@article{GoychukKharchenko2014, author = {Goychuk, Igor and Kharchenko, Vasyl O.}, title = {Anomalous features of diffusion in corrugated potentials with spatial correlations: Faster than normal, and other surprises}, series = {Physical review letters}, volume = {113}, journal = {Physical review letters}, number = {10}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.113.100601}, pages = {5}, year = {2014}, abstract = {Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius exp[-sigma(2)/(k(B)T(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, because of a temporal lack of self-averaging, transient subdiffusion emerges on the mesoscale, and it can readily reach macroscale even for moderately strong disorder fluctuations of sigma similar to 4 - 5k(B)T. Because of 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(B)T, or merely 0.05-0.075 eV.}, language = {en} } @article{Goychuk2015, author = {Goychuk, Igor}, title = {Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechano-chemical coupling and anharmonicity of tether}, series = {Physical biology : a journal for the fundamental understanding of biological systems}, volume = {12}, journal = {Physical biology : a journal for the fundamental understanding of biological systems}, number = {1}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1478-3967}, doi = {10.1088/1478-3975/12/1/016013}, pages = {14}, year = {2015}, abstract = {Here we generalize our previous model of molecular motors trafficking subdiffusing cargos in viscoelastic cytosol by (i) including mechano-chemical 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 the 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 mechano-chemical coupling. For realistic parameters, the maximal thermodynamic efficiency can transiently be 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.}, language = {en} } @misc{Goychuk2019, author = {Goychuk, Igor}, title = {Comment on "Anomalous Escape Governed by Thermal 1/f Noise" Reply (R. K. Singh)}, series = {Physical review letters}, volume = {123}, journal = {Physical review letters}, number = {23}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.123.238902}, pages = {1}, year = {2019}, language = {en} } @article{Goychuk2017, author = {Goychuk, Igor}, title = {Fractional Bhatnagar-Gross-Krook kinetic equation}, series = {The European physical journal : B, Condensed matter and complex systems}, volume = {90}, journal = {The European physical journal : B, Condensed matter and complex systems}, publisher = {Springer}, address = {New York}, issn = {1434-6028}, doi = {10.1140/epjb/e2017-80297-x}, pages = {13}, year = {2017}, abstract = {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. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.}, language = {en} } @article{Goychuk2019, author = {Goychuk, Igor}, title = {Fractional electron transfer kinetics and a quantum breaking of ergodicity}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {99}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {5}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.99.052136}, pages = {21}, year = {2019}, abstract = {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 nanoscaled systems like proteins, or molecular wires. Especially insightful is this framework in the semiclassical limit, where the environment can be treated classically, and an exact analytical treatment becomes feasible. Slow medium's dynamics is capable of enslaving ET and bringing it on the ensemble level from a quantum regime of nonadiabatic tunneling to the classical adiabatic regime, where electrons 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, also named Ohmic in the parlance of the famed spin-boson model. On the single particle level, ET always remains 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 typical, e.g., for protein macromolecules, and other viscoelastic media? Such a memory is vividly manifested by anomalous Cole-Cole dielectric response in such media. We address this question based both on accurate numerics and analytical theory. The ensemble theory remarkably agrees with the numerical dynamics of electronic populations, revealing a power-law relaxation tail even in a profoundly nonadiabatic electron transfer regime. In other words, ET in such media should typically display fractional kinetics. However, a profound difference with the numerically accurate results occurs for the distribution of residence times in the electronic states, both on the ensemble level and the level of single trajectories. Ergodicity is broken dynamically even in a more spectacular way than in the memoryless case. Our results question the applicability of all the existing and widely accepted ensemble theories of electron transfer in fractional, sub-Ohmic environments, on the level of single molecules, and provide a real challenge to face, both for theorists and experimentalists.}, language = {en} } @article{Goychuk2019, author = {Goychuk, Igor}, title = {Fractional Hydrodynamic Memory and Superdiffusion in Tilted Washboard Potentials}, series = {Physical review letters}, volume = {123}, journal = {Physical review letters}, number = {18}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.123.180603}, pages = {6}, year = {2019}, abstract = {Diffusion in tilted washboard potentials can paradoxically exceed free normal diffusion. The effect becomes much stronger in the underdamped case due to inertial effects. What happens upon inclusion of usually neglected fractional hydrodynamics memory effects (Basset-Boussinesq frictional force), which result in a heavy algebraic tail of the velocity autocorrelation function of the potential-free diffusion making it transiently superdiffusive? Will a giant enhancement of diffusion become even stronger, and the transient superdiffusion last even longer? These are the questions that we answer in this Letter based on an accurate numerical investigation. We show that a resonancelike enhancement of normal diffusion becomes indeed much stronger and sharper. Moreover, a long-lasting transient regime of superdiffusion, including Richardson-like diffusion, proportional to t(3) and ballistic supertransport, proportional to t(2), is revealed.}, language = {en} } @article{GoychukKharchenkoMetzler2014, author = {Goychuk, Igor and Kharchenko, Vasyl O. and Metzler, Ralf}, title = {How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport}, series = {PLoS one}, volume = {9}, journal = {PLoS one}, number = {3}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0091700}, pages = {7}, year = {2014}, abstract = {Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.}, language = {en} } @article{Goychuk2014, author = {Goychuk, Igor}, title = {Life and death of stationary linear response in anomalous continuous time random walk dynamics}, series = {Communications in theoretical physics : a series journal of the Chinese Physical Society (A)}, volume = {62}, journal = {Communications in theoretical physics : a series journal of the Chinese Physical Society (A)}, number = {4}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0253-6102}, pages = {497 -- 504}, year = {2014}, abstract = {Linear theory of stationary response in systems at thermal equilibrium requires to find equilibrium correlation function of unperturbed responding system. 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 systems at thermal equilibrium. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response at thermal equilibrium is absent, in accordance with some recent studies. The absence of such stationary response (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 matter for ergodic dynamics close to normal, rather than strongly deviating.}, language = {en} } @article{Goychuk2015, author = {Goychuk, Igor}, title = {Modeling magnetosensitive ion channels in the viscoelastic environment of living cells}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.92.042711}, pages = {18}, year = {2015}, abstract = {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 can 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 (five to seven) 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 the viscoelasticity of the 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 the explanation of the origin of such anomalous kinetics for other ionic channels whose sensors move in a viscoelastic environment provided by either cytosol or biological membrane, in a quite general context, beyond the fascinating hypothesis of magnetosensitive ionic channels we explore.}, language = {en} } @misc{Goychuk2016, author = {Goychuk, Igor}, title = {Molecular machines operating on the nanoscale: from classical to quantum}, series = {Beilstein journal of nanotechnology}, volume = {7}, journal = {Beilstein journal of nanotechnology}, publisher = {Beilstein-Institut zur F{\~A}\Prderung der Chemischen Wissenschaften}, address = {Frankfurt, Main}, issn = {2190-4286}, doi = {10.3762/bjnano.7.31}, pages = {328 -- 350}, year = {2016}, abstract = {The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the 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. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.}, language = {en} }