Stochastic Conformational Roadmaps for Computing Ensemble Properties of Molecular Motion

Abstract

Abstract.A key intuition behind probabilistic roadmap planners for motion planning is that many collision-free paths potentially exist between two given robot configurations. Hence the connectivity of a robot's free space can be captured effectively by a network of randomly sampled configurations. In this paper, a similar intuition is exploited to preprocess molecular motion pathways and efficiently compute their ensemble properties, i.e., properties characterizing the average behavior of many pathways. We construct a directed graph, called stochastic conformational roadmap, whose nodes are randomly sampled molecule conformations. A roadmap compactly encodes many molecular motion pathways. Ensemble properties are computed by viewing the roadmap as a Markov chain. A salient feature of this new approach is that it examines all the paths in the roadmap simultaneously, rather than one at a time as classic methods such as Monte Carlo (MC) simulation would do. It also avoids the localminima problem encountered by the classic methods. Tests of the approach on two important biological problems show that it produces more accurate results and achieves several orders of magnitude reduction in computation time, compared with MC simulation.

Multi-Resolution Rigidity-Based Sampling of Protein Conformational Paths

“…Another class of methods sample the conformational space efficiently by perturbing the molecular structure at certain degrees of freedom and using geometric and biophysical constraints to guide the search. The search is done using various techniques such as normal mode analysis [24,27], elastic network [7,17], robotic motion planning [2,4,5] and more. These methods are usually faster than MD but do not result in physical pathways due to randomness in the search and the approximations being used.…”

The Stochastic Motion Roadmap: A Sampling Framework for Planning with Markov Motion Uncertainty

“…Apaydin et al previously explored the connection between probabilistic roadmaps and stochastic motions using Stochastic Roadmap Simulation (SRS), a method designed specifically for molecular conformation spaces [4,5]. SRS, which formalizes random walks in a roadmap as a Markov Chain, has been successfully applied to predict average behavior of molecular motion pathways of proteins and requires orders of magnitude less computation time than traditional MonteCarlo molecular simulations.…”

“…PRM's were previously extended to explore stochastic motion in molecular conformation spaces [4,5], but without a planning component to optimize actions. Our SMR formulation is applicable to a variety of decision-based robotics problems.…”

The Stochastic Motion Roadmap: A Sampling Framework for Planning with Markov Motion Uncertainty

“…Apaydin et al previously explored the connection between probabilistic roadmaps and stochastic motions using Stochastic Roadmap Simulation (SRS), a method designed specifically for molecular conformation spaces [4,5]. SRS, which formalizes random walks in a roadmap as a Markov Chain, has been successfully applied to predict average behavior of molecular motion pathways of proteins and requires orders of magnitude less computation time than traditional Monte-Carlo molecular simulations.…”

“…In SMR, "stochastic" refers to the motion of the robot, not to the sampling of states. PRM's were previously extended to explore stochastic motion in molecular conformation spaces [4,5], but without a planning component to optimize actions. Our SMR formulation is applicable to a variety of decision-based robotics problems.…”