Locating landmarks on high-dimensional free energy surfaces

Proceedings of the National Academy of Sciences of the United States of America

Volumn 112, Issue 11, 2015, Pages 3235-3240

  Chen, Ming ^a   Yu, Tang Qing ^b   Tuckerman, Mark E ^a,b,c  

^a NEW YORK UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c NEW YORK UNIVERSITY SHANGHAI   (China)

Author keywords

Activation relaxation; Free energy surface; Machine learning; Network representation; Stochastic optimization

Indexed keywords

ALGORITHM; ARTICLE; CONFORMATIONAL TRANSITION; HIGH DIMENSIONAL FREE ENERGY SURFACE; MACHINE LEARNING; MOLECULAR BIOLOGY; MOLECULAR DYNAMICS; MOLECULAR MODEL; MONTE CARLO METHOD; PRIORITY JOURNAL; STOCHASTIC MODEL;

EID: 84925296467     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1418241112     Document Type: Article

References (40)

1. Rosso L, et al. (2002) On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles. J Chem Phys 116:4389-4402.
2. Maragliano L, Vanden-Eijnden E (2006) A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations. Chem Phys Lett 426(1-3):168-175.
3. Abrams JB, Tuckerman ME (2008) Efficient and direct generation of multidimensional free energy surfaces via adiabatic dynamics without coordinate transformations. J Phys Chem B 112(49):15742-15757.
4. Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci USA 99(20):12562-12566.
5. Bonomi M, Parrinello M (2010) Enhanced sampling in the well-tempered ensemble. Phys Rev Lett 104(19):190601.
6. Darve E, Rodríguez-Gómez D, Pohorille A (2008) Adaptive biasing force method for scalar and vector free energy calculations. J Chem Phys 128(14):144120.
7. Hénin J, Fiorin G, Chipot C, Klein ML (2010) Exploring multidimensional free energy landscapes using time-dependent biases on collective variables. J Chem Theory Comput 6(1):35-47.
8. Chen M, Cuendet MA, Tuckerman ME (2012) Heating and flooding: A unified approach for rapid generation of free energy surfaces. J Chem Phys 137(2):024102.
9. Morishita T, Itoh SG, Okumura H, Mikami M (2012) Free-energy calculation via meanforce dynamics using a logarithmic energy landscape. Phys Rev E Stat Nonlin Soft Matter Phys 85(6 Pt 2):066702.
10. Piana S, Laio A (2008) Advillin folding takes place on a hypersurface of small dimensionality. Phys Rev Lett 101(20):208101.
11. Das P, Moll M, Stamati H, Kavraki LE, Clementi C (2006) Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction. Proc Natl Acad Sci USA 103(26):9885-9890.
12. Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319-2323.
13. Coifman RR, et al. (2005) Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. Proc Natl Acad Sci USA 102(21): 7426-7431.
14. Rohrdanz MA, Zheng W, Maggioni M, Clementi C (2011) Determination of reaction coordinates via locally scaled diffusion map. J Chem Phys 134(12):124116.
15. Tribello GA, Ceriotti M, Parrinello M (2010) A self-learning algorithm for biased molecular dynamics. Proc Natl Acad Sci USA 107(41):17509-17514.
16. Ceriotti M, Tribello GA, Parrinello M (2011) From the cover: Simplifying the representation of complex free-energy landscapes using sketch-map. Proc Natl Acad Sci USA 108(32):13023-13028.
17. Henkelman G, Uberuaga BP, Jónsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113(22): 9901-9904.
18. Henkelman G, Jónsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111(15): 7010-7022.
19. Munro LJ, Wales DJ (1999) Defect migration in crystalline silicon. Phys Rev B 59: 3969-3980.
20. Barkema GT, Mousseau N (1996) Event-based relaxation of continuous disordered systems. Phys Rev Lett 77(21):4358-4361.
21. Malek R, Mousseau N (2000) Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 62(6 Pt A):7723-7728.
22. Wales DJ (2002) Discrete path sampling. Mol Phys 100(20):3285-3305.
23. Widrow B, Stearns SD (1985) Adaptive Signal Processing (Prentice-Hall, Upper Saddle River, NJ).
24. Bottou L (2004) Stochastic learning. Advanced Lectures on Machine Learning, Lecture Notes in Artificial Intelligence, LNAI 3176, eds Bousquet O, von Luxburg U (Springer, Berlin), pp 146-168.
25. Valsson O, Parrinello M (2014) Variational approach to enhanced sampling and free energy calculations. Phys Rev Lett 113(9):090601.
26. E W, Engquist B (2002) The heterogeneous multiscale methods. Commun Math Sci 1(1):87-132.
27. Gear WC, et al. (2003) Equation-free, coarse-grained multiscale computation: Enabling macroscopic simulators to perform system-level analysis. Commun Math Sci 1(4):715-762.
28. Maragliano L, Fischer A, Vanden-Eijnden E, Ciccotti G (2006) String method in collective variables: Minimum free energy paths and isocommittor surfaces. J Chem Phys 125(2):024106.
29. Samanta A, Chen M, Yu T-Q, Tuckerman M, E W (2014) Sampling saddle points on a free energy surface. J Chem Phys 140(16):164109.
30. E W, Zhou X (2011) The gentlest ascent dynamics. Nonlinearity 24(6):1831-1842.
31. Samanta A, E W (2012) Atomistic simulations of rare events using gentlest ascent dynamics. J Chem Phys 136(12):124104.
32. Borkar VS (2008) Stochastic Approximation: A Dynamical Systems Viewpoint (Cambridge Univ Press, New York).
33. Strodel B, Wales DJ (2008) Free energy surfaces from an extended harmonic superposition approach and kinetics for alanine dipeptide. Chem Phys Lett 466(4-6):105-115.
34. Rosso L, Abrams JB, Tuckerman ME (2005) Mapping the backbone dihedral free-energy surfaces in small peptides in solution using adiabatic free-energy dynamics. J Phys Chem B 109(9):4162-4167.
35. EW, Ren W, Vanden-Eijnden E (2002) String method for the study of rare events. Phys Rev B 66:052301.
36. Rappoport D, Galvin CJ, Zubarev DYu, Aspuru-Guzik A (2014) Complex chemical reaction networks from heuristics-aided quantum chemistry. J Chem Theory Comput 10(3):897-907.
37. Tuckerman ME, et al. (2000) Exploiting multiple levels of parallelism in molecular dynamics based calculations via modern techniques and software paradigms on distributed memory computers. Comput Phys Commun 128:333-376.
38. MacKerell AD, et al. (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102(18):3586-3616.
39. Tuckerman ME, Martyna GJ, Berne BJ (1992) Reversible multiple time scale molecular dynamics. J Chem Phys 97:1990-2001.
40. Ester M, Kriegel H-p, Jörg S, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Proceedings of 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96), eds Simoudis E, Han J, Fayyad U (AAAI Press, Menlo Park, CA), pp 226-231.