Viscoelastic subdiffusion, transport and anomalous rate processes in multistablepotentials: in and out of thermal equilibrium, influence of time-periodic andstochastic fields
Final Report Abstract
The primary goal of this project was to investigate viscoelastic subdiffusion in nonlinear potentials such as bistable potentials, washboard and ratchet potentials driven by either time-periodic or stochastic fields. Such processes are described by a nonlinear generalized Langevin equation (GLE) with algebraically decaying memory kernel and a correspondingly correlated thermal noise, similar to fractional Langevin equation. The project took advantage of the route of memory kernel approximation by a sum of exponentials (Prony series expansion) and a corresponding multi-scale multi-dimensional Markovian embedding of non-Markovian GLE dynamics. Such an approach has earlier been shown to be numerically accurate on exactly solvable non-Markovian fractional diffusion problems and can be also considered as independent approach to anomalous dynamics. This methodology has been elaborated further and successfully applied to study a large circle of nonlinear physical problems of interest, most of which were investigated for the first time. They can be divided into the two groups: (1) basic models of driven noisy transport generalized towards anomalous diffusion, i.e. basic models of nonequilibrium statistical physics, and (2) biophysical models pertinent to molecular motors and ion channels. First, it has been shown that subdiffusive rocking Brownian ratchets of this viscoelastic kind are genuine fractional Brownian motors characterized by a non-zero stalling force and capable to do a useful work. Stochastic energetics of such ratchets has been investigated and it has been shown that they can be characterized by a fractional power, and fractional thermodynamic efficiency. The standard power and thermodynamic efficiency decline algebraically in time. Nevertheless, transiently on a long time scale thermodynamic efficiency of fractional Brownian motors is comparable with their normal diffusion counterpart, which is rather surprising. Furthermore, it has been shown that optimization of fractional subdiffusive current versus temperature for a periodic driving is of a genuine stochastic resonance (SR) nature. The occurrence of such a genuine non-Markovian SR for subdiffusive systems is really surprising. Second, a model of on-off flashing potential subdiffusive ratchets has been introduced and studied for both periodic and stochastic potential modulations. For a periodic flashing and in the presence of inertial effects, fractional subdiffusive current co-exists with resonance and synchronization effects. This paradoxical feature is a benchmark of viscoelastic subdiffusive dynamics which is mostly ergodic. Subdiffusive current can even be inverted and flow into the counter-intuitive direction under a nontrivial synchronization condition. Clearly, such characteristic features are physically simple impossible for another kind of fractional subdiffusion based on divergent mean residence time in traps. This is one of profound conclusions from the research work done. Third, we proposed and developed several pertinent models of subdiffusive cargo transport in living cells based on a well-known flashing ratchet model of molecular motors by (i) generalizing it towards subdiffusive overdamped dynamics of a compound particle, and (ii) coupling a normal diffusion molecular motor moving on microtubule to subdiffusive (when free) cargo by an elastic linker. Our models explain why and under which conditions one and the same molecular motors in the same cell can realize both normal and subdiffusive transport of subdiffusing cargos, in accordance with some experimental work. It has been shown that a perfect ratchet transport, where the motor steps are perfectly synchronized with the random flashes of binding potential, is possible in spite of subdiffusion. Here, we elucidated a physical mechanism of how subdiffusional slowness can be overcame by molecular motors in living cells. By taking into account a bidirectional mechano-chemical coupling it has been shown that enzymatic turnovers of the molecular motor can become anomalously slow and scale sublinearly in time under a load. This is the first time when such an anomalous enzyme kinetics, which cannot be characterized by a turnover number because of the influence of subdiffusive viscoelastic interior of living cells, is predicted from a physical model deeply rooted in the very foundations of statistical mechanics. Astonishingly, the motor transport can proceed very fast in absolute terms in this anomalous transport regime and be thermodynamically highly efficient (transiently over 50% efficiency). As a general conclusion from this research, it can be very misleading to associate subdiffusional transport with slowness and deteriorated efficiency. Fourth, we developed a model of hypothetical magnetosensitive ion channels tentatively responsible (one of the current hypotheses) for sensing weak magnetic fields by various animals (birds, bats, rats, bees, fishes, etc). Our model succinctly shows that the origin of both stretched exponential dependence and a power law dependence in the distribution of dwelling times measured for several really existing ion channels can be rooted in the viscoelasticity of the environment in which the channel operates. The project resulted in a number of very surprising and even paradoxical results which lay the ground for a follow-up research of a broad interdisciplinary interest which is mostly welcome and expected.
Publications
- (2012): Flashing subdiffusive ratchets in viscoelastic media, New J. Phys., 14, 043042
Kharchenko, V. and Goychuk, I.
(See online at https://doi.org/10.1088/1367-2630/14/4/043042) - (2012): Fractional Brownian motors and Stochastic Resonance, Phys. Rev. E 85, 051131
Goychuk, I. and Kharchenko, V.
(See online at https://doi.org/10.1103/PhysRevE.85.051131) - (2012): Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower. Phys. Rev. E 86, 021113
Goychuk, I.
(See online at https://doi.org/10.1103/PhysRevE.86.021113) - Viscoelastic Subdiffusion: Generalized Langevin Equation Approach, in: Advances in Chemical Physics, edited by S. A. Rice and A. R. Dinner (John Wiley & Sons, Hoboken, NJ, 2012), Vol. 150, pp. 187-253
Goychuk, I.
- (2013): Subdiffusive rocking ratchets in viscoelastic media: Transport optimization and thermodynamic efficiency in overdamped regime, Phys. Rev. E 87, 052119
Kharchenko, V.O. and Goychuk, I.
(See online at https://doi.org/10.1103/PhysRevE.87.052119) - (2014): Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises, Phys. Rev. Lett. 113, 100601
Goychuk, I., Kharchenko, V. O.
(See online at https://doi.org/10.1103/PhysRevLett.113.100601) - (2014): How molecular motors work in the crowded environment of living cells: coexistence and efficiency of normal and anomalous transport, PLoS ONE 9, e91700
Goychuk, I., Kharchenko, V.O., Metzler, R.
(See online at https://doi.org/10.1371/journal.pone.0091700) - (2014): Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion, Phys. Chem. Chem. Phys. 16 , 16524
Goychuk, I., Kharchenko, V.O., Metzler, R.
(See online at https://doi.org/10.1039/c4cp01234h) - (2015): Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechanochemical coupling and anharmonicity of tether, Physical Biology 12, 016013
Goychuk, I.
(See online at https://doi.org/10.1088/1478-3975/12/1/016013) - (2015): Modeling magnetosensitive ion channels in viscoelastic environment of living cells, Phys. Rev. E 92 , 042711
Goychuk, I.
(See online at https://doi.org/10.1103/PhysRevE.92.042711)
