arXiv subjects

Madan Rao

Publications and source records attributed to Madan Rao.

At least 55 records · Page 3Linked to original sources

arXiv2013

Quantitative analysis of intra-Golgi transport reveals inter-cisternal exchange for all cargo

The mechanisms controlling the transport of proteins across the Golgi stack of mammalian and plant cells is the subject of intense debate, with two models, cisternal progression and inter-cisternal exchange, emerging as major contenders. A variety of transport experiments have claimed support for each of these models. We reevaluate these experiments using a single quantitative coarse-grained framework of intra-Golgi transport that accounts for both transport models and their many variants. Our analysis makes a definitive case for the existence of inter-cisternal exchange both for small membrane proteins (VSVG) and large protein complexes (procollagen) -- this implies that membrane structures larger than the typical protein-coated vesicles must be involved in transport. Notwithstanding, we find that current observations on protein transport cannot rule out cisternal progression as contributing significantly to the transport process. To discriminate between the different models of intra-Golgi transport, we suggest experiments and an analysis based on our extended theoretical framework that compare the dynamics of transiting and resident proteins.

q-bio.SC↗

arXiv2013

Condensation and Intermittency in an Open Boundary Aggregation-Fragmentation Model

We study real space condensation in aggregation-fragmentation models where the total mass is not conserved, as in phenomena like cloud formation and intracellular trafficking. We study the scaling properties of the system with influx and outflux of mass at the boundaries using numerical simulations, supplemented by analytical results in the absence of fragmentation. The system is found to undergo a phase transition to an unusual condensate phase, characterized by strong intermittency and giant fluctuations of the total mass. A related phase transition also occurs for biased movement of large masses, but with some crucial differences which we highlight.

cond-mat.stat-mech↗

arXiv2012

Non-affine displacements in crystalline solids in the harmonic limit

A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor ${\mathsf D}$ as well as a positive definite scalar $χ$ measuring non-affinity, i.e. the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of $χ$ and ${\mathsf D}$ and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution $P(χ, {\mathsf D})$ and the two point spatial correlation functions for $χ$ and ${\mathsf D}$. We show that non-affine and affine deformations are coupled even in a harmonic solid, with a strength that depends on the size of the coarse graining volume $Ω$ and dimensionality. As a corollary to our work, we identify the field, $h_χ$, conjugate to $χ$ and show that this field may be tuned to produce a transition to a state where the ensemble average, $<χ>$, and the correlation length of $χ$ diverge. Our work should be useful as a template for understanding non-affine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of non-affine displacements in melting, plastic flow and the glass transition.

cond-mat.stat-mech↗

arXiv2012

Patterning of polar active filaments on a tense cylindrical membrane

We study the dynamics and patterning of polar contractile filaments on the surface of a cylindrical cell using active hydrodynamic equations that incorporate couplings between curvature and filament orientation. Cables and rings spontaneously emerge as steady state configurations on the cylinder, and can be stationary or moving, helical or segments moving along helical trajectories. Contractility induces coalescence of proximal rings. We observe phase transitions in the steady state patterns upon changing cell diameter and make several testable predictions. Our results are relevant to the dynamics and patterning of a variety of active biopolymers in cylindrical cells.

cond-mat.soft↗

arXiv2012

Soft Active Matter

In this review we summarize theoretical progress in the field of active matter, placing it in the context of recent experiments. Our approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of the review is to integrate the several approaches proposed in the literature, from semi-microscopic to phenomenological. In particular, we first consider "dry" systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium, and clarify the differences and similarities between two types of orientationally ordered states, the nematic and the polar. We then consider the active hydrodynamics of a suspension, and relate as well as contrast it with the dry case. We further highlight various large-scale instabilities of these nonequilibrium states of matter. We discuss and connect various semi-microscopic derivations of the continuum theory, highlighting the unifying and generic nature of the continuum model. Throughout the review, we discuss the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular materials. We suggest promising extensions towards greater realism in specific contexts from cell biology to ethology, and remark on some exotic active-matter analogues. Lastly, we summarize the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents.

cond-mat.soft↗

arXiv2012

Atomistic simulations of a multicomponent asymmetric lipid bilayer

The cell membrane is inherently asymmetric and heterogeneous in its composition, a feature that is crucial for its function. Using atomistic molecular dynamics simulations, the physical properties of a 3-component asymmetric mixed lipid bilayer system comprising of an unsaturated POPC (palmitoyl-oleoyl-phosphatidyl-choline), a saturated SM (sphingomyelin) and cholesterol are investigated. In these simulations, the initial stages of liquid ordered, $l_o$, domain formation are observed and such domains are found to be highly enriched in cholesterol and SM. The current simulations also suggest that the cholesterol molecules may partition into these SM-dominated regions in the ratio of $3:1$ when compared to POPC-dominated regions. SM molecules exhibit a measurable tilt and long range tilt correlations are observed within the $l_o$ domain as a consequence of the asymmetry of the bilayer, with implications to local membrane deformation and budding. Tagged particle diffusion for SM and cholesterol molecules, which reflects spatial variations in the physical environment encountered by the tagged particle, is computed and compared with recent experimental results obtained from high resolution microscopy.

cond-mat.soft↗

arXiv2012

Phase behavior of two-component lipid membranes: theory and experiments

The structure of the ripple phase of phospholipid membranes remains poorly understood in spite of a large number of theoretical studies, with many experimentally established structural features of this phase unaccounted for. In this article we present a phenomenological theory of phase transitions in single- and two-component achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing {\it lipid chain melting}, and a vector order parameter describing the {\it tilt of the hydrocarbon chains} below the chain-melting transition. This model reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure. In addition, it predicts a variant of this phase which does not seem to have been experimentally observed. Using this model we have calculated generic phase diagrams of two-component membranes. We have also determined the phase diagram of a two-component lipid membrane from x-ray diffraction studies on aligned multilayers. This phase diagram is found to be in good agreement with that calculated from the model.

cond-mat.soft↗

arXiv2012

Nonequilibrium phase transitions in active contractile polar filaments

We study the patterning and fluctuations of a collection of active contractile polar filaments on a two dimensional substrate, using a continuum description in the presence of athermal noise, parameterised by an active temperature $T_A$. The steady states generically consist of arrays of inward pointing asters and show a continuous transition from a moving aster street to a stationary aster lattice. In contrast to its equilibrium counterpart, this active crystal shows true long range order at low $T_A$. On increasing $T_A$, the asters remodel with a distribution of lifetimes; concomitantly we find novel phase transitions characterised by polar and bond-orientational order.

cond-mat.soft↗

arXiv2011

Non-affine fields in solid-solid transformations: the structure and stability of a product droplet

We describe the microstructure, shape and dynamics of growth of a droplet of martensite nucleating in a parent austenite during a solid-solid transformation, using a Landau theory written in terms of conventional affine, elastic deformations and {\em non-affine} degrees of freedom. Non-affineness, $ϕ$, serves as a source of strain incompatibility and screens long-ranged elastic interactions. It is produced wherever the local stress exceeds a threshold and anneals diffusively thereafter. A description in terms of $ϕ$ is inevitable when the separation between defect pairs, possibly generated during the course of the transformation, is small. Using a variational calculation, we find three types of stable solutions ({\hv I}, {\hv II} and {\hv III}) for the structure of the product droplet depending on the scaled mobilities of $ϕ$ parallel and perpendicular to the parent-product interface and the stress threshold. In {\hv I}, $ϕ$ is vanishingly small, {\hv II} involves large $ϕ$ localized in regions of high stress within the parent-product interface and {\hv III} where $ϕ$ completely wets the parent-product interface. While width $l$ and size $W$ of the twins follows $l\propto\sqrt{W}$ in solution {\hv I}, this relation does not hold for {\hv II} or {\hv III}. We obtain a dynamical phase diagram featuring these solutions and argue that they represent specific microstructures such as twinned or dislocated martensites.

cond-mat.mtrl-sci↗

arXiv2011

A multi-species model with interconversion, chipping and injection

Motivated by the phenomenology of transport through the Golgi apparatus of cells, we study a multi-species model with boundary injection of one species of particle, interconversion between the different species of particle, and driven diffusive movement of particles through the system by chipping of a single particle from a site. The model is analysed in one dimension using equations for particle currents. It is found that, depending on the rates of various processes and the asymmetry in the hopping, the system may exist either in a steady phase, in which the average mass at each site attains a time-independent value, or in a "growing" phase, in which the total mass grows indefinitely in time, even in a finite system. The growing phases have interesting spatial structure. In particular, we find phases in which some spatial regions of the system have a constant average mass, while other regions show unbounded growth.

cond-mat.stat-mech↗

arXiv2011

Bidirectional transport in a multispecies TASEP model

We study a minimal lattice model which describes bidirectional transport of "particles" driven along a one dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies and organelles such as mitochondria. This minimal model, a multi-species totally asymmetric exclusion process (TASEP) with directional switching, can provide a framework for understanding the interplay between the switching dynamics of individual particles and the collective movement of particles in 1-dimension. When switching is much faster than translocation, the steady state density and current profiles of the particles are homogeneous in the bulk and are well described by a Mean-Field (MF) theory, as determined by comparison to a Monte Carlo simulation. In this limit, we construct a non-equilibrium phase diagram. Away from this fast switching regime, the MF theory fails, although the average bulk density profile still remains homogeneous. We study the steady state behaviour as a function of the ratio of the translocation and net switching rates, Q, and find a unique first-order phase transition at a finite Q associated with a discontinuous change of the bulk density. When the switching rate is decreased further (keeping translocation rate fixed), the system approaches a jammed phase with a net current that tends to zero as J ~ 1/Q.

cond-mat.stat-mech↗

arXiv2010

Theory of the asymmetric ripple phase in achiral lipid membranes

We present a phenomenological theory of phase transitions in achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing lipid chain melting, and a vector order parameter describing the tilt of the hydrocarbon chains below the chain-melting transition. Existing theoretical models fail to account for all the observed features of the phase diagram, in particular the detailed microstructure of the asymmetric ripple phase lying between the fluid and the tilted gel phase. In contrast, our two-component theory reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure.

cond-mat.soft↗

arXiv2010

Non-affine heterogeneities and droplet fluctuations in an equilibrium crystalline solid

We show, using molecular dynamics simulations, that a two-dimensional Lennard-Jones solid is subject to droplet fluctuations characterized by {\em non-affine} deviations from local crystallinity. The fraction of particles in these droplets increases as the mean density of the solid decreases and approaches $\approx 20$% of the total number in the vicinity of the fluid-solid phase boundary. We monitor the geometry, local equation of state, density correlations and van Hove functions of these droplets and show that some of these droplets are fluid-like and compact, while some are glassy and string-like. We provide evidence that these non-affine heterogeneities should be interpreted as being droplet fluctuations from nearby, metastable minima.

cond-mat.mtrl-sci↗

arXiv2010

Plasticity and reversibility of structural transitions in a model solid

We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be decomposed additively into separate elastic and plastic contributions. The plastic strain, produced when the local stress crosses a threshold, is governed by a phenomenological equation of motion. We investigate the dynamics of shape of an initially square solid as it is cycled through a transformation protocol consisting of (1) a quench across the transition (2) deformation by an external stress and finally (3) reverse transformation back to the parent state. We show that shape recovery at the end of this cycle depends on crucially on the presence of plasticity in components of the strain responsible for the transformation.

cond-mat.mtrl-sci↗

arXiv2010

Space-time approach to microstructure selection in solid-solid transitions

Nucleation of a solid in solid is initiated by the appearance of distinct dynamical heterogeneities, consisting of `active' particles whose trajectories show an abrupt transition from ballistic to diffusive, coincident with the discontinuous transition in microstructure from a {\it twinned martensite} to {\it ferrite}. The active particles exhibit intermittent jamming and flow. The nature of active particle trajectories decides the fate of the transforming solid -- on suppressing single particle diffusion, the transformation proceeds via rare string-like correlated excitations, giving rise to twinned martensitic nuclei. These string-like excitations flow along ridges in the potential energy topography set up by inactive particles. We characterize this transition using a thermodynamics in the space of trajectories in terms of a dynamical action for the active particles confined by the inactive particles. Our study brings together the physics of glass, jamming, plasticity and solid nucleation.

cond-mat.mtrl-sci↗

arXiv2009

Competition between folding and aggregation in a model for protein solutions

We study the thermodynamic and kinetic consequences of the competition between single-protein folding and protein-protein aggregation using a phenomenological model, in which the proteins can be in the unfolded (U), misfolded (M) or folded (F) states. The phase diagram shows the coexistence between a phase with aggregates of misfolded proteins and a phase of isolated proteins (U or F) in solution. The spinodal at low protein concentrations shows non-monotonic behavior with temperature, with implications for the stability of solutions of folded proteins at low temperatures. We follow the dynamics upon "quenching" from the U-phase (cooling) or the F-phase (heating) to the metastable or unstable part of the phase diagram that results in aggregation. We describe how interesting consequences to the distribution of aggregate size, and growth kinetics arise from the competition between folding and aggregation.

cond-mat.soft↗

arXiv2009

Dynamics of a stiff biopolymer in an actively contractile background: buckling, stiffening and negative dissipation

We present a generic theory for the dynamics of a stiff filament under tension, in an active medium with orientational correlations, such as a microtubule in contractile actin. In sharp contrast to the case of a passive medium, we find the filament can stiffen, and possibly oscillate, \textit{or} buckle, depending on the contractile or tensile nature of the activity \textit{and} the filament-medium anchoring interaction. We present experiments on the behaviour of microtubules in the growth cone of a neuron, which provide evidence for these apparently opposing behaviours. We also demonstrate a strong violation of the fluctuation-dissipation (FD) relation in the effective dynamics of the filament, including a negative FD ratio. Our approach is also of relevance to the dynamics of axons, and our model equations bear a remarkable formal similarity to those in recent work [PNAS (2001) {\bf 98}:14380-14385] on auditory hair cells. Detailed tests of our predictions can be made using a single filament in actomyosin extracts or bacterial suspensions.

cond-mat.soft↗

arXiv2008

Equilibrium properties of a grafted polyelectrolyte with explicit counterions

We study the equilibrium conformations of a grafted polyelectrolyte (PE) in the presence of explicit counterions (CI) using Monte Carlo simulations. The interplay between attractive Lennard-Jones interactions (parametrized by epsilon), and electrostatics (parametrized by A = q^2l_B/a, where q =counterion valency, l_B = Bjerrum length and a = monomer diameter), results in a variety of conformations, characterized as extended (E), pearls with m beads (P_m), sausage (S) and globular (G). For large epsilon, we observe a transition from G -> P_2 -> P_3 -> . . . -> S -> G with increasing A, i.e., a change from poor to good, to reentrant poor solvent, whereas, at lower epsilon, the sequence of transitions is, E -> S -> G. The conformation changes are directly related to the nature of binding of CI onto the PE. The transition between S -> G is continuous and associated with critical fluctuations in the shape driven by fluctuations in the fraction of condensed CI.

cond-mat.soft↗