Dynamic Graphical Models of Molecular Kinetics

Abstract

Most current molecular dynamics simulation and analysis methods rely on the idea that the molecular system can be characterized by a single global state, e.g., a Markov State in a Markov State Model (MSM). In this approach, molecules can be extensively sampled and analyzed when they only possess a few metastable states, such as small to medium-sized proteins. However this approach breaks down in frustrated systems and in large protein assemblies, where the number of global meta-stable states may grow exponentially with the system size. Here, we introduce Dynamic Graphical Models (DGMs), which build upon the idea of Ising models, and describe molecules as assemblies of coupled subsystems. The switching of each sub-system state is only governed by the states of itself and its neighbors. DGMs need many fewer parameters than MSMs or other global-state models, in particular we do not need to observe all global system configurations to estimate them. Therefore, DGMs can predict new, previously unobserved, molecular configurations. Here, we demonstrate that DGMs can faithfully describe molecular thermodynamics and kinetics and predict previously unobserved metastable states for Ising models and protein simulations.

Machine learning approaches for analyzing and enhancing molecular dynamics simulations

“…In recent work [18], Olsson and Noé have extended the notion of encoding a global molecular configuration, x, into encoding several local configurations x 1 , x 2 ,..., x j , each representing a partition of the original global molecular structure into a local substructure. To model the time evolution of x the propagator or conditional distribution p(x t |x t−τ ) is written in terms of the substructures:…”

Independent Markov Decomposition: Towards modeling kinetics of biomolecular complexes

“…To this end, Noé & Olsson (24) have recently proposed dynamic graphical models which attempts to decompose protein systems in a way similar to Ising or Potts models -subsystems with states or "spins" that are coupled to one another.…”

“…As protein complexes become larger, the number of uncoupled or weakly coupled subsystems increases. If each of these subsystems contain two or more substates, the number of global systems states increases exponentially (24). Therefore, any model treating the whole system by means of a global state poses requirements on the MD sampling that are fundamentally unscalable.…”

“…To this end, Noé & Olsson (24) have recently proposed dynamic graphical models which attempts to decompose protein systems in a way similar to Ising or Potts models – subsystems with states or “spins” that are coupled to one another. Dibak et al (29, 30) have developed a coupling of MSMs with reaction-diffusion dynamics in order to establish an infrastructure in which MSMs can be integrated into whole-cell models.…”

“…Modeling subsystems of a constant size effectively restricts the number of states that need to be sampled reversibly to a constant. Therefore exponentially less sampling is required for modeling smaller subsystems as compared to a global model (15, 24).…”