PhD Seminar • Bioinformatics — Protein Structure Constrained Dynamics and the Rank 3 Positive Semidefinite Matrix Manifold

Xiao-Bo Li, PhD candidate
David R. Cheriton School of Computer Science

Elastic network models (ENMs) model a protein structure as a network of nodes, where neighbouring nodes are connected by springs. A Hookean spring potential energy is used to model nearby pairwise atomic interactions. This model allows the normal mode displacements of the protein to be calculated efficiently. Squaring the inter-atomic distances in the Hookean potential gives a new potential that is a function of the positive semidefinite (PSD) Gram matrix. The PSD potential suggests the PSD Gram matrix is another object that can be used to model ENMs. Since the Gram matrix is a rank 3 PSD matrix, modelling protein dynamics with Gram matrices can be formulated as a rank 3 PSD matrix manifold optimization problem with constraints. The formulation of this constrained optimization problem is discussed in this seminar.