224 research outputs found
Diffusive Dynamics of the Reaction Coordinate for Protein Folding Funnels
The quantitative description of model protein folding kinetics using a
diffusive collective reaction coordinate is examined. Direct folding kinetics,
diffusional coefficients and free energy profiles are determined from Monte
Carlo simulations of a 27-mer, 3 letter code lattice model, which corresponds
roughly to a small helical protein. Analytic folding calculations, using simple
diffusive rate theory, agree extremely well with the full simulation results.
Folding in this system is best seen as a diffusive, funnel-like process.Comment: LaTeX 12 pages, figures include
A New Monte Carlo Algorithm for Protein Folding
We demonstrate that the recently proposed pruned-enriched Rosenbluth method
(P. Grassberger, Phys. Rev. E 56 (1997) 3682) leads to extremely efficient
algorithms for the folding of simple model proteins. We test them on several
models for lattice heteropolymers, and compare to published Monte Carlo
studies. In all cases our algorithms are faster than all previous ones, and in
several cases we find new minimal energy states. In addition to ground states,
our algorithms give estimates for the partition sum at finite temperatures.Comment: 4 pages, Latex incl. 3 eps-figs., submitted to Phys. Rev. Lett.,
revised version with changes in the tex
Statics, metastable states and barriers in protein folding: A replica variational approach
Protein folding is analyzed using a replica variational formalism to
investigate some free energy landscape characteristics relevant for dynamics. A
random contact interaction model that satisfies the minimum frustration
principle is used to describe the coil-globule transition (characterized by
T_CG), glass transitions (by T_A and T_K) and folding transition (by T_F).
Trapping on the free energy landscape is characterized by two characteristic
temperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which are
similar to those found in mean field theories of the Potts glass. 1)Above T_A,
the free energy landscape is monotonous and polymer is melted both dynamically
and statically. 2)Between T_A and T_K, the melted phase is still dominant
thermodynamically, but frozen metastable states, exponentially large in number,
appear. 3)A few lowest minima become thermodynamically dominant below T_K,
where the polymer is totally frozen. In the temperature range between T_A and
T_K, barriers between metastable states are shown to grow with decreasing
temperature suggesting super-Arrhenius behavior in a sufficiently large system.
Due to evolutionary constraints on fast folding, the folding temperature T_F is
expected to be higher than T_K, but may or may not be higher than T_A. Diverse
scenarios of the folding kinetics are discussed based on phase diagrams that
take into account the dynamical transition, as well as the static ones.Comment: 41 pages, LaTeX, 9 EPS figure
Viscosity Dependence of the Folding Rates of Proteins
The viscosity dependence of the folding rates for four sequences (the native
state of three sequences is a beta-sheet, while the fourth forms an
alpha-helix) is calculated for off-lattice models of proteins. Assuming that
the dynamics is given by the Langevin equation we show that the folding rates
increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and
have a maximum at intermediate values. The Kramers theory of barrier crossing
provides a quantitative fit of the numerical results. By mapping the simulation
results to real proteins we estimate that for optimized sequences the time
scale for forming a four turn \alpha-helix topology is about 500 nanoseconds,
whereas the time scale for forming a beta-sheet topology is about 10
microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at
http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical
Review Letter
Reply to Comment on "Criterion that Determines the Foldability of Proteins"
We point out that the correlation between folding times and in protein-like heteropolymer models where
and are the collapse and folding transition temperatures
was already established in 1993 before the other presumed equivalent criterion
(folding times correlating with alone) was suggested. We argue that the
folding times for these models show no useful correlation with the energy gap
even if restricted to the ensemble of compact structures as suggested by
Karplus and Shakhnovich (cond-mat/9606037).Comment: 6 pages, Latex, 2 Postscript figures. Plots explicitly showing the
lack of correlation between folding time and energy gap are adde
Folding in two-dimenensional off-lattice models of proteins
Model off-lattice sequences in two dimensions are constructed so that their
native states are close to an on-lattice target. The Hamiltonian involves the
Lennard-Jones and harmonic interactions. The native states of these sequences
are determined with a high degree of certainty through Monte Carlo processes.
The sequences are characterized thermodynamically and kinetically. It is shown
that the rank-ordering-based scheme of the assignment of contact energies
typically fails in off-lattice models even though it generates high stability
of on-lattice sequences. Similar to the on-lattice case, Go-like modeling, in
which the interaction potentials are restricted to the native contacts in a
target shape, gives rise to good folding properties. Involving other contacts
deteriorates these properties.Comment: REVTeX, 9 pages, 8 EPS figure
Modeling study on the validity of a possibly simplified representation of proteins
The folding characteristics of sequences reduced with a possibly simplified
representation of five types of residues are shown to be similar to their
original ones with the natural set of residues (20 types or 20 letters). The
reduced sequences have a good foldability and fold to the same native structure
of their optimized original ones. A large ground state gap for the native
structure shows the thermodynamic stability of the reduced sequences. The
general validity of such a five-letter reduction is further studied via the
correlation between the reduced sequences and the original ones. As a
comparison, a reduction with two letters is found not to reproduce the native
structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure
Scaling of folding properties in simple models of proteins
Scaling of folding properties of proteins is studied in a toy system -- the
lattice Go model with various two- and three- dimensional geometries of the
maximally compact native states. Characteristic folding times grow as power
laws with the system size. The corresponding exponents are not universal.
Scaling of the thermodynamic stability also indicates size-related
deterioration of the folding properties.Comment: REVTeX, 4 pages, 4 EPS figures, PRL (in press
Coarse grained description of the protein folding
We consider two- and three-dimensional lattice models of proteins which were
characterized previously. We coarse grain their folding dynamics by reducing it
to transitions between effective states. We consider two methods of selection
of the effective states. The first method is based on the steepest descent
mapping of states to underlying local energy minima and the other involves an
additional projection to maximally compact conformations. Both methods generate
connectivity patterns that allow to distinguish between the good and bad
folders. Connectivity graphs corresponding to the folding funnel have few loops
and are thus tree-like. The Arrhenius law for the median folding time of a
16-monomer sequence is established and the corresponding barrier is related to
easily identifiable kinetic trap states.Comment: REVTeX, 9 pages, 15 EPS figures, to appear in Phys. Rev.
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