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 local-minima 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.
Work completed at the University of North Carolina at Chapel Hill.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
N.M. Amato, O.B. Bayazit, L.K. Dale, C. Jones, and D. Vallejo. OBPRM: An obstacle-based PRM for 3D workspaces. In P.K. Agarwal et al., editors, Robotics: The Algorithmic Perspective: 1998 Workshop on the Algorithmic Foundations of Robotics, pages 155–168. A. K. Peters, Wellesley, MA, 1998.
N.M. Amato, K.A. Dill, and G. Song. Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures. In Proc. ACM Int. Conf. on Computational Biology (RECOMB), pages 2–11, 2002.
M.S. Apaydin, D.L. Brutlag, C. Guestrin, D. Hsu, and J.C. Latombe. Stochastic roadmap simulation: An efficient representation and algorithm for analyzing molecular motion. In Proc. ACM Int. Conf. on Computational Biology (RECOMB), pages 12–21, 2002.
M.S. Apaydin, C.E. Guestrin, Chris Varma, D.L. Brutlag, and J.C. Latombe. Stochastic roadmap simulation for the study of ligand-protein interactions. Bioinformatics, 18(supplement 2 ): 18S - 26S, 2002.
M.S. Apaydin, A.P. Singh, D.L. Brutlag, and J.C. Latombe. Capturing molecular energy landscapes with probabilistic conformational roadmaps. In Proc. IEEE Int. Conf. on Robotics & Automation, pages 932–939, 2001.
J. Barraquand and J.C. Latombe. Robot motion planning: A distributed representation approach. Int. J. Robotics Research, 10 (6): 628–649, 1991.
F.C. Bernstein et al. The protein data bank: A computer-based archival file for macro-molecular structure. J. Mol. Biol., 112 (3): 535–542, 1977.
R. Bohlin and L.E. Kavraki. Path planning using lazy PRM. In Proc. IEEE Int. Conf. on Robotics & Automation, pages 521–528, 2000.
V. Boor, M.H. Overmars, and F. van der Stappen. The Gaussian sampling strategy for probabilistic roadmap planners. In Proc. IEEE Int. Conf. on Robotics & Automation, pages 1018–1023, 1999.
C.J. Camacho and S. Vajda. Protein docking along smooth association pathways. Proc. Nat. Acad. Sei. USA, 98 (19): 10636–10641, 2001.
R. Du, V. Pande, A.Y. Grosberg, T. Tanaka, and E. Shakhnovich. On the transition coordinate for protein folding. J. Chem. Phys., 108 (l): 334–350, 1998.
J.M. Haile. Molecular Dynamics Simulation: Elementary Methods. John Wiley & Sons, New York, 1992.
D. Hsu, J.C. Latombe, and R. Motwani. Path planning in expansive configuration spaces. Int. J. Computational Geometry & Applications, 9 (4 & 5): 495–512, 1999.
IBM Blue Gene Team. Blue gene: A vision for protein science using a petaflop supercomputer. IBM Systems Journal, 40 (2): 310–327, 2001.
M.H. Kalos and P.A. Whitlock. Monte Carlo Methods, volume 1. John Wiley & Son, New York, 1986.
L.E. Kavraki, P. Svestka, J.C. Latombe, and M.H. Overmars. Probabilistic roadmaps for path planning in high-dimensional configuration space. IEEE Trans, on Robotics & Automation, 12 (4): 566–580, 1996.
S.M. LaValle and J.J. Kuffner. Randomized kinodynamic planning. Int. J. Robotics Research, 20 (5): 278–400, 2001.
A.R. Leach. Molecular Modelling: Principles and Applications. Longman, Essex, England, 1996.
M.Cieplak, M.Henkel, J. Karbowski, and J.R.Banavar. Master equation approach to protein folding and kinetic traps. Phys. Rev. Let., 80: 3654, 1998.
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller. Equations of state calculations by fast computing machines. J. Chem. Phys., 21: 1087–1092, 1953.
G.M. Morris, D.S. Goodsell, R.S. Halliday, R. Huey, W.E. Hart, R.K. Belew, and A.J. Olson. Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. J. Comput. Chem., 19 (14): 1639–1662, 1998.
V.S. Pande et al. Atomistic protein folding simulations on the hundreds of microsecond timescale using worldwide distributed computing. Biopolymers, to appear.
Y. Saad. Iterative Methods for Sparse Linear Systems. PWS, New York, 1996.
G. Sanchez and J.C. Latombe. On delaying collision checking in PRM planning— application to multi-robot coordination. Int. J. Robotics Research, 21 (1): 5–26, 2002.
T. Siméon, J.P. Laumond, and F. Lamiraux. Move3D: A generic platform for motion planning. In Proc. IEEE Int. Symp. on Assembly & Task Planning, 2001.
A.P. Singh and D.L. Brutlag. Hierarchical protein structure superposition using both secondary structure and atomic representations. In Proc. Int. Conf. on Intelligent Systems for Molecular Biology, pages 284–293, 1997.
A.P. Singh, J.C. Latombe, and D.L. Brutlag. A motion planning approach to flexible ligand binding. In Proc. Int. Conf. on Intelligent Systems for Molecular Biology, pages 252–261, 1999.
K. Smith and B. Honig. Evaluation of the conformational free energies of loops in proteins. Proteins: Structure, Function, and Genetics, 18: 119–132, 1994.
G. Song and N.M. Amato. Using motion planning to study protein folding pathways. In Proc. ACM Int. Conf. on Computational Biology (RECOMB), pages 287–296, 2001.
S. Sun, PD. Thomas, and K.A. Dill. A simple protein folding algorithm using a binary code and secondary structure constraints. Protein Engineering, 8: 769–778, 1995.
H. Taylor and S. Karlin. An Introduction to Stochastic Modeling. Academic Press, New York, 1994.
C. Varma. Computing protein-ligand interaction kinetics using Markov methods. Master’s thesis, Dept. of Computer Science, Stanford University, Stanford, CA, 2002.
J. Wang, P.A. Kollman, and I.D. Kuntz. Flexible ligand docking: A multiple strategy approach. Proteins: Structure, Function, and Genetics, 36 (1): 1–19, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Apaydın, M.S., Brutlag, D.L., Guestrin, C., Hsu, D., Latombe, JC. (2004). Stochastic Conformational Roadmaps for Computing Ensemble Properties of Molecular Motion. In: Boissonnat, JD., Burdick, J., Goldberg, K., Hutchinson, S. (eds) Algorithmic Foundations of Robotics V. Springer Tracts in Advanced Robotics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45058-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-45058-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07341-0
Online ISBN: 978-3-540-45058-0
eBook Packages: Springer Book Archive