Entropy-driven spatial organization of highly confined polymers: lessons for the bacterial chromosome

Caulobacter chromosome segregation is an ordered multistep process

Despite its fundamental nature, bacterial chromosome segregation remains poorly understood. Viewing segregation as a single process caused multiple proposed mechanisms to appear in conflict and failed to explain how asymmetrically dividing bacteria break symmetry to move only one of their chromosomes. Here, we demonstrate that the ParA ATPase extends from one cell pole and pulls the chromosome by retracting upon association with the ParB DNA-binding protein. Surprisingly, ParA disruption has a specific effect on chromosome segregation that only perturbs the latter stages of this process. Using quantitative high-resolution imaging, we demonstrate that this specificity results from the multistep nature of chromosome translocation. We propose that Caulobacter chromosome segregation follows an ordered pathway of events with distinct functions and mechanisms. Initiation releases polar tethering of the origin of replication, distinction spatially differentiates the two chromosomes, and commitment irreversibly translocates the distal centromeric locus. Thus, much as eukaryotic mitosis involves a sequence of distinct subprocesses, Caulobacter cells also segregate their chromosomes through an orchestrated series of steps. We discuss how the multistep view of bacterial chromosome segregation can help to explain and reconcile outstanding puzzles and frame future investigation.

Biopolymer organization upon confinement

Biopolymers in vivo are typically subject to spatial restraints, either as a result of molecular crowding in the cellular medium or of direct spatial confinement. DNA in living organisms provides a prototypical example of a confined biopolymer. Confinement prompts a number of biophysics questions. For instance, how can the high level of packing be compatible with the necessity to access and process the genomic material? What mechanisms can be adopted in vivo to avoid the excessive geometrical and topological entanglement of dense phases of biopolymers? These and other fundamental questions have been addressed in recent years by both experimental and theoretical means. A review of the results, particularly of those obtained by numerical studies, is presented here. The review is mostly devoted to DNA packaging inside bacteriophages, which is the best studied example both experimentally and theoretically. Recent selected biophysical studies of the bacterial genome organization and of chromosome segregation in eukaryotes are also covered.

A mathematical model for timing the release from sequestration and the resultant Brownian migration of SeqA clusters in E. coli

DNA replication in Escherichia coli is initiated by DnaA binding to oriC, the replication origin. During the process of assembly of the replication factory, the DnaA is released back into the cytoplasm, where it is competent to reinitiate replication. Premature reinitiation is prevented by binding SeqA to newly formed GATC sites near the replication origin. Resolution of the resulting SeqA cluster is one aspect of timing for reinitiation. A Markov model accounting for the competition between SeqA binding and methylation for one or several GATC sites relates the timing to reaction rates, and consequently to the concentrations of SeqA and methylase. A model is proposed for segregation, the motion of the two daughter DNAs into opposite poles of the cell before septation. This model assumes that the binding of SeqA and its subsequent clustering results in loops from both daughter nucleoids attached to the SeqA cluster at the GATC sites. As desequestration occurs, the cluster is divided in two, one associated with each daughter. As the loops of DNA uncoil, the two subclusters migrate apart due to the Brownian ratchet effect of the DNA loop.

From self-assembled vesicles to protocells

Self-assembled vesicles are essential components of primitive cells. We review the importance of vesicles during the origins of life, fundamental thermodynamics and kinetics of self-assembly, and experimental models of simple vesicles, focusing on prebiotically plausible fatty acids and their derivatives. We review recent work on interactions of simple vesicles with RNA and other studies of the transition from vesicles to protocells. Finally we discuss current challenges in understanding the biophysics of protocells, as well as conceptual questions in information transmission and self-replication.

Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.

Strong intranucleoid interactions organize the Escherichia coli chromosome into a nucleoid filament

The stochasticity of chromosome organization was investigated by fluorescently labeling genetic loci in live Escherichia coli cells. In spite of the common assumption that the chromosome is well modeled by an unstructured polymer, measurements of the locus distributions reveal that the E. coli chromosome is precisely organized into a nucleoid filament with a linear order. Loci in the body of the nucleoid show a precision of positioning within the cell of better than 10% of the cell length. The precision of interlocus distance of genomically-proximate loci was better than 4% of the cell length. The measured dependence of the precision of interlocus distance on genomic distance singles out intranucleoid interactions as the mechanism responsible for chromosome organization. From the magnitude of the variance, we infer the existence of an as-yet uncharacterized higher-order DNA organization in bacteria. We demonstrate that both the stochastic and average structure of the nucleoid is captured by a fluctuating elastic filament model.

Towards building a chromosome segregation machine

All organisms, from bacteria to humans, face the daunting task of replicating, packaging and segregating up to two metres (about 6 x 10(9) base pairs) of DNA when each cell divides. This task is carried out up to a trillion times during the development of a human from a single fertilized cell. The strategy by which DNA is replicated is now well understood. But when it comes to packaging and segregating a genome, the mechanisms are only beginning to be understood and are often as variable as the organisms in which they are studied.

A challenge to vaccinology: living organisms trap information

Life couples reproduction of the cell machinery with replication of the genetic program. Both processes are linked to the expression of some information. Over time, reproduction can enhance the information of the machine. We show that accumulation of valuable information results from degradative processes required to make room for novel entities. Degradation systems act as Maxwell's demons, using energy not to make room per se, but to prevent degradation of what has some functional features. This myopic process will accumulate information, whatever its source, in a ratchet-like manner. The consequence is that genes acquired by horizontal transfer as well as viruses will tend to perpetuate in niches where they are functional, creating recurrent conditions for emergence of diseases.

Entropic organization of interphase chromosomes

Chromosomes are not distributed randomly in nuclei. Appropriate positioning can activate (or repress) genes by bringing them closer to active (or inactive) compartments like euchromatin (or heterochromatin), and this is usually assumed to be driven by specific local forces (e.g., involving H bonds between nucleosomes or between nucleosomes and the lamina). Using Monte Carlo simulations, we demonstrate that nonspecific (entropic) forces acting alone are sufficient to position and shape self-avoiding polymers within a confining sphere in the ways seen in nuclei. We suggest that they can drive long flexible polymers (representing gene-rich chromosomes) to the interior, compact/thick ones (and heterochromatin) to the periphery, looped (but not linear) ones into appropriately shaped (ellipsoidal) territories, and polymers with large terminal beads (representing centromeric heterochromatin) into peripheral chromocenters. Flexible polymers tend to intermingle less than others, which is in accord with observations that gene-dense (and so flexible) chromosomes make poor translocation partners. Thus, entropic forces probably participate in the self-organization of chromosomes within nuclei.

Self-avoiding polymer trapped inside a cylindrical pore: Flory free energy and unexpected dynamics

We study the elastic and dynamic behavior of a self-avoiding chain confined inside a cylindrical pore using a Flory-type approach and molecular-dynamics simulations. In the Hookean regime, we find that the effective spring constant of the chain is given by keff approximately N(-1)D(-gamma), where N is the number of monomers and D the diameter of the pore. While the Flory approach reproduces the earlier scaling result gamma=1/3, our simulations confirm a more recent numerical result gamma approximately 0.9 for the computationally accessible regimes. In the absence of hydrodynamic interactions, the relaxation dynamics of a stretched-and-released chain in this regime is characterized by a global relaxation time tauR approximately N2Dgamma with the same exponent gamma for keff. We also discuss how chain relaxation under confinement is influenced by hydrodynamic interactions. In the presence (or absence) of the hydrodynamic interaction, the finite-size effect observed in keff is shown to persist in chain relaxation, resulting in tauR markedly different from previous results.

Linking topology of tethered polymer rings with applications to chromosome segregation and estimation of the knotting length

The Gauss linking number (Ca) of two flexible polymer rings which are tethered to one another is investigated. For ideal random walks, mean linking-squared varies with the square root of polymer length while for self-avoiding walks, linking-squared increases logarithmically with polymer length. The free-energy cost of linking of polymer rings is therefore strongly dependent on degree of self-avoidance, i.e., on intersegment excluded volume. Scaling arguments and numerical data are used to determine the free-energy cost of fixed linking number in both the fluctuation and large-Ca regimes; for ideal random walks, for |Ca|>N;{1/4} , the free energy of catenation is found to grow proportional, variant|Ca/N;{1/4}|;{4/3} . When excluded volume interactions between segments are present, the free energy rapidly approaches a linear dependence on Gauss linking (dF/dCa approximately 3.7k_{B}T) , suggestive of a novel "catenation condensation" effect. These results are used to show that condensation of long entangled polymers along their length, so as to increase excluded volume while decreasing number of statistical segments, can drive disentanglement if a mechanism is present to permit topology change. For chromosomal DNA molecules, lengthwise condensation is therefore an effective means to bias topoisomerases to eliminate catenations between replicated chromatids. The results for mean-square catenation are also used to provide a simple approximate estimate for the "knotting length," or number of segments required to have a knot along a single circular polymer, explaining why the knotting length ranges from approximately 300 for an ideal random walk to 10;{6} for a self-avoiding walk.

Non-specific interactions are sufficient to explain the position of heterochromatic chromocenters and nucleoli in interphase nuclei

The organization of the eukaryote nucleus into functional compartments arises by self-organization both through specific protein-protein and protein-DNA interactions and non-specific interactions that lead to entropic effects, such as e.g. depletion attraction. While many specific interactions have so far been demonstrated, the contributions of non-specific interactions are still unclear. We used coarse-grained molecular dynamics simulations of previously published models for Arabidopsis thaliana chromatin organization to show that non-specific interactions can explain the in vivo localization of nucleoli and chromocenters. Also, we quantitatively demonstrate that chromatin looping contributes to the formation of chromosome territories. Our results are consistent with the previously published Rosette model for Arabidopsis chromatin organization and suggest that chromocenter-associated loops play a role in suppressing chromocenter clustering.

Design features of a mitotic spindle: balancing tension and compression at a single microtubule kinetochore interface in budding yeast

Accurate segregation of duplicated chromosomes ensures that daughter cells get one and only one copy of each chromosome. Errors in chromosome segregation result in aneuploidy and have severe consequences on human health. Incorrect chromosome number and chromosomal instability are hallmarks of tumor cells. Hence, segregation errors are thought to be a major cause of tumorigenesis. A study of the physical mechanical basis of chromosome segregation is essential to understand the processes that can lead to errors. Tremendous progress has been made in recent years in identifying the proteins necessary for chromosome movement and segregation, but the mechanism and structure of critical force generating components and the molecular basis of centromere stiffness remain poorly understood.

Bacteria as computers making computers

Various efforts to integrate biological knowledge into networks of interactions have produced a lively microbial systems biology. Putting molecular biology and computer sciences in perspective, we review another trend in systems biology, in which recursivity and information replace the usual concepts of differential equations, feedback and feedforward loops and the like. Noting that the processes of gene expression separate the genome from the cell machinery, we analyse the role of the separation between machine and program in computers. However, computers do not make computers. For cells to make cells requires a specific organization of the genetic program, which we investigate using available knowledge. Microbial genomes are organized into a paleome (the name emphasizes the role of the corresponding functions from the time of the origin of life), comprising a constructor and a replicator, and a cenome (emphasizing community-relevant genes), made up of genes that permit life in a particular context. The cell duplication process supposes rejuvenation of the machine and replication of the program. The paleome also possesses genes that enable information to accumulate in a ratchet-like process down the generations. The systems biology must include the dynamics of information creation in its future developments.

Entropic unfolding of DNA molecules in nanofluidic channels

Single DNA molecules confined to nanoscale fluidic channels extend along the channel axis in order to minimize their conformational free energy. When such molecules are forced into a nanoscale fluidic channel under the application of an external electric field, monomers near the middle of the DNA molecule may enter first, resulting in a folded configuration with less entropy than an unfolded molecule. The increased free energy of a folded molecule results in two effects: an increase in extension factor per unit length for each segment of the molecule, and a spatially localized force that causes the molecule to spontaneously unfold. The ratio of this unfolding force to hydrodynamic friction per DNA contour length is measured in nanochannels with two different diameters.

Kinetochores and microtubules wed without a ring

Proper chromosome segregation in mitosis requires tethering of spindle microtubules to the kinetochore. Using electron tomography of mammalian cells, McIntosh et al. (2008) now report the presence of fibrils that connect the inner kinetochore to the curved protofilaments at microtubule ends, suggesting a new model for force generation in chromosome movement.

Caulobacter requires a dedicated mechanism to initiate chromosome segregation

Chromosome segregation in bacteria is rapid and directed, but the mechanisms responsible for this movement are still unclear. We show that Caulobacter crescentus makes use of and requires a dedicated mechanism to initiate chromosome segregation. Caulobacter has a single circular chromosome whose origin of replication is positioned at one cell pole. Upon initiation of replication, an 8-kb region of the chromosome containing both the origin and parS moves rapidly to the opposite pole. This movement requires the highly conserved ParABS locus that is essential in Caulobacter. We use chromosomal inversions and in vivo time-lapse imaging to show that parS is the Caulobacter site of force exertion, independent of its position in the chromosome. When parS is moved farther from the origin, the cell waits for parS to be replicated before segregation can begin. Also, a mutation in the ATPase domain of ParA halts segregation without affecting replication initiation. Chromosome segregation in Caulobacter cannot occur unless a dedicated parS guiding mechanism initiates movement.

Compression and stretching of a self-avoiding chain in cylindrical nanopores

Force-induced deformations of a self-avoiding chain confined inside a cylindrical cavity, with diameter D, are probed using molecular dynamics simulations, scaling analysis, and analytical calculations. We obtain and confirm a simple scaling relation -fD approximately R(-9/4) in the strong-compression regime, while for weak deformations, we find fD = -A(R/R0) + B(R/R0)(-2), where A and B are constants, f the external force, and R the chain extension (with R0 its unperturbed value). For a strong stretch, we present a universal, analytical force-extension relation. Our results can be used to analyze the behavior of biomolecules in confinement.

Conformation and dynamics of DNA confined in slitlike nanofluidic channels

Using laser fluorescence microscopy, we study the shape and dynamics of individual DNA molecules in slitlike nanochannels confined to a fraction of their bulk radius of gyration. With a confinement size spanning 2 orders of magnitude, we observe a transition from the de Gennes regime to the Odijk regime in the scaling of both the radius of gyration and the relaxation time. The radius of gyration and the relaxation time follow the predicted scaling in the de Gennes regime, while, unexpectedly, the relaxation time shows a sharp decrease in the Odijk regime. The radius of gyration remains constant in the Odijk regime. Additionally, we report the first measurements of the effect of confinement on the shape anisotropy.

Structure and dynamics of interphase chromosomes

During interphase chromosomes decondense, but fluorescent in situ hybridization experiments reveal the existence of distinct territories occupied by individual chromosomes inside the nuclei of most eukaryotic cells. We use computer simulations to show that the existence and stability of territories is a kinetic effect that can be explained without invoking an underlying nuclear scaffold or protein-mediated interactions between DNA sequences. In particular, we show that the experimentally observed territory shapes and spatial distances between marked chromosome sites for human, Drosophila, and budding yeast chromosomes can be reproduced by a parameter-free minimal model of decondensing chromosomes. Our results suggest that the observed interphase structure and dynamics are due to generic polymer effects: confined Brownian motion conserving the local topological state of long chain molecules and segregation of mutually unentangled chains due to topological constraints.

Intracellular mobility of plasmid DNA is limited by the ParA family of partitioning systems

The highly conserved ParA family of partitioning systems is responsible for positioning DNA and protein complexes in bacteria. In Escherichia coli, plasmids that rely upon these systems are positioned at mid-cell and are repositioned at the quarter-cell positions after replication. How they remain fixed at these positions throughout the cell cycle is unknown. We use fluorescence recovery after photobleaching and time-lapse microscopy to measure plasmid mobility in living E. coli cells. We find that a minimalized version of plasmid RK2 that lacks its Par system is highly mobile, that the intact RK2 plasmid is relatively immobile, and that the addition of a Par system to the minimalized RK2 plasmid limits its mobility to that of the intact RK2. Mobility is thus the default state, and Par systems are required not only to position plasmids, but also to hold them at these positions. The intervention of Par systems is required continuously throughout the cell cycle to restrict plasmid movement that would, if unrestricted, subvert the segregation process. Our results reveal an important function for Par systems in plasmid DNA segregation that is likely to be conserved in bacteria.

MukB colocalizes with the oriC region and is required for organization of the two Escherichia coli chromosome arms into separate cell halves

The circular Escherichia coli chromosome is organized by bidirectional replication into two equal left and right arms (replichores). Each arm occupies a separate cell half, with the origin of replication (oriC) at mid-cell. E. coli MukBEF belongs to the ubiquitous family of SMC protein complexes that play key roles in chromosome organization and processing. In mukBEF mutants, viability is restricted to low temperature with production of anucleate cells, reflecting chromosome segregation defects. We show that in mukB mutant cells, the two chromosome arms do not separate into distinct cell halves, but extend from pole to pole with the oriC region located at the old pole. Mutations in topA, encoding topoisomerase I, do not suppress the aberrant positioning of chromosomal loci in mukB cells, despite suppressing the temperature-sensitivity and production of anucleate cells. Furthermore, we show that MukB and the oriC region generally colocalize throughout the cell cycle, even when oriC localization is aberrant. We propose that MukBEF initiates the normal bidirectional organization of the chromosome from the oriC region.

Time scale of entropic segregation of flexible polymers in confinement: implications for chromosome segregation in filamentous bacteria

We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. This result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation.

Chromosome segregation in Escherichia coli division: a free energy-driven string model

Although the mechanisms of eukaryotic chromosome segregation and cell division have been elucidated to a certain extent, those for bacteria remain largely unknown. Here we present a computational string model for simulating the dynamics of Escherichia coli chromosome segregation. A novel thermal-average force field accounting for stretching, bending, volume exclusion, friction and random fluctuation is introduced. A Langevin equation is used to simulate the chromosome structural changes. The mechanism of chromosome segregation is thereby postulated as a result of free energy-driven structural optimization with replication introduced chromosomal mass increase. Predictions of the model agree well with observations of fluorescence labeled chromosome loci movement in living cells. The results demonstrate the possibility of a mechanism of chromosome segregation that does not involve cytoskeletal guidance or advanced apparatus in an E. coli cell. The model also shows that DNA condensation of locally compacted domains is a requirement for successful chromosome segregation. Simulations also imply that the shape-determining protein MreB may play a role in the segregation via modification of the membrane pressure.

Confined space and effective interactions of multiple self-avoiding chains

We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semidilute solutions. Our main result is that the free energy for overlapping n chains is independent of chain length and scales as n9/4, slowly crossing over to n3, as n increases. For strongly confined polymers inside a spherical cavity, we show that rearranging the chains does not cost an additional free energy. Our results imply that, during cell cycle, global reorganization of eukaryotic chromosomes in a large cell nucleus could be readily achieved.

Swollen-to-globular transition of a self-avoiding polymer confined in a soft tube

Monte Carlo simulations are presented for the structural transition of a self-avoiding polymer confined in an elastic soft tube, within the Helfrich energy model for the description of a fluctuating surface. Based on the simulation data of the maximum extension of the confined polymer in the tube and of the tube radius, a swollen-to-globular transition is identified where the confined polymer undergoes an abrupt transition from a shape elongated along the tube axis to a globule that is of much smaller dimensions than that of an unperturbed polymer. An extended regime in the parameter space has been explored where various scaling properties can be viewed.

DNA-protein interactions and bacterial chromosome architecture

Bacteria, like eukaryotic organisms, must compact the DNA molecule comprising their genome and form a functional chromosome. Yet, bacteria do it differently. A number of factors contribute to genome compaction and organization in bacteria, including entropic effects, supercoiling and DNA-protein interactions. A gamut of new experimental techniques have allowed new advances in the investigation of these factors, and spurred much interest in the dynamic response of the chromosome to environmental cues, segregation, and architecture, during both exponential and stationary phases. We review these recent developments with emphasis on the multifaceted roles that DNA-protein interactions play.