Tight coupling in thermal Brownian motors

We study analytically a thermal Brownian motor model and calculate exactly the Onsager coefficients. We show how the reciprocity relation holds and that the determinant of the Onsager matrix vanishes. Such condition implies that the device is built with tight coupling. This explains why Carnot's efficiency can be achieved in the limit of infinitely slow velocities. We also prove that the efficiency at maximum power has the maximum possible value, which corresponds to the Curzon-Alhborn bound. Finally, we discuss the model acting as a Brownian refrigerator

Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments

Single molecule mechanical unfolding experiments are beginning to provide profiles of the complex energy landscape of biomolecules. In order to obtain reliable estimates of the energy landscape characteristics it is necessary to combine the experimental measurements with sound theoretical models and simulations. Here, we show how by using temperature as a variable in mechanical unfolding of biomolecules in laser optical tweezer or AFM experiments the roughness of the energy landscape can be measured without making any assumptions about the underlying reaction oordinate. The efficacy of the formalism is illustrated by reviewing experimental results that have directly measured roughness in a protein-protein complex. The roughness model can also be used to interpret experiments on forced-unfolding of proteins in which temperature is varied. Estimates of other aspects of the energy landscape such as free energy barriers or the transition state (TS) locations could depend on the precise model used to analyze the experimental data. We illustrate the inherent difficulties in obtaining the transition state location from loading rate or force-dependent unfolding rates. Because the transition state moves as the force or the loading rate is varied it is in general difficult to invert the experimental data unless the curvature at the top of the one dimensional free energy profile is large, i.e the barrier is sharp. The independence of the TS location on force holds good only for brittle or hard biomolecules whereas the TS location changes considerably if the molecule is soft or plastic. We also comment on the usefulness of extension of the molecule as a surrogate reaction coordinate especially in the context of force-quench refolding of proteins and RNA.Comment: 44 pages, 7 figure

Scale-free energy dissipation and dynamic phase transition in stochastic sandpiles

We study numerically scaling properties of the distribution of cumulative energy dissipated in an avalanche and the dynamic phase transition in a stochastic directed cellular automaton [B. Tadi\'c and D. Dhar, Phys. Rev. Lett. {\bf 79}, 1519 (1997)] in d=1+1 dimensions. In the critical steady state occurring for the probability of toppling $p\ge p^\star$= 0.70548, the dissipated energy distribution exhibits scaling behavior with new scaling exponents $\tau_E$ and D_E for slope and cut-off energy, respectively, indicating that the sandpile surface is a fractal. In contrast to avalanche exponents, the energy exponents appear to be p- dependent in the region $p^\star \le p <1$, however the product $(\tau_E-1)D_E$ remains universal. We estimate the roughness exponent of the transverse section of the pile as $\chi =0.44\pm 0.04$. Critical exponents characterizing the dynamic phase transition at $p^\star$ are obtained by direct simulation and scaling analysis of the survival probability distribution and the average outflow current. The transition belongs to a new universality class with the critical exponents $\nu_\| =\gamma =1.22 \pm 0.02$, $\beta =0.56\pm 0.02$ and $\nu_\bot = 0.761 \pm 0.029$, with apparent violation of hyperscaling. Generalized hyperscaling relation leads to $\beta + \beta ^\prime = (d-1)\nu_\bot$, where $\beta ^\prime = 0.195 \pm 0.012$ is the exponent governed by the ultimate survival probability

Spontaneous Oscillations of Collective Molecular Motors

We analyze a simple stochastic model to describe motor molecules which cooperate in large groups and present a physical mechanism which can lead to oscillatory motion if the motors are elastically coupled to their environment. Beyond a critical fuel concentration, the non-moving state of the system becomes unstable with respect to a mode with angular frequency omega. We present a perturbative description of the system near the instability and demonstrate that oscillation frequencies are determined by the typical timescales of the motors.Comment: 11 pages, Revtex, 4 pages Figure

Islands of conformational stability for Filopodia

Filopodia are long, thin protrusions formed when bundles of fibers grow outwardly from a cell surface while remaining closed in a membrane tube. We study the subtle issue of the mechanical stability of such filopodia and how this depends on the deformation of the membrane that arises when the fiber bundle adopts a helical configuration. We calculate the ground state conformation of such filopodia, taking into account the steric interaction between the membrane and the enclosed semiflexible fiber bundle. For typical filopodia we find that a minimum number of fibers is required for filopodium stability. Our calculation elucidates how experimentally observed filopodia can obviate the classical Euler buckling condition and remain stable up to several tens of . We briefly discuss how experimental observation of the results obtained in this work for the helical-like deformations of enclosing membrane tubes in filopodia could possibly be observed in the acrosomal reactions of the sea cucumber Thyone, and the horseshoe crab Limulus. Any realistic future theories for filopodium stability are likely to rely on an accurate treatment of such steric effects, as analysed in this work

Energetics of rocked inhomogeneous ratchets

We study the efficiency of frictional thermal ratchets driven by finite frequency driving force and in contact with a heat bath. The efficiency exhibits varied behavior with driving frequency. Both nonmonotonic and monotonic behavior have been observed. In particular the magnitude of efficiency in finite frequency regime may be more than the efficiency in the adiabatic regime. This is our central result for rocked ratchets. We also show that for the simple potential we have chosen, the presence of only spatial asymmetry (homogeneous system) or only frictional ratchet (symmetric potential profile), the adiabatic efficiency is always more than in the nonadiabatic case.Comment: 5 figure

Hopping motion of lattice gases through nonsymmetric potentials under strong bias conditions

The hopping motion of lattice gases through potentials without mirror-reflection symmetry is investigated under various bias conditions. The model of 2 particles on a ring with 4 sites is solved explicitly; the resulting current in a sawtooth potential is discussed. The current of lattice gases in extended systems consisting of periodic repetitions of segments with sawtooth potentials is studied for different concentrations and values of the bias. Rectification effects are observed, similar to the single-particle case. A mean-field approximation for the current in the case of strong bias acting against the highest barriers in the system is made and compared with numerical simulations. The particle-vacancy symmetry of the model is discussed.Comment: 8 pages (incl. 6 eps figures); RevTeX 3.

Breaking of general rotational symmetries by multi-dimensional classical ratchets

We demonstrate that a particle driven by a set of spatially uncorrelated, independent colored noise forces in a bounded, multidimensional potential exhibits rotations that are independent of the initial conditions. We calculate the particle currents in terms of the noise statistics and the potential asymmetries by deriving an n-dimensional Fokker-Planck equation in the small correlation time limit. We analyze a variety of flow patterns for various potential structures, generating various combinations of laminar and rotational flows.Comment: Accepted, Physical Review

Congruent evolution of genetic and environmental robustness in microRNA

Genetic robustness, the preservation of an optimal phenotype in the face of mutations, is critical to the understanding of evolution as phenotypically expressed genetic variation is the fuel of natural selection. The origin of genetic robustness, whether it evolves directly by natural selection or it is a correlated byproduct of other phenotypic traits, is, however, unresolved. Examining microRNA (miRNA) genes of several eukaryotic species, Borenstein and Ruppin (Borenstein et al. 2006, PNAS 103: 6593), showed that the structure of miRNA precursor stem-loops exhibits significantly increased mutational robustness in comparison with a sample of random RNA sequences with the same stem-loop structure. The observed robustness was found to be uncorrelated with traditional measures of environmental robustness -- implying that miRNA sequences show evidence of the direct evolution of genetic robustness. These findings are surprising as theoretical results indicate that the direct evolution of robustness requires high mutation rates and/or large effective population sizes only found among RNA viruses, not multicellular eukaryotes. Introducing a novel measure of environmental robustness based on the equilibrium thermodynamic ensemble of secondary structures of the miRNA precursor sequences we demonstrate that the biophysics of RNA folding, induces a high level of correlation between genetic (mutational) and environmental (thermodynamic) robustness, as expected from the theory of plastogenetic congruence introduced by Ancel and Fontana (Ancel et al. 2000, J. Exp. Zool. 288: 242). In light of theoretical considerations we believe that this correlation strongly suggests that genetic robustness observed in miRNA sequences is the byproduct of selection for environmental robustness.Comment: Accepted for publication in Mol. Biol. Evol. Supplemental Information available as a separate pdf file from http://angel.elte.hu:/~ssolo/miRNA_supp_mat.pd

Reversible quantum Brownian heat engines for electrons

Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.Comment: Physical Review Letters, accepted (July 2002