Master Equation Approach to Protein Folding and Kinetic Traps

  title={Master Equation Approach to Protein Folding and Kinetic Traps},
  author={Marek Cieplak and Malte Henkel and Jan Karbowski and Jayanth R. Banavar},
  journal={Physical Review Letters},
The master equation for 12-monomer lattice heteropolymers is solved numerically and the time evolution of the occupancy of the native state is determined. At low temperatures, the median folding time follows the Arrhenius law and is governed by the longest relaxation time. For good folders significant kinetic traps appear in the folding funnel, whereas for bad folders the traps also occur in non-native energy valleys. 
The role of the energy gap in protein folding dynamics
It is shown that for certain models of the transition probabilities between the different states of the protein, the relaxation to the native state is accelerated by increasing the gap, whereas for others it is slowed down.
Kinetic nonoptimality and vibrational stability of proteins
Scaling of folding times in Go models of proteins and of decoy structures with the Lennard–Jones potentials in the native contacts reveal power law trends when studied under optimal folding
Folding kinetics of proteins and cold denaturation.
  • O. Collet
  • Chemistry, Physics
    The Journal of chemical physics
  • 2008
The study of the conformational space as function of the temperature permits to elucidate the folding kinetics of a lattice model of protein and shows that the activation barriers of the system decrease faster than the temperature as the temperature is decreased.
Cooperativity in two‐state protein folding kinetics
A solvable model that predicts the folding kinetics of two‐state proteins from their native structures based on conditional chain entropies and it predicts well the average Φ‐values for secondary structures.
A characteristic temperature related to the combined probability, PL, to stay in the non-native minima during folding coincides with the temperature of the fastest folding, which yields an easy numerical way to determine conditions of the optimal folding.
Energy landscape and dynamics of an HP lattice model of proteins —The role of anisotropy
We present the results of exact numerical studies of the energy landscape and the dynamics of a 12-monomer chain comprised of two types of amino acids called the HP model. We benchmark our findings
Reliable protein folding on complex energy landscapes: the free energy reaction path.
A theory predicts that proteins with complex energy landscapes can fold reliably to their native state; reliable folding can occur as an equilibrium or out-of-equilibrium process; and reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy.
N ov 2 00 3 Cooperativity in Two-State Protein Folding Kinetics
We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes
Master equation approach to finding the rate-limiting steps in biopolymer folding.
The rate-limiting searching method has been tested for a simplified hairpin folding kinetics model, and it may provide a general transition state searching method for biopolymer folding.
Analyzing the biopolymer folding rates and pathways using kinetic cluster method.
A kinetic cluster method enables us to analyze biopolymer folding kinetics with discrete rate-limiting steps by classifying biopolymers conformations into pre-equilibrated clusters and the temperature dependence of the folding rate can be analyzed from the interplay between the stabilities of the on- Pathway and off-pathway conformations and from the kinetic partitioning between different intercluster pathways.


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