Interaction-controlled Brownian motion in a tilted periodic potential

Vortex motion and nonlinear response in coupled noisy phase oscillator lattices under shear stress

Vortex motion in coupled phase oscillator lattices is analogous to the dislocation motion in crystals. A single vortex exhibits a glide motion by force at the boundaries. Thermal fluctuations induce the glide motion even below the critical point corresponding to the Peierls stress. The random drift motion is approximated as a random walk in a tilted potential. If the temperature is high, vortices are spontaneously generated. A nonlinear response where the frequency profile is relatively flat in the central region and changes sharply near the boundaries is observed when the vortex density becomes large and nonuniform.

Dynamic and Thermodynamic Bounds for Collective Motor-Driven Transport

Molecular motors work collectively to transport cargo within cells, with anywhere from one to several hundred motors towing a single cargo. For a broad class of collective-transport systems, we use tools from stochastic thermodynamics to derive a new lower bound for the entropy production rate which is tighter than the second law. This implies new bounds on the velocity, efficiency, and precision of general transport systems and a set of analytic Pareto frontiers for identical motors. In a specific model, we identify conditions for saturation of these Pareto frontiers.

Nonequilibrium master equation for interacting Brownian particles in a deep-well periodic potential

Employing a creation and annihilation operator formulation, we derive an approximate many-body master equation describing discrete hopping from the more general continuous description of Brownian motion on a deep-well nonequilibrium periodic potential. The many-body master equation describes interactions of arbitrary strength and range arising from a "top-hat" two-body interaction potential. We show that this master equation reduces to the well-known asymmetric simple exclusion process and the zero range process in certain regimes. We also use the creation and annihilation operator formalism to derive results for the steady-state drift and the number fluctuations in special cases, including the unexplored limit of weak interparticle interactions.

Brownian particles driven by spatially periodic noise

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as [Formula: see text] with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.

Internal energy and information flows mediate input and output power in bipartite molecular machines

Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the general design principles governing how biomolecular machines achieve effective free-energy transduction in light of these challenges. We use a model of two strongly coupled stochastic rotary motors to explore the effect of coupling strength between components of a molecular machine. We observe prominent thermodynamic characteristics at intermediate coupling strength, near that which maximizes output power: a maximum in power and information transduced from the upstream to the downstream system, and equal subsystem entropy production rates. These observations are unified through a bound on the machine's input and output power, which accounts for both the energy and information transduced between subsystems.

Negative resistance for colloids driven over two barriers in a microchannel

When considering the flow of currents through obstacles, one core expectation is that the total resistance of sequential single resistors is additive. While this rule is most commonly applied to electronic circuits, it also applies to other transport phenomena such as the flow of colloids or nanoparticles through channels containing multiple obstacles, as long as these obstacles are sufficiently far apart. Here we explore the breakdown of this additivity for fluids of repulsive colloids driven over two energetic barriers in a microchannel, using real-space microscopy experiments, particle-resolved simulations, and dynamical density functional theory. If the barrier separation is comparable to the particle correlation length, the resistance is highly non-additive, such that the resistance added by the second barrier can be significantly higher or lower than that of the first. Surprisingly, in some cases the second barrier can even add a negative resistance, such that two identical barriers are easier to cross than a single one. We explain this counterintuitive observation in terms of the structuring of particles trapped between the barriers.

Nonequilibrium Energy Transduction in Stochastic Strongly Coupled Rotary Motors

Living systems at the molecular scale are composed of many constituents with strong and heterogeneous interactions, operating far from equilibrium, and subject to strong fluctuations. These conditions pose significant challenges to efficient, precise, and rapid free energy transduction, yet nature has evolved numerous molecular machines that do just this. Using a simple model of the ingenious rotary machine F_oF₁-ATP synthase, we investigate the interplay between nonequilibrium driving forces, thermal fluctuations, and interactions between strongly coupled subsystems. This model reveals design principles for effective free energy transduction. Most notably, while tight coupling is intuitively appealing, we find that output power is maximized at intermediate-strength coupling, which permits lubrication by stochastic fluctuations with only minimal slippage.

Enhancement of mobility in an interacting colloidal system under feedback control

Feedback control schemes are a promising way to manipulate transport properties of driven colloidal suspensions. In the present article, we suggest a feedback scheme to enhance the collective transport of colloidal particles with repulsive interactions through a one-dimensional tilted washboard potential. The control is modeled by a harmonic confining potential, mimicking an optical "trap," with the center of this trap moving with the (instantaneous) mean particle position. Our theoretical analysis is based on the Smoluchowski equation combined with dynamical density functional theory for systems with hard-core or ultrasoft (Gaussian) interactions. For either type of interaction, we find that the feedback control can lead to an enhancement of the mobility by several orders of magnitude relative to the uncontrolled case. The largest effects occur for intermediate stiffness of the trap and large particle numbers. Moreover, in some regions of the parameter space the feedback control induces oscillations of the mean velocity. Finally, we show that the enhancement of mobility is robust against a small time delay in implementing the feedback control.

Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential

We report a Brownian dynamics simulation study of a two-dimensional system of repulsive colloidal particles in a channel geometry with a sinusoidal substrate potential under influence of a constant driving. The effect of this driving on the structure, mobility, and diffusion is discussed as well as the appearance of kink and antikink solitons. The competing order principles of the hexagonal crystal structure, the period of the substrate, and the layering due to the confining walls can be either commensurable or incommensurable. The combination of those three leads to new effects. The simultaneous occurrence of kinks and antikinks can be observed, due to the energy difference between boundary- and midlanes, and similarities to the electron-hole conductivity in a semiconductor can be found.

Synchronization of elastically coupled processive molecular motors and regulation of cargo transport

The collective work of motor proteins plays an important role in cellular transport processes. Since measuring intermotor coupling and hence a comparison to theoretical predictions is difficult, we introduce the synchronization as an alternative observable for motor cooperativity. This synchronization can be determined from the ratio of the mean times of motor resting and stepping. Results from a multistate Markov chain model and Brownian dynamics simulations, describing the elastically coupled motors, coincide well. Our model can explain the experimentally observed effect of strongly increased transport velocities and powers by the synchronization and coupling of myosin V and kinesin I.

Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

Effects of phase disorder on transport of globally coupled Brownian motors

The transport of N globally coupled Brownian motors driven by a periodic force with phase disorder is investigated. An approximate theoretical analysis of the model is presented. The effects of the phase disorder and the driving strength of the periodic force on the transport of the coupled Brownian motors are discussed both theoretically and numerically. It is found that the increase of the periodical driving force decreases the average velocity, while the coupled particles may benefit from the phase disorder to enhance collective transport.

Particle diode: rectification of interacting Brownian ratchets

Transport of Brownian particles interacting with each other via the Morse potential is investigated in the presence of an ac driving force applied locally at one end of the chain. By using numerical simulations, we find that the system can behave as a particle diode for both overdamped and underdamped cases. For low frequencies, the transport from the free end to the ac acting end is prohibited, while the transport from the ac acting end to the free end is permitted. However, the polarity of the particle diode will reverse for medium frequencies. There exists an optimal value of the well depth of the interaction potential at which the average velocity takes its maximum. The average velocity υ decreases monotonically with the system size N by a power law υ ∝ N(-1).

Nanoimaging for protein misfolding diseases

Misfolding and aggregation of proteins are widespread phenomena leading to the development of numerous neurodegenerative disorders such as Parkinson's, Alzheimer's, and Huntington's diseases. Each of these diseases is linked to structural misfolding and aggregation of a particular protein. The aggregated forms of the protein induce the development of a particular disease at all levels, leading to neuronal dysfunction and loss. Because protein refolding is frequently accompanied by transient association of partially folded intermediates, the propensity to aggregate is considered a general characteristic of the majority of proteins. X-ray crystallography, nuclear magnetic resonance, electron microscopy, and atomic force microscopy have provided important information on the structure of aggregates. However, fundamental questions, such as why the misfolded conformation of the protein is formed, and why this state is important for self-assembly, remain unanswered. Although it is well known that the same protein under pathological conditions can lead to the formation of aggregates with diverse biological consequences, the conditions leading to misfolding and the formation of the disease prone complexes are unclear, complicating any development of efficient prevention of the diseases. Misfolded states exist transiently, so answering these questions requires the use of novel approaches and methods. Progress has been made during the past few years, when recently developed ensemble methods and single-molecule biophysics techniques were applied to the problem of the protein misfolding. In this review, the impacts of these studies on the understanding of the mechanisms of the protein self-assembly into aggregates and on the development of treatments of the diseases are discussed.

Cooperativity of self-organized Brownian motors pulling on soft cargoes

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.

Effects of rotation on the nonlinear friction of a damped dimer sliding on a periodic substrate

Rotational effects on the nonlinear sliding friction of a damped dimer moving over a substrate are studied within a largely one-dimensional model. The model consists of two masses connected rigidly, internally damped, and sliding over a sinusoidal (substrate) potential while being free to rotate in the plane containing the masses and the direction of sliding. Numerical simulations of the dynamics performed by throwing the dimer with an initial center of mass velocity along the substrate direction show a richness of phenomena including the appearance of three separate regimes of motion. The orientation of the dimer performs tiny oscillations around values that are essentially constant in each regime. The constant orientations form an intricate pattern determined by the ratio of the dimer length to the substrate wavelength as well as by the initial orientations chosen. Corresponding evolution of the center of mass velocity consists, respectively, of regular oscillations in the first and the third regimes, but a power law decay in the second regime; the center of mass motion is effectively damped in this regime because of the coupling to the rotation. Depending on the initial orientation of the dimer, there is considerable variation in the overall behavior. For small initial angles to the vertical, an interesting formal connection can be established to earlier results known in the literature for a vibrating, rather than rotating, dimer. But for large angles, on which we focus in the present paper, quite different evolution occurs. Some of the numerical observations are explained successfully on the basis of approximate analytical arguments but others pose puzzling problems.

Current control in a tilted washboard potential via time-delayed feedback

We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.