13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- sidechain CSAW method. We developed the all-atom self-avoiding walk method as a coarse-grained ab initio protein folding simulation method with atom details[3]. Since crank model can provide atom locations for backbone atoms, the central problem is how to determine the sidechain atom coordinates if the atom coordinates are known for a backbone structure in arbitrary orientation. Thanks for the knowledge of amino acid structure, we have the atom coordinates for sidechain in some special orientation. As a consequence, we can determine the sidechain atom coordinates by matching amino acid to the backbone of a crank. As the structure of 20 amino acids are well determined by experiment observation, we have the atom coordinates for any type of residues, including backbone obs BB X and sidechain obs SC X . The only problem is that the observed amino acid structure are usually not in the same orientation as in crank model. If the backbone parts N-Cα-C-O of observed amino acid structure overlap with crank model, it is obvious that the crank sidechain atom will be determined by obs SC crank SC X X= . 4. Pivot algorithm The protein chain is simulated by a series of cranks connected at Cα atom. The chain conformation will change when the torsion angle φ and ψ are modified. In order to create a new conformation in AA-CSAW, we pivot the chain at certain randomly selected Cα atom by changing φ and ψ to specified values (Figure 2). The crank chain pivot procedure can be summarized as following steps. 1. Start with initial chain. 2. Choose a crank randomly as pivot point and change the torsion angles 3. Rotate end portion about pivot point. 4. Check atom overlaps. If no overlap, accept and update chain conformation. 5. If overlap, go to 2. Figure 2. Pivot polypeptide chain by changing torsion angles 5. Non-covalent Interactions and structure energy In AA-CSAW, we consider the most important non-covalent interactions in water solution, such as hydrophobic effect, hydrogen bonding. Hydrophobic residues, such as Alanine, Valine and Phenylalanine, tend to congregate in an aqueous (i.e. water) environment. The absence of hydrogen bonding between water and non-polar groups constitutes an important source of the protein stability in aqueous solution, known as hydrophobic effect. With the help of such effect, a hydrophobic core is usually formed in globular protein. The assembly of hydrophobic residues is thus considered as the driving force of the collapse of peptide chain[4]. Hydrophobicity is usually expressed as the Gibbs energies of transfer from water into the reference state. When globular protein fold from denature to native structure, hydrophobic residues come together and free energy decrease. The transfer hydrophobic amino acid residues from cyclohexane
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