Surfing on protein waves: modeling the bacterial genome partitioning

International audienceControlled motion and positioning of colloids and macromolecular complexes in a fluid, as well as catalytic particles in active environments, are fundamental processes in physics, chemistry and biology. Here we focus on an active biological system for which precise experimental results are available. Our work is fully inspired by studies of one of the most widespread and ancient mechanisms of liquid phase macromolecular segregation and positioning known in nature: bacterial DNA segregation systems. Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component, fueled by adenosine triphosphate machinery called the partition complex. We can distinguish two steps: (i) a process of phase transition [2,3] to built a membraneless region of high protein concentration (partition complex) (ii) the action of molecular motor action upon the complex to create a chemical force. We present a phenomenological model [1] accounting for the dynamics 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 volumetric chemophoresis force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This description captures experimental observations: dynamic oscillations of complex components, complex separation and symmetrical positioning. The predictions of our model are in agreement with and provide substantial insight into recent experiments. From a non-linear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and travelling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry. We also discuss the phase transition mechanism giving rise to macromolecular assembly of proteins. Our predictions are compared to Super Resolution microscopy and microbiology experiments [1,2,3].[1] Walter J.-C., Dorignac J., Lorman V., Rech J., Bouet J.-Y., Nollmann M., Palmeri J., Parmeggiani A. and Geniet F., Phys. Rev. Lett. 119, 028101 (2017).[2] Debaugny R., Sanchez A., Rech J., Labourdette D., Dorignac J., Geniet F., Palmeri J., Parmeggiani A., Boudsocq, Leberre V., Walter* J.-C. and Bouet* J.-Y Mol. Syst. Biol. 14, e8516 (2018)[3] David G., Walter J.-C., Broedersz C., Dorignac J., Geniet F., Parmeggiani A., Walliser N.-O. and Palmeri J., submitted to Phys. Rev. Lett. [arXiv/1811.09234] (2019)

Surfing on protein waves: modeling the bacterial genome partitioning

International audienceControlled motion and positioning of colloids and macromolecular complexes in a fluid, as well as catalytic particles in active environments, are fundamental processes in physics, chemistry and biology. Here we focus on an active biological system for which precise experimental results are available. Our work is fully inspired by studies of one of the most widespread and ancient mechanisms of liquid phase macromolecular segregation and positioning known in nature: bacterial DNA segregation systems. Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component, fueled by adenosine triphosphate machinery called the partition complex. We can distinguish two steps: (i) a process of phase transition [2,3] to built a membraneless region of high protein concentration (partition complex) (ii) the action of molecular motor action upon the complex to create a chemical force. We mainly present a phenomenological model of reaction-diffusion for two families of proteins [1] describing the step (ii), the dynamics of the segregation of paired chromosomes. We also discuss the step (i) the phase transition mechanism giving rise to macromolecular assembly of proteins. Our predictions are compared to Super Resolution microscopy and microbiology experiments [1,2,3].[1] Walter J.-C., Dorignac J., Lorman V., Rech J., Bouet J.-Y., Nollmann M., Palmeri J., Parmeggiani A. and Geniet F., Phys. Rev. Lett. 119, 028101 (2017).[2] Debaugny R., Sanchez A., Rech J., Labourdette D., Dorignac J., Geniet F., Palmeri J., Parmeggiani A., Boudsocq, Leberre V., Walter* J.-C. and Bouet* J.-Y Mol. Syst. Biol. 14, e8516 (2018)[3] David G., Walter J.-C., Broedersz C., Dorignac J., Geniet F., Parmeggiani A., Walliser N.-O. and Palmeri J., submitted to Phys. Rev. Lett. [arXiv/1811.09234] (2019)

Unwinding Dynamics of a Helically Wrapped Polymer

We study the rotational dynamics of a flexible polymer initially wrapped around a rigid rod and unwinding from it. This dynamics is of interest in several problems in biology and constitutes a fundamental instance of polymer relaxation from a state of minimal entropy. We investigate the dynamics of several quantities such as the total and local winding angles and metric quantities. The results of simulations performed in two and three dimensions, with and without self-avoidance, are explained by a theory based on scaling arguments and on a balance between frictional and entropic forces. The early stage of the dynamics is particularly rich, being characterized by three coexisting phases.Comment: 9 pages, 9 figure

Unwinding relaxation dynamics of polymers

The relaxation dynamics of a polymer wound around a fixed obstacle constitutes a fundamental instance of polymer with twist and torque and it is of relevance also for DNA denaturation dynamics. We investigate it by simulations and Langevin equation analysis. The latter predicts a relaxation time scaling as a power of the polymer length times a logarithmic correction related to the equilibrium fluctuations of the winding angle. The numerical data support this result and show that at short times the winding angle decreases as a power-law. This is also in agreement with the Langevin equation provided a winding-dependent friction is used, suggesting that such reduced description of the system captures the basic features of the problem.Comment: 4 pages, 5 figures. Accepted for publication in Phys. Rev. Let

Rotational dynamics of entangled polymers

Some recent results on the rotational dynamics of polymers are reviewed and extended. We focus here on the relaxation of a polymer, either flexible or semiflexible, initially wrapped around a rigid rod. We also study the steady polymer rotation generated by a constant torque on the rod. The interplay of frictional and entropic forces leads to a complex dynamical behavior characterized by non-trivial universal exponents. The results are based on extensive simulations of polymers undergoing Rouse dynamics and on an analytical approach using force balance and scaling arguments. The analytical results are in general in good agreement with the simulations, showing how a simplified approach can correctly capture the complex dynamical behavior of rotating polymers.Comment: 13 pages; 7 figures; proceedings of the International Workshop on "Brownian Motion in Confined Geometries", Max Planck Institute for the Physics of Complex Systems in Dresden from 17 - 21 March 2014; to appear in EPJ-S

Probing Hybridization parameters from microarray experiments: nearest neighbor model and beyond

In this article it is shown how optimized and dedicated microarray experiments can be used to study the thermodynamics of DNA hybridization for a large number of different conformations in a highly parallel fashion. In particular, free energy penalties for mismatches are obtained in two independent ways and are shown to be correlated with values from melting experiments in solution reported in the literature. The additivity principle, which is at the basis of the nearest-neighbor model, and according to which the penalty for two isolated mismatches is equal to the sum of the independent penalties, is thoroughly tested. Additivity is shown to break down for a mismatch distance below 5 nt. The behavior of mismatches in the vicinity of the helix edges, and the behavior of tandem mismatches are also investigated. Finally, some thermodynamic outlying sequences are observed and highlighted. These sequences contain combinations of GA mismatches. The analysis of the microarray data reported in this article provides new insights on the DNA hybridization parameters and can help to increase the accuracy of hybridization-based technologies.Comment: 13 pages, 11 figures, 1 table, Supplementary Data available in Appendi

Motor proteins traffic regulation by supply-demand balance of resources

In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerised tubulin heterodimers). We present analytical results for the density profiles of bound motors, the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir.Comment: 31 pages, 10 figure

Torque-Induced Rotational Dynamics in Polymers: Torsional Blobs and Thinning

By using the blob theory and computer simulations, we investigate the properties of a linear polymer performing a stationary rotational motion around a long impenetrable rod. In particular, in the simulations the rotation is induced by a torque applied to the end of the polymer that is tethered to the rod. Three different regimes are found, in close analogy with the case of polymers pulled by a constant force at one end. For low torques the polymer rotates maintaining its equilibrium conformation. At intermediate torques the polymer assumes a trumpet shape, being composed by blobs of increasing size. At even larger torques the polymer is partially wrapped around the rod. We derive several scaling relations between various quantities as angular velocity, elongation and torque. The analytical predictions match the simulation data well. Interestingly, we find a "thinning" regime where the torque has a very weak (logarithmic) dependence on the angular velocity. We discuss the origin of this behavior, which has no counterpart in polymers pulled by an applied force.Comment: 30 pages, 8 figures, 1 TOC figure; video abstract at https://youtu.be/LwicoSkh3m