Implementation of the simulated annealing and replica exchange Monte Carlo algorithms for protein folding in the HP model in Python (2.7.6) and using NumPy library (1.8.0).
Hydrophobic-polar protein folding (HP) model is used in the study of the general principles of protein folding. The idea of the HP model is based on the observation that a key role in the process of folding has the hydrophobic effect - tendency of hydrophobic amino acids to aggregate and 'hide' from the water molecules. Amino acids are over the alphabet {H,P}, where H is hydrophobic and P polar amino acid and they are located on the square lattice.
Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method that allows sampling the set of possible configurations of protein, according to any probability distribution (here the Boltzmann distribution). The algorithm generates a Markov chain in which each state x^{t+1} depends only on the previous state x^t. The algorithm uses a proposal density Q(x'; x^t ), which depends on the current state x^t, to generate a new proposed sample x'. This proposal is "accepted" as the next value (x^{t+1}=x') if \alpha drawn from U(0,1) satisfies.
For more details see [1].
Usage:
$ python replica_exchange.pyOutput is the trajectory of replica at the lowest temperature in the pdb format.
Usage:
$ python simulated_annealing.pyOutput is the trajectory in the pdb format.
You can visualizate trajectory in the pdb format using PyMOL:
$ pymol trajectory.pdband then in PyMOL console:
PyMOL> run show[1] Dill, KA, Bromberg, S, Yue, K, Fiebig, KM, Yee, DP, Thomas, PD, Chan, HS (1995). Principles of protein folding--a perspective from simple exact models. Protein Sci., 4, 4:561-602.