arXiv subjects

Igor Goychuk

Publications and source records attributed to Igor Goychuk.

At least 19 recordsLinked to original sources

arXiv2020

Finite-range viscoelastic subdiffusion in disordered systems with inclusion of inertial effects

This work justifies the paradigmatic importance of viscoelastic subdiffusion in random environments for cellular biological systems. This model displays several remarkable features, which makes it an attractive paradigm to explain the physical nature of biological subdiffusion. In particular, it combines viscoelasticity with distinct non-ergodic features. We extend this model to make it suitable for the subdiffusion of lipids in disordered biological membranes upon including the inertial effects. For lipids, the inertial effects occur in the range of picoseconds, and a power-law decaying viscoelastic memory extends over the range of several nanoseconds. Thus, in the absence of disorder, diffusion would become normal on a time scale beyond this memory range. However, both experimentally and in some molecular-dynamical simulations, the time range of lipid subdiffusion extends far beyond the viscoelastic memory range. We study three 1d models of correlated quenched Gaussian disorder to explain the puzzle: singular short-range (exponentially correlated), smooth short-range (Gaussian-correlated), and smooth long-range (power-law correlated) disorder. For a moderate disorder strength, transient viscoelastic subdiffusion changes into the subdiffusion caused by the randomness of the environment. It is characterized by a time-dependent power-law exponent of subdiffusion, which can show nonmonotonous behavior, in agreement with some recent molecular-dynamical simulations. Moreover, the spatial distribution of test particles in this disorder-dominated regime is shown to be a non-Gaussian, exponential power distribution, which also correlates well with molecular-dynamical findings and experiments. Furthermore, this subdiffusion is nonergodic with single-trajectory averages showing a broad scatter, in agreement with experimental observations for subdiffusion of various particles in living cells.

cond-mat.stat-mech↗

arXiv2020

Hydrodynamic memory can boost enormously driven nonlinear diffusion and transport

Hydrodynamic memory force or Basset force is known since the 19th-century. Its influence on Brownian motion remains, however, mostly unexplored. Here, we investigate its role in nonlinear transport and diffusion within a paradigmatic model of tilted washboard potential. In this model, a giant enhancement of driven diffusion over its potential-free limit presents a well-established paradoxical phenomenon. In the overdamped limit, it occurs at a critical tilt of vanishing potential barriers. However, for weak damping, it takes place surprisingly at another critical tilt, where the potential barriers are clearly expressed. Recently we showed that Basset force could make such a diffusion enhancement enormously large. In this paper, we discover that even for moderately strong damping, where the overdamped theory works very well when the memory effects are negligible, substantial hydrodynamic memory unexpectedly makes a strong impact. First, the diffusion boost occurs at non-vanishing potential barriers and can be orders of magnitude larger. Second, transient anomalous diffusion regimes emerge over many time decades and potential periods. Third, particles' mobility can also be dramatically enhanced, and a long transient super-transport regime emerges.

cond-mat.stat-mech↗

arXiv2019

Fractional electron transfer kinetics and a quantum breaking of ergodicity

The dissipative curve-crossing problem provides a paradigm for electron-transfer (ET) processes in condensed media. It establishes the simplest conceptual test bed to study the influence of the medium's dynamics on ET kinetics both on the ensemble level, and on the level of single particles. Single electron description is particularly important for nanoscale systems. Slow medium's dynamics is capable to enslave ET and bring it on the ensemble level from a quantum regime of non-adiabatic tunneling to the classical adiabatic regime, where electrons just follow the nuclei rearrangements. This classical adiabatic textbook picture contradicts, however, in a very spectacular fashion to the statistics of single electron transitions, even in the Debye, memoryless media, named also Ohmic in the parlance of the famed spin-boson model. On the single particle level, ET remains always quantum and this was named a quantum breaking of ergodicity in the adiabatic ET regime. What happens in the case of subdiffusive, fractional, or sub-Ohmic medium's dynamics, which is featured by power-law decaying dynamical memory effects pertinent e.g. for protein macromolecules, and other viscoelastic media? Such a memory is vividly manifested by anomalous Cole-Cole dielectric response typical for such media. This is the question which is addressed in this work based both on precise numerics and analytical semi-classical theory. The ensemble theory remarkably agrees with the numerical dynamics of electronic populations, revealing a power law relaxation tail even in a deeply non-adiabatic electron transfer regime. However, a profound difference with the numerically accurate results emerges for the distribution of residence times in the electronic states, both on the ensemble level and on the level of single trajectories. Ergodicity is broken dynamically even in a more spectacular way than in the memoryless case.

cond-mat.stat-mech↗

arXiv2018

Perfect anomalous transport of subdiffusive cargos by molecular motors in viscoelastic cytosol

Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed at each motor step along microtubule on average. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms.

physics.bio-ph↗

arXiv2018

Viscoelastic subdiffusion in a random Gaussian environment

Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several $k_BT$, in the units of thermal energy), and strong (5-10 $k_BT$) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compare with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.

cond-mat.stat-mech↗

arXiv2017

Comment on "Large Fluctuations for Spatial Diffusion of Cold Atoms" [arXiv:1701.03357]

A comment on the Letter by E. Aghion, D. Kessler, and E. Barkai, Phys. Rev. Lett. 118, 260601 (2017). An important criterion on finite kinetic temperature of the system of cold atoms is established. It is shown that the kinetic temperature becomes infinite in Fig. 1 of the commented paper in the course of time, i.e. the considered model system becomes asymptotically infinitely hot. Moreover, within this model the behavior of the squared width of the spatial distribution of atoms at the half of its maximum is very different from the variance of the particle positions. In particular, in the discussed Fig. 1 the former one increases sub-ballistically in time, while the variance grows super-ballistically, which corresponds to a heating phase. This leads to a profound ambiguity in definition and classification of anomalous diffusion. All in all, the model in the commented paper simply does not fit to experiments with cold atoms.

cond-mat.stat-mech↗

arXiv2017

Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations

Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-stationary potential fluctuations whose root mean squared amplitude grows with distance. We show here that extremely persistent, macroscopic ultraslow logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems. Combining results from extensive simulations with a scaling approach we elucidate the physical mechanism of this unusual subdiffusion. In particular, we explain why with growing temperature and/or time a first crossover occurs to standard, power-law subdiffusion, with a time-dependent power law exponent, and then a second crossover occurs to normal diffusion with a disorder-renormalized diffusion coefficient. Interestingly, the initial, nominally ultraslow diffusion turns out to be much faster than the universal de Gennes-Baessler-Zwanzig limit of the renormalized normal diffusion, which physically cannot be attained at sufficiently low temperatures and/or for strong disorder. The ultraslow diffusion is also non-ergodic and displays a local bias phenomenon. Our simple scaling theory not only explains our numerical findings, but qualitatively has also a predictive character.

cond-mat.stat-mech↗

arXiv2017

Fractional Bhatnagar-Gross-Krook kinetic equation

The linear Boltzmann equation approach is generalized to describe fractional superdiffusive transport of the Levy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional linear Boltzmann equation approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP.

cond-mat.stat-mech↗

arXiv2016

Molecular machines operating on nanoscale: from classical to quantum

The main physical features and operating principles of isothermal nanomachines in microworld are reviewed, which are common for both classical and quantum machines. Especial attention is paid to the dual and constructive role of dissipation and thermal fluctuations, fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. Our exposition allows to spot some common fallacies which continue to plague the literature, in particular, erroneous beliefs that one should minimize friction and lower the temperature to arrive at a high performance of Brownian machines, and that thermodynamic efficiency at maximum power cannot exceed one-half. The emerging topic of anomalous molecular motors operating sub-diffusively but highly efficiently in viscoelastic environment of living cells is also discussed.

cond-mat.mes-hall↗

arXiv2015

Quantum breaking of ergodicity in semi-classical charge transfer dynamics

Does electron transfer (ET) kinetics within a single-electron trajectory description always coincide with the ensemble description? This fundamental question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem of quantum Landau-Zener tunneling between two electronic states with overdamped classical reaction coordinate. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer a profound breaking of ergodicity occurs. The ensemble survival probability remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and inverse MLD rate. However, near to adiabatic regime, the single-electron survival probability is clearly non-exponential but possesses an exponential tail which agrees well with the ensemble description. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of nonadiabatic quantum tunneling rate on a single particle level.

cond-mat.mes-hall↗

arXiv2015

Modeling magnetosensitive ion channels in viscoelastic environment of living cells

We propose and study a model of hypothetical magnetosensitive ionic channels which are long thought to be a possible candidate to explain the influence of weak magnetic fields on living organisms ranging from magnetotactic bacteria to fishes, birds, rats, bats and other mammals including humans. The core of the model is provided by a short chain of magnetosomes serving as a sensor which is coupled by elastic linkers to the gating elements of ion channels forming a small cluster in the cell membrane. The magnetic sensor is fixed by one end on cytoskeleton elements attached to the membrane and is exposed to viscoelastic cytosol. Its free end can reorient stochastically and subdiffusively in viscoelastic cytosol responding to external magnetic field changes and open the gates of coupled ion channels. The sensor dynamics is generally bistable due to bistability of the gates which can be in two states with probabilities which depend on the sensor orientation. For realistic parameters, it is shown that this model channel can operate in the magnetic field of Earth for a small number (5 to 7) of single-domain magnetosomes constituting the sensor rod each of which has a typical size found in magnetotactic bacteria and other organisms, or even just one sufficiently large nanoparticle of a characteristic size also found in nature. It is shown that due to viscoelasticity of medium the bistable gating dynamics generally exhibits power law and stretched exponential distributions of the residence times of the channels in their open and closed states. This provides a generic physical mechanism for explanation of the origin of such anomalous kinetics for other ionic channels whose sensors move in viscoelastic environment provided by either cytosol or biological membrane, in a quite general context, beyond the fascinating hypothesis of magnetosensitive ionic channels we explore.

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↗

arXiv2015

Comment on "Non-Normalizable Densities in Strong Anomalous Diffusion: Beyond the Central Limit Theorem"

A comment on the Letter by A. Rebenshtok, S. Denisov, P. Hänggi, and E. Barkai, Phys. Rev. Lett., vol. 112, 110601 (2014). It is shown that the recent claims that the particle distributions or densities can become non-normalizable in the case of anomalous Levy walk diffusion cannot be justified. In particular, one can define a normalizable finite-time density which become infinite covariant density (ICD) in the limit of infinite time. The former one can be used to find any generalized moment, while the latter one does not. In this respect, we point out that any decent real or numerical experiment is done in finite time. Hence, ICD does not correspond to any physical reality, contrary to the claims made.

cond-mat.stat-mech↗

arXiv2014

Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechanochemical coupling and anharmonicity of tether

Here we generalize our previous model of molecular motors trafficking subdiffusing cargos in viscoelastic cytosol by (i) including mechanochemical coupling between cyclic conformational fluctuations of the motor protein driven by the reaction of ATP hydrolysis and its translational motion within the simplest two-state model of hand-over-hand motion of kinesin, and also (ii) by taking into account the anharmonicity of the tether between the motor and cargo (its maximally possible extension length). It is shown that the major earlier results such as occurrence of normal versus anomalous transport depending on the amplitude of binding potential, cargo size and the motor turnover frequency not only survive in this more realistic model, but the results also look very similar for the correspondingly adjusted parameters. However, this more realistic model displays a substantially larger thermodynamic efficiency due to a bidirectional mechanochemical coupling. For realistic parameters, the maximal thermodynamic efficiency can be transiently about 50% as observed for kinesins, and even larger, surprisingly also in a novel strongly anomalous (sub)transport regime, where the motor enzymatic turnovers become also anomalously slow and cannot be characterized by a turnover rate. Here anomalously slow dynamics of the cargo enforces anomalously slow cyclic kinetics of the motor protein.

physics.bio-ph↗

arXiv2014

Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises

Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius $\exp[-σ^2/(k_BT^2)]$ temperature-dependence in disordered systems. Here we show that unbiased diffusion remains asymptotically normal also in the presence of spatial correlations decaying to zero. However, due to a temporal lack of self-averaging transient subdiffusion emerges on mesoscale, and it can readily reach macroscale even for moderately strong disorder fluctuations of $σ\sim 4-5\, k_BT$. Due to its nonergodic origin such subdiffusion exhibits a large scatter in single trajectory averages. However, at odds with intuition, it occurs essentially faster than one expects from the normal diffusion in the absence of correlations. We apply these results to diffusion of regulatory proteins on DNA molecules and predict that such diffusion should be anomalous, but much faster than earlier expected on a typical length of genes for a realistic energy disorder of several room $k_BT$, or merely $0.05-0.075$ eV.

cond-mat.stat-mech↗

arXiv2014

Stochastic modeling of excitable dynamics: improved Langevin model for mesoscopic channel noise

Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject within the last decade, and the traditional biophysical models of neuronal dynamics such as Hodgkin-Huxley model have been generalized to incorporate such effects. There still exists but a controversy on how to do it in a proper and computationally efficient way. Here we introduce an improved Langevin description of stochastic Hodgkin-Huxley dynamics with natural boundary conditions for gating variables. It consistently describes the channel noise variance in a good agreement with discrete state model. Moreover, we show by comparison with our improved Langevin model that two earlier Langevin models by Fox and Lu also work excellently starting from several hundreds of ion channels upon imposing numerically reflecting boundary conditions for gating variables.

q-bio.NC↗

arXiv2014

Life and death of stationary linear response in anomalous continuous time random walk dynamics

Linear theory of stationary response in thermal systems subjected to external perturbations requires to find equilibrium correlation function of the responding system variable in the absence of external perturbations. Studies of the response of the systems exhibiting anomalously slow dynamics are often based on the continuous time random walk description (CTRW) with divergent mean waiting times. The bulk of the literature on anomalous response contains linear response functions like one by Cole-Cole calculated from such a CTRW theory and applied to thermal systems. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response is absent, in accordance with some recent studies. The absence of stationary response at thermal equilibrium (or dying to zero non-stationary response in aging experiments) would confirm CTRW with divergent mean waiting times as underlying physical relaxation mechanism, but reject it otherwise. We show that the absence of stationary response is closely related to the breaking of ergodicity of the corresponding dynamical variable. As an important new result, we derive a generalized Cole-Cole response within ergodic CTRW dynamics with finite waiting time. Moreover, we provide a physically reasonable explanation of the origin and wide presence of 1/f noise in condensed systems for ergodic dynamics close to normal, rather than mostly deviating.

cond-mat.stat-mech↗

arXiv2013

Molecular motors transporting cargos in viscoelastic cytosol: how to beat subdiffusion with a power stroke?

Anomalously slow passive diffusion, $\langle δx^2(t)\rangle\simeq t^α$, with $0<α<1$, of larger tracers such as messenger RNA and endogenous submicron granules in the cytoplasm of living biological cells has been demonstrated in a number of experiments and has been attributed to the viscoelastic physical nature of the cellular cytoplasm. This finding provokes the question to which extent active intracellular transport is affected by this viscoelastic environment: does the subdiffusion of free submicron cargo such as vesicles and organelles always imply anomalously slow transport by molecular motors such as kinesins, that is, directed transport characterized by a sublinear growth of the mean distance, $\langle x(t)\rangle\simeq t^{α_{\rm eff}}$, with $0<α_{\rm eff}<1$? Here we study a generic model approach combining the commonly accepted two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubule driven by a flashing binding potential. The motor is elastically coupled to a cargo particle, which in turn is subject to the viscoelastic cytoplasmic environment. Depending on the physical parameters of cargo size, loading force, amplitude of the binding potential, and the turnover frequency of the molecular motor, the transport can be both normal ($α_{\rm eff}=1$) and anomalous ($α\leq α_{\rm eff}<1$). In particular, we demonstrate in detail how highly efficient normal motor transport can emerge despite the anomalously slow passive diffusion of cargo particles, and how the active motion of the same motor in the same cell may turn anomalously slow when the parameters are changed.

physics.bio-ph↗