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arXiv2013

Maximum power operation of interacting molecular motors

We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the non-interacting system, in a wide range of biologically compatible scenarios. We furthermore consider the case where the motor-motor interaction directly affects the internal chemical cycle and investigate the effect on the system dynamics and thermodynamics.

cond-mat.stat-mech↗

arXiv2013

Sacrificial bonds and hidden length in biomaterials -- a kinetic, constitutive description of strength and toughness in bone

Sacrificial bonds and hidden length in structural molecules account for the greatly increased fracture toughness of biological materials compared to synthetic materials without such structural features, by providing a molecular-scale mechanism for energy dissipation. One example is in the polymeric glue connection between collagen fibrils in animal bone. In this paper, we propose a simple kinetic model that describes the breakage of sacrificial bonds and the release of hidden length, based on Bell's theory. We postulate a master equation governing the rates of bond breakage and formation. This enables us to predict the mechanical behavior of a quasi-one-dimensional ensemble of polymers at different stretching rates. We find that both the rupture peak heights and maximum stretching distance increase with the stretching rate. In addition, our theory naturally permits the possibility of self-healing in such biological structures.

cond-mat.soft↗

arXiv2013

Optimal Channel Efficiency in a Sensory Network

We show that the entropy of the distribution of avalanche lifetimes in the Kinouchi-Copelli model always achieves a maximum jointly with the dynamic range. This is noteworthy and nontrivial because while the dynamic range is an equilibrium average measure of the sensibility of a sensory system to a stimulus, the entropy of relaxation times is a purely dynamical quantity, independent of the stimulus rate, that can be interpreted as the efficiency of the network seen as a communication channel. The newly found optimization occurs for all topologies we tested, even when the distribution of avalanche lifetimes itself is not a power-law and when the entropy of the size distribution of avalanches is not concomitantly maximized, strongly suggesting that dynamical rules allowing a proper temporal matching of the states of the interacting neurons is the key for achieving good performance in information processing, rather than increasing the number of available units.

physics.bio-ph↗

arXiv2013

Elastic Properties and Line Tension of Self-Assembled Bilayer Membranes

The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. Finally the region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.

physics.bio-ph↗

arXiv2013

Uniform asymptotic approximation of diffusion to a small target

The problem of the time required for a diffusing molecule, within a large bounded domain, to first locate a small target is prevalent in biological modeling. Here we study this problem for a small spherical target. We develop uniform in time asymptotic expansions in the target radius of the solution to the corresponding diffusion equation. Our approach is based on combining short-time expansions using pseudo-potential approximations with long-time expansions based on first eigenvalue and eigenfunction approximations. These expansions allow the calculation of corresponding expansions of the first passage time density for the diffusing molecule to find the target. We demonstrate the accuracy of our method in approximating the first passage time density and related statistics for the spherically symmetric problem where the domain is a large concentric sphere about a small target centered at the origin.

physics.bio-ph↗

arXiv2012

Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin Model

An analytic formula for the density of states of Wako-Saito-Munoz-Eaton model, for a simple class of beta-hairpins, is obtained. Under certain simplifying assumptions on the structure of the native contacts and the values of local entropy, the partition function zeros are also obtained in analytic forms. The zeros are uniformly distributed on a circle, exhibiting a first-order-like nature of the folding transition. After introducing hydrophobic core at the central region of the hairpin, the zeros are shown to distribute uniformly on two concentric circles corresponding to the hydrophobic collapse and the transition to the fully folded conformations. The dependence of the distribution of the zeros on the position of the hydrophobic core, is shown to have a clear physical interpretation. The exact partition function zeros for a hairpin with a more complex structure of native contacts, the 16 C-terminal residues of streptococcal protein G B1, are also numerically computed, and their loci are also shown to be closely approximated by concentric circles.

cond-mat.stat-mech↗

arXiv2013

Rerouting Excitation Transfer in the Fenna-Matthews-Olson Complex

We investigate, using the Hierarchy method, the entanglement and the excitation transfer efficiency of the Fenna-Matthews-Olson complex under two different local modifications: the suppression of transitions between particular sites and localized changes to the protein environment. We find that inhibiting the connection between the site-5 and site-6, or disconnecting site-5 from the complex completely, leads to an dramatic enhancement of the entanglement between site-6 and site-7. Similarly, the transfer efficiency actually increases if site-5 is disconnected from the complex entirely. We further show that if site-5 and site-7 are conjointly removed, the efficiency falls. This suggests that while not contributing to the transport efficiency in a normal complex, site-5 introduces a redundant transport route in case of damage to site-7. Our results suggest an overall robustness of excitation energy transfer in the FMO complex under mutations, local defects, and other abnormal situations.

q-bio.BM↗

arXiv2013

Elasticity of cross-linked semiflexible biopolymers under tension

Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced inter-chain bonds (cross-links) represented by harmonic springs. Within this model, we compute the force-extension curve and the differential stiffness exactly and discuss several limiting cases. Cross-links effectively stiffen the chain pair by reducing thermal fluctuations transverse to the force and alignment direction. The extra alignment due to cross-links increases both with growing number and with growing strength of the cross-links, and is most prominent for small force f. For large f, the additional, cross-link-induced extension is subdominant except for the case of linking the chains rigidly and continuously along their contour. In this combined limit, we recover asymptotically the elasticity of a weakly bending wormlike chain without constraints, stiffened by a factor four. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.

physics.bio-ph↗

arXiv2013

Linear surface roughness growth and flow smoothening in a three-dimensional biofilm model

The sessile microbial communities known as biofilms exhibit varying architectures as environmental factors are varied, which for immersed biofilms includes the shear rate of the surrounding flow. Here we modify an established agent-based biofilm model to include affine flow, and employ it to analyse the growth of surface roughness of single-species, three-dimensional biofilms. We find linear growth laws for surface geometry in both horizontal and vertical directions, and measure the thickness of the active surface layer, which is shown to anti-correlate with roughness. Flow is shown to monotonically reduce surface roughness without affecting the thickness of the active layer. We argue that the rapid roughening is due to non-local surface interactions mediated by the nutrient field, which are curtailed when advection competes with diffusion. We further argue the need for simplified models to elucidate the underlying mechanisms coupling flow to growth.

physics.bio-ph↗

arXiv2013

Anomalous diffusion of proteins in sheared lipid membranes

We use coarse grained molecular dynamics simulations to investigate diffusion properties of sheared lipid membranes with embedded transmembrane proteins. In membranes without proteins, we find normal in-plane diffusion of lipids in all flow conditions. Protein embedded membranes behave quite differently: by imposing a simple shear flow and sliding the monolayers of the membrane over each other, the motion of protein clusters becomes strongly superdiffusive in the shear direction. In such a circumstance, subdiffusion regime is predominant perpendicular to the flow. We show that superdiffusion is a result of accelerated chaotic motions of protein--lipid complexes within the membrane voids, which are generated by hydrophobic mismatch or the transport of lipids by proteins.

physics.bio-ph↗

arXiv2013

Quantification of noise in the bifunctionality-induced post-translational modification

We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation. The resultant analytical expression of phosphorylated response regulators are then used to quantify the noise profile of biologically motivated single and branched pathways. Enhancement and reduction of noise in terms of extra phosphate outflux and influx, respectively, have been analyzed for the branched system. Furthermore, role of fluctuations of the network output in the regulation of a promoter with random activation/deactivation dynamics has been analyzed.

q-bio.SC↗

arXiv2013

Elastic models of the fast traps of carnivorous Dionaea and Aldrovanda

The carnivorous aquatic Waterwheel Plant (Aldrovanda vesiculosa L.) and the closely related terrestrial Venus Flytrap (Dionaea muscipula SOL. EX J. ELLIS) both feature elaborate snap-traps, which shut after reception of an external mechanical stimulus by prey animals. Although Aldrovanda is usually considered as a miniature aquatic Dionaea, the shutting mechanisms of the two plants are actually quite different. The fast shutting of Aldrovanda is indeed based on a simple swelling/shrinking mechanism, while the movement of Dionaea's traps is accelerated by the snap-buckling of the lobes. The purpose of this Report is to describe several key improvements to the elastic models that have recently been introduced to elucidate these movements [Poppinga and Joyeux, Phys. Rev. E 84, 041928 (2011)]. In particular, a precise mechanism for the action of the motor cells of Aldrovanda is proposed, the facts that the opening of the leaves of Dionaea is an irreversible mechanism based on growth and that the strain field is anisotropic and much smaller on the inner than on the outer surface of the leaves during shutting are taken properly into account, and a more accurate formula for calculating mean curvatures is used. The improvements brought to the model are described in detail and the physical consequences of these improvements are discussed.

physics.bio-ph↗

arXiv2013

Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

We investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allow to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.

physics.bio-ph↗

arXiv2013

Effect of magnesium ions on dielectric relaxation in semidilute DNA aqueous solutions

The effect of magnesium ion Mg2+ on the dielectric relaxation of semidilute DNA aqueous solutions has been studied by means of dielectric spectroscopy in the 100 Hz-100 MHz frequency range. De Gennes-Pfeuty-Dobrynin semidilute solution correlation length is the pertinent fundamental length scale for sufficiently low concentration of added salt, describing the collective properties of Mg-DNA solutions. No relaxation fingerprint of the DNA denaturation bubbles, leading to exposed hydrophobic core scaling, was detected at low DNA concentrations, thus indicating an increased stability of the double-stranded conformation in Mg-DNA solutions as compared to the case of Na-DNA solutions. Some changes are detected in the behavior of the fundamental length scale pertaining to the single molecule DNA properties, reflecting modified electrostatic screening effects of the Odijk-Skolnick-Fixman type. All results consistently demonstrate that Mg2+ ions interact with DNA in a similar way as Na1+ ions do, their effect being mostly describable through an enhanced screening.

physics.bio-ph↗

arXiv2013

Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

We use Brownian dynamics simulations to study the permeation properties of a generic electrostatic model of a biological ion channel as a function of the fixed charge $Q_f$ at its selectivity filter. We reconcile the recently-discovered discrete calcium conduction bands M0 ($Q_f$=1e), M1 (3e), M2 (5e) with the set of sodium conduction bands L0 (0.5-0.7e), L1 (1.5-2e) thereby obtaining a completed pattern of conduction and selectivity bands v $Q_f$ for the sodium-calcium channels family. An increase of $Q_f$ leads to an increase of calcium selectivity: L0 (sodium selective, non-blocking channel) -> M0 (non-selective channel) -> L1 (sodium selective channel with divalent block) -> M1 (calcium selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is identified with the eukaryotic (DEKA) sodium channel, and L1/L2 (speculatively) with the bacterial NaChBac channel. The scheme created is able to account for the experimentally observed mutation-induced transformations between non-selective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrier-less conduction. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca/Na valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

physics.bio-ph↗

arXiv2013

Twist neutrality, a zero sum rule for oriented closed space curves with applications to circular DNA

The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Studies of molecules that are intrinsically chiral, such as double-stranded DNA, is one example. Their properties generally depend on the local geometry, i.e. on curvature and torsion, yet the paths of closed molecules are globally restricted by topology. Molecules that fulfill a twist neutrality condition, a zero sum rule for the incremental change in the rate of winding along the curve, will behave neutrally to strain. This has implications for plasmids. For small circular microDNAs it follows that there must exist a minimum length for these to be double-stranded. It also follows that all microDNAs longer than the minimum length must be concave. This counterintuitive result is consistent with the kink-like appearance which has been observed for circular DNA. A prediction for the total negative curvature of a circular microDNA is given as a function of its length.

physics.bio-ph↗

arXiv2013

Local immobilization of particles in mass transfer described by the equation of the Jeffreys type

We consider the equation of the Jeffreys type as the basic one in three different models of mass transfer, namely, the Jeffreys type and two-phase models, and the $D_1$ approximation to the linear Boltzmann equation. We study two classic 1 + 1D problems in the framework of each model. The first problem is the transfer of a substance initially confined in a point. The second problem is the transfer of a substance from a stationary point source. We calculate the mean-square displacement (MSD) for the solutions of the first problem. The temporal behaviour of the MSD in the framework of the first and third models is found to be the same as that in the Brownian motion described by the standard Langevin equation. Besides, we find a remarkable phenomenon when a portion of the substance does not move.

cond-mat.stat-mech↗

arXiv2014

Collective behavior of penetrable self-propelled rods in two dimensions

Collective behavior of self-propelled particles is observed on a microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays. The properties of such systems depend both on their dimensionality and the interactions between their particles. We introduce a model for self-propelled rods in two dimensions that interact via a separation-shifted Lennard-Jones potential. Due to the finite potential barrier, the rods are able to cross. This model allows us to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can occasionally escape to the third dimension in order to pass each other. Our quasi-two-dimensional self-propelled particles describe a class of active systems that encompasses microswimmers close to a wall and filaments propelled on a substrate. Using Monte Carlo simulations, we first determine the isotropic-nematic transition for passive rods. Using Brownian dynamics simulations, we characterize cluster formation of self-propelled rods as a function of propulsion strength, noise, and energy barrier. Contrary to rods with an infinite potential barrier, an increase of the propulsion strength does not only favor alignment but also effectively decreases the potential barrier that prevents crossing of rods. We thus find a clustering window with a maximum cluster size at medium propulsion strengths.

cond-mat.soft↗