226 research outputs found
Exactness of the cluster variation method and factorization of the equilibrium probability for the Wako-Saito-Munoz-Eaton model of protein folding
I study the properties of the equilibrium probability distribution of a
protein folding model originally introduced by Wako and Saito, and later
reconsidered by Munoz and Eaton. The model is a one-dimensional model with
binary variables and many-body, long-range interactions, which has been solved
exactly through a mapping to a two-dimensional model of binary variables with
local constraints. Here I show that the equilibrium probability of this
two-dimensional model factors into the product of local cluster probabilities,
each raised to a suitable exponent. The clusters involved are single sites,
nearest-neighbour pairs and square plaquettes, and the exponents are the
coefficients of the entropy expansion of the cluster variation method. As a
consequence, the cluster variation method is exact for this model.Comment: 14 pages, 1 figur
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
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
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
The Phase Diagram of the Gonihedric 3d Ising Model via CVM
We use the cluster variation method (CVM) to investigate the phase structure
of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The
geometrical spin cluster boundaries in these systems serve as models for the
string worldsheets of the gonihedric string embedded in . The models
are interesting from the statistical mechanical point of view because they have
a vanishing bare surface tension. As a result the action depends only on the
angles of the discrete surface and not on the area, which is the antithesis of
the standard 3d Ising model.
The results obtained with the CVM are in good agreement with Monte Carlo
simulations for the critical temperatures and the order of the transition as
the self-avoidance coupling is varied. The value of the magnetization
critical exponent , calculated with the cluster
variation--Pad\`e approximant method, is also close to the simulation results.Comment: 8 pages text (LaTex) + 3 eps figures bundled together with uufile
Downhill versus two-state protein folding in a statistical mechanical model
The authors address the problem of downhill protein folding in the framework
of a simple statistical mechanical model, which allows an exact solution for
the equilibrium and a semianalytical treatment of the kinetics. Focusing on
protein 1BBL, a candidate for downhill folding behavior, and comparing it to
the WW domain of protein PIN1, a two-state folder of comparable size, the
authors show that there are qualitative differences in both the equilibrium and
kinetic properties of the two molecules. However, the barrierless scenario
which would be expected if 1BBL were a true downhill folder is observed only at
low enough temperature.Comment: 20 pages, 13 figure
Rigorous results on the local equilibrium kinetics of a protein folding model
A local equilibrium approach for the kinetics of a simplified protein folding
model, whose equilibrium thermodynamics is exactly solvable, was developed in
[M. Zamparo and A. Pelizzola, Phys. Rev. Lett. 97, 068106 (2006)]. Important
properties of this approach are (i) the free energy decreases with time, (ii)
the exact equilibrium is recovered in the infinite time limit, (iii) the
equilibration rate is an upper bound of the exact one and (iv) computational
complexity is polynomial in the number of variables. Moreover, (v) this method
is equivalent to another approximate approach to the kinetics: the path
probability method. In this paper we give detailed rigorous proofs for the
above results.Comment: 25 pages, RevTeX 4, to be published in JSTA
Cluster variation - Pade` approximants method for the simple cubic Ising model
The cluster variation - Pade` approximant method is a recently proposed tool,
based on the extrapolation of low/high temperature results obtained with the
cluster variation method, for the determination of critical parameters in
Ising-like models. Here the method is applied to the three-dimensional simple
cubic Ising model, and new results, obtained with an 18-site basic cluster, are
reported. Other techniques for extracting non-classical critical exponents are
also applied and their results compared with those by the cluster variation -
Pade` approximant method.Comment: 8 RevTeX pages, 3 PostScript figure
Equilibrium properties and force-driven unfolding pathways of RNA molecules
The mechanical unfolding of a simple RNA hairpin and of a 236--bases portion
of the Tetrahymena thermophila ribozyme is studied by means of an Ising--like
model. Phase diagrams and free energy landscapes are computed exactly and
suggest a simple two--state behaviour for the hairpin and the presence of
intermediate states for the ribozyme. Nonequilibrium simulations give the
possible unfolding pathways for the ribozyme, and the dominant pathway
corresponds to the experimentally observed one.Comment: Main text + appendix, to appear in Phys. Rev. Let
Effects of confinement on thermal stability and folding kinetics in a simple Ising-like model
In cellular environment, confinement and macromulecular crowding play an
important role on thermal stability and folding kinetics of a protein. We have
resorted to a generalized version of the Wako-Saito-Munoz-Eaton model for
protein folding to study the behavior of six different protein structures
confined between two walls. Changing the distance 2R between the walls, we
found, in accordance with previous studies, two confinement regimes: starting
from large R and decreasing R, confinement first enhances the stability of the
folded state as long as this is compact and until a given value of R; then a
further decrease of R leads to a decrease of folding temperature and folding
rate. We found that in the low confinement regime both unfolding temperatures
and logarithm of folding rates scale as R-{\gamma} where {\gamma} values lie in
between 1.42 and 2.35
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