Chemophoresis as a driving force for intracellular organization: Theory and application to plasmid partitioning

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.

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.

Adhesive Dynamics Simulations of Highly Polyvalent DNA Motors

Molecular motors, such as myosin and kinesin, perform diverse tasks ranging from vesical transport to bulk muscle contraction. Synthetic molecular motors may eventually be harnessed to perform similar tasks in versatile synthetic systems. The most promising type of synthetic molecular motor, the DNA walker, can undergo processive motion but generally exhibits low speeds and virtually no capacity for force generation. However, we recently showed that highly polyvalent DNA motors (HPDMs) can rival biological motors by translocating at micrometer per minute speeds and generating 100+ pN of force. Accordingly, DNA nanotechnology-based designs may hold promise for the creation of synthetic, force-generating nanomotors. However, the dependencies of HPDM speed and force on tunable design parameters are poorly understood and difficult to characterize experimentally. To overcome this challenge, we present RoloSim, an adhesive dynamics software package for fine-grained simulations of HPDM translocation. RoloSim uses biophysical models for DNA duplex formation and dissociation kinetics to explicitly model tens of thousands of molecular scale interactions. These molecular interactions are then used to calculate the nano- and microscale motions of the motor. We use RoloSim to uncover how motor force and speed scale with several tunable motor properties such as motor size and DNA duplex length. Our results support our previously defined hypothesis that force scales linearly with polyvalency. We also demonstrate that HPDMs can be steered with external force, and we provide design parameters for novel HPDM-based molecular sensor and nanomachine designs.

Distinct architectural requirements for the parS centromeric sequence of the pSM19035 plasmid partition machinery

Three-component ParABS partition systems ensure stable inheritance of many bacterial chromosomes and low-copy-number plasmids. ParA localizes to the nucleoid through its ATP-dependent nonspecific DNA-binding activity, whereas centromere-like parS-DNA and ParB form partition complexes that activate ParA-ATPase to drive the system dynamics. The essential parS sequence arrangements vary among ParABS systems, reflecting the architectural diversity of their partition complexes. Here, we focus on the pSM19035 plasmid partition system that uses a ParB_pSM of the ribbon-helix-helix (RHH) family. We show that parS_pSM with four or more contiguous ParB_pSM-binding sequence repeats is required to assemble a stable ParA_pSM-ParB_pSM complex and efficiently activate the ParA_pSM-ATPase, stimulating complex disassembly. Disruption of the contiguity of the parS_pSM sequence array destabilizes the ParA_pSM-ParB_pSM complex and prevents efficient ATPase activation. Our findings reveal the unique architecture of the pSM19035 partition complex and how it interacts with nucleoid-bound ParA_pSM-ATP.

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.

CTP and parS coordinate ParB partition complex dynamics and ParA-ATPase activation for ParABS-mediated DNA partitioning

ParABS partition systems, comprising the centromere-like DNA sequence parS, the parS-binding ParB-CTPase, and the nucleoid-binding ParA-ATPase, ensure faithful segregation of bacterial chromosomes and low-copy-number plasmids. F-plasmid partition complexes containing ParB_F and parS_F move by generating and following a local concentration gradient of nucleoid-bound ParA_F. However, the process through which ParB_F activates ParA_F-ATPase has not been defined. We studied CTP- and parS_F-modulated ParA_F-ParB_F complex assembly, in which DNA-bound ParA_F-ATP dimers are activated for ATP hydrolysis by interacting with two ParB_F N-terminal domains. CTP or parS_F enhances the ATPase rate without significantly accelerating ParA_F-ParB_F complex assembly. Together, parS_F and CTP accelerate ParA_F-ParB_F assembly without further significant increase in ATPase rate. Magnetic-tweezers experiments showed that CTP promotes multiple ParB_F loading onto parS_F-containing DNA, generating condensed partition complex-like assemblies. We propose that ParB_F in the partition complex adopts a conformation that enhances ParB_F-ParB_F and ParA_F-ParB_F interactions promoting efficient partitioning.

CTP and parS coordinate ParB partition complex dynamics and ParA-ATPase activation for ParABS-mediated DNA partitioning

ParABS partition systems, comprising the centromere-like DNA sequence parS, the parS-binding ParB-CTPase, and the nucleoid-binding ParA-ATPase, ensure faithful segregation of bacterial chromosomes and low-copy-number plasmids. F-plasmid partition complexes containing ParB_F and parS_F move by generating and following a local concentration gradient of nucleoid-bound ParA_F. However, the process through which ParB_F activates ParA_F-ATPase has not been defined. We studied CTP- and parS_F-modulated ParA_F-ParB_F complex assembly, in which DNA-bound ParA_F-ATP dimers are activated for ATP hydrolysis by interacting with two ParB_F N-terminal domains. CTP or parS_F enhances the ATPase rate without significantly accelerating ParA_F-ParB_F complex assembly. Together, parS_F and CTP accelerate ParA_F-ParB_F assembly without further significant increase in ATPase rate. Magnetic-tweezers experiments showed that CTP promotes multiple ParB_F loading onto parS_F-containing DNA, generating condensed partition complex-like assemblies. We propose that ParB_F in the partition complex adopts a conformation that enhances ParB_F-ParB_F and ParA_F-ParB_F interactions promoting efficient partitioning.

Burnt bridge ratchet motor force scales linearly with polyvalency: a computational study

Nano- and micro-scale burnt bridge ratchet motors, which translocate via "guide" molecules that bind to and degrade a field of "fuel" molecules, have recently emerged in several biological and engineering contexts. The capacity of these motors to generate mechanical forces remains an open question. Here, chemomechanical modeling suggests that BBR force scales linearly with the steady-state number of guide-fuel bonds.

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.

Physical Views on ParABS-Mediated DNA Segregation

In this chapter, we will focus on ParABS: an apparently simple, three-component system, required for the segregation of bacterial chromosomes and plasmids. We will specifically describe how biophysical measurements combined with physical modeling advanced our understanding of the mechanism of ParABS-mediated complex assembly, segregation and positioning.

Nucleoid-mediated positioning and transport in bacteria

Precise management of the spatiotemporal position of subcellular components is critical to a number of essential processes in the bacterial cell. The bacterial nucleoid is a highly structured yet dynamic object that undergoes significant reorganization during the relatively short cell cycle, e.g. during gene expression, chromosome replication, and segregation. Although the nucleoid takes up a large fraction of the volume of the cell, the mobility of macromolecules within these dense regions is relatively high and recent results suggest that the nucleoid plays an integral role of dynamic localization in a host of seemingly disparate cellular processes. Here, we review a number of recent reports of nucleoid-mediated positioning and transport in the model bacteria Escherichia coli. These results viewed as a whole suggest that the dynamic, cellular-scale structure of the nucleoid may be a key driver of positioning and transport within the cell. This model of a global, default positioning and transport system may help resolve many unanswered questions about the mechanisms of partitioning and segregation in bacteria.

The E. coli MinCDE system in the regulation of protein patterns and gradients

Molecular self-organziation, also regarded as pattern formation, is crucial for the correct distribution of cellular content. The processes leading to spatiotemporal patterns often involve a multitude of molecules interacting in complex networks, so that only very few cellular pattern-forming systems can be regarded as well understood. Due to its compositional simplicity, the Escherichia coli MinCDE system has, thus, become a paradigm for protein pattern formation. This biological reaction diffusion system spatiotemporally positions the division machinery in E. coli and is closely related to ParA-type ATPases involved in most aspects of spatiotemporal organization in bacteria. The ATPase MinD and the ATPase-activating protein MinE self-organize on the membrane as a reaction matrix. In vivo, these two proteins typically oscillate from pole-to-pole, while in vitro they can form a variety of distinct patterns. MinC is a passenger protein supposedly operating as a downstream cue of the system, coupling it to the division machinery. The MinCDE system has helped to extract not only the principles underlying intracellular patterns, but also how they are shaped by cellular boundaries. Moreover, it serves as a model to investigate how patterns can confer information through specific and non-specific interactions with other molecules. Here, we review how the three Min proteins self-organize to form patterns, their response to geometric boundaries, and how these patterns can in turn induce patterns of other molecules, focusing primarily on experimental approaches and developments.

Mesoscopic non-equilibrium measures can reveal intrinsic features of the active driving

Biological assemblies such as chromosomes, membranes, and the cytoskeleton are driven out of equilibrium at the nanoscale by enzymatic activity and molecular motors. Similar non-equilibrium dynamics can be realized in synthetic systems, such as chemically fueled colloidal particles. Characterizing the stochastic non-equilibrium dynamics of such active soft assemblies still remains a challenge. Recently, new non-invasive approaches have been proposed to determine the non-equilibrium behavior, which are based on detecting broken detailed balance in the stochastic trajectories of several coordinates of the system. Inspired by the method of two-point microrheology, in which the equilibrium fluctuations of a pair of probe particles reveal the viscoelastic response of an equilibrium system, here, we investigate whether we can extend such an approach to non-equilibrium assemblies: can one extract information on the nature of the active driving in a system from the analysis of a two-point non-equilibrium measure? We address this question theoretically in the context of a class of elastic systems, driven out of equilibrium by a spatially heterogeneous stochastic internal driving. We consider several scenarios for the spatial features of the internal driving that may be relevant in biological and synthetic systems, and investigate how such features of the active noise may be reflected in the long-range scaling behavior of two-point non-equilibrium measures.

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.

Self-organised segregation of bacterial chromosomal origins

The chromosomal replication origin region (ori) of characterised bacteria is dynamically positioned throughout the cell cycle. In slowly growing Escherichia coli, ori is maintained at mid-cell from birth until its replication, after which newly replicated sister oris move to opposite quarter positions. Here, we provide an explanation for ori positioning based on the self-organisation of the Structural Maintenance of Chromosomes complex, MukBEF, which forms dynamically positioned clusters on the chromosome. We propose that a non-trivial feedback between the self-organising gradient of MukBEF complexes and the oris leads to accurate ori positioning. We find excellent agreement with quantitative experimental measurements and confirm key predictions. Specifically, we show that oris exhibit biased motion towards MukBEF clusters, rather than mid-cell. Our findings suggest that MukBEF and oris act together as a self-organising system in chromosome organisation-segregation and introduces protein self-organisation as an important consideration for future studies of chromosome dynamics.

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.

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.

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

Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component machinery, fueled by adenosine triphosphate, called the partition complex. We present a phenomenological model accounting for the dynamic activity of this system that is also relevant for the physics of catalytic particles in active environments. The model is obtained by coupling simple linear reaction-diffusion equations with a proteophoresis, or "volumetric" chemophoresis, force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This minimal description captures most known experimental observations: dynamic oscillations of complex components, complex separation, and subsequent symmetrical positioning. The predictions of our model are in phenomenological agreement with and provide substantial insight into recent experiments. From a nonlinear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and traveling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry.

Brownian Ratchet Mechanism for Faithful Segregation of Low-Copy-Number Plasmids

Bacterial plasmids are extrachromosomal DNA that provides selective advantages for bacterial survival. Plasmid partitioning can be remarkably robust. For high-copy-number plasmids, diffusion ensures that both daughter cells inherit plasmids after cell division. In contrast, most low-copy-number plasmids need to be actively partitioned by a conserved tripartite ParA-type system. ParA is an ATPase that binds to chromosomal DNA; ParB is the stimulator of the ParA ATPase and specifically binds to the plasmid at a centromere-like site, parS. ParB stimulation of the ParA ATPase releases ParA from the bacterial chromosome, after which it takes a long time to reset its DNA-binding affinity. We previously demonstrated in vitro that the ParA system can exploit this biochemical asymmetry for directed cargo transport. Multiple ParA-ParB bonds can bridge a parS-coated cargo to a DNA carpet, and they can work collectively as a Brownian ratchet that directs persistent cargo movement with a ParA-depletion zone trailing behind. By extending this model, we suggest that a similar Brownian ratchet mechanism recapitulates the full range of actively segregated plasmid motilities observed in vivo. We demonstrate that plasmid motility is tuned as the replenishment rate of the ParA-depletion zone progressively increases relative to the cargo speed, evolving from diffusion to pole-to-pole oscillation, local excursions, and, finally, immobility. When the plasmid replicates, the daughters largely display motilities similar to that of their mother, except that when the single-focus progenitor is locally excursive, the daughter foci undergo directed segregation. We show that directed segregation maximizes the fidelity of plasmid partition. Given that local excursion and directed segregation are the most commonly observed modes of plasmid motility in vivo, we suggest that the operation of the ParA-type partition system has been shaped by evolution for high fidelity of plasmid segregation.

DNA-relay mechanism is sufficient to explain ParA-dependent intracellular transport and patterning of single and multiple cargos

Spatial ordering of macromolecular components inside cells is important for cellular physiology and replication. In bacteria, ParA/B systems are known to generate various intracellular patterns that underlie the transport and partitioning of low-copy-number cargos such as plasmids. ParA/B systems consist of ParA, an ATPase that dimerizes and binds DNA upon ATP binding, and ParB, a protein that binds the cargo and stimulates ParA ATPase activity. Inside cells, ParA is asymmetrically distributed, forming a propagating wave that is followed by the ParB-rich cargo. These correlated dynamics lead to cargo oscillation or equidistant spacing over the nucleoid depending on whether the cargo is in single or multiple copies. Currently, there is no model that explains how these different spatial patterns arise and relate to each other. Here, we test a simple DNA-relay model that has no imposed asymmetry and that only considers the ParA/ParB biochemistry and the known fluctuating and elastic dynamics of chromosomal loci. Stochastic simulations with experimentally derived parameters demonstrate that this model is sufficient to reproduce the signature patterns of ParA/B systems: the propagating ParA gradient correlated with the cargo dynamics, the single-cargo oscillatory motion, and the multicargo equidistant patterning. Stochasticity of ATP hydrolysis breaks the initial symmetry in ParA distribution, resulting in imbalance of elastic force acting on the cargo. Our results may apply beyond ParA/B systems as they reveal how a minimal system of two players, one binding to DNA and the other modulating this binding, can transform directionally random DNA fluctuations into directed motion and intracellular patterning.

Self-propulsion and interactions of catalytic particles in a chemically active medium

Enzymatic "machines," such as catalytic rods or colloids, can self-propel and interact by generating gradients of their substrates. We theoretically investigate the behaviors of such machines in a chemically active environment where their catalytic substrates are continuously synthesized and destroyed, as occurs in living cells. We show how the kinetic properties of the medium modulate self-propulsion and pairwise interactions between machines, with the latter controlled by a tunable characteristic interaction range analogous to the Debye screening length in an electrolytic solution. Finally, we discuss the effective force arising between interacting machines and possible biological applications, such as partitioning of bacterial plasmids.

Operational Principles for the Dynamics of the In Vitro ParA-ParB System

In many bacteria the ParA-ParB protein system is responsible for actively segregating DNA during replication. ParB proteins move by interacting with DNA bound ParA-ATP, stimulating their unbinding by catalyzing hydrolysis, that leads to rectified motion due to the creation of a wake of depleted ParA. Recent in vitro experiments have shown that a ParB covered magnetic bead can move with constant speed over a DNA covered substrate that is bound by ParA. It has been suggested that the formation of a gradient in ParA leads to diffusion-ratchet like motion of the ParB bead but how it forms and generates a force is still a matter of exploration. Here we develop a deterministic model for the in vitro ParA-ParB system and show that a ParA gradient can spontaneously form due to any amount of initial spatial noise in bound ParA. The speed of the bead is independent of this noise but depends on the ratio of the range of ParA-ParB force on the bead to that of removal of surface bound ParA by ParB. We find that at a particular ratio the speed attains a maximal value. We also consider ParA rebinding (including cooperativity) and ParA surface diffusion independently as mechanisms for ParA recovery on the surface. Depending on whether the DNA covered surface is undersaturated or saturated with ParA, we find that the bead can accelerate persistently or potentially stall. Our model highlights key requirements of the ParA-ParB driving force that are necessary for directed motion in the in vitro system that may provide insight into the in vivo dynamics of the ParA-ParB system.

Segregating genetic material is essential for cell survival over multiple generations. The process underlying the required spatio-temporal organization of DNA is mediated by the ParA-ParB-parS system. Recently, experiments have shown that directed motion can be reconstituted in vitro. In these experiments, a magnetic bead was covered with the protein ParB and was able to move ballistically over a surface of DNA that was bound by the protein ParA. How does this active transport spontaneously emerge? In this paper we present a deterministic model for the dynamics of ParA-ParB proteins. We show how spatial noise in surface bound ParA is sufficient for the creation of a gradient in ParA that can drive motion of ParB in vitro. The model explains certain key aspects of the in vitro ParA-ParB system and leads to testable predictions.

Directed and persistent movement arises from mechanochemistry of the ParA/ParB system

The segregation of DNA before cell division is essential for faithful genetic inheritance. In many bacteria, segregation of low-copy number plasmids involves an active partition system composed of a nonspecific DNA-binding ATPase, ParA, and its stimulator protein ParB. The ParA/ParB system drives directed and persistent movement of DNA cargo both in vivo and in vitro. Filament-based models akin to actin/microtubule-driven motility were proposed for plasmid segregation mediated by ParA. Recent experiments challenge this view and suggest that ParA/ParB system motility is driven by a diffusion ratchet mechanism in which ParB-coated plasmid both creates and follows a ParA gradient on the nucleoid surface. However, the detailed mechanism of ParA/ParB-mediated directed and persistent movement remains unknown. Here, we develop a theoretical model describing ParA/ParB-mediated motility. We show that the ParA/ParB system can work as a Brownian ratchet, which effectively couples the ATPase-dependent cycling of ParA-nucleoid affinity to the motion of the ParB-bound cargo. Paradoxically, this resulting processive motion relies on quenching diffusive plasmid motion through a large number of transient ParA/ParB-mediated tethers to the nucleoid surface. Our work thus sheds light on an emergent phenomenon in which nonmotor proteins work collectively via mechanochemical coupling to propel cargos-an ingenious solution shaped by evolution to cope with the lack of processive motor proteins in bacteria.

A moving ParA gradient on the nucleoid directs subcellular cargo transport via a chemophoresis force

DNA segregation is a critical process for all life, and although there is a relatively good understanding of eukaryotic mitosis, the mechanism in bacteria remains unclear. The small size of a bacterial cell and the number of factors involved in its subcellular organization make it difficult to study individual systems under controlled conditions in vivo. We developed a cell-free technique to reconstitute and visualize bacterial ParA-mediated segregation systems. Our studies provide direct evidence for a mode of transport that does not use a classical cytoskeletal filament or motor protein. Instead, we demonstrate that ParA-type DNA segregation systems can establish a propagating ParA ATPase gradient on the nucleoid surface, which generates the force required for the directed movement of spatially confined cargoes, such as plasmids or large organelles, and distributes multiple cargos equidistant to each other inside cells. Here we present the critical principles of our diffusion-ratchet model of ParA-mediated transport and expand on the mathematically derived chemophoresis force using experimentally-determined biochemical and cellular parameters.

Physical modeling of chromosome segregation in escherichia coli reveals impact of force and DNA relaxation

The physical mechanism by which Escherichia coli segregates copies of its chromosome for partitioning into daughter cells is unknown, partly due to the difficulty in interpreting the complex dynamic behavior during segregation. Analysis of previous chromosome segregation measurements in E. coli demonstrates that the origin of replication exhibits processive motion with a mean displacement that scales as t(0.32). In this work, we develop a model for segregation of chromosomal DNA as a Rouse polymer in a viscoelastic medium with a force applied to a single monomer. Our model demonstrates that the observed power-law scaling of the mean displacement and the behavior of the velocity autocorrelation function is captured by accounting for the relaxation of the polymer chain and the viscoelastic environment. We show that the ratio of the mean displacement to the variance of the displacement during segregation events is a critical metric that eliminates the compounding effects of polymer and medium dynamics and provides the segregation force. We calculate the force of oriC segregation in E. coli to be ∼0.49 pN.

Competing ParA structures space bacterial plasmids equally over the nucleoid

Low copy number plasmids in bacteria require segregation for stable inheritance through cell division. This is often achieved by a parABC locus, comprising an ATPase ParA, DNA-binding protein ParB and a parC region, encoding ParB-binding sites. These minimal components space plasmids equally over the nucleoid, yet the underlying mechanism is not understood. Here we investigate a model where ParA-ATP can dynamically associate to the nucleoid and is hydrolyzed by plasmid-associated ParB, thereby creating nucleoid-bound, self-organizing ParA concentration gradients. We show mathematically that differences between competing ParA concentrations on either side of a plasmid can specify regular plasmid positioning. Such positioning can be achieved regardless of the exact mechanism of plasmid movement, including plasmid diffusion with ParA-mediated immobilization or directed plasmid motion induced by ParB/parC-stimulated ParA structure disassembly. However, we find experimentally that parABC from Escherichia coli plasmid pB171 increases plasmid mobility, inconsistent with diffusion/immobilization. Instead our observations favor directed plasmid motion. Our model predicts less oscillatory ParA dynamics than previously believed, a prediction we verify experimentally. We also show that ParA localization and plasmid positioning depend on the underlying nucleoid morphology, indicating that the chromosomal architecture constrains ParA structure formation. Our directed motion model unifies previously contradictory models for plasmid segregation and provides a robust mechanistic basis for self-organized plasmid spacing that may be widely applicable.

Evidence for a DNA-relay mechanism in ParABS-mediated chromosome segregation

The widely conserved ParABS system plays a major role in bacterial chromosome segregation. How the components of this system work together to generate translocation force and directional motion remains uncertain. Here, we combine biochemical approaches, quantitative imaging and mathematical modeling to examine the mechanism by which ParA drives the translocation of the ParB/parS partition complex in Caulobacter crescentus. Our experiments, together with simulations grounded on experimentally-determined biochemical and cellular parameters, suggest a novel 'DNA-relay' mechanism in which the chromosome plays a mechanical function. In this model, DNA-bound ParA-ATP dimers serve as transient tethers that harness the elastic dynamics of the chromosome to relay the partition complex from one DNA region to another across a ParA-ATP dimer gradient. Since ParA-like proteins are implicated in the partitioning of various cytoplasmic cargos, the conservation of their DNA-binding activity suggests that the DNA-relay mechanism may be a general form of intracellular transport in bacteria.DOI: http://dx.doi.org/10.7554/eLife.02758.001.

A propagating ATPase gradient drives transport of surface-confined cellular cargo

The faithful segregation of duplicated genetic material into daughter cells is critical to all organisms. In many bacteria, the segregation of chromosomes involves transport of "centromere-like" loci over the main body of the chromosome, the nucleoid, mediated by a two-protein partition system: a nonspecific DNA-binding ATPase, ParA, and an ATPase stimulator, ParB, which binds to the centromere-like loci. These systems have previously been proposed to function through a filament-based mechanism, analogous to actin- or microtubule-based movement. Here, we reconstituted the F-plasmid partition system using a DNA-carpeted flow cell as an artificial nucleoid surface and magnetic beads coated with plasmid partition complexes as surface-confined cargo. This minimal system recapitulated directed cargo motion driven by a surface ATPase gradient that propagated with the cargo. The dynamics are consistent with a diffusion-ratchet model, whereby the cargo dynamically establishes, and interacts with, a concentration gradient of the ATPase. A chemophoresis force ensues as the cargo perpetually chases the ATPase gradient, allowing the cargo to essentially "surf" the nucleoid on a continuously traveling wave of the ATPase. Demonstration of this non-filament-based motility mechanism in a biological context establishes a distinct class of motor system used for the transport and positioning of large cellular cargo.