Stochastic Thermodynamics, Active Matter and Driven Systems
Title and abstract
  1. Tripti Bameta

Collective force generation by multiple rigid filaments and molecular motors

Force generated by multiple filaments or motor in collective is not always additive but show a unique behaviour at equilibrium. Inspired by real biological phenomenon, we give models of both biofilaments and motors and derive exact analytical expression of two filament/motor velocity. As a result, show that maximum force generated by group of filaments/motors show additivity (stall force of N filaments/motors is N times the stall force of one filament/motor), at equilibrium point. Moreover, we correlate deviation from additivity to efficiency like quantity of the filament/motor model. Furthermore, with this result in hand, we analyse a few present models.

 

  1. Sakuntala Chatterjee

Optimal methylation noise for best chemotactic performance of E. coli

In response to a concentration gradient of chemo-attractant, E. coli bacterium modulates the rotational bias of flagellar motors that control its run-and-tumble motion, to migrate towards regions of high chemo-attractant concentration. Presence of stochastic noise in the biochemical pathway of the cell has important consequence on the switching mechanism of motor bias, which in turn affects the runs and tumbles of the cell in a significant way. We use a standard description to model the intra-cellular reaction network in terms of coupled time-evolution of three stochastic variables, kinase activity, methylation level and CheY-P protein level, and study the effect of methylation noise on the chemotactic performance of the cell. A good performance consists of reaching the favorable region quickly and localizing there in the long time limit. Our simulations show that the best performance is obtained at an optimal noise strength. We show that when the CheY-P level falls below a certain (noise-dependent) threshold, the cell tends to move down the concentration gradient of the nutrient, which impairs its chemotactic response. This threshold value decreases as noise is increased, and this effect is responsible for noise-induced enhancement of chemotactic performance.

 

  1. Debasish Chaudhuri

Entropy production and linear response in active Brownian particles

Non-equilibrium dynamics of several active Brownian systems are modeled in terms of nonlinear velocity dependent force, e.g., in the energy depot model or the Rayleigh-Helmholtz model. We derive the entropy production using Fokker-Planck equation, and the ratio of forward and time- reversed path probabilities. The distribution of stochastic entropy production is obtained and it obeys fluctuation theorem symmetry. The steady-state response function obeys a modified fluctuation-dissipation relation.

 

  1. Debashish Chowdhury

Motoring alone and in a traffic at nano-scale: stochastic kinetics on networks

A molecular motor is a macromolecular `active' device that walks along a filamentous track utilizing a part of input energy to perform mechanical work. Some motors, while walking along their respective tracks in a step-by-step manner, use the track as a template to carry out template-directed polymerization. Such information processing motors are often referred to as `tape-copying Turing machines'. In this talk I focus on such a motor and analyze its stochastic kinetics, both at the single motor level and in traffic congestion. I present results obtained by using graph theoretical framework for Markov processes on a network of chemo-mechanical states. We address the question of validity of some macroscopic laws of physics and chemical kinetics, even on the average, at the nano-scale of molecular motors. We also indicate novel mechanisms of control of traffic flow of these interacting `self-driven' agents.

 

  1. Hugues Chaté

Recent progress and outstanding problems in dilute, aligning, dry active matter

The speaker will give an overview of our current knowledge of dilute, aligning, dry active matter, emphasizing recent progress and important pending theoretical questions. Among the topics covered, depending on time:

  • A quantitative assessment of the Toner-Tu theory of flocking
  • The effect of topological defects on the stability of orientationally-ordered phases
  • Fluctuations and long-range order in 2D active nematics
  • The ‘Vicsek-shake’ class: apolar particles with ferromagnetic alignment
  • Fragility of the Vicsek class (fore-aft asymmetry, quenched disorder)
     
  1. Shankar Ghosh

Multiscale flows in an highly viscous fluids

TBA

 

  1. Anupam Kundu

Fluctuations and correlations in a single file process

Studying the dynamics of an active particle or a locally driven particle traveling in a crowded environment is a frequent problem in physics and biology. Consequently, determination of the statistical properties of system both in stationary and non-stationary regime are important questions. In this talk I will discuss about the scaling properties of fluctuations and correlations in this system.

 

  1. Cesare Nardini

Scalar field theories of active systems: irreversible processes and `bubbly’ phase separation

Collaborators: F. Caballero, M. Cates, E. Fodor, J. Tailleur, E. Tjhung, F. van Wijland

Purely repulsive but active particles are known to undergo phase separation, at odd with what happens for passive particles. Such inherently non-equilibrium phenomena, if looked at coarse-grained level, can be understood by an approximate mapping to equilibrium systems presenting liquid-gas phase separation. I will discuss our recent efforts to pinpoint the non-equilibrium, irreversible, signatures of phase separation in active matter. I will focus on coarse grained approaches where only the density of particles is retained as macroscopic variable (scalar field theories) and show how we can measure unambiguously the degree of irreversibility in the dynamics. The same measures performed at the level of particle models, yields very similar results, supporting the idea that reversibility is mostly broken at the interfaces between the two phases and restored away from it. Moreover, I will show that scalar field theories point out more subtle irreversible processes. In particular, I will show that the dense phase is not uniform as one would expect from an equilibrium system, but instead supports dilute droplets, continuously created by nucleation and expelled deterministically. Importantly, such `bubbly phase’ is mirrored by a phase where phase separation is arrested and dense droplet cannot grow beyond a certain size, similar to micro-phase separation seen in experiments of active colloids. These results are unveiled with a combination of numerical simulations, mean-field calculations and renormalisation group analysis.

 

  1. Shraddha Mishra

Phase ordering dynamics in a collection of self propelled particles in inhomogeneous medium

We study the phase-ordering dynamics of a collection of self-propelled polar particles on {\it homogeneous} and {\it inhomogeneous} substrate in two-dimensions. We write the coarse-grained hydrodynamic equations of motion for density and local velocity fields for inhomogeneous media, where the inhomogeneity is introduced as an external disorder field quenched in time and random in space. In homogeneous system, phase ordering dynamics of the density is faster, as compared to its equilibrium counterpart, and the size of domain grows linearly with time. However, the local velocity field follows the same growth dynamics as an equilibrium non-conserved vector order parameter of $O(2)$ symmetry follows in two-dimensions. For inhomogeneous system, we find a disorder dependent growth of both the density and the local velocity fields. The domain boundaries become rough with increasing disorder strength. Two-point correlation function for the local velocity and the density show scaling for different strength of disorder; although, for fixed disorder strength the velocity shows good scaling collapse, whereas the density does not.

 

  1. Ranjith Padinhateeri

Role of active disassembly in biology

I will discuss some examples from biology where ATP-dependent activity leads to disassembly. In chromatin, non-equilibrium activity plays a major role in the disassembly of nucleosomes. In cytoskeletal filaments, ATP/GTP-dependent activity is crucial for disassembly of the filaments. Our studies show that active disassembly is crucial in maintaining various biologically relevant ``states’’ in different living systems.

 

  1. Punyabrata Pradhan

Characterizing fluctuations in driven active- and passive-matter systems

Characterizing fluctuations in a many-particle system is fundamental to the formulation of statistical mechanics. Unlike in equilibrium, where fluctuations are obtained from the Boltzmann distribution, there is no unified principle to characterize fluctuations in non-equilibrium. In this talk, I would discuss static and dynamical properties of fluctuations in active- and passive-matter systems, which are inherently driven out of equilibrium, and explore if a statistical mechanics framework could be constructed to understand them better.

 

  1. Samriddhi Sankar Ray

Collective motion in a turbulent flow: Adapting the Vicsek model

TBA

 

  1. Masaki Sano

Topological Defects Control Collective Dynamics in Neural Stem Cells

Self-motility is an important character of living matter. Ranging from filamentous bacteria to mobile cells, ensembles of self-propelled particles generate highly non-trivial collective behaviors. In such dynamical collective behaviors, order and disorder can be well characterized by using nematic order parameter and the concept of topological defects in many cases. I will talk about 3D structure formation from 2D sheet of neural stem cells where topological defects become the center for 3D mound formation. This morphological change is reproduced by a simple mathematical model of active matter. Quantitative analysis of the dynamics will be described.

 

  1. Sanjib Sabhapandit

Fluctuation theorem for entropy production of a partial system in the weak coupling limit

Small systems in contact with a heat bath evolve by stochastic dynamics. We show that, when one such small system is weakly coupled to another one, it is possible to infer the presence of such weak coupling by observing the violation of the steady state fluctuation theorem for the partial entropy production of the observed system. We give a general mechanism due to which the violation of the fluctuation theorem can be significant, even for weak coupling. We analytically demonstrate on a realistic model system that this mechanism can be realized by applying an external random force to the system. In other words, we find a new fluctuation theorem for the entropy production of a partial system, in the limit of weak coupling.

 

  1. Udo Seifert

Universal features of current fluctuations of driven and active systems

Stochastic thermodynamics provides a comprehensive framework for describing fluctuating driven systems leading, inter alia, to the fluctuation theorem that constrains the fluctuations of the current associated with entropy production. The recently discovered thermodynamic uncertainty relation constrains the typical fluctuation of any current in terms of the entropy production rate associated with the driving or active mechanism [1]. Generalizations exist for the extreme fluctuations on the large-deviation level [2].

I will introduce the basic concepts behind these recent development and illustrate how they can be used to infer a universal bound on the efficiency of, e.g., a molecular motor just from experimental data [3]. Likewise, our recent universal classification of the large deviation function for a generic active particle might be used to infer hidden aspects of the driving mechanism [4].

  1. A. C. Barato and U.S., Phys. Rev. Lett. 114, 158101, 2015
  2. P. Pietzonka, A.C. Barato, and U.S., Phys. Rev. E 93, 052145, 2016
  3. P. Pietzonka, A. C. Barato, and U.S., J. Stat. Mech., 124004, 2016
  4. P. Pietzonka, K. Kleinbeck, and U.S., New J. Phys., 18, 052001, 2016

 

  1. Michael Shelley

Some problems in cellular biomechanics involving active processes

I will discuss the interaction of theory and simulation with experimental measurements of active processes within the cell. This includes understanding the force transduction mechanisms underlying nuclear migration, spindle positioning and oscillations, as well as how active displacement domains of chromatin might be forming in the interphase nucleus.

 

  1. Aditi Simha

Binary mixtures of active and passive particles on a 2-dimensional frictional substrate

Binary mixtures of active and passive particles exhibit interesting and diverse properties arising from activity and the asymmetry of particles. I will present some results on a study of such systems. Specifically, we study the dynamics of passive particles induced by the surrounding active medium and look at how their presence effects motility induced aggregation of active particles.

 

  1. Thomas Speck

Heat and entropy production for active Brownian particles

The consistent identification of fluctuating work, heat, and entropy production is at the heart of stochastic thermodynamics. I will discuss the situation for active Brownian particles, a minimal model system of active matter combining directed motion with volume exclusion, and the related active Ornstein-Uhlenbeck process. I will propose an identification based on the concept of reservoirs and earlier work on frame invariance in stochastic thermodynamics, and discuss ramifications.

 

  1. Leihan Tang

Beyond Kuramoto: a unifying theory of autoinduced oscillation in cell populations

Collective oscillations are ubiquitous in the biological world. In 1975, Kuramoto proposed a model of globally coupled oscillators with distributed frequencies that exhibits an entrainment transition at critical coupling strength. Yet in many well-studied cell populations, such as dictyostelium and neuronal cell culture, chemical waves emerge only when the local cell density exceeds a critical value. Mechanistic interpretation of the observed phenomena is challenging due to the often incomplete knowledge about the underlying complex molecular and cellular processes. Here we attempt a general theory of collective oscillation in cell populations from nonequilibrium thermodynamics. Our key observation is that, in the examples examined, the response function of individual units shows a phase lead over a periodic signal on the low frequency side. Such behavior is ruled out by the fluctuation-dissipation theorem (FDT) for equilibrium systems. On the other hand, using the well-known Kramers-Kronig relation, we prove that driven adaptive systems must have this type of nonequilibrium response in a certain frequency domain[1, 2]. The phase lead allows individual adaptive units to inject energy to the signaling field. Collective oscillation develops through a Hopf bifurcation when the coupling is sufficiently strong or local cell number sufficiently high. Interestingly, for partially adaptive systems, collective oscillation comes to arrest when cell density exceeds an upper threshold, in contrast to that of the Kuramoto model where stronger coupling implies more perfect synchronization. As the response function of a cell to a chosen signal is often more accessible than a full characterization of the relevant intracellular network, our work suggests a novel experimental methodology to decipher collective oscillations from mesoscopic cellular behavior.

Work supported in part by the NSFC under grant 11635002, and by the RGC of the HKSAR under grant 12301514.

Key words: adaptive circuit; fluctuation-dissipation theorem; stochastic thermodynamics; autoinduced oscillation; cell-cell communication.

  1. S.-W. Wang, Y. Lan, and L.-H. Tang, J. Stat. Mech., P07025 (2015); S.-W. Wang, K. Kawaguchi, S.-i. Sasa, and L.-H. Tang, Phys. Rev. Lett. 117, 070601 (2016).
  2. S.-W. Wang and L.-H. Tang, arXiv:1611.04089; in preparation.

 

  1. Shashi Thutupalli

A motility-induced phase transition drives Myxococcus xanthus aggregation

A hallmark of living systems is their ability to generate dynamic and complex spatial patterns at the molecular, cellular, and multicellular levels. Many such systems rely on biochemical and genetic signalling mechanisms that, when coupled together, can produce large-scale patterns such as periodicity and oscillation of the Min proteins inside a single Escherichia coli bacterium, spiral waves of cyclic AMP and multicellular aggregation of the amoeba Dictyostelium discoideum, and the arrangement of specific body segments in developing animals from flies to humans. However, long-range order and patterning can emerge through purely mechanical interactions. Here, we study the starvation-induced aggregation of gliding Myxococcus xanthus bacteria and show that these cells induce a phase separation of the population by tuning their motility over time. By experimentally varying the density and speed of gliding cells, tracking individual cells in large populations, and comparing to simulations of a simple active-Brownian particle model, we are able to map out the phase diagram of aggregation and understand the dynamics of density fluctuations. We further track changes in motility of the wild-type during starvation and show that a reduction of the reversal frequency and an increase in gliding speed change the rotational Peclet number to drive aggregation.

 

  1. Julia M. Yeomans

Topology in Biology

Active materials such as bacteria, molecular motors and self-propelled colloids, are Nature’s engines. They continuously transform chemical energy from their environment to mechanical work. Dense active matter shows mesoscale turbulence, the emergence of chaotic flow structures characterised by high vorticity and topological defects.

I shall discuss how dense active matter might be harnessed to provide energy, and the connection of mesoscale turbulence to cell motility and cell division. In particular I shall give examples of topological defects in biological systems.