Graphical Causal Modeling of Protein Structural and Dynamical Features

Abstract

The causal relationship between protein structural features and conformational dynamics is difficult to isolate experimentally because even seemingly small perturbations, such as point mutations, can simultaneously alter many physical properties of proteins. Using molecular dynamics simulation trajectories for a series of point mutations at a single solvent-exposed position on the protein GB1, for which experimental NMR spin relaxation data also are available [1], effects of various types of inter-residue interactions are isolated via a graph-theory-based approach to causal modeling [2] previously applied in the biological sciences mainly to functional MRI studies [3] and genomics [4]. This approach produces directed acyclic graphs (DAGs) in which protein structural features such as hydrogen bonds, inter-residue contacts, and order parameters are encoded as nodes; the presence of an edge in the graph implies a causal relationship between features and the directionality of the edge implies the direction of causation.[1] Mayer, KL et al. (2003). Nat. Struct. Biol. 10: 962-965.[2] Pearl, J. (2000). Cambridge University Press, London; Pearl, J. (2009). Statistics Surveys. 3:96-146; Spirtes et al. (2000). MIT Press, Cambridge.[3] Eichler, M. (2005). Phil. Trans. R. Soc. B. 360(1457): 953-967.[4] Maathius, MH et al. (2009). Ann. Stat. 37(6A): 3133-3164.