arXiv subjects

Alexander Y. Grosberg

Publications and source records attributed to Alexander Y. Grosberg.

At least 19 recordsLinked to original sources

arXiv2026

Roadmap for Condensates in Cell Biology

Biomolecular condensates govern essential cellular processes yet elude description by traditional equilibrium models. This roadmap, distilled from structured discussions at a workshop and reflecting the consensus of its participants, clarifies key concepts for researchers, funding bodies, and journals. After unifying terminology that often separates disciplines, we outline the core physics of condensate formation, review their biological roles, and identify outstanding challenges in nonequilibrium theory, multiscale simulation, and quantitative in-cell measurements. We close with a forward-looking outlook to guide coordinated efforts toward predictive, experimentally anchored understanding and control of biomolecular condensates.

physics.bio-ph↗

arXiv2023

Activity-driven phase transition causes coherent flows of chromatin

We discover a new type of nonequilibrium phase transition in a model of chromatin dynamics, which accounts for the coherent motions that have been observed in experiment. The coherent motion is due to the long-range cooperation of molecular motors tethered to chromatin. Cooperation occurs if each motor acts simultaneously on the polymer and the surrounding solvent, exerting on them equal and opposite forces. This drives the flow of solvent past the polymer, which in turn affects the orientation of nearby motors and, if the drive is strong enough, an active polar (``ferromagnetic'') phase of motors can spontaneously form. Depending on boundary conditions, either transverse flows, or sustained longitudinal oscillations and waves are possible. Predicted time and length scales are consistent with experiments. We now have in hand a coarse-grained description of chromatin dynamics which reproduces the directed coherent flows of chromatin seen in experiments. This field-theoretic description can be analytically coupled to other features of the nuclear environment such as fluctuating or porous boundaries, local heterogeneities in the distribution of chromatin or its activity, leading to insights on the effects of activity on the cell nucleus and its contents.

cond-mat.soft↗

arXiv2023

Model chromatin flows: numerical analysis of linear and nonlinear hydrodynamics inside a sphere

We solve a hydrodynamic model of active chromatin dynamics, within a confined geometry simulating the cell nucleus. Using both analytical and numerical methods, we describe the behavior of the chromatin polymer driven by the activity of motors having polar symmetry, both in the linear response regime as well as in the long-term, fully nonlinear regime of the flows. The introduction of a boundary induces a particular geometry in the flows of chromatin, which we describe using vector spherical harmonics, a tool which greatly simplifies both our analytical and numerical approaches. We find that the long-term behavior of this model in confinement is dominated by steady, transverse flows of chromatin which circulate around the spherical domain. These circulating flows are found to be robust to perturbations, and their characteristic size is set by the size of the domain. This gives us further insight into active chromatin dynamics in the cell nucleus, and provides a foundation for development of further, more complex models of active chromatin dynamics.

cond-mat.soft↗

arXiv2022

Stretching of a fractal polymer around a disc reveals KPZ-like statistics

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. Here by means of the scaling analyses and computer simulations we examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius $R$. Surprisingly, we reveal that the typical excursions of the polymer away from the surface scale as $Δ\sim R^β$, with the Kardar-Parisi-Zhang (KPZ) growth exponent $β=1/3$, for any fractal dimension of the chain. Moreover, we find that the curvature-induced correlation length of a fractal chain behaves as $S^* \sim R^{1/z}$ with the KPZ dynamic exponent $z=3/2$, suggesting that the crossover from flat to curved geometry of a stretched polymer corresponds to the crossover from large to short time scales in the KPZ stochastic growth. Thus, we argue that curvature of an underlying boundary furnishes universal KPZ-like statistics to the stretched fractal paths, which further suggests numerous connections with several branches of mathematical physics.

cond-mat.soft↗

arXiv2022

Reentrant Transitions in a Mixture of Small and Big Particles Interacting via Soft Repulsive Potential

We report the first observation of temperature-controlled reentrant transition in simulations of mixtures of small and big particles interacting via soft repulsive potential in 2D. As temperature increases, the system passes from a fluid mixture, to a crystal of big particles in a fluid of small particles and back to a fluid mixture. Solidification is driven by entropy gain of small particles which overcomes the free energy cost of confining big ones. Melting results from enhanced interpenetration of particles at high temperature which reduces the entropic forces that stabilize the crystal.

cond-mat.soft↗

arXiv2020

Non-Equilibrium Interaction Between Catalytic Colloids: Boundary Conditions and Penetration Depth

Spherical colloids that catalyze the interconversion reaction $A \leftrightharpoons B$ between solute molecules $A$ and $B$ whose concentration at infinity is maintained away from equilibrium effectively interact due to the non-uniform fields of solute concentrations. We show that this long range $1/r$ interaction is suppressed via a mechanism that is superficially reminiscent but qualitatively very different from electrostatic screening: catalytic activity drives the concentrations of solute molecules towards their equilibrium values and reduces the chemical imbalance that drives the interaction between the colloids. The imposed non-equilibrium boundary conditions give rise to a variety of geometry-dependent scenarios; while long-range interactions are suppressed (except for a finite penetration depth) in the bulk of the colloid solution in 3D, they can persist in quasi-2D geometry in which the colloids but not the solutes are confined to a surface, resulting in the formation of clusters or Wigner crystals, depending on the sign of the interaction between colloids.

cond-mat.soft↗

arXiv2018

Dynamical response of a system of passive or active swimmers to time-periodic forcing

The presence of active forces in various biological and artificial systems may change how those systems behaves under forcing. We present a minimal model of a suspension of passive or active swimmers driven on the boundaries by time-dependent forcing. In particular, we consider a time-periodic drive from which we determine the linear response functions of the suspension. The meaning of these response functions are interpreted in terms of the storage and dissipation of energy through the particles within the system. We find that while a slowly driven active system responds in a way similar to a passive system with a re-defined diffusion constant, a rapidly driven active system exhibits a novel behavior related to a change in the motoring activity of the particles due to the external drive.

cond-mat.soft↗

arXiv2018

Generalized Flory Theory for Rotational Symmetry Breaking of Complex Macromolecules

We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. We analyze this transition using a variational mean-field theory that combines the Gibbs-Bogolyubov-Feynman inequality with the concept of the Laplacian matrix. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of this Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension Eventually, the variational free energy landscape develops a complex structure with multiple competing minima.

cond-mat.soft↗

arXiv2018

Active sorting of particles as an illustration of the Gibbs mixing paradox

The Gibbs Mixing Paradox is a conceptual touchstone for understanding mixtures in statistical mechanics. While debates over the theoretical subtleties of particle distinguishability continue to this day, we seek to extend the discussion in another direction by considering devices which can only distinguish particles with limited accuracy. We introduce two illustrative models of sorting devices which are designed to separate a binary mixture, but which sometimes make mistakes. In the first model, discrimination between particle types is passive and sorting is driven, while the second model is based on an active proofreading network, where both discrimination and sorting have a tunable active component. We show that the performance of these devices may be enhanced out of equilibrium, and we further probe how the quality of particle sorting is maintained by trade-offs between the time taken and the energy dissipated. Considering these examples, we demonstrate how increasing the similarity between particles gradually increases the work required to sort them, eliminating the paradox, while preserving the limits imposed by standard equilibrium statistical mechanics.

cond-mat.stat-mech↗

arXiv2018

Colloidomers: freely-jointed polymers made of droplets

An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or `colloidomers'. The distribution of cluster sizes is consistent with a polymerization process in which the droplets achieve their prescribed valence. Conformational dynamics reveals that the chains are freely-jointed, such that the end-to-end length scales with the number of bonds $N$ as $N^ν$, where $ν\approx3/4$, in agreement with the Flory theory in 2D. The chain diffusion coefficient $D$ approximately scales as $D\propto N^{-ν}$, as predicted by the Zimm model. Unlike molecular polymers, colloidomers can be repeatedly assembled and disassembled under temperature cycling, allowing for reconfigurable, responsive matter.

cond-mat.soft↗

arXiv2018

Pressure and Flow of Exponentially Self-Correlated Active Particles

Microscopic swimming particles, which dissipate energy to execute persistent directed motion, are a classic example of a non-equilibrium system. We investigate the non-interacting Ornstein--Uhlenbeck Particle (OUP), which is propelled through a viscous medium by a force which is correlated over a finite time. We obtain an exact expression for the steady state phase-space density of a single OUP confined by a quadratic potential, and use the result to explore more complex geometries, both through analytical approximations and numerical simulations. In a "Casimir"-style setup involving two narrowly-spaced walls, we describe a particle-trapping phenomenon, which leads to a repulsive effective interaction between the walls; while in a two-dimensional annulus geometry, we observe net stresses which resemble the Laplace pressure.

cond-mat.soft↗

arXiv2018

Memory Effects in Active Particles with Exponentially Correlated Propulsion

The Ornstein--Uhlenbeck Particle (OUP) model imagines a microscopic swimmer propelled by an active force which is correlated with itself on a finite time-scale. Here we investigate the influence of external potentials on an ideal suspension of OUPs, in both one and two spatial dimensions, with particular attention paid to the pressure exerted on "confining walls". We employ a mathematical connection between the local density of OUPs and the statistics of their propulsion force to demonstrate the existence of an equation of state in one dimension. In higher dimensions we show that active particles generate a non-conservative force field in the surrounding medium. A simplified far-from-equilibrium model is proposed to account for OUP behaviour in the vicinity of potentials. Building on this, we interpret simulations of OUPs in more complicated situations involving asymmetrical and spatially curved potentials, characterising the inhomogeneous local stresses which result in terms of competing active length-scales.

cond-mat.soft↗

arXiv2016

Quasi-Equilibrium Self-Assembly of Small RNA Viruses

We propose a description for the quasi-equilibrium self-assembly of small, single-stranded (ss) RNA viruses whose capsid proteins (CPs) have flexible, positively charged, disordered tails that associate with the negatively charged RNA genome molecules. We describe the assembly of such viruses as the interplay between two coupled phase-transition like events: the formation of the protein shell (the capsid) by CPs and the condensation of a large ss viral RNA molecule. Electrostatic repulsion between the CPs competes with attractive hydrophobic interactions and attractive interaction between neutralized RNA segments mediated by the tail-groups. An assembly diagram is derived in terms of the strength of attractive interactions between CPs and between CPs and the RNA molecules. It is compared with the results of recent studies of viral assembly. We demonstrate that the conventional theory of self-assembly, which does describe the assembly of \textit{empty} capsids, is in general not applicable to the self-assembly of RNA-encapsidating virions.

cond-mat.soft↗

arXiv2015

Artificial Rheotaxis

Motility is a basic feature of living microorganisms, and how it works is often determined by environmental cues. Recent efforts have focused on develop- ing artificial systems that can mimic microorganisms, and in particular their self-propulsion. Here, we report on the design and characterization of syn- thetic self-propelled particles that migrate upstream, known as positive rheo- taxis. This phenomenon results from a purely physical mechanism involving the interplay between the polarity of the particles and their alignment by a viscous torque. We show quantitative agreement between experimental data and a simple model of an overdamped Brownian pendulum. The model no- tably predicts the existence of a stagnation point in a diverging flow. We take advantage of this property to demonstrate that our active particles can sense and predictably organize in an imposed flow. Our colloidal system represents an important step towards the realization of biomimetic micro-systems withthe ability to sense and respond to environmental changes

cond-mat.soft↗

arXiv2015

A perturbative theory for Brownian vortexes

Brownian vortexes are stochastic machines that use static non-conservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak non-conservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

cond-mat.soft↗

arXiv2015

From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers

We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius $R$, at large $R$, obeys, in the scaling sense, $ΔS \sim R^2/(a^2L)$, with $a$ bond length (or Kuhn segment) and $L$ defined as an average spanning distance. We show that this estimate is valid up to at most the logarithmic correction for any tree. We do so by explicitly computing the largest eigenvalues of Kramers matrices for both regular and "sparse" 3-branched trees, uncovering on the way their peculiar mathematical properties.

cond-mat.stat-mech↗

arXiv2015

Activity induced phase separation

We consider a mixture of passive (i.e., Brownian) and active (e.g., bacterial or colloidal swimmers) particles, and analyze the stability conditions of either uniformly mixed or phase segregated steady states consisting of phases enriched with different types of particles. We show that in sufficiently dilute mixtures the system behaves as if it were exposed to two separate heat baths of uneven temperatures. It can be described within a second virial approximation neglecting three body and higher order collisions. In this approximation, we define non-equilibrium "chemical potentials" whose gradients govern diffusion fluxes and a non-equilibrium "osmotic pressure", which governs the mechanical stability of the interface.

cond-mat.stat-mech↗

arXiv2014

Understanding the dynamics of rings in the melt in terms of annealed tree model

Dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in the light of the recently developed Flory theory of unentangled rings which maps every ring on an annealed branched polymer and establishes that the backbone associated with each ring follows self-avoiding rather than Gaussian random walk statistics. We find the scaling of ring relaxation time and diffusion coefficient with ring length, as well as time dependence of stress relaxation modulus, zero shear viscosity and mean square averaged displacements of both individual monomers and ring's mass center. Our results agree within error bars with all available experimental and simulations data of the ring melt, although the quality of the data so far is insufficient to make a definitive judgment for or against the annealed tree theory. In the end we review briefly the relation between our findings and experimental data on chromatin dynamics.

cond-mat.soft↗