Combining Experiments and Simulations Using the Maximum Entropy Principle

PLoS Computational Biology

Volumn 10, Issue 2, 2014, Pages

  Boomsma, Wouter ^a   Ferkinghoff Borg, Jesper ^b   Lindorff Larsen, Kresten ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

MAXIMUM ENTROPY METHODS;

COMPUTATIONAL BIOLOGY; MAXIMUM ENTROPY PRINCIPLE; MAXIMUM-ENTROPY; MODEL AND ALGORITHMS; NATURAL TOOLS; PRINCIPLE OF MAXIMUM ENTROPY; PROBABILITY: DISTRIBUTIONS; QUANTITATIVE AGREEMENT; RESULTS OF COMPUTER MODELING; SEQUENCE ANALYSIS;

PROBABILITY DISTRIBUTIONS;

ACCURACY; ANALYTIC METHOD; ARTICLE; CONCEPTUAL FRAMEWORK; CONFORMATIONAL TRANSITION; DATA ANALYSIS; ENTROPY; MACROMOLECULE; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MAXIMUM ENTROPY PRINCIPLE; MOLECULAR DYNAMICS; MOLECULAR MODEL; PROBABILITY; REPRODUCIBILITY; STRUCTURE ANALYSIS; THEORETICAL STUDY; BIOLOGICAL MODEL; BIOLOGY; CHEMICAL STRUCTURE; CHEMISTRY; COMPUTER SIMULATION; UNCERTAINTY;

MACROMOLECULE;

COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; ENTROPY; MACROMOLECULAR SUBSTANCES; MODELS, BIOLOGICAL; MODELS, MOLECULAR; MOLECULAR DYNAMICS SIMULATION; UNCERTAINTY;

EID: 84895736343     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1003406     Document Type: Article

References (53)

1. Jaynes ET, (1957) Information theory and statistical mechanics. Phys Rev 106: 620.
2. Granot-Atedgi E, Tkaik G, Segev R, Schneidman E, (2013) Stimulus-dependent maximum entropy models of neural population codes. PLOS Comput Biol 9: e1002922 doi:10.1371/journal.pcbi.1002922.
3. Locasale JW, Wolf-Yadlin A, (2009) Maximum entropy reconstructions of dynamic signaling networks from quantitative proteomics data. PLOS One 4: e6522 doi:10.1371/journal.pone.0006522.
4. Carmichael SP, Shell MS, (2012) A new multiscale algorithm and its application to coarse-grained peptide models for self-assembly. J Phys Chem B 116: 8383-8393.
5. Lapedes AS, Giraud BG, Liu L, Stormo GD, (1999) Correlated mutations in models of protein sequences: phylogenetic and structural effects. Lect Notes Monogr Ser 33: 236-256.
6. Morcos F, Pagnani A, Lunt B, Bertolino A, Marks DS, et al. (2011) Direct-coupling analysis of residue coevolution captures native contacts across many protein families. Proc Natl Acad Sci U S A 108: E1293-E1301.
7. Klepeis JL, Lindorff-Larsen K, Dror RO, Shaw DE, (2009) Long-timescale molecular dynamics simulations of protein structure and function. Curr Opin Struct Biol 19: 120-127.
8. Norgaard AB, Ferkinghoff-Borg J, Lindorff-Larsen K, (2008) Experimental parameterization of an energy function for the simulation of unfolded proteins. Biophys J 94: 182-192.
9. Pitera JW, Chodera JD, (2012) On the use of experimental observations to bias simulated ensembles. J Chem Theory Comput 8: 3445-3451.
10. Roux B, Weare J, (2013) On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method. J Chem Phys 138: 084107.
11. Cavalli A, Camilloni C, Vendruscolo M, (2013) Molecular dynamics simulations with replica averaged structural restraints generate structural ensembles according to the maximum entropy principle. J Chem Phys 138: 094112.
12. Shannon CE, Weaver W, (1948) A mathematical theory of communication. Bell System Technical Journal 27: 379-423, 623-656.
13. Kullback S, Leibler RA, (1951) On information and sufficiency. Ann Math Statist 22: 79-86.
14. Jaynes ET, (1968) Prior probabilities. IEEE Trans Syst Sci Cybern 4: 227-241.
15. Hobson A, (1969) A new theorem of information theory. J Stat Phys 1: 383-391.
16. Shore J, Johnson R, (1980) Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Trans Inf Theory 26: 26-37.
17. Jaynes E (1979) Where do we stand on maximum entropy? In: Levine R, Tribus M, editors. The Maximum Entropy Formalism. Cambridge, MA: MIT Press. pp. 1-104.
18. Lindorff-Larsen K, Maragakis P, Piana S, Eastwood MP, Dror RO, et al. (2012) Systematic validation of protein force fields against experimental data. PLOS One 7: e32131 doi:10.1371/journal.pone.0032131.
19. Leaver-Fay A, O'Meara MJ, Tyka M, Jacak R, Song Y, et al. (2013) Chapter six- scientific benchmarks for guiding macromolecular energy function improvement. In: Keating AE, editor. Methods in Protein Design, Academic Press, Volume 523 of Methods in Enzymology. pp. 109-143.
20. Best RB, Hummer G, (2009) Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides. J Phys Chem B 113: 9004-9015.
21. Tyka MD, Jung K, Baker D, (2012) Efficient sampling of protein conformational space using fast loop building and batch minimization on highly parallel computers. J Comput Chem 33: 2483-2491.
22. Raval A, Piana S, Eastwood MP, Dror RO, Shaw DE, (2012) Refinement of protein structure homology models via long, all-atom molecular dynamics simulations. Proteins 80: 2071-2079.
23. Rieping W, Habeck M, Nilges M, (2005) Inferential structure determination. Science 309: 303-306.
24. Habeck M, Rieping W, Nilges M, (2006) Weighting of experimental evidence in macromolecular structure determination. Proc Natl Acad Sci U S A 103: 1756-1761.
25. Vendruscolo M, (2007) Determination of conformationally heterogeneous states of proteins. Curr Opin Struct Biol 17: 15-20.
26. Scheek RM, Torda AE, Kemmink J, van Gunsteren WF (1991) Structure determination by NMR: The modeling of NMR parameters as ensemble averages. In: Hoch JC, Poulsen FM, Redfield C, editors. Computational aspects of the Study of Biological Macromolecules by Nuclear Magnetic Resonance Spectroscopy. New York: Plenum Press. pp. 209-217.
27. Kim Y, Prestegard J, (1989) A dynamic model for the structure of acyl carrier protein in solution. Biochemistry 28: 8792-8797.
28. Kuriyan J, Ösapay K, Burley SK, Brünger AT, Hendrickson WA, et al. (1991) Exploration of disorder in protein structures by x-ray restrained molecular dynamics. Proteins 10: 340-358.
29. Levin EJ, Kondrashov DA, Wesenberg GE, Phillips GN, (2007) Ensemble refinement of protein crystal structures: validation and application. Structure 15: 1040-1052.
30. Burnley BT, Afonine PV, Adams PD, Gros P, (2012) Modelling dynamics in protein crystal structures by ensemble refinement. eLife 1: e00311.
31. Lindorff-Larsen K, Best RB, DePristo MA, Dobson CM, Vendruscolo M, (2005) Simultaneous determination of protein structure and dynamics. Nature 433: 128-132.
32. Lange OF, Lakomek NA, Farès C, Schröder GF, Walter KF, et al. (2008) Recognition dynamics up to microseconds revealed from an rdc-derived ubiquitin ensemble in solution. Science 320: 1471-1475.
33. Roux B, Islam SM, (2013) Restrained-ensemble molecular dynamics simulations based on distance histograms from double electron-electron resonance spectroscopy. J Phys Chem B 117: 4733-4739.
34. Lindorff-Larsen K, Kristjansdottir S, Teilum K, Fieber W, Dobson CM, et al. (2004) Determination of an ensemble of structures representing the denatured state of the bovine acyl-coenzyme A binding protein. J Am Chem Soc 126: 3291-3299.
35. Jo S, Im W, (2011) Transmembrane helix orientation and dynamics: insights from ensemble dynamics with solid-state nmr observables. Biophys J 100: 2913-2921.
36. Dedmon MM, Lindorff-Larsen K, Christodoulou J, Vendruscolo M, Dobson CM, (2005) Mapping long-range interactions in α-synuclein using spin-label NMR and ensemble molecular dynamics simulations. J Am Chem Soc 127: 476-477.
37. Richter B, Gsponer J, Várnai P, Salvatella X, Vendruscolo M, (2007) The MUMO (minimal underrestraining minimal over-restraining) method for the determination of native state ensembles of proteins. J Biomol NMR 37: 117-135.
38. Lindorff-Larsen K, Ferkinghoff-Borg J, (2009) Similarity measures for protein ensembles. PLOS One 4: e4203 doi:10.1371/journal.pone.0004203.
39. Burling FT, Weis WI, Flaherty KM, Brunger AT, (1996) Direct observation of protein salvation and discrete disorder with experimental crystallographic phases. Science 271: 72-77.
40. van Gunsteren WF, Dolenc J, Mark AE, (2008) Molecular simulation as an aid to experimentalists. Curr Opin Struct Biol 18: 149-153.
41. Bricogne G, (1984) Maximum entropy and the foundations of direct methods. Acta Crystallogr A 40: 410-445.
42. Róz'ycki B, Kim YC, Hummer G, (2011) SAXS ensemble refinement of ESCRT-III CHMP3 conformational transitions. Structure 19: 109-116.
43. Groth M, Malicka J, Czaplewski C, Ołdziej S, Łankiewicz L, et al. (1999) Maximum entropy approach to the determination of solution conformation of exible polypeptides by global conformational analysis and NMR spectroscopy - application to DNS1-c-[D-A2bu2, Trp4, Leu5]-enkephalin and DNS1-c-[D-A2bu2, Trp4, D-Leu5] enkephalin. J Biomol NMR 15: 315-330.
44. Massad T, Jarvet J, Tanner R, Tomson K, Smirnova J, et al. (2007) Maximum entropy reconstruction of joint φ, ψ-distribution with a coil-library prior: the backbone conformation of the peptide hormone motilin in aqueous solution from φ and ψ-dependent J-couplings. J Biomol NMR 38: 107-123.
45. Genheden S, Ryde U, (2012) Will molecular dynamics simulations of proteins ever reach equilibrium? Phys Chem Chem Phys 14: 8662-8677.
46. Thomas MU, (1979) Technical note - a generalized maximum entropy principle. Oper Res 27: 1188-1196.
47. Golan A, Judge G, Miller D (1996) Maximum entropy econometrics: robust estimation with limited data. Series in financial economics and quantitative analysis. San Francisco: Wiley. 307 pp.
48. Dudík M, Phillips SJ, Schapire RE, (2007) Maximum entropy density estimation with generalized regularization and an application to species distribution modeling. J Mach Learn Res 8: 1217-1260.
49. Donoho DL, Johnstone IM, Hoch JC, Stern AS, (1992) Maximum entropy and the nearly black object. J R Stat Soc Series B Stat Methodol 54: 41-81.
50. Gull S, Daniell G, (1978) Image reconstruction from incomplete and noisy data. Nature 272: 686-690.
51. Olsson S, Frellsen J, Boomsma W, Mardia KV, Hamelryck T, (2013) Inference of structure ensembles from sparse, averaged data. PLOS One 8: e79439 doi:101371/journal.pone0079439.
52. Wang LP, Chen J, Van Voorhis T, (2012) Systematic parametrization of polarizable force fields from quantum chemistry data. J Chem Theory Comput 9: 452-460.
53. Olsson S, Boomsma W, Frellsen J, Bottaro S, Harder T, et al. (2011) Generative probabilistic models extend the scope of inferential structure determination. Journal of Magnetic Resonance 213: 182-186.