13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- All-Atom CSAW: An Ab Initio Protein Folding Method Weitao Sun1* 1 Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China * Corresponding author: sunwt@tsinghua.edu.cn Abstract Conditioned Self-Avoiding Walk (CSAW) was first developed as a tool to simulate protein folding Based on CSAW algorithm, All-atom Conditioned Self-Avoiding Walk (AA-CSAW) was developed around 2007. The polypeptide chain is simulated as effectively rigid cranks -Ca-CO-NH- units lined by covalent bonds. Bond lengths and bond angles are set as fixed optimal values. All-atom amino acid sidechain is attached to very Ca atom. The structure of polypeptide is fully described by backbone dihedral angles φ, ψ and the sidechain dihedral angles χ. A trial structure is randomly generated by pivoting the polypeptide chain and sidechains. In the pivot algorithm, the backbone dihedral angles φ, ψ for each residue are chosen according to probability distributions in Ramachandran plot. The dihedral angle distributions are improved by 3-residue fragment set investigation. The effective energy of protein structure is constructed by considering hydrophobic effect, desolvation effect and hydrogen bonding interaction. An appropriate three dimensional structure is accepted with a probability according to Metropolis scheme. In order to evaluate the accepted structures in Monte Carlo simulations, the ratio of secondary structure content to radius of gyration is introduced. CASP09 target example shows that AA-CSAW is an efficient and promising ab initio method. Keywords protein folding simulation, self-avoiding walk, coarse-grained, sidechain atom 1. Introduction In physiological conditions, globular protein folds from randomly coiled polypeptide chain into a characteristic three-dimensional structure in water solution. Protein folding is a stochastic process and there are huge amount of protein molecules in organism. The observable macroscopic properties have microscopic interpretations based on collective molecule behaviors. Meanwhile, individual protein molecule undergoes a Brownian motion and it’s hard to describe the movements of each molecule. In addition, protein structure is at the edge of thermo-equilibrium. Delicate balance between entropy-enthalpy exist throughout the folding process. We believe that statistical thermodynamics is a prior way for protein folding problem. Polypeptide chains in solutions incessantly change shape and position by thermal agitation. This Brownian motion can be characterized in more quantitative fashion by the use of phenomenological models. One such model is summarized by the Langevin equation of motion[1, 2]. Monte Carlo (MC) simulation samples typical configurations from a Boltzmann distribution determined by potential energy and temperature of the system. Monte Carlo method solves the stochastic models without consideration of the analytical representations of the system. It is clear that the Monte Carlo model does not represent the dynamic behavior of the real system directly. According to the ergodicity theorem, “time average” will converge to the “configuration average” in a large system. Estimations from MC simulations often correspond very well with those from MD simulations. In All-tom CSAW method[3]., we first set up an initial unfolded structure. Then the structure is pivoted by randomly choosing backbone dihedral angles ψφ, and sidechain torsion angle χ. This candidate structure is checked by self-avoiding walk criteria to make sure that there are no atom overlaps. The structure energy is calculated for the pivoted peptide chain. A Metropolis scheme is used to determine if the new structure should be accepted. If accepted, this pivoted structure is saved and used as the starting point for the next loop. Otherwise, the structure is restored to the one before pivot. Then a new pivot is carried out in the next loop.
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