Data-Driven Coarse-Graining using Space-Time Diffusion Maps

Dynamical systems with many degrees of freedom arise in a wide range of applications, including large scale molecular dynamics, climate and weather studies, and electrical power networks. The challenge in simulation is normally to extract statistical information, for example the average propensity of a given state of the system or the average time that elapses between certain events. Simulation data is easy to generate but often poorly utilized. The goal of this project is the development of a data-driven method for the automatic detection of a simplified description of the system based on a set of collective variables which can be used within efficient statistical extraction procedures. These slowest degrees of freedom are typically the most important ones. The dynamics are characterised as fluctuations in the vicinity of given state punctuated by relatively rare events describing transitions between the states. Efficiently identifying collective variables is the crucial first step in the design of coarse-grained models which can allow many order of magnitude increases in the accessible simulation timescale. By automatically finding collective variables, we can greatly simplify rapid study and comparison of many systems. The research builds on the technique of diffusion maps, whereby the eigenfunctions of a diffusion operator are used to characterise the metastable (slowly changing) states of the system.

The potential impact of automatic coarse-graining will be felt most profoundly in fields such as rational drug design, where it is necessary to select specific drug molecules for their properties in interaction with some target, e.g. a protein. Bio-molecular simulation depends on the use of very specialised and intensely developed simulation codes which are the products of many years of development and government investment. In order to accelerate the implementation and testing of novel algorithms in this important area, this project includes a detailed plan for software development within the EPSRC-funded MIST (Molecular Integrator Software Tools) platform. Testing of the software methodology will be conducted via collaborations with chemists and pharmaceutical chemists, including researchers at Rice University (Houston, Texas) and Memorial Sloan Kettering Cancer Research Center (New York).

This project has the potential to influence at least three important application fields: macromolecular simulation, geophysical fluid modelling, and the design of power networks. The latter two areas are increasingly important in the context of the evolving global climate, both for understanding and predicting changes in global (e.g. hurricane development) and local (e.g. tidal surge) weather behaviours and for the design of a stable power grid with the proliferation of power sources and changing power demand.

The macromolecular modelling area is the principal application developed in the project. In order to accelerate the development -> algorithm -> model -> simulation pipeline (which can, in some cases, evolve on a decadal timescale), this project will take advantage of the Molecular Integrator Software Tools (MIST) package developed within a previous EPSRC-funded research project. MIST facilitates a write-once-run-everywhere approach to algorithm design. Previously, MIST has been shown to allow the implementation of a continuous tempering strategy (the use of a defined temperature schedule) within AMBER, GROMACS and other molecular simulation codes. It is currently being enhanced to include algorithms for constraints and for adaptive thermostatic control. The current project will take MIST to the next level by establishing additional functionalities in the form of an analysis toolset with decision maker that will allow adaptive determination of collective variables as well as the selection of seeds for subsequent phase space exploration.

Benchmarking in an area such as macromolecular modelling is a nontrivial task, thus the project will include collaboration with well placed researchers from chemistry and pharma communities who can provide use cases (initial conditions and parameter values) which are relevant for large scale modelling. As an important demonstration, we will collaborate with John Chodera (Memorial Sloan Kettering Cancer Center, New York), who is engaged in using biomolecular simulation for drug design. The goal here is to apply our method to the problem of kinase inhibitor design for use in treating cancer and other diseases. The challenge is to accurately account for the complex large-scale conformational changes between active and various inactive states of the more than 500 human kinases. An efficient automated scheme for identifying the relevant collective variables for each kinase is vital to enabling the rapid computation of conformational free energies that play a critical role in inhibitor selectivity. By using well-studied kinase systems such as Abl and Src for which ~1 ms of aggregate simulation data is available and for which good collective variables are known, we can validate the approach before applying it to a large-scale survey of kinase conformational dynamics that will be performed on the Folding@home distributed computing platform.