1,551 research outputs found
Ratcheted molecular-dynamics simulations identify efficiently the transition state of protein folding
The atomistic characterization of the transition state is a fundamental step
to improve the understanding of the folding mechanism and the function of
proteins. From a computational point of view, the identification of the
conformations that build out the transition state is particularly cumbersome,
mainly because of the large computational cost of generating a
statistically-sound set of folding trajectories. Here we show that a biasing
algorithm, based on the physics of the ratchet-and-pawl, can be used to
identify efficiently the transition state. The basic idea is that the
algorithmic ratchet exerts a force on the protein when it is climbing the
free-energy barrier, while it is inactive when it is descending. The transition
state can be identified as the point of the trajectory where the ratchet
changes regime. Besides discussing this strategy in general terms, we test it
within a protein model whose transition state can be studied independently by
plain molecular dynamics simulations. Finally, we show its power in
explicit-solvent simulations, obtaining and characterizing a set of
transition--state conformations for ACBP and CI2
Protein folding rates correlate with heterogeneity of folding mechanism
By observing trends in the folding kinetics of experimental 2-state proteins
at their transition midpoints, and by observing trends in the barrier heights
of numerous simulations of coarse grained, C-alpha model, Go proteins, we show
that folding rates correlate with the degree of heterogeneity in the formation
of native contacts. Statistically significant correlations are observed between
folding rates and measures of heterogeneity inherent in the native topology, as
well as between rates and the variance in the distribution of either
experimentally measured or simulated phi-values.Comment: 11 pages, 3 figures, 1 tabl
Accelerated Sampling of Boltzmann distributions
The sampling of Boltzmann distributions by stochastic Markov processes, can
be strongly limited by the crossing time of high (free) energy barriers. As a
result, the system may stay trapped in metastable states, and the relaxation
time to the equilibrium Boltzmann distribution may be very large compared to
the available computational time. In this paper, we show how, by a simple
modification of the Hamiltonian, one can dramatically decrease the relaxation
time of the system, while retaining the same equilibrium distribution. The
method is illustrated on the case of the one-dimensional double-well potential
Steady-state fluctuations of a genetic feedback loop:an exact solution
Genetic feedback loops in cells break detailed balance and involve
bimolecular reactions; hence exact solutions revealing the nature of the
stochastic fluctuations in these loops are lacking. We here consider the master
equation for a gene regulatory feedback loop: a gene produces protein which
then binds to the promoter of the same gene and regulates its expression. The
protein degrades in its free and bound forms. This network breaks detailed
balance and involves a single bimolecular reaction step. We provide an exact
solution of the steady-state master equation for arbitrary values of the
parameters, and present simplified solutions for a number of special cases. The
full parametric dependence of the analytical non-equilibrium steady-state
probability distribution is verified by direct numerical solution of the master
equations. For the case where the degradation rate of bound and free protein is
the same, our solution is at variance with a previous claim of an exact
solution (Hornos et al, Phys. Rev. E {\bf 72}, 051907 (2005) and subsequent
studies). We show explicitly that this is due to an unphysical formulation of
the underlying master equation in those studies.Comment: 31 pages, 3 figures. Accepted for publication in the Journal of
Chemical Physics (2012
Steady-state simulations using weighted ensemble path sampling
We extend the weighted ensemble (WE) path sampling method to perform rigorous
statistical sampling for systems at steady state. The straightforward
steady-state implementation of WE is directly practical for simple landscapes,
but not when significant metastable intermediates states are present. We
therefore develop an enhanced WE scheme, building on existing ideas, which
accelerates attainment of steady state in complex systems. We apply both WE
approaches to several model systems confirming their correctness and efficiency
by comparison with brute-force results. The enhanced version is significantly
faster than the brute force and straightforward WE for systems with WE bins
that accurately reflect the reaction coordinate(s). The new WE methods can also
be applied to equilibrium sampling, since equilibrium is a steady state
What thermodynamic features characterize good and bad folders? Results from a simplified off-lattice protein model
The thermodynamics of the small SH3 protein domain is studied by means of a
simplified model where each bead-like amino acid interacts with the others
through a contact potential controlled by a 20x20 random matrix. Good folding
sequences, characterized by a low native energy, display three main
thermodynamical phases, namely a coil-like phase, an unfolded globule and a
folded phase (plus other two phases, namely frozen and random coil, populated
only at extremes temperatures). Interestingly, the unfolded globule has some
regions already structured. Poorly designed sequences, on the other hand,
display a wide transition from the random coil to a frozen state. The
comparison with the analytic theory of heteropolymers is discussed
Single-molecule Studies Of p53 Sliding Along DNA
2 more articles on this page.
Deciphering the folding kinetics of transmembrane helical proteins
Nearly a quarter of genomic sequences and almost half of all receptors that
are likely to be targets for drug design are integral membrane proteins.
Understanding the detailed mechanisms of the folding of membrane proteins is a
largely unsolved, key problem in structural biology. Here, we introduce a
general model and use computer simulations to study the equilibrium properties
and the folding kinetics of a -based two helix bundle fragment
(comprised of 66 amino-acids) of Bacteriorhodopsin. Various intermediates are
identified and their free energy are calculated toghether with the free energy
barrier between them. In 40% of folding trajectories, the folding rate is
considerably increased by the presence of non-obligatory intermediates acting
as traps. In all cases, a substantial portion of the helices is rapidly formed.
This initial stage is followed by a long period of consolidation of the helices
accompanied by their correct packing within the membrane. Our results provide
the framework for understanding the variety of folding pathways of helical
transmembrane proteins
How accurate are polymer models in the analysis of Forster resonance energy transfer experiments on proteins?
Single molecule Forster resonance energy transfer (FRET) experiments are used
to infer the properties of the denatured state ensemble (DSE) of proteins. From
the measured average FRET efficiency, , the distance distribution P(R) is
inferred by assuming that the DSE can be described as a polymer. The single
parameter in the appropriate polymer model (Gaussian chain, Wormlike chain, or
Self-avoiding walk) for P(R) is determined by equating the calculated and
measured . In order to assess the accuracy of this "standard procedure," we
consider the generalized Rouse model (GRM), whose properties [ and P(R)] can
be analytically computed, and the Molecular Transfer Model for protein L for
which accurate simulations can be carried out as a function of guanadinium
hydrochloride (GdmCl) concentration. Using the precisely computed for the
GRM and protein L, we infer P(R) using the standard procedure. We find that the
mean end-to-end distance can be accurately inferred (less than 10% relative
error) using and polymer models for P(R). However, the value extracted for
the radius of gyration (Rg) and the persistence length (lp) are less accurate.
The relative error in the inferred R-g and lp, with respect to the exact
values, can be as large as 25% at the highest GdmCl concentration. We propose a
self-consistency test, requiring measurements of by attaching dyes to
different residues in the protein, to assess the validity of describing DSE
using the Gaussian model. Application of the self-consistency test to the GRM
shows that even for this simple model the Gaussian P(R) is inadequate. Analysis
of experimental data of FRET efficiencies for the cold shock protein shows that
at there are significant deviations in the DSE P(R) from the Gaussian model.Comment: 31 pages, 9 figure
Exact Solution of the Munoz-Eaton Model for Protein Folding
A transfer-matrix formalism is introduced to evaluate exactly the partition
function of the Munoz-Eaton model, relating the folding kinetics of proteins of
known structure to their thermodynamics and topology. This technique can be
used for a generic protein, for any choice of the energy and entropy
parameters, and in principle allows the model to be used as a first tool to
characterize the dynamics of a protein of known native state and equilibrium
population. Applications to a -hairpin and to protein CI-2, with
comparisons to previous results, are also shown.Comment: 4 pages, 5 figures, RevTeX 4. To be published in Phys. Rev. Let
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