A novel kinetic model to demonstrate the independent effects of ATP and ADP/Pi concentrations on sarcomere function.

Understanding muscle contraction mechanisms is a standing challenge, and one of the approaches has been to create models of the sarcomere-the basic contractile unit of striated muscle. While these models have been successful in elucidating many aspects of muscle contraction, they fall short in explaining the energetics of functional phenomena, such as rigor, and in particular, their dependence on the concentrations of the biomolecules involved in the cross-bridge cycle. Our hypothesis posits that the stochastic time delay between ATP adsorption and ADP/Pi release in the cross-bridge cycle necessitates a modeling approach where the rates of these two reaction steps are controlled by two independent parts of the total free energy change of the hydrolysis reaction.

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.

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.

Symmetry-based classification of forces driving chromatin dynamics.

Chromatin - the functional form of DNA in the cell - exists in the form of a polymer immersed in a nucleoplasmic fluid inside the cell nucleus. Both chromatin and nucleoplasm are subject to active forces resulting from local biological processes. This activity leads to non-equilibrium phenomena, affecting chromatin organization and dynamics, yet the underlying physics is far from understood.

Stretching of a Fractal Polymer around a Disc Reveals Kardar-Parisi-Zhang Scaling.

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. We use scaling analysis and computer simulations to examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. We reveal that the typical excursions of the polymer away from the surface and curvature-induced correlation length scale as Δ∼R^{β} and S^{*}∼R^{1/z}, respectively, with the Kardar-Parisi-Zhang (KPZ) growth β=1/3 and dynamic exponents z=3/2.

Reentrant transitions in a mixture of small and big particles interacting via soft repulsive potential.

We report an observation of a temperature-controlled reentrant transition in simulations of mixtures of small and big particles interacting via a soft repulsive potential in two dimensions. 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.

Tethered tracer in a mixture of hot and cold Brownian particles: can activity pacify fluctuations?

We study how an interacting mixture of components with differing levels of activity can affect the fluctuations of an embedded object such as a tracer. In particular, we consider a simple model of a tracer that is harmonically bound within a mixture of hot and cold Brownian particles, which, like a mixture of active and passive particles, can phase separate. By measuring the fluctuations of the tracer, we find that this collective behavior gives rise to an effective temperature for the tracer.

Non-equilibrium interaction between catalytic colloids: boundary conditions and penetration depth.

Spherical colloids that catalyze the interconversion reaction A⇋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.

Three-body problem for Langevin dynamics with different temperatures.

A mixture of Brownian particles at different temperatures has been a useful model for studying the out-of-equilibrium properties of systems made up of microscopic components with differing levels of activity. This model was previously studied analytically for two-particle interactions in the dilute limit, yielding a Boltzmann-like two-particle distribution with an effective temperature. Like the Newtonian two- and three-body problems, we ask here whether the two-particle results can be extended to three-particle interactions to get the three-particle distributions.

Comment on "Osmotic pressure of compressed lattice knots".

In a recent paper, E. J. Janse van Rensburg has presented computational data enumerating the conformations of closed circular self-avoiding lattice polymers with knots confined in a cubic box, and claimed to have observed a negative osmotic pressure in the system.

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.

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.

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.

Confining annealed branched polymers inside spherical capsids.

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R dependence.

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 nonequilibrium system. We investigate the noninteracting 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.

Flory theory of randomly branched polymers.

Randomly branched polymer chains (or trees) are a classical subject of polymer physics with connections to the theory of magnetic systems, percolation and critical phenomena. More recently, the model has been reconsidered for RNA, supercoiled DNA and the crumpling of topologically-constrained polymers. While solvable in the ideal case, little is known exactly about randomly branched polymers with volume interactions.

Direct observation of DNA knots using a solid-state nanopore.

Long DNA molecules can self-entangle into knots. Experimental techniques for observing such DNA knots (primarily gel electrophoresis) are limited to bulk methods and circular molecules below 10 kilobase pairs in length. Here, we show that solid-state nanopores can be used to directly observe individual knots in both linear and circular single DNA molecules of arbitrary length.

Minimal Surfaces on Unconcatenated Polymer Rings in Melt.

In order to quantify the effect of mutual threading on conformations and dynamics of unconcatenated and unknotted rings in the melt we computationally examine their minimal surfaces. We found a linear scaling of the surface area with the ring length. Minimal surfaces allow for an unambiguous algorithmic definition of mutual threading between rings.

Scale-Dependent Viscosity in Polymer Fluids.

In this communication, we use simple physical arguments to construct a "phase diagram" of various frequency and wave vector-dependent regimes of effective viscosity for polymer fluids, including nonentangled and entangled melts, semidilute solutions without and with hydrodynamic interactions, as well as the more exotic case of a melt of unconcatenated ring polymers.

Sequence Dependence of Viral RNA Encapsidation.

We develop a Flory mean-field theory for viral RNA (vRNA) molecules that extends the current RNA folding algorithms to include interactions between different sections of the secondary structure. The theory is applied to sequence-selective vRNA encapsidation. The dependence on sequence enters through a single parameter: the largest eigenvalue of the Kramers matrix of the branched polymer obtained by coarse graining the secondary structure.

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 developing artificial systems that can mimic microorganisms, in particular their self-propulsion. We report on the design and characterization of synthetic self-propelled particles that migrate upstream, known as positive rheotaxis.