Characterizing Potentials by a Generalized Boltzmann Factor

Based on the concept of a nonequilibrium steady state, we present a novel method to experimentally determine energy landscapes acting on colloidal systems. By measuring the stationary probability distribution and the current in the system, we explore potential landscapes with barriers up to several hundred \kT. As an illustration, we use this approach to measure the effective diffusion coefficient of a colloidal particle moving in a tilted potential

The Einstein relation generalized to non-equilibrium

The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime. For a colloidal particle driven along a periodic potential imposed by laser traps, we test the recent theoretical generalization of the Einstein relation to the non-equilibrium regime which involves an integral over measurable velocity correlation functions

Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential

We study the motion of an overdamped colloidal particle in a time-dependent non-harmonic potential. We demonstrate the first law-like balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy

Finite sampling effects on generalized fluctuation-dissipation relations for steady states

We study the effects of the finite number of experimental data on the computation of a generalized fluctuation-dissipation relation around a nonequilibrium steady state of a Brownian particle in a toroidal optical trap. We show that the finite sampling has two different effects, which can give rise to a poor estimate of the linear response function. The first concerns the accessibility of the generalized fluctuation-dissipation relation due to the finite number of actual perturbations imposed to the control parameter. The second concerns the propagation of the error made at the initial sampling of the external perturbation of the system. This can be highly enhanced by introducing an estimator which corrects the error of the initial sampled condition. When these two effects are taken into account in the data analysis, the generalized fluctuation-dissipation relation is verified experimentally

Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle

Entropy production for mechanically or chemically driven biomolecules

Entropy production along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium. For a molecule manipulated mechanically by an AFM or an optical tweezer, entropy production (or annihilation) occurs in the molecular conformation proper or in the surrounding medium. Within a Langevin dynamics, a unique identification of these two contributions is possible. The total entropy change obeys an integral fluctuation theorem and a class of further exact relations, which we prove for arbitrarily coupled slow degrees of freedom including hydrodynamic interactions. These theoretical results can therefore also be applied to driven colloidal systems. For transitions between different internal conformations of a biomolecule involving unbalanced chemical reactions, we provide a thermodynamically consistent formulation and identify again the two sources of entropy production, which obey similar exact relations. We clarify the particular role degenerate states have in such a description

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt

On Replacement Strategies in Steady State Evolutionary Algorithms

Steady State models of Evolutionary Algorithms are widely used, yet surprisingly little attention has been paid to the effects arising from different replacement strategies. This paper explores the use of mathematical models to characterise the selection pressures arising in a selection-only environment. The first part brings together models for the behaviour of seven different replacement mechanisms and provides expressions for various proposed indicators of Evolutionary Algorithm behaviour. Some of these have been derived elsewhere, and are included for completeness, but the majority are new to this paper. These theoretical indicators are used to compare the behaviour of the different strategies. The second part of this paper examines the practical relevance of these indicators as predictors for algorithms' relative performance in terms of optimisation time and reliability. It is not the intention of this paper to come up with a "one size fits all" recommendation for choice of replacement strategy. Although some strategies may have little to recommend them, the relative ranking of others is shown to depend on the intended use of the algorithm to be implemented, as reflected in the choice of performance metrics. © 2007 by the Massachusetts Institute of Technology

The Clinical Variability of Maternally Inherited Diabetes and Deafness Is Associated with the Degree of Heteroplasmy in Blood Leukocytes

Context: Maternally inherited diabetes and deafness (MIDD) is a rare form of diabetes with a matrilineal transmission, sensorineural hearing loss, and macular pattern dystrophy due to an A to G transition at position 3243 of mitochondrial DNA (mtDNA) (m.3243A>G). The phenotypic heterogeneity of MIDD may be the consequence of different levels of mutated mtDNA among mitochondria in a given tissue. Objective: The aim of the present study was thus to ascertain the correlation between the severity of the phenotype in patients with MIDD and the level of heteroplasmy in the blood leukocytes. Participants: The GEDIAM prospective multicenter register was initiated in 1995. Eighty-nine Europid patients from this register, with MIDD and the mtDNA 3243A>G mutation, were included. Patients with MELAS (mitochondrial encephalomyopathy, lactic acidosis, and stroke-like episodes) or with mitochondrial diabetes related to other mutations or to deletions of mtDNA were excluded. Results: A significant negative correlation was found between levels of heteroplasmy and age of the patients at the time of sampling for molecular analysis, age at the diagnosis of diabetes, and body mass index. After adjustment for age at sampling for molecular study and gender, the correlation between heteroplasmy levels and age at the diagnosis of diabetes was no more significant. The two other correlations remained significant. A significant positive correlation between levels of heteroplasmy and HbA1c was also found and remained significant after adjustment for age at molecular sampling and gender. Conclusions: These results support the hypothesis that heteroplasmy levels are at least one of the determinants of the severity of the phenotype in MIDD. Heteroplasmy levels are at least one of the determinants of the severity of the phenotype of maternally inherited diabetes and deafness