Fractional Brownian motors and stochastic resonance

Roughness induced current reversal in fractional hydrodynamic memory

The existence of a corrugated surface is of great importance and ubiquity in biological systems, exhibiting diverse dynamic behaviors. However, it has remained unclear whether such rough surface leads to the current reversal in fractional hydrodynamic memory. We investigate the transport of a particle within a rough potential under external forces in a subdiffusive media with fractional hydrodynamic memory. The results demonstrate that roughness induces current reversal and a transition from no transport to transport. These phenomena are analyzed through the subdiffusion, Peclet number, useful work, input power, and thermodynamic efficiency. The analysis reveals that transport results from energy conversion, wherein time-dependent periodic force is partially converted into mechanical energy to drive transport against load, and partially dissipated through environmental absorption. In addition, the findings indicate that the size and shape of ratchet tune the occurrence and disappearance of the current reversal, and control the number of times of the current reversal occurring. Furthermore, we find that temperature, friction, and load tune transport, resonant-like activity, and enhanced stability of the system, as evidenced by thermodynamic efficiency. These findings may have implications for understanding dynamics in biological systems and may be relevant for applications involving molecular devices for particle separation at the mesoscopic scale.

High-temperature ratchets driven by deterministic and stochastic fluctuations

We consider the overdamped dynamics of a Brownian particle in an arbitrary spatial periodic and time-dependent potential on the basis of an exact solution for the probability density in the form of a power series in the inverse friction coefficient. The expression for the average velocity of a Brownian ratchet is simplified in the high-temperature consideration when only the first terms of the series can be used. For the potential of an additive-multiplicative form (a sum of a time-independent contribution and a time-dependent multiplicative perturbation), general explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations. For qualitative and quantitative analysis of these dependences, we choose illustrative examples for spatial harmonic fluctuations: with deterministic time dependences of a relaxation type and stochastic time dependences describing Markovian dichotomous and harmonic noise processes. We explore the influence of fluctuation types on the ratchet effect and demonstrate its enhancement in the case of harmonic noise.

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 on average at each motor step along microtubule. 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.

Molecular machines operating on the nanoscale: from classical to quantum

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.

Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling

The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.

Modeling magnetosensitive ion channels in the 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 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.

Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion

The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.

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

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.

How molecular motors work in the crowded environment of living cells: coexistence and efficiency of normal and anomalous transport

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.

Subdiffusive rocking ratchets in viscoelastic media: transport optimization and thermodynamic efficiency in overdamped regime

We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of a non-Markovian generalized Langevin equation approach and associated multidimensional Markovian embedding dynamics. Viscoelastic deformations of the medium caused by the transport particle are modeled by a set of auxiliary Brownian quasiparticles elastically coupled to the transport particle and characterized by a hierarchy of relaxation times which obey a fractal scaling. The most slowly relaxing deformations which cannot immediately follow to the moving particle imprint long-range memory about its previous positions and cause subdiffusion and anomalous transport on a sufficiently long time scale. This anomalous behavior is combined with normal diffusion and transport on an initial time scale of overdamped motion. Anomalously slow directed transport in a periodic ratchet potential with broken space inversion symmetry emerges due to a violation of the thermal detailed balance by a zero-mean periodic driving and is optimized with frequency of driving, its amplitude, and temperature. Such optimized anomalous transport can be low dispersive and characterized by a large generalized Peclet number. Moreover, we show that overdamped subdiffusive ratchets can sustain a substantial load and do useful work. The corresponding thermodynamic efficiency decays algebraically in time since the useful work done against a load scales sublinearly with time following to the transport particle position, but the energy pumped by an external force scales with time linearly. Nevertheless, it can be transiently appreciably high and compare well with the thermodynamical efficiency of the normal diffusion overdamped ratchets on sufficiently long temporal and spatial scales.