Frank Noé and J. C Smith (2007)
Transition Networks: A Unifying Theme for Molecular Simulation and Computer Science
In: Mathematical Modeling of Biological Systems, Volume I, ed. by A. Deutsch, L. Brusch, H. Byrne, G. de Vries and H.-P. Herzel , chap. 11, pp. 121–137, Birkhäuser Boston. (ISBN: 978-0-8176-4557-1 (Print) 978-0-8176-4558-8 (Online)).
A transition network (TN) is a graph-theoretical concept describing the transitions between (meta)stable states of dynamical systems. Here, we review methods to generate and analyze a TN for molecular systems. The appropriate identification of states and transitions from the potential energy surface of the molecule is discussed. We describe a formalism transforming a TN on a static energy surface into a time-dependent dynamic TN that yields the population probabilities for each system state and the interstate transition rates. Three analysis methods that help in understanding the dynamics of the molecular system based on the TN are discussed: (1) Disconnectivity graphs allow important features of the energy surface captured in a static TN to be visualized, (2) graph-theoretical methods enable the computation of the best transition paths between two predefined states of the TN, and (3) statistical methods from complex network analysis identify important features of the TN topology. A broad review of the literature is given, and some open research directions are discussed.
