Fluctuation Theorems

Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical relationships for free energy changes. They describe the statistical fluctuations in time-averaged properties of many-particle systems such as fluids driven to nonequilibrium states, and provide some of the very few analytical expressions that describe nonequilibrium states. Quantitative predictions on fluctuations in small systems that are monitored over short periods can also be made, and therefore the fluctuation theorems allow thermodynamic concepts to be extended to apply to finite systems. For this reason, fluctuation theorems are anticipated to play an important role in the design of nanotechnological devices and in understanding biological processes. These theorems, their physical significance and results for experimental and model systems are discussed.Comment: A review, submitted to Annual Reviews in Physical Chemistry, July 2007 Acknowledgements corrected in revisio

Experimental study of the fluctuation theorem in a nonequilibrium steady state

The fluctuation theorem (FT) quantifies the probability of second law violations in small systems over short time scales. While this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state, there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state. The asymptotic application of the FT to such nonequilibrium steady states has been referred to in the literature as the steady-state fluctuation theorem (or SSFT). In this paper, we demonstrate experimentally the application of the FT to nonequilibrium steady states, using a colloidal particle localized in a translating optical trap. Furthermore, we show, for this colloidal system, that the FT holds under nonequilibrium steady states for all time, and not just in the long time limit, as in the SSFT

Conformational isomers of linear rotaxanes

We examine a simple model of rotaxane structure, with 3 asymmetric rings interacting via repulsive power-law forces. This interlocked molecule exhibits conformational isomerisation which is different from that of molecules whose connectedness is through covalent bonds. The rings are free to translate along and rotate around the axle, and hence weak interaction forces between the rings can lead to distinct rotamer states. We use energy minimisation to determine these states exactly, and show that there can be transitions from asymmetric to symmetric states by varying the bond lengths. We also use classical statistical mechanics to show the effect of thermal noise

Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations

Brownian dynamics simulations are used to study the detachment of a particle from a substrate. Although the model is simple and generic, we attempt to map its energy, length and time scales onto a specific experimental system, namely a bead that is weakly bound to a cell and then removed by an optical tweezer. The external driving force arises from the combined optical tweezer and substrate potentials, and thermal fluctuations are taken into account by a Brownian force. The Jarzynski equality and Crooks' fluctuation theorem are applied to obtain the equilibrium free energy difference between the final and initial states. To this end, we sample non--equilibrium work trajectories for various tweezer pulling rates. We argue that this methodology should also be feasible experimentally for the envisioned system. Furthermore, we outline how the measurement of a whole free energy profile would allow the experimentalist to retrieve the unknown substrate potential by means of a suitable deconvolution. The influence of the pulling rate on the accuracy of the results is investigated, and umbrella sampling is used to obtain the equilibrium probability of particle escape for a variety of trap potentials.Comment: 21 pages, 11 figures, To appear in Soft Matte

Non-equilibrium umbrella sampling applied to force spectroscopy of soft matter

Physical systems often respond on a timescale which is longer than that of the measurement. This is particularly true in soft matter where direct experimental measurement, for example in force spectroscopy, drives the soft system out of equilibrium and provides a non-equilibrium measure. Here we demonstrate experimentally for the first time that equilibrium physical quantities (such as the mean square displacement) can be obtained from non-equilibrium measurements via umbrella sampling. Our model experimental system is a bead fluctuating in a time-varying optical trap. We also show this for simulated force spectroscopy on a complex soft molecule--a piston-rotaxane

Coarse-graining intramolecular hydrodynamic interaction in dilute solutions of flexible polymers

We present a scheme for coarse-graining hydrodynamic interactions in an isolated flexible homopolymer molecule in solution. In contrast to the conventional bead-spring model that employs spherical beads of fixed radii to represent the hydrodynamic characteristics of coarse-grained segments, we show that our procedure leads naturally to a discrete model of a polymer molecule as a chain of orientable and stretchable Gaussian blobs. This model accounts for both intrablob and interblob hydrodynamic interactions, which depend on the instantaneous shapes of the blobs. In Brownian dynamics simulations of initially stretched chains relaxing under quiescent conditions, the transient evolution of the mean-square end-to-end distance and first normal stress difference obtained with the Gaussian-blob model are found to be less sensitive to the degree of coarse graining, in comparison with the conventional bead-spring model with Rotne-Prager-Yamakawa hydrodynamic interactions

Using molecular imaging to assess the delivery and infection of protease activated virus in animal model of myocardial infarction

Cardiovascular diseases remain the greatest cause of death in the US and gene therapy has the potential to be an effective therapy. In this study, we demonstrated MMP-9 based protease-activatable virus (PAV) for selective infection of myocardial infarct (MI) that is associated with active MMP-9 expression. To test the specificity of PAV, we used expression of a far-red fluorescence protein (iRFP) delivered by the PAV together with a dual PET/NIRF imaging agent specific for active MMP-9 activity at the site of MI in a murine model. Calibrated fluorescence imaging employed a highly-sensitive intensified camera, laser diode excitation sources, and filtration schemes based upon the spectra of iRFP and the NIRF agent. One to two days after ligation of the left anterior descending artery, the PAV or WT AAV9 virus encoding for iRFP (5x1010 genomic particles) and radiolabeled MMP-9 imaging agent (3 nmol) were injected intravenously (i.v.). PET imaging showed MMP activity was associated with adverse tissue remodeling at the site of the MI. One week after, animals were again injected i.v. with the MMP-9 agent (3 nmol) and 18-24 h later, the animals were euthanized and the hearts were harvested, sliced, and imaged for congruent iRFP transgene expression and NIRF signals associated with MMP-9 tissue activity. The fluorescent margins of iRFP and NIRF contrasted tissues were quantified in terms Standard International units of mW/cm2/sr. The sensitivity, specificity, and accuracy of PAV and WT targeting to sites of MI was determined from these calibrated fluorescence measurements. The PAV demonstrated significantly higher delivery performance than that of the WT AAV9 virus

Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales

We experimentally demonstrate the fluctuation theorem, which predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales, by following the trajectory of a colloidal particle captured in an optical trap that is translated relative to surrounding water molecules. From each particle trajectory, we calculate the entropy production/consumption over the duration of the trajectory and determine the fraction of second law–defying trajectories. Our results show entropy consumption can occur over colloidal length and time scales

Getting the inactive active : implications for public health policy

Epidemiological data have established that a sedentary lifestyle increases the incidence of at least 17 medical conditions. The evidence is strongest for coronary heart disease. A sedentary lifestyle is now the normal lifestyle for the majority of the populations in developed countries and relapse from regular physical activity is also high. Thus there is clear need for public policy aimed at increasing the physical activity levels in the population. Policy makers have begun to respond to this need and recently Scottish and English plans for increasing physical activity levels in the populations have been published

A Polymer End-Tethered to a Potential Stripe: A Simple Example of an Escape Transition

ABSTRACT: We study the problem of a single ideal polymer chain tethered to a surface at the midpoint of a repulsive potential stripe. If the potential is very weak, the chain remains unperturbed. However, as the potential is increased, the chain conformation undergoes a sudden change. The chain forms a tether to the edge of the stripe and moves most of the monomers off to the region of lower potential. This is a simple example of an escape transition previously discussed for compression of polymer chains. We show how these two systems are analogous and clear up some controversy regarding the exact form of the force versus height curve for the compressive system