial physiology, including to the nucleoid dynamics, to limit detrimental costs leading to their counter-selection. We show that large DNA circles, whether from a natural plasmid or excised from the chromosome tend to localize in a dynamic manner in a zone separating the nucleoid from the cytoplasm at the edge of the nucleoid. This localization is in good agreement with silico simulations of DNA circles in the nucleoid volume. Subcellular positioning systems counteract this tendency, allowing replicons to enter the nucleoid space. In enterobacteria, these systems are found in replicons above 25 kb, defining the limit with small randomly segregated plasmids. Larger replicons carry at least one of the three described family of systems, ParAB, ParRM, and StbA. Replicons above 180 kb all carry a ParAB system, suggesting this system is specifically required in the cases of large replicons. Simulations demonstrated that replicon size profoundly affects localization, compaction, and dynamics of DNA circles in the nucleoid volume. The present work suggests that presence of partition systems on the larger plasmids or chromids is not only due to selection for accurate segregation but also to counteract their unmixing with the chromosome and consequent exclusion from the nucleoid.

Highly Polyvalent DNA Motors Generate 100+ pN of Force via Autochemophoresis

Motor proteins such as myosin, kinesin, and dynein are essential to eukaryotic life and power countless processes including muscle contraction, wound closure, cargo transport, and cell division. The design of synthetic nanomachines that can reproduce the functions of these motors is a longstanding goal in the field of nanotechnology. DNA walkers, which are programmed to "walk" along defined tracks via the burnt bridge Brownian ratchet mechanism, are among the most promising synthetic mimics of these motor proteins. While these DNA-based motors can perform useful tasks such as cargo transport, they have not been shown to be capable of cooperating to generate large collective forces for tasks akin to muscle contraction. In this work, we demonstrate that highly polyvalent DNA motors (HPDMs), which can be viewed as cooperative teams of thousands of DNA walkers attached to a microsphere, can generate and sustain substantial forces in the 100+ pN regime. Specifically, we show that HPDMs can generate forces that can unzip and shear DNA duplexes (∼12 and ∼50 pN, respectively) and rupture biotin-streptavidin bonds (∼100-150 pN). To help explain these results, we present a variant of the burnt-bridge Brownian ratchet mechanism that we term autochemophoresis, wherein many individual force generating units generate a self-propagating chemomechanical gradient that produces large collective forces. In addition, we demonstrate the potential of this work to impact future engineering applications by harnessing HPDM autochemophoresis to deposit "molecular ink" via mechanical bond rupture. This work expands the capabilities of synthetic DNA motors to mimic the force-generating functions of biological motors. Our work also builds upon previous observations of autochemophoresis in bacterial transport processes, indicating that autochemophoresis may be a fundamental mechanism of pN-scale force generation in living systems.

Can a Flux-Based Mechanism Explain Protein Cluster Positioning in a Three-Dimensional Cell Geometry?

The plane of bacterial cell division must be precisely positioned. In the bacterium Myxococcus xanthus, the proteins PomX and PomY form a large cluster, which is tethered to the nucleoid by the ATPase PomZ and moves in a stochastic but biased manner toward midcell where it initiates cell division. Previously, a positioning mechanism based on the fluxes of PomZ on the nucleoid was proposed. However, the cluster dynamics was analyzed in a reduced, one-dimensional geometry. Here, we introduce a mathematical model that accounts for the three-dimensional shape of the nucleoid, such that nucleoid-bound PomZ dimers can diffuse past the cluster without interacting with it. Using stochastic simulations, we find that the cluster still moves to and localizes at midcell. Redistribution of PomZ by diffusion in the cytosol is essential for this cluster dynamics. Our mechanism also positions two clusters equidistantly on the nucleoid, as observed for low-copy-number plasmid partitioning. We conclude that a flux-based mechanism allows for cluster positioning in a biologically realistic three-dimensional cell geometry.

DNA segregation under Par protein control

The spatial organization of DNA is mediated by the Par protein system in some bacteria. ParB binds specifically to the parS sequence on DNA and orchestrates its motion by interacting with ParA bound to the nucleoid. In the case of plasmids, a single ParB bound plasmid is observed to execute oscillations between cell poles while multiple plasmids eventually settle at equal distances from each other along the cell's length. While the potential mechanism underlying the ParA-ParB interaction has been discussed, it remains unclear whether ParB-complex oscillations are stable limit cycles or merely decaying transients to a fixed point. How are dynamics affected by substrate length and the number of complexes? We present a deterministic model for ParA-ParB driven DNA segregation where the transition between stable arrangements and oscillatory behaviour depends only on five parameters: ParB-complex number, substrate length, ParA concentration, ParA hydrolysis rate and the ratio of the lengthscale over which the ParB complex stimulates ParA hydrolysis to the lengthscale over which ParA interacts with the ParB complex. When the system is buffered and the ParA rebinding rate is constant we find that ParB-complex dynamics is independent of substrate length and complex number above a minimum system size. Conversely, when ParA resources are limited, we find that changing substrate length and increasing complex number leads to counteracting mechanisms that can both generate or subdue oscillatory dynamics. We argue that cells may be poised near a critical level of ParA so that they can transition from oscillatory to fixed point dynamics as the cell cycle progresses so that they can both measure their size and faithfully partition their genetic material. Lastly, we show that by modifying the availability of ParA or depletion zone size, we can capture some of the observed differences in ParB-complex positioning between replicating chromosomes in B. subtilis cells and low-copy plasmids in E. coli cells.

Diffusiophoresis in Cells: A General Nonequilibrium, Nonmotor Mechanism for the Metabolism-Dependent Transport of Particles in Cells

The more we learn about the cytoplasm of cells, the more we realize that the cytoplasm is not uniform but instead is highly inhomogeneous. In any inhomogeneous solution, there are concentration gradients, and particles move either up or down these gradients due to a mechanism called diffusiophoresis. I estimate that inside metabolically active cells, the dynamics of particles can be strongly accelerated by diffusiophoresis, provided that they are at least tens of nanometers across. The dynamics of smaller objects, such as single proteins, are largely unaffected.

Self-organization principles of intracellular pattern formation

Dynamic patterning of specific proteins is essential for the spatio-temporal regulation of many important intracellular processes in prokaryotes, eukaryotes and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. In this article, we review quantitative models for intracellular Min protein patterns in Escherichia coli, Cdc42 polarization in Saccharomyces cerevisiae and the bipolar PAR protein patterns found in Caenorhabditis elegans. By analysing the molecular processes driving these systems we derive a theoretical perspective on general principles underlying self-organized pattern formation. We argue that intracellular pattern formation is not captured by concepts such as ‘activators’, ‘inhibitors’ or ‘substrate depletion’. Instead, intracellular pattern formation is based on the redistribution of proteins by cytosolic diffusion, and the cycling of proteins between distinct conformational states. Therefore, mass-conserving reaction–diffusion equations provide the most appropriate framework to study intracellular pattern formation. We conclude that directed transport, e.g. cytosolic diffusion along an actively maintained cytosolic gradient, is the key process underlying pattern formation. Thus the basic principle of self-organization is the establishment and maintenance of directed transport by intracellular protein dynamics.

This article is part of the theme issue ‘Self-organization in cell biology’.

Subcellular Organization: A Critical Feature of Bacterial Cell Replication

Spatial organization is a hallmark of all living systems. Even bacteria, the smallest forms of cellular life, display defined shapes and complex internal organization, showcasing a highly structured genome, cytoskeletal filaments, localized scaffolding structures, dynamic spatial patterns, active transport, and occasionally, intracellular organelles. Spatial order is required for faithful and efficient cellular replication and offers a powerful means for the development of unique biological properties. Here, we discuss organizational features of bacterial cells and highlight how bacteria have evolved diverse spatial mechanisms to overcome challenges cells face as self-replicating entities.

Center Finding in E. coli and the Role of Mathematical Modeling: Past, Present and Future

We review the key role played by mathematical modeling in elucidating two center-finding patterning systems in Escherichia coli: midcell division positioning by the MinCDE system and DNA partitioning by the ParABS system. We focus particularly on how, despite much experimental effort, these systems were simply too complex to unravel by experiments alone, and instead required key injections of quantitative, mathematical thinking. We conclude the review by analyzing the frequency of modeling approaches in microbiology over time. We find that while such methods are increasing in popularity, they are still probably heavily under-utilized for optimal progress on complex biological questions.

A conserved mechanism drives partition complex assembly on bacterial chromosomes and plasmids

Chromosome and plasmid segregation in bacteria are mostly driven by ParABS systems. These DNA partitioning machineries rely on large nucleoprotein complexes assembled on centromere sites (parS). However, the mechanism of how a few parS-bound ParB proteins nucleate the formation of highly concentrated ParB clusters remains unclear despite several proposed physico-mathematical models. We discriminated between these different models by varying some key parameters in vivo using the F plasmid partition system. We found that "Nucleation & caging" is the only coherent model recapitulating in vivo data. We also showed that the stochastic self-assembly of partition complexes (i) is a robust mechanism, (ii) does not directly involve ParA ATPase, (iii) results in a dynamic structure of discrete size independent of ParB concentration, and (iv) is not perturbed by active transcription but is by protein complexes. We refined the "Nucleation & caging" model and successfully applied it to the chromosomally encoded Par system of Vibrio cholerae, indicating that this stochastic self-assembly mechanism is widely conserved from plasmids to chromosomes.

Regulation of Pom cluster dynamics in Myxococcus xanthus

Precise positioning of the cell division site is essential for the correct segregation of the genetic material into the two daughter cells. In the bacterium Myxococcus xanthus, the proteins PomX and PomY form a cluster on the chromosome that performs a biased random walk to midcell and positively regulates cell division there. PomZ, an ATPase, is necessary for tethering of the cluster to the nucleoid and regulates its movement towards midcell. It has remained unclear how the cluster dynamics change when the biochemical parameters, such as the attachment rates of PomZ dimers to the nucleoid and the cluster, the ATP hydrolysis rate of PomZ or the mobility of PomZ interacting with the nucleoid and cluster, are varied. To answer these questions, we investigate a one-dimensional model that includes the nucleoid, the Pom cluster and PomZ proteins. We find that a mechanism based on the diffusive PomZ fluxes on the nucleoid into the cluster can explain the latter's midnucleoid localization for a broad parameter range. Furthermore, there is an ATP hydrolysis rate that minimizes the time the cluster needs to reach midnucleoid. If the dynamics of PomZ on the nucleoid is slow relative to the cluster's velocity, we observe oscillatory cluster movements around midnucleoid. To understand midnucleoid localization, we developed a semi-analytical approach that dissects the net movement of the cluster into its components: the difference in PomZ fluxes into the cluster from either side, the force exerted by a single PomZ dimer on the cluster and the effective friction coefficient of the cluster. Importantly, we predict that the Pom cluster oscillates around midnucleoid if the diffusivity of PomZ on the nucleoid is reduced. A similar approach to that applied here may also prove useful for cargo localization in ParABS systems.

Self-organized system-size oscillation of a stochastic lattice-gas model

The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.