arXiv subjects

Alex J. Levine

Publications and source records attributed to Alex J. Levine.

At least 19 recordsLinked to original sources

arXiv2021

Braiding dynamics in semiflexible filament bundles under oscillatory forcing

We examine the nonequilibrium production of topological defects -- braids -- in semiflexible filament bundles under cycles of compression and tension. During these cycles, the period of compression facilitates the thermally activated pair production of braid/anti-braid pairs, which then may separate when the bundle is under tension. As result, appropriately tuned alternating periods of compression and extension should lead to the proliferation of braid defects in a bundle so that linear density of these pairs far exceeds that expected in thermal equilibrium. Secondly, we examine the slow extension of braided bundles under tension, showing that their end-to-end length creeps nonmonotonically under a fixed force due to braid deformation and the motion of the braid pair along the bundle. We conclude with a few speculations regarding experiments on semiflexible filament bundles and their networks.

cond-mat.soft↗

arXiv2020

Microcircuit synchronization and heavy tailed synaptic weight distribution in preBötzinger Complex contribute to generation of breathing rhythm

The preBötzinger Complex, the mammalian inspiratory rhythm generator, encodes inspiratory time as motor pattern. Spike synchronization throughout this sparsely connected network generates inspiratory bursts albeit with variable latencies after preinspiratory activity onset in each breathing cycle. Using preBötC rhythmogenic microcircuit minimal models, we examined the variability in probability and latency to burst, mimicking experiments. Among various physiologically plausible graphs of 1000 point neurons with experimentally determined neuronal and synaptic parameters, directed Erdős-Rényi graphs best captured the experimentally observed dynamics. Mechanistically, preBötC (de)synchronization and oscillatory dynamics are regulated by the efferent connectivity of spiking neurons that gates the amplification of modest preinspiratory activity through input convergence. Furthermore, to replicate experiments, a lognormal distribution of synaptic weights was necessary to augment the efficacy of convergent coincident inputs. These mechanisms enable exceptionally robust yet flexible preBötC attractor dynamics that, we postulate, represent universal temporal-processing and decision-making computational motifs throughout the brain.

q-bio.NC↗

arXiv2020

Disordered biopolymer filament bundles: Topological defects and kinks

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate analytically, numerically and experimentally that such bundles can be kinked, i.e., have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross links; a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross links, the last two effects lead to the topologically protected kinked states. Finally, we explore numerically and analytically the transition of the metastable kinked state to the stable straight bundle.

cond-mat.soft↗

arXiv2020

Geometrically-induced localization of flexural waves on thin warped physical membranes

We consider the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved. The stress-free configuration is specified by a quenched height field, whose Fourier components are drawn from a Gaussian distribution with power law variance. Gaussian curvature couples the in-plane stretching to out-of-plane bending. Integrating out the faster stretching modes yields a wave equation for undulations in the presence of an effective random potential, determined purely by geometry. We show that at long times/lengths, the undulation intensity obeys a diffusion equation. The diffusion coefficient is found to be frequency dependent and sensitive to the quenched height field distribution. Finally, we consider the effect of coherent backscattering corrections, yielding a weak localization correction that decreases the diffusion coefficient proportional to the logarithm of the system size, and induces a localization transition at large amplitude of the quenched height field. The localization transition is confirmed via a self-consistent extension to the strong disorder regime.

cond-mat.soft↗

arXiv2020

Directed force propagation in semiflexible networks

We consider the propagation of tension along specific filament of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogenous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network.

cond-mat.soft↗

arXiv2020

The effects of curvature on the propagation of undulatory waves in lower dimensional elastic materials

The mechanics of lower dimensional elastic structures depends strongly on the geometry of their stress-free state. Elastic deformations separate into in-plane stretching and lower energy out-of-plane bending deformations. For elastic structures with a curved stress-free state, these two elastic modes are coupled within linear elasticity. We investigate the effect of that curvature-induced coupling on wave propagation in lower dimensional elastic structures, focusing on the simplest example -- a curved elastic rod. We find that the dispersion relation of the waves becomes gapped in the presence of finite curvature; bending modes are absent below a frequency proportional to the curvature of the rod. By studying the scattering of undulatory waves off regions of uniform curvature, we find that undulatory waves with frequencies in the gap associated with the curved region tunnel through that curved region via conversion into compression waves. These results should be directly applicable to the spectrum and spatial distribution of phonon modes in a number of curved rod-like elastic solids, including carbon nanotubes and biopolymer filaments.

cond-mat.soft↗

arXiv2020

Dynamics of undulatory fluctuations of semiflexible filaments in a network

We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, whose value depends on the filament's instantaneous end-to-end length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the Martin-Siggia-Rose-Janssen-de-Domincis formalism, and compute the time-dependent correlation functions of transverse undulations and of the filament's end-to-end distance. The relaxational dynamics of the modes below a characteristic wavelength $\sqrt{κ/τ_R}$, set by the filament's bending modulus $κ$ and spring-renormalized tension $τ_{R}$, are changed by the boundary spring. This occurs near the cross-over frequency between tension- and bending-dominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross-linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks' collective shear response. The system's dynamic shear modulus is predicted to exhibit the well-known crossover with increasing frequency from $ω^{1/2}$ to $ω^{3/4}$, but the inclusion of the the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.

cond-mat.soft↗

arXiv2020

Dynamical phase separation on rhythmogenic neuronal networks

We explore the dynamics of the preBötzinger complex, the mammalian central pattern generator with $N \sim 10^3$ neurons, which produces a collective metronomic signal that times the inspiration. Our analysis is based on a simple firing-rate model of excitatory neurons with dendritic adaptation (the Feldman Del Negro model [Nat. Rev. Neurosci. 7, 232 (2006), Phys. Rev. E 2010 :051911]) interacting on a fixed, directed Erdős-Rényi network. In the all-to-all coupled variant of the model, there is spontaneous symmetry breaking in which some fraction of the neurons become stuck in a high firing-rate state, while others become quiescent. This separation into firing and non-firing clusters persists into more sparsely connected networks, and is partially determined by $k$-cores in the directed graphs. The model has a number of features of the dynamical phase diagram that violate the predictions of mean-field analysis. In particular, we observe in the simulated networks that stable oscillations do not persist in the large-N limit, in contradiction to the predictions of mean-field theory. Moreover, we observe that the oscillations in these sparse networks are remarkably robust in response to killing neurons, surviving until only $\approx 20 \%$ of the network remains. This robustness is consistent with experiment.

q-bio.NC↗

arXiv2019

The equilibrium fluctuations of a semiflexible filament cross linked into a network

We examine the equilibrium fluctuation spectrum of a constituent semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network, and its elastic compliance. Most significantly, the network's compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament's fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following: (i) network tension, (ii) filament bending stiffness, or (iii) network compliance. We propose that one can use observed filament fluctuations as a noninvasive probe of network tension, and we provide the necessary response function to quantitatively analyze this sort of "tension microrheology" in cross linked semiflexible filament networks.

cond-mat.soft↗

arXiv2019

The conformation of a semiflexible filament in a quenched random potential

Motivated by the observation of the storage of excess elastic free energy - (prestress) -- in cross linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross linking to other filaments is assumed to have a finite correlation length $ξ$ and mean strength $V_{0}$. We examine statistical distribution of curvature in filament with thermal persistence length $\ell_{P}$ and length $L_0$ in the limit that $\ell_{P} \gg L_0$. We compare our theoretical predictions to finite element Brownian dynamics simulations. Lastly we comment on the validity of replica field techniques in addressing these questions.

cond-mat.soft↗

arXiv2017

Encoding Mechano-Memories in Actin Networks

Understanding the response of complex materials to external force is central to fields ranging from materials science to biology. Here, we describe a novel type of mechanical adaptation in cross-linked networks of F-actin, a ubuiquitous protein found in eukaryotic cells. We show that shear stress changes its nonlinear mechanical response even long after that stress is removed. The duration, magnitude and direction of forcing history all impact changes in mechanical response. The `memory' of the forcing history is long-lived, but can be erased by force application in the opposite direction. We further show that the observed mechanical adaptation is consistent with stress-dependent changes in the nematic order of the constituent filaments. Thus, this mechano-memory is a type of nonlinear hysteretic response in which an applied, "training" strain modifies the nonlinear elasticity. This demonstrates that F-actin networks can encode analog read-write mechano-memories, which can be used for adaptation to mechanical stimuli.

cond-mat.soft↗

arXiv2015

Using an ion trap with two temperature reservoirs to explore nonequilibrium physics

Using a combination of molecular dynamics simulations and fundamental statistical mechanics, we analyze the position and velocity distribution of a trapped ion immersed in two ideal gases at differing temperatures. Such a system has been realized in the recently developed MOTion trap architecture. This system has the potential to serve as platform for studying nonequilibrium statistical mechanics in a controlled environment. As examples, we demonstrate a non-Maxwell Boltzmann velocity ionic distribution in the trap, the breakdown of the fluctuation-dissipation theorem, and position-velocity sorting, wherein high-velocity ionic states are over represented at points of high potential energy. We propose experiments to test these predictions.

cond-mat.stat-mech↗

arXiv2013

Shape transitions in soft spheres regulated by elasticity

We study elasticity-driven morphological transitions of soft spherical core shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.

cond-mat.soft↗

arXiv2013

High-energy deformation of filaments with internal structure and localized torque-induced melting of DNA

We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single standed DNA chain. This construct, studied by Qu et al. [Europhys. Lett., $\bf{94}$, 18003, 2011], displays nonlinear strain softening associated with the local melting of the double stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented worm-like chain model, the helix coil worm-like chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented worm-like chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.

cond-mat.soft↗

arXiv2011

Intermolecular adhesion in conjugated polymers: The role of the band gap and solitonic excitations

Conjugated polymers are soft, one-dimensional conductors that admit complex interactions between their polymeric, conformational degrees of freedom and their electronic ones. The presence of extended electronic states along their backbone allows for inter-chain electronic tunneling at points where these polymers make near passes. Using a combination of analytic modeling and Hartree-Fock numerical calculations, we study the localized electronic states that form due to such close encounters between semiconducting conjugated polymers and explore how these states lead to chain--chain binding. We also study the interaction of these inter-chain binding sites with solitonic excitations on the chains. From these results and a modified Poland-Scheraga model, we determine the equilibrium structures of paired-chains formed by intermolecular electronic tunneling. We calculate the energetic ground state of such pairs and show the effective thermal persistence length of the paired chains can vary over an order of magnitude due to the intermolecular binding mechanism.

cond-mat.soft↗

arXiv2010

The Affine-Nonaffine Transition in Anisotropic Semiflexible Networks

We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to non-affine cross-over controlled by the ratio of the filament length to the non-affinity length. Deep in the non-affine regime, however, these anisotropic networks exhibit a much more complex mechanical response characterized by a vanishing linear response regime for highly ordered networks and a generically more complex dependence of the shear modulus upon the direction of shear relative to the nematic director. We show that these features can be understood in terms of a generalized floppy modes analysis of the non-affine mechanics and a type of cooperative Euler buckling.

cond-mat.soft↗

arXiv2008

Rhythmogenic neuronal networks, pacemakers, and k-cores

Neuronal networks are controlled by a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a minimal model of the preBotzinger complex, a small neuronal network that controls the breathing rhythm of mammals through periodic firing bursts. We show that the properties of a such a randomly connected network of identical excitatory neurons are fundamentally different from those of uniformly connected neuronal networks as described by mean-field theory. We show that (i) the connectivity properties of the networks determines the location of emergent pacemakers that trigger the firing bursts and (ii) that the collective desensitization that terminates the firing bursts is determined again by the network connectivity, through k-core clusters of neurons.

q-bio.NC↗

arXiv2008

Effective Viscosity of a Dilute Suspension of Membrane-bound Inclusions

When particulate suspensions are sheared, perturbations in the shear flows around the rigid particles increase the local energy dissipation, so that the viscosity of the suspension is effectively higher than that of the solvent. For bulk (three-dimensional) fluids, understanding this viscosity enhancement is a classic problem in hydrodynamics that originated over a century ago with Einstein's study of a dilute suspension of spherical particles. \cite{Einstein1} In this paper, we investigate the analogous problem of the effective viscosity of a suspension of disks embedded in a two-dimensional membrane or interface. Unlike the hydrodynamics of bulk fluids, low-Reynolds number membrane hydrodynamics is characterized by an inherent length scale generated by the coupling of the membrane to the bulk fluids that surround it. As a result, we find that the size of the particles in the suspension relative to this hydrodynamic length scale has a dramatic effect on the effective viscosity of the suspension. Our study also helps to elucidate the mathematical tools needed to solve the mixed boundary value problems that generically arise when considering the motion of rigid inclusions in fluid membranes.

cond-mat.soft↗