title: Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps.
abstract: Identification of the collective coordinates that describe rare events in complex molecular transitions such as protein folding has been a key challenge in the theoretical molecular sciences. In the Diffusion Map approach, one assumes that the molecular configurations sampled have been generated by a diffusion process, and one uses the eigenfunctions of the corresponding diffusion operator as reaction coordinates. While diffusion coordinates (DCs) appear to provide a good approximation to the true dynamical reaction coordinates, they are not parametrized using dynamical information. Thus, their approximation quality could not, as yet, be validated, nor could the diffusion map eigenvalues be used to compute relaxation rate constants of the system. Here we combine the Diffusion Map approach with the recently proposed Variational Approach for Conformation Dynamics (VAC). Diffusion Map coordinates are used as a basis set, and their optimal linear combination is sought using the VAC, which employs time-correlation information on the molecular dynamics (MD) trajectories. We have applied this approach to ultra-long MD simulations of the Fip35 WW domain and found that the first DCs are indeed a good approximation to the true reaction coordinates of the system, but they could be further improved using the VAC. Using the Diffusion Map basis, excellent approximations to the relaxation rates of the system are obtained. Finally, we evaluate the quality of different metric spaces and find that pairwise minimal root-mean-square deviation performs poorly, while operating in the recently introduced kinetic maps based on the time-lagged independent component analysis gives the best performance.
authors.affiliation: Center for Theoretical Biological Physics and Department of Chemistry, Rice University , 6100 Main Street, Houston, Texas 77005, United States.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Boninsegna
authors.affiliation: Maxwell Institute for Mathematical Sciences and School of Mathematics, The University of Edinburgh , Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom.
authors.forename: Gianpaolo
authors.initials: G
authors.lastname: Gobbo
authors.affiliation: Department of Mathematics, Computer Science and Bioinformatics, Freie Universität Berlin , Arnimallee 6, 14195 Berlin, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Noé
authors.affiliation: Center for Theoretical Biological Physics and Department of Chemistry, Rice University , 6100 Main Street, Houston, Texas 77005, United States.
authors.forename: Cecilia
authors.initials: C
authors.lastname: Clementi
mesh_terms: D004058:Diffusion; D006801:Humans; D007700:Kinetics; D008390:Markov Chains; D056004:Molecular Dynamics Simulation; D016296:Mutagenesis; D000072340:NIMA-Interacting Peptidylprolyl Isomerase; D019696:Peptidylprolyl Isomerase / Q000737:chemistry / Q000235:genetics / Q000378:metabolism; D017510:Protein Folding; D017434:Protein Structure, Tertiary; D011506:Proteins / Q000737:chemistry* / Q000378:metabolism
chemical_list: D000072340:NIMA-Interacting Peptidylprolyl Isomerase; D011506:Proteins; C000606846:PIN1 protein, human; D019696:Peptidylprolyl Isomerase