On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example

We suggest and discuss a simple model of an ideal gas under the piston to gain an insight into the workings of the Jarzynski identity connecting the average exponential of the work over the non-equilibrium trajectories with the equilibrium free energy. We show that the Jarzynski identity is valid for our system due to the very rapid molecules belonging to the tail of the Maxwell distribution. For the most interesting extreme, when the system volume is large, while the piston is moving with large speed (compared to thermal velocity) for a very short time, the necessary number of independent experimental runs to obtain a reasonable approximation for the free energy from averaging the non-equilibrium work grows exponentially with the system size.Comment: 15 pages, 7 figures, submitted to JP

Topologically Driven Swelling of a Polymer Loop

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius are generated for loops of up to N=3000 segments. Gyration radii of trivially knotted loops are found to follow a power law similar to that of self avoiding walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200

Probability distributions of the work in the 2D-Ising model

Probability distributions of the magnetic work are computed for the 2D Ising model by means of Monte Carlo simulations. The system is first prepared at equilibrium for three temperatures below, at and above the critical point. A magnetic field is then applied and grown linearly at different rates. Probability distributions of the work are stored and free energy differences computed using the Jarzynski equality. Consistency is checked and the dynamics of the system is analyzed. Free energies and dissipated works are reproduced with simple models. The critical exponent $\delta$ is estimated in an usual manner.Comment: 12 pages, 6 figures. Comments are welcom

Polymer translocation through a nanopore - a showcase of anomalous diffusion

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {\em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $\alpha = 2/(2\nu+2-\gamma_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {\em fractional} diffusion equation which is solved exactly in the interval $0 <s < N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $$, and $- < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev.

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure

Residence Time Statistics for Normal and Fractional Diffusion in a Force Field

We investigate statistics of occupation times for an over-damped Brownian particle in an external force field. A backward Fokker-Planck equation introduced by Majumdar and Comtet describing the distribution of occupation times is solved. The solution gives a general relation between occupation time statistics and probability currents which are found from solutions of the corresponding problem of first passage time. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker-Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding potential rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking.Comment: 12 page

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

Overexpressed hPTTG1 promotes breast cancer cell invasion and metastasis by regulating GEF-H1/RhoA signalling

Human pituitary tumour-transforming gene 1 (hPTTG1) is an oncogenic transcription factor that is overexpressed in many tumour types, especially tumours with metastatic abilities. However, how hPTTG1 overexpression drives metastasis is not yet clear. As a transcription factor, hPTTG1 may promote metastasis by activating target genes that are involved in the metastatic process. Here, we showed that Rho guanine nucleotide exchange factor-H1 (GEF-H1) was transcriptionally activated by hPTTG1, thereby promoting breast cancer metastasis. Luciferase reporter analyses and chromatin immunoprecipitation (ChIP) assays showed that hPTTG1 directly bound and activated the GEF-H1 gene promoter. In this study, RNA interference-mediated knockdown of hPTTG1 in highly metastatic breast tumour cells decreased GEF-H1 expression and RhoA activation, thereby reducing cell motility and invasion, and interfering with cytoskeletal remodelling in vitro, and impairing the tumour metastasis in vivo. The restoration of GEF-H1 expression in hPTTG1-knockdown cells rescued the hPTTG1-knockdown effects on cytoskeletal changes in vitro and tumour metastasis in vivo. Conversely, ectopic expression of hPTTG1 in non-metastatic breast tumour cells induced cytoskeletal rearrangements, and allowed these cells to metastasise in a mouse model by orthotopic implantation. In human tumour samples, hPTTG1 expression was also correlated to GEF-H1 expression in aggressive breast carcinoma. Altogether, these findings definitively establish a role for hPTTG1 in activating the GEF-H1/RhoA pathway as a newly identified mechanism in breast cancer metastasis

Unique Structure and Dynamics of the EphA5 Ligand Binding Domain Mediate Its Binding Specificity as Revealed by X-ray Crystallography, NMR and MD Simulations

10.1371/journal.pone.0074040PLoS ONE89-POLN

Rapid and convenient method for preparing masters for microcontact printing with 1–12 µm features

Mechanical scribing can be employed to create surfaces with recessed features. Through replica molding elastomeric copies of these scribed surfaces are created that function as stamps for microcontact printing. It is shown that this new method for creating masters for microcontact printing can be performed with a computer-controlled milling machine (CNC), making this method particularly straightforward and accessible to a large technical community that does not need to work in a particle free environment. Thus, no clean room, or other specialized equipment is required, as is commonly needed to prepare masters. Time-of-flight secondary ion mass spectrometry confirms surface pattering by this method. Finally, it is shown that feature size in the scribed master can be controlled by varying the force on the tip during scribing