arXiv subjects

Madan Rao

Publications and source records attributed to Madan Rao.

At least 37 records · Page 2Linked to original sources

arXiv2018

Cascade of transitions in molecular information theory

Biological organisms are open, adaptve systems that can respond to changes in environment in specific ways. Adaptation and response can be posed as an optimization problem, with a tradeoff between the benefit obtained from a response and the cost of producing environment-specific responses. Using recent results in stochastic thermodynamics, we formulate the cost as the mutual information between the environment and the stochastic response. The problem of designing an optimally performing network now reduces to a problem in rate distortion theory -- a branch of information theory that deals with lossy data compression. We find that as the cost of unit information goes down, the system undergoes a sequence of transitions, corresponding to the recruitment of an increasing number of responses, thus improving response specificity as well as the net payoff. We derive formal equations for the transition points and exactly solve them for special cases. The first transition point, also called the {\it coding transition}, demarcates the boundary between a passive response and an active decision-making by the system. We study this transition point in detail, and derive three classes of asymptotic behavior, corresponding to the three limiting distributions of the statistics of extreme values. Our work points to the necessity of a union between information theory and the theory of adaptive biomolecular networks, in particular metabolic networks.

cond-mat.stat-mech↗

arXiv2018

Soft inclusion in a confined fluctuating active gel

We study stochastic dynamics of a point and extended inclusion within a one dimensional confined active viscoelastic gel. We show that the dynamics of a point inclusion can be described by a Langevin equation with a confining potential and multiplicative noise. Using a systematic adiabatic elimination over the fast variables, we arrive at an overdamped equation with a proper definition of the multiplicative noise. To highlight various features and to appeal to different biological contexts, we treat the inclusion in turn as a rigid extended element, an elastic element and a viscoelastic (Kelvin-Voigt) element. The dynamics for the shape and position of the extended inclusion can be described by coupled Langevin equations. Deriving exact expressions for the corresponding steady state probability distributions, we find that the active noise induces an attraction to the edges of the confining domain. In the presence of a competing centering force, we find that the shape of the probability distribution exhibits a sharp transition upon varying the amplitude of the active noise. Our results could help understanding the positioning and deformability of biological inclusions, eg. organelles in cells, or nucleus and cells within tissues.

physics.bio-ph↗

arXiv2018

Maximal fluctuations of confined actomyosin gels: dynamics of the cell nucleus

We investigate the effect of stress fluctuations on the stochastic dynamics of an inclusion embedded in a viscous gel. We show that, in non-equilibrium systems, stress fluctuations give rise to an effective attraction towards the boundaries of the confining domain, which is reminiscent of an active Casimir effect. We apply this generic result to the dynamics of deformations of the cell nucleus and we demonstrate the appearance of a fluctuation maximum at a critical level of activity, in agreement with recent experiments [E. Makhija, D. S. Jokhun, and G. V. Shivashankar, Proc. Natl. Acad. Sci. U.S.A. 113, E32 (2016)].

physics.bio-ph↗

arXiv2017

Interacting passive advective scalars in an active medium

Recent experimental studies, both in vivo and in vitro, have revealed that membrane components that bind to the cortical actomyosin meshwork are driven by active fluctuations, whereas membrane components that do not bind to cortical actin are not. Here we study the statistics of density fluc- tuations and dynamics of particles advected in an active quasi-two dimensional medium comprising self-propelled filaments with no net orientational order, using a combination of agent-based Brow- nian dynamics simulations and analytical calculations. The particles interact with each other and with the self-propelled active filaments via steric interactions. We find that the particles show a tendency to cluster and their density fluctuations reflect their binding to and driving by the active filaments. The late-time dynamics of tagged particles is diffusive, with an active diffusion coefficient that is independent of (or at most weakly-dependent on) temperature at low temperatures. Our results are in qualitative agreement with the experiments mentioned above. In addition, we make predictions that can be tested in future experiments.

physics.bio-ph↗

arXiv2017

Covariant Active Hydrodynamics of Shape-Changing Epithelial Monolayers

During the early-stages of embryo development, morphogenesis--- the emergence of shape and form in living organisms--- is almost exclusively associated with monolayers of tightly bound epithelial cells. To understand how such tissues change their shape, we construct a fully covariant active-hydrodynamic theory. At the cellular scale, stresses arise from apical contractility, mechanical response and the constraint of constant cell volume. Tissue-scale deformations emerge due to the balance between such cell-autonomous stresses and the displacement and shear of a low Reynolds number embedding fluid. Tissues with arbitrary curvature or shape can be described, providing a general framework for epithelial monolayer morphology. Analysis of the stability of flat monolayers reveals two generic shape instabilities: passive constrained-buckling, and actively-driven tissue deformation. The active instability can be further categorised into two types, corresponding to cell shape changes that are either "squamous to columnar" or "regular-prism to truncated-pyramid". The deformations resulting from the latter qualitatively reproduce in vivo observations of the onset of both mesoderm and posterior midgut invaginations, which take place during gastrulation in the fruit fly Drosophila melanogaster.

cond-mat.soft↗

arXiv2017

Activity controls fragility: A Random First Order Transition Theory for an active glass

How does nonequilibrium activity modify the approach to a glass? This is an important question, since many experiments reveal the near-glassy nature of the cell interior, remodelled by activity. However, different simulations of dense assemblies of active particles, parametrised by a self-propulsion force, $f_0$, and persistence time, $τ_p$, appear to make contradictory predictions about the influence of activity on characteristic features of glass, such as fragility. This calls for a broad conceptual framework to understand active glasses; here we extend the Random First-Order Transition (RFOT) theory to a dense assembly of self-propelled particles. We compute the active contribution to the configurational entropy using an effective medium approach - that of a single particle in a caging-potential. This simple active extension of RFOT provides excellent quantitative fits to existing simulation results. We find that whereas $f_0$ always inhibits glassiness, the effect of $τ_p$ is more subtle and depends on the microscopic details of activity. In doing so, the theory automatically resolves the apparent contradiction between the simulation models. The theory also makes several testable predictions, which we verify by both existing and new simulation data, and should be viewed as a step towards a more rigorous analytical treatment of active glass.

cond-mat.soft↗

arXiv2017

A universal lower bound on the free energy cost of molecular measurements

The living cell uses a variety of molecular receptors to read and process chemical signals that vary in space and time. We model the dynamics of such molecular level measurements as Markov processes in steady state, with a coupling between the receptor and the signal. We prove exactly that, when the the signal dynamics is not perturbed by the receptors, the free energy consumed by the measurement process is lower bounded by a quantity proportional to the mutual information. Our result is completely independent of the receptor architecture and dependent on signal properties alone, and therefore holds as a general principle for molecular information processing.

cond-mat.stat-mech↗

arXiv2017

Glassy swirls of active dumbbells

The dynamics of a dense binary mixture of soft dumbbells, each subject to an active propulsion force and thermal fluctuations, shows a sudden arrest, first to a translational then to a rotational glass, as one reduces temperature $T$ or the self-propulsion force $f$. Is the temperature-induced glass different from the activity-induced glass? To address this question, we monitor the dynamics along an iso-relaxation-time contour in the $(T-f)$ plane. We find dramatic differences both in the fragility and in the nature of dynamical heterogeneity which characterise the onset of glass formation - the activity-induced glass exhibits large swirls or vortices, whose scale is set by activity, and appears to diverge as one approaches the glass transition. This large collective swirling movement should have implications for collective cell migration in epithelial layers.

cond-mat.soft↗

arXiv2017

Emergent Structures in an Active Polar Fluid : dynamics of shape, scattering and merger

Spatially localised defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar 'actin' filaments and 'myosin' motor proteins that (un)bind to filaments and exert active contractile stresses. These emergent defect structures are characterized by distinct textures and can be either static or mobile - we derive effective equations of motion for these 'extended particles' and analyse their shape, kinetics, interactions and scattering. Depending on the impact parameter and propulsion speed, these active defects undergo elastic scattering or merger. Our results are relevant for the dynamics of actomyosin-dense structures at the cell cortex, reconstituted actomyosin complexes and 2D active colloidal gels.

physics.bio-ph↗

arXiv2016

Active fluidization in dense glassy systems

Dense soft glasses show strong collective caging behavior at sufficiently low temperatures. Using molecular dynamics simulations of a model glass former, we show that the incorporation of activity or self-propulsion, f0, can induce cage breaking and fluidization, resulting in a disappearance of the glassy phase beyond a critical f0 . The diffusion coefficient crosses over from being strongly to weakly temperature dependent as f0 is increased. In addition, we demonstrate that activity induces a crossover from a fragile to a strong glass and a tendency for clustering of active particles. Our results are of direct relevance to the collective dynamics of dense active colloidal glasses and to recent experiments on tagged particle diffusion in living cells.

cond-mat.soft↗

arXiv2016

Nonequilibrium mechanisms underlying de novo biogenesis of Golgi cisternae

A central issue in cell biology is the physico-chemical basis of organelle biogenesis in intracellular trafficking pathways, its most impressive manifestation being the biogenesis of Golgi cisternae. At a basic level, such morphologically and chemically distinct compartments should arise from an interplay between the molecular transport and chemical maturation. Here, we formulate analytically tractable, minimalist models, that incorporate this interplay between transport and chemical progression in physical space, and explore the conditions for de novo biogenesis of distinct cisternae. We propose new quantitative measures that can discriminate between the various models of transport in a qualitative manner- this includes measures of the dynamics in steady state and the dynamical response to perturbations of the kind amenable to live-cell imaging.

physics.bio-ph↗

arXiv2016

Actomyosin pulsation and symmetry breaking flows in a confined active elastomer subject to affine and nonaffine deformations

Tissue remodelling in diverse developmental contexts require cell shape changes that have been associated with pulsation and flow of the actomyosin cytoskeleton. Here we describe the dynamics of the actomyosin cytoskeleton as a confined active elastomer embedded in the cytosol and subject to turnover of its components. Under affine deformations (homogeneous deformation over a spatially coarse-grained scale), the active elastomer exhibits spontaneous oscillations, propagating waves, contractile collapse and spatiotemporal chaos. The collective nonlinear dynamics shows nucleation, growth and coalescence of actomyosin-dense regions which, beyond a threshold, spontaneously move as a spatially localized traveling front towards one of the boundaries. However, large myosin-induced contractile stresses, can lead to nonaffine deformations due to actin turnover. This results in a transient actin network, that naturally accommodates intranetwork flows of the actomyosin dense regions as a consequence of filament unbinding and rebinding. Our work suggests that the driving force for the spontaneous movement comes from the actomyosin-dense region itself and not the cell boundary. We verify the many predictions of our study in Drosophila embryonic epithelial cells undergoing neighbour exchange during a collective process of tissue extension called germband extension.

physics.bio-ph↗

arXiv2016

Phase segregation of passive advective particles in an active medium

Localized contractile configurations or asters spontaneously appear and disappear as emergent structures in the collective stochastic dynamics of active polar actomyosin filaments. Passive parti- cles which (un)bind to the active filaments get advected into the asters, forming transient clusters. We study the phase segregation of such passive advective scalars in a medium of dynamic asters, as a function of the aster density and the ratio of the rates of aster remodeling to particle diffusion. The dynamics of coarsening shows strong violation of Porod behaviour, suggesting diffuse interfaces. The phase segregated steady state shows strongly fluctuations characterized by multiscaling and in- termittency. We expect these unique nonequilibrium features to manifest in the actin-dependent molecular clustering at the cell surface.

cond-mat.soft↗

arXiv2015

Active remodeling of chromatin and implications for in-vivo folding

Recent high resolution experiments have provided a quantitative description of the statistical properties of interphase chromatin at large scales. These findings have stimulated a search for generic physical interactions that give rise to such specific statistical conformations. Here, we show that an active chromatin model of in-vivo folding, based on the interplay between polymer elasticity, confinement, topological constraints and active stresses arising from the (un)binding of ATP-dependent chromatin-remodeling proteins gives rise to steady state conformations consistent with these experiments. Our results lead us to conjecture that the chromatin conformation resulting from this active folding optimizes information storage by co-locating gene loci which share transcription resources.

physics.bio-ph↗

arXiv2015

Pre-yield non-affine fluctuations and a hidden critical point in strained crystals

A crystalline solid exhibits thermally induced localised {\em non-affine} droplets in the absence of external stress. Here we show that upon an imposed shear, the size of these droplets grow until they percolate at a critical strain, well {\em below} the value at which the solid begins to yield. This critical point does not manifest in bulk thermodynamic or mechanical properties, but is {\em hidden} and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. Slow relaxation of stress and an-elasticity appear as observable dynamical consequences of this hidden criticality. Our results may be directly verified in colloidal crystals with video microscopy techniques but are expected to have more general validity.

cond-mat.mtrl-sci↗

arXiv2014

Activating membranes

We present a general dynamical theory of a membrane coupled to an actin cortex containing polymerizing filaments with active stresses and currents, and demonstrate that active membrane dynamics [Phys. Rev. Lett \textbf{84}, 3494 (2000)] and spontaneous shape oscillations emerge from this description. We also consider membrane instabilities and patterns induced by the presence of filaments with polar orientational correlations in the tangent plane of the membrane. The dynamical features we predict should be seen in a variety of cellular contexts involving the dynamics of the membrane-cytoskeleton composite and cytoskeletal extracts coupled to synthetic vesicles.

physics.bio-ph↗

arXiv2014

Organelle morphogenesis by active remodeling

Intracellular organelles are subject to a steady flux of lipids and proteins through active, energy consuming transport processes. Active fission and fusion are promoted by GTPases, e.g., Arf-Coatamer and the Rab-Snare complexes, which both sense and generate local membrane curvature. Here we investigate through Dynamical Triangulation Monte Carlo simulations, the role that these active processes play in determining the morphology and compositional segregation in closed membranes. Our results suggest that the ramified morphologies of organelles observed in-vivo are a consequence of driven nonequilibrium processes rather than equilibrium forces.

physics.bio-ph↗

arXiv2013

Bilayer registry in a multicomponent asymmetric membrane : dependence on lipid composition and chain length

A question of considerable interest to cell membrane biology is whether phase segregated domains across an asymmetric bilayer are strongly correlated with each other and whether phase segregation in one leaflet can induce segregation in the other. We answer both these questions in the affirmative, using an atomistic molecular dynamics simulation to study the equilibrium statistical properties of a 3-component {\em asymmetric} lipid bilayer comprising an unsaturated POPC (palmitoyl-oleoyl-phosphatidyl-choline), a saturated SM (sphingomyelin) and cholesterol with different composition ratios. Our simulations are done by fixing the composition of the upper leaflet to be at the coexistence of the liquid ordered ($l_o$) - liquid disordered ($l_d$) phases, while the composition of the lower leaflet is varied from the phase coexistence regime to the mixed $l_d$ phase, across a first-order phase boundary. In the regime of phase coexistence in each leaflet, we find strong transbilayer correlations of the $l_o$ domains across the two leaflets, resulting in {\it bilayer registry}. This transbilayer correlation depends sensitively upon the chain length of the participating lipids and possibly other features of lipid chemistry, such as degree of saturation. We find that the $l_o$ domains in the upper leaflet can {\em induce} phase segregation in the lower leaflet, when the latter is nominally in the mixed ($l_d$) phase.

physics.bio-ph↗