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arXiv2010

Crowding effects in non-equilibrium transport through nano-channels

Transport through nano-channels plays an important role in many biological processes and industrial applications. Gaining insights into the functioning of biological transport processes and the design of man-made nano-devices requires an understanding of the basic physics of such transport. A simple exclusion process has proven to be very useful in ex- plaining the properties of several artificial and biological nano-channels. It is particularly useful for modeling the influence of inter-particle interactions on transport characteristics. In this paper, we explore several models of the exclusion process using a mean field approach and computer simulations. We examine the effects of crowding inside the channel and its immediate vicinity on the mean flux and the transport times of single molecules. Finally, we discuss the robustness of the theory's predictions with respect to the crucial characteristics of the hindered diffusion in nano-channels that need to be included in the model.

cond-mat.stat-mech↗

arXiv2010

Electrostatic models of electron-driven proton transfer across a lipid membrane

We present two models for electron-driven uphill proton transport across lipid membranes, with the electron energy converted to the proton gradient via the electrostatic interaction. In the first model, associated with the cytochrome c oxidase complex in the inner mitochondria membranes, the electrostatic coupling to the site occupied by an electron lowers the energy level of the proton-binding site, making the proton transfer possible. In the second model, roughly describing the redox loop in a nitrate respiration of E. coli bacteria, an electron displaces a proton from the negative side of the membrane to a shuttle, which subsequently diffuses across the membrane and unloads the proton to its positive side. We show that both models can be described by the same approach, which can be significantly simplified if the system is separated into several clusters, with strong Coulomb interaction inside each cluster and weak transfer couplings between them. We derive and solve the equations of motion for the electron and proton creation/annihilation operators, taking into account the appropriate Coulomb terms, tunnel couplings, and the interaction with the environment. For the second model, these equations of motion are solved jointly with a Langevin-type equation for the shuttle position. We obtain expressions for the electron and proton currents and determine their dependence on the electron and proton voltage build-ups, on-site charging energies, reorganization energies, temperature, and other system parameters. We show that the quantum yield in our models can be up to 100% and the power-conversion efficiency can reach 35%.

cond-mat.mes-hall↗

arXiv2013

First-passage problems in DNA replication: effects of template tension on stepping and exonuclease activities of a DNA polymerase motor

A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits the template as the track for its own motor-like mechanical movement. In the polymerase mode it elongates the nascent DNA by one nucleotide in each step. But, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode. In the latter mode it excises the wrong nucleotide before switching back to its polymerase mode. We develop a stochastic kinetic model of DNA replication that mimics an {\it in-vitro} experiment where a single-stranded DNA, subjected to a mechanical tension $F$, is converted to a double-stranded DNA by a single DNAP. The $F$-dependence of the average rate of replication, which depends on the rates of both polymerase and exonuclease activities of the DNAP, is in good qualitative agreement with the corresponding experimental results. We introduce 9 novel distinct {\it conditional dwell times} of a DNAP. Using the methods of first-passage times, we also derive the exact analytical expressions for the probability distributions of these conditional dwell times. The predicted $F$-dependence of these distributions are, in principle, accessible to single-molecule experiments.

q-bio.SC↗

arXiv2016

Proofreading of DNA Polymerase: a new kinetic model with higher-order terminal effects

The fidelity of DNA replication by DNA polymerase (DNAP) has long been an important issue in biology. While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP which consists of both a polymerase site and an exonuclease (proofreading) site, there were quite few theoretical studies on the fidelity issue. The first model which explicitly considered both sites was proposed in 1970s' and the basic idea was widely accepted by later models. However, all these models did not systematically and rigorously investigate the dominant factor on DNAP fidelity, i.e, the higher-order terminal effects through which the polymerization pathway and the proofreading pathway coordinate to achieve high fidelity. In this paper, we propose a new and comprehensive kinetic model of DNAP based on some recent experimental observations, which includes previous models as special cases. We present a rigorous and unified treatment of the corresponding steady-state kinetic equations of any-order terminal effects, and derive analytical expressions for fidelity in terms of kinetic parameters under bio-relevant conditions. These expressions offer new insights on how the the higher-order terminal effects contribute substantially to the fidelity in an order-by-order way, and also show that the polymerization-and-proofreading mechanism is dominated only by very few key parameters. We then apply these results to calculate the fidelity of some real DNAPs, which are in good agreements with previous intuitive estimates given by experimentalists.

q-bio.SC↗

arXiv2013

Ion transport through a graphene nanopore

Molecular dynamics simulation is utilized to investigate the ionic transport of NaCl in solution through a graphene nanopore under an applied electric field. Results show the formation of concentration polarization layers in the vicinity of the graphene sheet. The non-uniformity of the ion distribution gives rise to an electric pressure which drives vortical motions in the fluid if the electric field is sufficiently strong to overcome the influence of viscosity and thermal fluctuations. The relative importance of hydrodynamic transport and thermal fluctuations in determining the pore conductivity is investigated. A second important effect that is observed is the mass transport of water through the nanopore, with an average velocity proportional to the applied voltage and independent of the pore diameter. The flux arises as a consequence of the asymmetry in the ion distribution with respect to reflection about the plane of the graphene sheet. The accumulation of liquid molecules in the vicinity of the nanopore due to reorientation of the water dipoles by the local electric field is seen to result in a local increasein the liquid density. Results confirm that the electric conductance is proportional to the nanopore diameter for the parameter regimes that we simulated. The occurrence of fluid vortices is found to result in an increase in the effective electrical conductance.

physics.bio-ph↗

arXiv2020

A Python based automated tracking routine for myosin II filaments

The study of motor protein dynamics within cytoskeletal networks is of high interest to physicists and biologists to understand how the dynamics and properties of individual motors lead to cooperative effects and control of overall network behaviour. Here, we report a method to detect and track muscular myosin II filaments within an actin network tethered to supported lipid bilayers. Based on the characteristic shape of myosin II filaments, this automated tracking routine allowed us to follow the position and orientation of myosin II filaments over time, and to reliably classify their dynamics into segments of diffusive and processive motion based on the analysis of displacements and angular changes between time steps. This automated, high throughput method will allow scientists to efficiently analyse motor dynamics in different conditions, and will grant access to more detailed information than provided by common tracking methods, without any need for time consuming manual tracking or generation of kymographs.

q-bio.SC↗

arXiv2016

Dynamics in Steady State In Vitro Acto-Myosin Networks

It is well known that many biochemical processes in the cell such as gene regulation, growth signals and activation of ion channels, rely on mechanical stimuli. However, the mechanism by which mechanical signals propagate through cells is not as well understood. In this review we focus on stress propagation in a minimal model for cell elasticity, actomyosin networks, which are comprised of a sub-family of cytoskeleton proteins. After giving an overview of th actomyosin network components, structure and evolution we review stress propagation in these materials as measured through the correlated motion of tracer beads. We also discuss the possibility to extract structural features of these networks from the same experiments. We show that stress transmission through these networks has two pathways, a quickly dissipative one through the bulk, and a long ranged weakly dissipative one through the pre-stressed actin network.

cond-mat.soft↗

arXiv2010

Segregation of receptor-ligand complexes in cell adhesion zones: Phase diagrams and role of thermal membrane roughness

The adhesion zone of immune cells, the 'immunological synapse', exhibits characteristic domains of receptor-ligand complexes. The domain formation is likely caused by a length difference of the receptor-ligand complexes, and has been investigated in experiments in which T cells adhere to supported membranes with anchored ligands. For supported membranes with two types of anchored ligands, MHCp and ICAM1, that bind to the receptors TCR and LFA1 in the cell membrane, the coexistence of domains of TCR-MHCp and LFA1-ICAM1 complexes in the cell adhesion zone has been observed for a wide range of ligand concentrations and affinities. For supported membranes with long and short ligands that bind to the same cell receptor CD2, in contrast, domain coexistence has been observed for a rather narrow ratio of ligand concentrations. In this article, we determine detailed phase diagrams for cells adhering to supported membranes with a statistical-physical model of cell adhesion. We find a characteristic difference between the adhesion scenarios in which two types of ligands in a supported membrane bind (i) to the same cell receptor or (ii) to two different cell receptors, which helps to explain the experimental observations. Our phase diagrams fully include thermal shape fluctuations of the cell membranes on nanometer scales, which lead to a critical point for the domain formation and to a cooperative binding of the receptors and ligands.

cond-mat.soft↗

arXiv2011

Condensation of actin filaments pushing against a barrier

We develop a model to describe the force generated by the polymerization of an array of parallel biofilaments. The filaments are assumed to be coupled only through mechanical contact with a movable barrier. We calculate the filament density distribution and the force-velocity relation with a mean-field approach combined with simulations. We identify two regimes: a non-condensed regime at low force in which filaments are spread out spatially, and a condensed regime at high force in which filaments accumulate near the barrier. We confirm a result previously known from other related studies, namely that the stall force is equal to N times the stall force of a single filament. In the model studied here, the approach to stalling is very slow, and the velocity is practically zero at forces significantly lower than the stall force.

cond-mat.stat-mech↗

arXiv2012

Requirements for contractility in disordered cytoskeletal bundles

Actomyosin contractility is essential for biological force generation, and is well understood in highly organized structures such as striated muscle. Additionally, actomyosin bundles devoid of this organization are known to contract both in vivo and in vitro, which cannot be described by standard muscle models. To narrow down the search for possible contraction mechanisms in these systems, we investigate their microscopic symmetries. We show that contractile behavior requires non-identical motors that generate large enough forces to probe the nonlinear elastic behavior of F-actin. This suggests a role for filament buckling in the contraction of these bundles, consistent with recent experimental results on reconstituted actomyosin bundles.

physics.bio-ph↗

arXiv2013

Active Gel Model of Amoeboid Cell Motility

We develop a model of amoeboid cell motility based on active gel theory. Modeling the motile apparatus of a eukaryotic cell as a confined layer of finite length of poroelastic active gel permeated by a solvent, we first show that, due to active stress and gel turnover, an initially static and homogeneous layer can undergo a contractile-type instability to a polarized moving state in which the rear is enriched in gel polymer. This agrees qualitatively with motile cells containing an actomyosin-rich uropod at their rear. We find that the gel layer settles into a steadily moving, inhomogeneous state at long times, sustained by a balance between contractility and filament turnover. In addition, our model predicts an optimal value of the gel-susbstrate adhesion leading to maximum layer speed, in agreement with cell motility assays. The model may be relevant to motility of cells translocating in complex, confining environments that can be mimicked experimentally by cell migration through microchannels.

physics.bio-ph↗

arXiv2013

Mesoscopic model for filament orientation in growing actin networks: the role of obstacle geometry

Propulsion by growing actin networks is a universal mechanism used in many different biological systems. Although the core molecular machinery for actin network growth is well preserved in most cases, the geometry of the propelled obstacle can vary considerably. In recent years, filament orientation distribution has emerged as an important observable characterizing the structure and dynamical state of the growing network. Here we derive several continuum equations for the orientation distribution of filaments growing behind stiff obstacles of various shapes and validate the predicted steady state orientation patterns by stochastic computer simulations based on discrete filaments. We use an ordinary differential equation approach to demonstrate that for flat obstacles of finite size, two fundamentally different orientation patterns peaked at either +35/-35 or +70/0/-70 degrees exhibit mutually exclusive stability, in agreement with earlier results for flat obstacles of very large lateral extension. We calculate and validate phase diagrams as a function of model parameters and show how this approach can be extended to obstacles with piecewise straight contours. For curved obstacles, we arrive at a partial differential equation in the continuum limit, which again is in good agreement with the computer simulations. In all cases, we can identify the same two fundamentally different orientation patterns, but only within an appropriate reference frame, which is adjusted to the local orientation of the obstacle contour. Our results suggest that two fundamentally different network architectures compete with each other in growing actin networks, irrespective of obstacle geometry, and clarify how simulated and electron tomography data have to be analyzed for non-flat obstacle geometries.

physics.bio-ph↗

arXiv2014

Efficiency of cellular information processing

We show that a rate of conditional Shannon entropy reduction, characterizing the learning of an internal process about an external process, is bounded by the thermodynamic entropy production. This approach allows for the definition of an informational efficiency that can be used to study cellular information processing. We analyze three models of increasing complexity inspired by the E. coli sensory network, where the external process is an external ligand concentration jumping between two values. We start with a simple model for which ATP must be consumed so that a protein inside the cell can learn about the external concentration. With a second model for a single receptor we show that the rate at which the receptor learns about the external environment can be nonzero even without any dissipation inside the cell since chemical work done by the external process compensates for this learning rate. The third model is more complete, also containing adaptation. For this model we show inter alia that a bacterium in an environment that changes at a very slow time-scale is quite inefficient, dissipating much more than it learns. Using the concept of a coarse-grained learning rate, we show for the model with adaptation that while the activity learns about the external signal the option of changing the methylation level increases the concentration range for which the learning rate is substantial.

physics.bio-ph↗

arXiv2014

Collective force generated by multiple biofilaments can exceed the sum of forces due to individual ones

Collective dynamics and force generation by cytoskeletal filaments are crucial in many cellular processes. Investigating growth dynamics of a bundle of N independent cytoskeletal filaments pushing against a wall, we show that chemical switching (ATP/GTP hydrolysis) leads to a collective phenomenon that is currently unknown. Obtaining force-velocity relations for different models that capture chemical switching, we show, analytically and numerically, that the collective stall force of N filaments is greater than N times the stall force of a single filament. Employing an exactly solvable toy model, we analytically prove the above result for N=2. We, further, numerically show the existence of this collective phenomenon, for N>=2, in realistic models (with random and sequential hydrolysis) that simulate actin and microtubule bundle growth. We make quantitative predictions for the excess forces, and argue that this collective effect is related to the non-equilibrium nature of chemical switching.

physics.bio-ph↗

arXiv2014

Stochastic dynamics and mechanosensitivity of myosin II minifilaments

Tissue cells are in a state of permanent mechanical tension that is maintained mainly by myosin II minifilaments, which are bipolar assemblies of tens of myosin II molecular motors contracting actin networks and bundles. Here we introduce a stochastic model for myosin II minifilaments as two small myosin II motor ensembles engaging in a stochastic tug-of-war. Each of the two ensembles is described by the parallel cluster model that allows us to use exact stochastic simulations and at the same time to keep important molecular details of the myosin II cross-bridge cycle. Our simulation and analytical results reveal a strong dependence of myosin II minifilament dynamics on environmental stiffness that is reminiscent of the cellular response to substrate stiffness. For small stiffness, minifilaments form transient crosslinks exerting short spikes of force with negligible mean. For large stiffness, minifilaments form near permanent crosslinks exerting a mean force which hardly depends on environmental elasticity. This functional switch arises because dissociation after the power stroke is suppressed by force (catch bonding) and because ensembles can no longer perform the power stroke at large forces. Symmetric myosin II minifilaments perform a random walk with an effective diffusion constant which decreases with increasing ensemble size, as demonstrated for rigid substrates with an analytical treatment.

q-bio.SC↗

arXiv2015

Single molecule thermodynamics of ATP synthesis by F$_1$-ATPase

F$_\mathrm{o}$F$_1$-ATP synthase is a factory for synthesizing ATP in virtually all cells. Its core machinery is the subcomplex F$_1$-motor (F$_1$-ATPase) and performs the reversible mechanochemical coupling. Isolated F$_1$-motor hydrolyzes ATP, which is accompanied by unidirectional rotation of its central $γ$-shaft. When a strong opposing torque is imposed, the $γ$-shaft rotates in the opposite direction and drives the F$_1$-motor to synthesize ATP. This mechanical-to-chemical free-energy transduction is the final and central step of the multistep cellular ATP-synthetic pathway. Here, we determined the amount of mechanical work exploited by the F$_1$-motor to synthesize an ATP molecule during forced rotations using methodology combining a nonequilibrium theory and single molecule measurements of responses to external torque. We found that the internal dissipation of the motor is negligible even during rotations far from a quasistatic process.

physics.bio-ph↗

arXiv2015

Many-body effects in tracer particle diffusion with applications for single-protein dynamics on DNA

30% of the DNA in E. coli bacteria is covered by proteins. Such high degree of crowding affect the dynamics of generic biological processes (e.g. gene regulation, DNA repair, protein diffusion etc.) in ways that are not yet fully understood. In this paper, we theoretically address the diffusion constant of a tracer particle in a one dimensional system surrounded by impenetrable crowder particles. While the tracer particle always stays on the lattice, crowder particles may unbind to a surrounding bulk and rebind at another or the same location. In this scenario we determine how the long time diffusion constant ${\cal D}$ (after many unbinding events) depends on (i) the unbinding rate of crowder particles $k_{\rm off}$, and (ii) crowder particle line density $ρ$, from simulations (Gillespie algorithm) and analytical calculations. For small $k_{\rm off}$, we find ${\cal D}\sim k_{\rm off}/ρ^2$ when crowder particles are immobile on the line, and ${\cal D}\sim \sqrt{D k_{\rm off}}/ρ$ when they are diffusing; $D$ is the free particle diffusion constant. For large $k_{\rm off}$, we find agreement with mean-field results which do not depend on $k_{\rm off}$. From literature values of $k_{\rm off}$ and $D$, we show that the small $k_{\rm off}$-limit is relevant for in vivo protein diffusion on a crowded DNA. Our results applies to single-molecule tracking experiments.

cond-mat.stat-mech↗

arXiv2016

Nonlinear self-adapting wave patterns

We propose a new type of traveling wave pattern, one that can adapt to the size of physical system in which it is embedded. Such a system arises when the initial state has an instability that extends down to zero wavevector, connecting at that point to two symmetry modes of the underlying dynamical system. The Min system of proteins in E. coli is such as system with the symmetry emerging from the global conservation of two proteins, MinD and MinE. For this and related systems, traveling waves can adiabatically deform as the system is increased in size without the increase in node number that would be expected for an oscillatory version of a Turing instability containing an allowed wavenumber band with a finite minimum.

q-bio.SC↗