0.8 Motion planning for proteins: biophysics and applications  (Page 5/10)

A prm-based approach

The research group of Nancy Amato has been working on roadmap-based methods to study the process of protein folding . They start with the known native structure of a protein, and incrementally find conformations more and more different from the native state, and build a roadmap using these conformations. The goal is to find a large ensemble of pathways between the native structure and unfolded structures, and to study these pathways and their properties. In their work, the degrees of freedom of the protein are assumed to be the φ and ψ backbone dihedral angles of each amino acid residue. The side chains are assumed to be rigidly attached to the backbone. In their initial work, they generated new conformations for their roadmaps by adjusting the backbone dihedral angles in the folded conformation randomly with various standard deviations. This approach worked well for very small proteins, but did not scale well.

A later sampling approach was based on counting native contacts . For the purposes of their method, a native contact was defined as any two alpha-carbons within 7 Å of each other in the folded state of the protein. A new conformation is generated at each step of the sampling phase of the roadmap construction by randomly perturbing some existing sample. The resulting structure was accepted with a probability as follows:

Once the samples are generated, an attempt is made to connect the k nearest neighbors of each node to the node itself. A series of conformations on the line connecting the two nodes are tested, and if their energy is below a threshold, the edge is included in the roadmap. The weight of the edge depends on the sequence of energies of the conformations computed along the connecting line. The probability of moving from the (i-1)th structure to the ith along the line is given by: