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.Comment: New J. Phys., 201

Giant number fluctuations in microbial ecologies

Statistical fluctuations in population sizes of microbes may be quite large depending on the nature of their underlying stochastic dynamics. For example, the variance of the population size of a microbe undergoing a pure birth process with unlimited resources is proportional to the square of its mean. We refer to such large fluctuations, with the variance growing as square of the mean, as Giant Number Fluctuations (GNF). Luria and Delbruck showed that spontaneous mutation processes in microbial populations exhibit GNF. We explore whether GNF can arise in other microbial ecologies. We study certain simple ecological models evolving via stochastic processes: (i) bi-directional mutation, (ii) lysis-lysogeny of bacteria by bacteriophage, and (iii) horizontal gene transfer (HGT). For the case of bi-directional mutation process, we show analytically exactly that the GNF relationship holds at large times. For the ecological model of bacteria undergoing lysis or lysogeny under viral infection, we show that if the viral population can be experimentally manipulated to stay quasi-stationary, the process of lysogeny maps essentially to one-way mutation process and hence the GNF property of the lysogens follows. Finally, we show that even the process of HGT may map to the mutation process at large times, and thereby exhibits GNF.Comment: 18 pages, 5 figure

Inhomogeneous Cooling of the Rough Granular Gas in Two Dimensions

We study the inhomogeneous clustered regime of a freely cooling granular gas of rough particles in two dimensions using large-scale event driven simulations and scaling arguments. During collisions, rough particles dissipate energy in both the normal and tangential directions of collision. In the inhomogeneous regime, translational kinetic energy and the rotational energy decay with time $t$ as power-laws $t^{-\theta_T}$ and $t^{-\theta_R}$. We numerically determine $\theta_T \approx 1$ and $\theta_R \approx 1.6$, independent of the coefficients of restitution. The inhomogeneous regime of the granular gas has been argued to be describable by the ballistic aggregation problem, where particles coalesce on contact. Using scaling arguments, we predict $\theta_T=1$ and $\theta_R=1$ for ballistic aggregation, $\theta_R$ being different from that obtained for the rough granular gas. Simulations of ballistic aggregation with rotational degrees of freedom are consistent with these exponents.Comment: 6 pages, 5 figure

Persistence of a Rouse polymer chain under transverse shear flow

We consider a single Rouse polymer chain in two dimensions in presence of a transverse shear flow along the $x$ direction and calculate the persistence probability $P_0(t)$ that the $x$ coordinate of a bead in the bulk of the chain does not return to its initial position up to time $t$. We show that the persistence decays at late times as a power law, $P_0(t)\sim t^{-\theta}$ with a nontrivial exponent $\theta$. The analytical estimate of $\theta=0.359...$ obtained using an independent interval approximation is in excellent agreement with the numerical value $\theta\approx 0.360\pm 0.001$.Comment: 6 page

Violation of Porod law in a freely cooling granular gas in one dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.Comment: 4 pages, 5 figure

Critical Dynamics of Dimers: Implications for the Glass Transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy vanishing phase transition, and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments and numerical diagonalizations of the master equation, we find non-exponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point, and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics

Spatial Structures and Giant Number Fluctuations in Models of Active Matter

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod law violation, by measuring subleading corrections to the number fluctuations.Comment: 5 pages, 3 figure