A geometrical approach to computing free-energy landscapes from short-ranged potentials

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

Volumn 110, Issue 1, 2013, Pages

  Holmes Cerfon, Miranda ^a   Gortler, Steven J ^a   Brenner, Michael P ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Self assembly; Sticky Brownian motion; Sticky spheres; Transition rates

Indexed keywords

ENERGY; FREE ENERGY LANDSCAPE; GEOMETRY; MATHEMATICAL COMPUTING; MATHEMATICAL PARAMETERS; PARTICLE SIZE; PRIORITY JOURNAL; REVIEW; SIMULATION; TEMPERATURE;

BIOPHYSICAL PROCESSES; CARBOXYLIC ACIDS; COLLOIDS; DNA, COMPLEMENTARY; FULLERENES; KINETICS; MODELS, THEORETICAL;

EID: 84871943759     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1211720110     Document Type: Review

References (52)

1. Wales DJ (2003) Energy Landscapes (Cambridge Univ Press, Cambridge, UK).
2. Stillinger F, Weber T (1984) Packing structures and transition in liquids and solids. Science 225:983-989.
3. Beberg AL, Ensign DL, Jayachandran G, Khaliq S, Pande VS (2009) Folding@home: Lessons from eight years of distributed computing. IEEE International Symposium on Parallel & Distributed Processing, May 23-29, 2009, IEEE Computer Society.
4. Meng G, Arkus N, Brenner MP, Manoharan VN (2010) The free-energy landscape of clusters of attractive hard spheres. Science 327(5965):560-563.
5. Bowman GR, Pande VS (2010) Protein folded states are kinetic hubs. Proc Natl Acad Sci USA 107(24):10890-10895.
6. Doye JPK, Wales DJ (1996) The structure and stability of atomic liquids: From clusters to bulk. Science 271:484-487. (Pubitemid 126552475)
7. Stillinger FH (1995) A topographic view of supercooled liquids and glass formation. Science 267(5206):1935-1939.
8. Onuchic JN, Luthey-Schulten Z, Wolynes PG (1997) Theory of protein folding: The energy landscape perspective. Annu Rev Phys Chem 48:545-600. (Pubitemid 127443918)
9. Liwo A, Lee J, Ripoll DR, Pillardy J, Scheraga HA (1999) Protein structure prediction by global optimization of a potential energy function. Proc Natl Acad Sci USA 96(10):5482-5485. (Pubitemid 29234643)
10. Wolynes PG (2005) Recent successes of the energy landscape theory of protein folding and function. Q Rev Biophys 38(4):405-410.
11. Rothemund PW (2006) Folding DNA to create nanoscale shapes and patterns. Nature 440(7082):297-302.
12. Clementi C (2008) Coarse-grained models of protein folding: Toy models or predictive tools? Curr Opin Struct Biol 18(1):10-15.
13. Maragliano L, Cottone G, Ciccotti G, Vanden-Eijnden E (2010) Mapping the network of pathways of CO diffusion in myoglobin. J Am Chem Soc 132(3):1010-1017.
14. Swendsen RH, Wang JS (1986) Replica Monte Carlo simulation of spin glasses. Phys Rev Lett 57(21):2607-2609.
15. Elber R, Karplus M (1987) A method for determining reaction paths in large molecules: Application to myoglobin. Chem Phys Lett 139:375-380.
16. Weinan E, Ren W, Vanden-Eijnden E (2002) String method for the study of rare events. Phys Rev B 66:052301.
17. Bolhuis PG, Chandler D, Dellago C, Geissler PL (2002) Transition path sampling: Throwing ropes over rough mountain passes, in the dark. Annu Rev Phys Chem 53:291-318.
18. Hummer G (2004) From transition paths to transition states and rate coefficients. J Chem Phys 120(2):516-523.
19. Abrams CF, Vanden-Eijnden E (2010) Large-scale conformational sampling of proteins using temperature-accelerated molecular dynamics. Proc Natl Acad Sci USA 107(11):4961-4966.
20. Wales DJ, Scheraga HA (1999) Global optimization of clusters, crystals, and biomolecules. Science 285(5432):1368-1372. (Pubitemid 29411661)
21. Carr JM, Trygubenko SA, Wales DJ (2005) Finding pathways between distant local minima. J Chem Phys 122(23):234903.
22. Wales DJ (2006) Energy landscapes: Calculating pathways and rates. Int Rev Phys Chem 25:237-282.
23. Henkelman G, Uberuaga B, Jonsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113:9901.
24. Noé F, Schütte C, Vanden-Eijnden E, Reich L, Weikl TR (2009) Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations. Proc Natl Acad Sci USA 106(45):19011-19016.
25. Hagen M, Jeijer E, Mooij G, Frenekl D, Lekkerkerker H (1993) Does C60 have a liquid phase? Nature 365:425-426.
26. n clusters. Chem Phys Lett 262: 167-174.
27. Gazzillo D, Giacometti A, Fantoni R, Sollich P (2006) Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions. Phys Rev E Stat Nonlin Soft Matter Phys 74(5 Pt 1):051407.
28. Dreyfus R, et al. (2009) Simple quantitative model for the reversible association of DNA coated colloids. Phys Rev Lett 102(4):048301.
29. Macfarlane R, et al. (2011) Nanoparticle superlattice engineering with DNA. Science 334(6053):204-208.
30. Rogers WB, Crocker JC (2011) Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling. Proc Natl Acad Sci USA 108(38):15687-15692.
31. Baxter R (1968) Percus-Yevick equation for hard spheres with surface adhesion. J Chem Phys 49:2770-2774.
32. Stell G (1991) Sticky spheres and related systems. J Stat Phys 63(5-6):1203-1221.
33. Miller MA, Frenkel D (2003) Competition of percolation and phase separation in a fluid of adhesive hard spheres. Phys Rev Lett 90(13):135702.
34. Gazzillo D, Giacometti A (2004) Analytic solutions for Baxter's model of sticky hard sphere fluids within closures different from the Percus-Yevick approximation. J Chem Phys 120(10):4742-4754.
35. Malins A, Williams SR, Eggers J, Tanaka H, Royall CP (2009) Geometric frustration in small colloidal clusters. J Phys Condens Matter 21(42):425103.
36. Wales DJ (2010) Energy landscapes of clusters bound by short-ranged potentials. ChemPhysChem 11(12):2491-2494.
37. Arkus N, Manoharan VN, Brenner MP (2009) Minimal energy clusters of hard spheres with short range attractions. Phys Rev Lett 103(11):118303.
38. Arkus N, Manoharan V, Brenner M (2011) Deriving finite sphere packings. SIAM J Discrete Math 25:1860-1901.
39. Allen MP, Tildesley DJ (1989) Computer Simulation of Liquids (Oxford Univ Press, Oxford).
40. Landau LD, Lifshitz EM (1978) Statistical Physics, Course of Theoretical Physics (Pergamon, Oxford), Vol 5.
41. Fatkullin I, Kovacic G, Vanden-Eijnden E (2010) Reduced dynamics of stochastically perturbed gradient flows. Commun Math Sci 8:439-461.
42. Calvo F, Doye JPK, Wales DJ (2012) Energy landscapes of colloidal clusters: Thermodynamics and rearrangement mechanisms. Nanoscale 4(4):1085-1100.
43. Asimow L, Roth B (1978) The rigidity of graphs. Trans Am Math Soc 245:279-289.
44. Gardiner C (2009) Stochastic Methods: A Handbook for the Natural and Social Sciences (Springer, Berlin), 4th Ed.
45. Ikeda N, Watanabe S (1981) Stochastic Differential Equations and Diffusion Processes (Elsevier, Amsterdam).
46. Metzner P, Schütte C, Vanden-Eijnden E (2006) Illustration of transition path theory on a collection of simple examples. J Chem Phys 125(8):084110.
47. Vanden-Eijnden E (2006) Transition path theory. Lect Note Phys 703:453-493.
48. Weinan E, Vanden-Eijnden E (2010) Transition-path theory and path-finding algorithms for the study of rare events. Annu Rev Phys Chem 61:391-420.
49. Schütte C, Noé F, Lu J, Sarich M, Vanden-Eijnden E (2011) Markov state models based on milestoning. J Chem Phys 134(20):204105.
50. Hormoz S, Brenner M (2011) Design principles for self-assembly with short-range interactions. Proc Natl Acad Sci USA 108:19885-19890.
51. Hoy R, Harwayne-Gidansky J, O'Hern C (2012) Structure of finite sphere packing via exact enumeration: Implications for colloidal crystal nucleation. Phys Rev E Stat Nonlin Soft Matter Phys 85(5):051403.
52. Sommese A, Wampler C (2005) Numerical Solution of Polynomial Systems Arising in Engineering and Science (World Scientific, Singapore).