534 research outputs found
Mechanical unfolding and refolding pathways of ubiquitin
Mechanical unfolding and refolding of ubiquitin are studied by Monte Carlo
simulations of a Go model with binary variables. The exponential dependence of
the time constants on the force is verified, and folding and unfolding lengths
are computed, with good agreement with experimental results. Furthermore, the
model exhibits intermediate kinetic states, as observed in experiments.
Unfolding and refolding pathways and intermediate states, obtained by tracing
single secondary structure elements, are consistent with simulations of
previous all-atom models and with the experimentally observed step sizes
Evaluation of free energy landscapes from manipulation experiments
A fluctuation relation, which is an extended form of the Jarzynski equality,
is introduced and discussed. We show how to apply this relation in order to
evaluate the free energy landscape of simple systems. These systems are
manipulated by varying the external field coupled with a systems' internal
characteristic variable. Two different manipulation protocols are here
considered: in the first case the external field is a linear function of time,
in the second case it is a periodic function of time. While for simple mean
field systems both the linear protocol and the oscillatory protocol provide a
reliable estimate of the free energy landscape, for a simple model
ofhomopolymer the oscillatory protocol turns out to be not reliable for this
purpose. We then discuss the possibility of application of the method here
presented to evaluate the free energy landscape of real systems, and the
practical limitations that one can face in the realization of an experimental
set-up
Work probability distribution in systems driven out of equilibrium
We derive the differential equation describing the time evolution of the work
probability distribution function of a stochastic system which is driven out of
equilibrium by the manipulation of a parameter. We consider both systems
described by their microscopic state or by a collective variable which
identifies a quasiequilibrium state. We show that the work probability
distribution can be represented by a path integral, which is dominated by
``classical'' paths in the large system size limit. We compare these results
with simulated manipulation of mean-field systems. We discuss the range of
applicability of the Jarzynski equality for evaluating the system free energy
using these out-of-equilibrium manipulations. Large fluctuations in the work
and the shape of the work distribution tails are also discussed
The distribution function of entropy flow in stochastic systems
We obtain a simple direct derivation of the differential equation governing
the entropy flow probability distribution function of a stochastic system first
obtained by Lebowitz and Spohn. Its solution agrees well with the experimental
results of Tietz et al [2006 {\it Phys. Rev. Lett.} {\bf 97} 050602]. A
trajectory-sampling algorithm allowing to evaluate the entropy flow
distribution function is introduced and discussed. This algorithm turns out to
be effective at finite times and in the case of time-dependent transition
rates, and is successfully applied to an asymmetric simple exclusion process
Heat flow in chains driven by thermal noise
We consider the large deviation function for a classical harmonic chain
composed of N particles driven at the end points by heat reservoirs, first
derived in the quantum regime by Saito and Dhar and in the classical regime by
Saito and Dhar and Kundu et al. Within a Langevin description we perform this
calculation on the basis of a standard path integral calculation in Fourier
space. The cumulant generating function yielding the large deviation function
is given in terms of a transmission Green's function and is consistent with the
fluctuation theorem. We find a simple expression for the tails of the heat
distribution which turn out to decay exponentially. We, moreover, consider an
extension of a single particle model suggested by Derrida and Brunet and
discuss the two-particle case. We also discuss the limit for large N and
present a closed expression for the cumulant generating function. Finally, we
present a derivation of the fluctuation theorem on the basis of a Fokker-Planck
description. This result is not restricted to the harmonic case but is valid
for a general interaction potential between the particles.Comment: Latex: 26 pages and 9 figures, appeared in J. Stat. Mech. P04005
(2012
Direction dependent mechanical unfolding and Green Fluorescent Protein as a force sensor
An Ising--like model of proteins is used to investigate the mechanical
unfolding of the Green Fluorescent Protein along different directions. When the
protein is pulled from its ends, we recover the major and minor unfolding
pathways observed in experiments. Upon varying the pulling direction, we find
the correct order of magnitude and ranking of the unfolding forces. Exploiting
the direction dependence of the unfolding force at equilibrium, we propose a
force sensor whose luminescence depends on the applied force.Comment: to appear in Phys Rev
Out-of-equilibrium versus dynamical and thermodynamical transitions for a model protein
Equilibrium and out-of-equilibrium transitions of an off-lattice protein
model have been identified and studied. In particular, the out-of-equilibrium
dynamics of the protein undergoing mechanical unfolding is investigated, and by
using a work fluctuation relation, the system free energy landscape is
evaluated. Three different structural transitions are identified along the
unfolding pathways. Furthermore, the reconstruction of the the free and
potential energy profiles in terms of inherent structure formalism allows us to
put in direct correspondence these transitions with the equilibrium thermal
transitions relevant for protein folding/unfolding. Through the study of the
fluctuations of the protein structure at different temperatures, we identify
the dynamical transitions, related to configurational rearrangements of the
protein, which are precursors of the thermal transitions.Comment: Proceedings of the "YKIS 2009 : Frontiers in Nonequilibrium Physics"
conference in Kyoto, August 2009. To appear in Progress of Theoretical
Physics Supplemen
Protein mechanical unfolding: a model with binary variables
A simple lattice model, recently introduced as a generalization of the
Wako--Sait\^o model of protein folding, is used to investigate the properties
of widely studied molecules under external forces. The equilibrium properties
of the model proteins, together with their energy landscape, are studied on the
basis of the exact solution of the model. Afterwards, the kinetic response of
the molecules to a force is considered, discussing both force clamp and dynamic
loading protocols and showing that theoretical expectations are verified. The
kinetic parameters characterizing the protein unfolding are evaluated by using
computer simulations and agree nicely with experimental results, when these are
available. Finally, the extended Jarzynski equality is exploited to investigate
the possibility of reconstructing the free energy landscape of proteins with
pulling experiments
Efficiency of molecular machines with continuous phase space
We consider a molecular machine described as a Brownian particle diffusing in
a tilted periodic potential. We evaluate the absorbed and released power of the
machine as a function of the applied molecular and chemical forces, by using
the fact that the times for completing a cycle in the forward and the backward
direction have the same distribution, and that the ratio of the corresponding
splitting probabilities can be simply expressed as a function of the applied
force. We explicitly evaluate the efficiency at maximum power for a simple
sawtooth potential. We also obtain the efficiency at maximum power for a broad
class of 2-D models of a Brownian machine and find that loosely coupled
machines operate with a smaller efficiency at maximum power than their strongly
coupled counterparts.Comment: To appear in EP
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