Showing papers by "Udo Seifert published in 2005"

Entropy production along a stochastic trajectory and an integral fluctuation theorem.

Abstract: For stochastic nonequilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and entropy production in the surrounding medium. The integrated sum of both $\ensuremath{\Delta}{s}_{\mathrm{tot}}$ is shown to obey a fluctuation theorem $⟨\mathrm{exp} [\ensuremath{-}\ensuremath{\Delta}{s}_{\mathrm{tot}}]⟩=1$ for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval.

Integral fluctuation theorem for the housekeeping heat

Abstract: The housekeeping heat Qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states By analysing the evolution of its probability distribution, we prove an integral fluctuation theorem exp[−βQhk] = 1 valid for arbitrary-driven transitions between steady states We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano–Sasa and the Jarzynski relation

Experimental test of the fluctuation theorem for a driven two-level system with time-dependent rates.

Abstract: A single defect center in diamond periodically excited by a laser is shown to provide a simple realization for a system obeying a fluctuation theorem for nonthermal noise. The distribution of these fluctuations is distinctly non-Gaussian, which has also been verified by numerical calculation. For driving protocols symmetric under time reversal a more restricted form of the theorem holds, which is also known from entropy fluctuations caused by thermal noise.

Fluctuation theorem for a single enzym or molecular motor

Abstract: Cyclically operating enzyms and molecular motors are shown to be restricted non-linearly by a fluctuation theorem that basically relates the number of backward steps to that of forward steps. Only if the rates obey a quasi-equilibrium form in terms of chemical potentials and mechanical load, this fluctuation theorem becomes the usual one for entropy fluctuations. Boundary terms can be subsumed under an entropy change if one defines a trajectory-dependent entropy of the enzym or motor. Explicit expressions are derived for a three-state motor with and without an intermediate state and an enzym with Michaelis-Menten kinetics.

Lateral diffusion of a protein on a fluctuating membrane

Abstract: Measurements of lateral diffusion of proteins in a membrane typically assume that the movement of the protein occurs in a flat plane. Real membranes, however, are subject to thermal fluctuations, leading to movement of an inclusion into the third dimension. We calculate the magnitude of this effect by projecting real three-dimensional diffusion onto an effective one on a flat plane. We consider both a protein that is free to diffuse in the membrane and one that also couples to the local curvature. For a freely diffusing inclusion the measured projected diffusion constant is up to 15% smaller than the actual value. Coupling to the curvature enhances diffusion significantly up to a factor of two.

Dissipated work in driven harmonic diffusive systems: General solution and application to stretching Rouse polymers

Abstract: We study n-dimensional diffusive motion in an externally driven harmonic potential. For these systems the probability distribution of the applied work is a Gaussian. We give explicit expressions for its mean and variance, which are determined by a non-local integral kernel relating the time-derivatives of the applied forces. As illustrations, we specialize our results to dragging a colloidal particle through a viscous fluid and to stretching a Rouse polymer with different protocols.

Effective adhesion strength of specifically bound vesicles.

Abstract: A theoretical approach has been undertaken in order to model the thermodynamic equilibrium of a 3D vesicle adhering to a flat substrate. The vesicle is treated in a canonical description with a fixed number of sites. A finite number of these sites are occupied by mobile ligands that are capable of interacting with a discrete number of receptors immobilized on the substrate. Explicit consideration of the bending energy of the vesicle shape has shown that the problem of the vesicle shape can be decoupled from the determination of the optimum allocation of ligands over the vesicle. The allocation of bound and free ligands in the vesicle can be determined as a function of the size of the contact zone, the ligand-receptor binding strength, and the concentration of the system constituents. Several approximate solutions for different regions of system parameters are determined and in particular, the distinction between receptor- and ligand-dominated equilibria is found to be important. The crossover between these two types of solutions is found to occur at a critical size of the contact zone. The presented approach enables the calculation of the effective adhesion strength of the vesicle and thus permits meaningful comparisons with relevant experiments as well as connecting the presented model with the proven success of the continuum approach for modeling the shapes of adhering vesicles. The behavior of the effective adhesion strength is analyzed in detail and several approximate expressions for it are given.

Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state

Abstract: In a nonequilibrium steady state, the violation of the fluctuation-dissipation theorem (FDT) is connected to breaking detailed balance. For the velocity correlations of a driven colloidal particle we calculate an explicit expression of the FDT violation. The equilibrium form of the FDT can be restored by measuring the velocity with respect to the local mean velocity.

Force spectroscopy of single multidomain biopolymers: a master equation approach.

Abstract: Experiments using atomic force microscopy for unfolding single multidomain biopolymers cover a broad range of time scales from equilibrium to non-equilibrium. A master equation approach allows to identify and treat coherently three dynamical regimes for increasing linear ramp velocity: i) an equilibrium regime, ii) a transient regime where refolding events still occur, and iii) a saw-tooth regime without any refolding events. For each regime, analytical approximations are derived and compared to numerically investigated examples. We analyze in the framework of this model also a periodic experimental protocol instead of a linear ramp. In this case, a major simplification arises if the dynamics can be restricted to an effectively two-dimensional subspace. For transitions with an intermediate meta-stable state, like Immunoglobulin27, a refined model allows to extract previously unknown molecular parameters related to this meta-stable state.

Force-induced de-adhesion of specifically bound vesicles: strong adhesion in competition with tether extraction.

Abstract: A theoretical study of the thermodynamic equilibrium between force-induced tether formation and the adhesion of vesicles mediated by specific ligand-receptor interactions has been performed. The formation of bonds between mobile ligands in the vesicle and immobile receptors on the substrate is examined within a thermodynamic approximation. The shape of a vesicle pulled with a point force is calculated within a continuous approach. The two approaches are merged self-consistently by the use of the effective adhesion potential produced by the collective action of the bonds. As a result, the shapes of the vesicle and the tether, as well as the number of formed bonds in the contact zone, are determined as a function of the force, and approximate analytic expressions for them are provided. The de-adhesion process is characterized by the construction of a phase diagram that is a function of the density of the ligands in the vesicle, the surface coverage by receptors, the ligand-receptor binding affinity, and the reduced volume of the vesicle. In all cases, the phase diagram contains three regions separated by two nonintersecting lines of critical forces. The first is the line of onset forces associated with a second-order shape transition from a spherical cap to a tethered vesicle. The second line is attributed to the detachment forces at which a first-order unbinding transition from a tethered shape to a free vesicle occurs.

Integral fluctuation theorem for the housekeeping heat

Abstract: The housekeeping heat $Q\hk$ is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analyzing the evolution of its probability distribution, we prove an integral fluctuation theorem $\mean{\exp[-\beta Q\hk]}=1$ valid for arbitrary driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation.