Two-dimensional model of elastically coupled molecular motors

A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins.Extensive Langevin simulations of the model are performed.We discuss the dependences of motion and efficiency on the model parameters,including the external force and the temperature.A good qualitative agreement with the expected behavior is observed.     

玻色-爱因斯坦凝聚体中非线性相互作用对量子共振棘流的影响

研究了玻色-爱因斯坦凝聚体中非线性相互作用对量子共振棘流的影响．满足量子共振条件的周期驱动使得波包在动量空间出现弹道扩散,当波包扩散具有特定方向时,系统就出现定向的动量流．弱非线性相互作用下的冷原子分成两簇,它们分别受到方向相反的稳定周期驱动力,以各自恒定的加速度沿相反方向运动．波包在动量空间的扩散表现为两个稳定的沿相反方向运动的峰．非线性相互作用的增强使得正方向运动的冷原子减少,负方向运动的冷原子增加,从而系统的动量流减弱甚至反转．当非线性相互作用足够强时,动量空间中的波包只有一个稳定的峰,且峰值对应的动量不随时间变化．此时冷原子受的周期驱动力为零,定向的动量流消失．     

Directed transport in equilibrium: A model study

It is generally believed that sustained directed transport in mechanical systems is not achievable under equilibrium conditions. In this article, by analyzing a simple model, we will show that directed motion under equilibrium conditions can take place and is not inconsistent with conservation of energy and the second law of thermodynamics. Our model demonstrates a novel symmetry breaking mechanism sustainable under equilibrium conditions and average uniform motion of the center of mass is a consequence of the sustained broken symmetry. The most important consequence of our results is that, no current condition for mechanical equilibrium is possibly non-universal.     

Feedback control in a coupled Brownian ratchet

On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.     

Transport of biomolecules in asymmetric nanofilter arrays

We propose a theoretical model for describing the electric-field-driven migration of rod-like biomolecules in nanofilters comprising a periodic array of shallow passages connecting deep wells. The electrophoretic migration of the biomolecules is modeled as transport of point-sized Brownian particles, with the orientational degree of freedom captured by an entropy term. Using appropriate projections, the formulation dimensionality is reduced to one physical dimension, requiring minimal computation and making it ideal for device design and optimization. Our formulation is used to assess the effect of slanted well walls on the energy landscape and resulting molecule mobility. Using this approach, we show that asymmetry in the well shape, such as a well with one slanted and one vertical wall, may be used for separation using low-frequency alternating-current fields because the mobility of a biomolecule is different in the two directions of travel. Our results show that, compared to methods using direct-current fields, the proposed method remains effective at higher field strengths and can achieve comparable separation using a significantly shorter device.     

Molecular Motor Cycles: From Ratchets to Networks

Molecular motor cycles are studied in the framework of stochastic ratchets in which the motor moves along a 1-dimensional track, can attain M internal states, and can undergo transitions between these levels at K spatial positions. These ratchets can be mapped onto a stochastic network of KM discrete states. The network is governed by a Master equation, fulfills a vertex rule, and satisfies detailed balance in the absence of enzymatic activity and external force. Any pathway of the motor cycle which leads to a forward or backward step of the motor corresponds to a certain sequence of transitions spanning this network. The dependence of the motor velocity on the transition rates can be determined for arbitrary values of K and M and exhibits some simple and universal features.     

Dynamic instability of collective myosin Ⅱ motors

Some kinds of muscles can oscillate spontaneously,which is related to the dynamic instability of the collective motors.Based on the two-state ratchet model and with consideration of the motor stiffness,the dynamics of collective myosin Ⅱmotors are studied.It is shown that when the motor stiffness is small,the velocity of the collective motors decreases monotonically with load increasing.When the motor stiffness becomes large,dynamic instability appears in the forcevelocity relationship of the collective-motor transport.For a large enough motor stiffness,the zero-velocity point lies in the unstable range of the force-velocity curve,and the motor system becomes unstable before the motion is stopped,so spontaneous oscillations can be generated if the system is elastically coupled to its environment via a spring.The oscillation frequency is related to the motor stiffness,motor binding rate,spring stiffness,and the width of the ATP excitation interval.For a medium motor stiffness,the zero-velocity point lies outside the unstable range of the force-velocity curve,and the motion will be stopped before the instability occurs.     

Coulomb Friction Driving Brownian Motors

We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation (linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein-Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.     

Coefficient of Performance at Maximum χ-Criterion for Feynman Ratchet as a Refrigerator

The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tomás et al., Phys. Rev. E 85 (2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χ is investigated.     

Current Reversal Due to Coupling Between Asymmetrical Driving Force and Ratchet Potential

Transport of a Brownian particle moving in a periodic potential is investigated in the presence of an asymmetric unbiased external force. The asymmetry of the external force and the asymmetry of the potential are the two ways of inducing a net current. It is found that the competition of the spatial asymmetry of potential with the temporal asymmetry of the external force leads to the phenomena like current reversal. The competition between the two opposite driving factors is a necessary but not a sufficient condition for current reversals.