arXiv subjects

Andriy Goychuk

Publications and source records attributed to Andriy Goychuk.

11 recordsLinked to original sources

arXiv2026

Dynamical mean-field theory of active, self-interacting heteropolymers

Analytical theories of polymer dynamics typically focus on the linear response around some steady state obtained via perturbative calculations. The present study derives a dynamical, nonlinear mean-field theory that yields unified access to the evolution of conformations, contact probabilities, and fluctuations of active polymers within a single analytical framework. As in previous mean-field descriptions of passive polymers, the object of interest is the two-point correlator, which is the lowest-order relevant observable in the general Langevin equation of a polymer. In contrast, the present focus is on active polymers driven by heterogeneous monomer-level kicks and spatially correlated active flows, while allowing nonreciprocal couplings, in the presence of hydrodynamic and contact interactions. Using a Gaussian closure to truncate higher-order correlations leads to a self-consistent diffusion equation for the chain correlations. In some cases, this can be further simplified to the dynamics of pairwise squared separations in closed form. In the continuum limit, the theory reveals useful analogies to similar mean-field approximations for reaction-diffusion systems, as well as fractional diffusion in different scale-free regimes. Deriving asymptotic solutions in different parameter regimes of the continuum limit recovers the scalings of coiled, globular, and self-avoiding polymers, thus validating the theory. Applied to hydrodynamically coupled active polymers, such as chromatin, the framework predicts a sequence of crossover scalings between coiled, swollen, and hyper-compacted fractal states.

cond-mat.soft↗

arXiv2026

Active fluctuations induce buckling of living surfaces

Active tissues exhibit tension fluctuations that are correlated in space and time. We study a minimal overdamped surface model in which such fluctuations enter as a zero-mean, multiplicative modulation of the local surface tension. Although the deterministic elastic dynamics (tension plus bending) stabilizes the flat state for all nonzero wave numbers, we find that sufficiently persistent active fluctuations generate positive ensemble growth rates for a finite band of Fourier modes, leading to stochastic buckling with wavelength selection. A non-Markovian theory based on the Novikov--Furutsu theorem captures the instability threshold and unstable band observed in simulations.

cond-mat.soft↗

arXiv2025

Externally driven condensates show translation-induced polarization, directed coalescence, and anomalous diffusion in viscoelastic media

Phase separation into compositionally and physically distinct domains is ubiquitous in (non)living matter ranging from alloys and emulsions to biomolecular condensates in cells. The organization of these domains can be controlled, for example, by nonequilibrium chemical reactions, external fields, or mechanical stresses. In this context, stationary states can emerge from effective long-range interactions resembling the electrostatics of charges. As shown here, externally controlled dynamic states, such as condensate motion, lead to an effective polarization and dipolar force fields even for microscopically nonpolarizable matter. The dipole-dipole interactions resulting from this \emph{translation-induced polarization} cause directed coalescence of domains. This coarsening mechanism complements Ostwald ripening and coalescence due to Brownian motion or Marangoni flows, and has implications for controlling domains by electric fields or concentration gradients. Interestingly, the chemical potential gradients around a domain that nucleates material are exactly opposite to the hydrodynamic pressure gradients around an impermeable colloid that pushes the fluid, suggesting a competition between phase separation and hydrodynamics. In addition to chemical control, the motion of domains can also be driven by mechanical stresses. An example is the cell interior, where mechanical stresses are actively generated by molecular motors and opposed by passive viscoelastic stresses in the cytoplasm and nucleoplasm. The resulting fluid flows lead to Brownian motion with a suppressed or enhanced size scaling which modifies collision-coalescence. For active stresses with a long correlation time, the domains show superdiffusion on intermediate time scales. Together, these findings shed new light on the dynamics of domains in viscoelastic media and conserved order parameters in general.

cond-mat.soft↗

arXiv2024

Self-consistent sharp interface theory of active condensate dynamics

Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for non-uniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel non-equilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries.

physics.bio-ph↗

arXiv2024

Hidden nonreciprocity as a stabilizing effective potential in active matter

Nonreciprocal interactions are known to produce distinctive dynamics in active matter. To shed light on how the stationary state of such systems is affected by breaking reciprocity, we consider interacting particles propelled by persistent noise, where reciprocity is broken by a transverse force perpendicular to the gradient of the interaction energy. Focusing on the steady-state distribution of positions, we show that the nonreciprocal coupling helps keep the system at its stable configurations. Specifically, we demonstrate this effect for a variety of active systems whose stable configurations are energy minima, finding that the nonreciprocal coupling stiffens springs, aligns spins, and improves associative memory. In contrast, the transverse force does not change the stationary distribution of positions at all when the noise is thermal. Preliminary simulations suggest that this nonreciprocal coupling plays a similar stabilizing role in other active systems, such as those exhibiting motility-induced phase separation, whose stable configurations are not energy minima.

cond-mat.stat-mech↗

arXiv2024

Delayed excitations induce polymer looping and coherent motion

We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.

cond-mat.soft↗

arXiv2023

Enzyme-enriched condensates show self-propulsion, positioning, and coexistence

Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing non-equilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move towards the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.

physics.bio-ph↗

arXiv2022

Geometry-induced patterns through mechanochemical coupling

Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic changes of cell shape. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the resulting rich dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves that do not occur in systems with a fixed membrane shape. Our work reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.

nlin.PS↗

arXiv2019

Protein recruitment through indirect mechanochemical interactions

Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation, and is strongly affected by membrane composition.

physics.bio-ph↗

arXiv2018

Morphology and Motility of Cells on Soft Substrates

Recent experiments suggest that the interplay between cells and the mechanics of their substrate gives rise to a diversity of morphological and migrational behaviors. Here, we develop a Cellular Potts Model of polarizing cells on a visco-elastic substrate. We compare our model with experiments on endothelial cells plated on polyacrylamide hydrogels to constrain model parameters and test predictions. Our analysis reveals that morphology and migratory behavior are determined by an intricate interplay between cellular polarization and substrate strain gradients generated by traction forces exerted by cells (self-haptotaxis).

physics.bio-ph↗

arXiv2015

Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay

We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around -1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence.

q-bio.NC↗