Potts Hamiltonian models of protein co-variation, free energy landscapes, and evolutionary fitness

Current Opinion in Structural Biology

Volumn 43, Issue , 2017, Pages 55-62

  Levy, Ronald M ^a   Haldane, Allan ^a   Flynn, William F ^a,b  

^a Temple University   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AMINO ACID SEQUENCE; GENE MUTATION; MOLECULAR EVOLUTION; POTTS HAMILTONIAN MODEL; PRIORITY JOURNAL; PROTEIN CONFORMATION; PROTEIN FAMILY; PROTEIN FUNCTION; PROTEIN STRUCTURE; REVIEW; SEQUENCE ALIGNMENT; STATISTICAL MODEL; CHEMISTRY; EPISTASIS; GENETICS; METABOLISM; MOLECULAR MODEL; THERMODYNAMICS;

PROTEIN;

EPISTASIS, GENETIC; EVOLUTION, MOLECULAR; MODELS, MOLECULAR; PROTEINS; THERMODYNAMICS;

EID: 84996528086     PISSN: 0959440X     EISSN: 1879033X     Source Type: Journal    
DOI: 10.1016/j.sbi.2016.11.004     Document Type: Review

References (69)

1. 1 de Juan, D., Pazos, F., Valencia, A., Emerging methods in protein co-evolution. Nat Rev Genet 14 (2013), 249–261, 10.1038/nrg3414.
2. 2 Stein, R.R., Marks, D.S., Sander, C., Inferring pairwise interactions from biological data using maximum-entropy probability models. PLoS Comput Biol, 11, 2015, e1004182, 10.1371/journal.pcbi.1004182.
3. 3 Serohijos, A.W., Shakhnovich, E.I., Merging molecular mechanism and evolution: theory and computation at the interface of biophysics and evolutionary population genetics. Curr Opin Struct Biol 26 (2014), 84–91, 10.1016/j.sbi.2014.05.005.
4. 4 Neuwald, A.F., Gleaning structural and functional information from correlations in protein multiple sequence alignments. Curr Opin Struct Biol 38 (2016), 1–8, 10.1016/j.sbi.2016.04.006.
5. 5 Mzard, M., Mora, T., Constraint satisfaction problems and neural networks: a statistical physics perspective. J Physiol Paris 103 (2009), 107–113, 10.1016/j.jphysparis.2009.05.013.
6. 6 Mora, T., Bialek, W., Are biological systems poised at criticality?. J Stat Phys 144 (2011), 268–302, 10.1007/s10955-011-0229-4.
7. 7 Mortazavi, A., Williams, B.A., McCue, K., Schaeffer, L., Wold, B., Mapping and quantifying mammalian transcriptomes by RNA-Seq. Nat Methods 5 (2008), 621–628, 10.1038/nmeth.1226.
8. 8 Jabara, C.B., Jones, C.D., Roach, J., Anderson, J.A., Swanstrom, R., Accurate sampling and deep sequencing of the HIV-1 protease gene using a primer ID. Proc Natl Acad Sci U S A 108 (2011), 20166–20171, 10.1073/pnas.1110064108.
9. 9 Flynn, W.F., Chang, M.W., Tan, Z., Oliveira, G., Yuan, J., Okulicz, J.F., Torbett, B.E., Levy, R.M., Deep sequencing of protease inhibitor resistant HIV patient isolates reveals patterns of correlated mutations in Gag and protease. PLOS Comput Biol, 11, 2015, e1004249, 10.1371/journal.pcbi.1004249.
10. 10 Socolich, M., Lockless, S.W., Russ, W.P., Lee, H., Gardner, K.H., Ranganathan, R., Evolutionary information for specifying a protein fold. Nature 437 (2005), 512–518, 10.1038/nature03991.
11. 11 Russ, W.P., Lowery, D.M., Mishra, P., Yaffe, M.B., Ranganathan, R., Natural-like function in artificial WW domains. Nature 437 (2005), 579–583, 10.1038/nature03990.
12. 12 Liu, Z., Chen, J., Thirumalai, D., On the accuracy of inferring energetic coupling between distant sites in protein families from evolutionary imprints: illustrations using lattice model. Proteins Struct Funct Bioinform 77 (2009), 823–831, 10.1002/prot.22498.
13. 13 Weigt, M., White, R.A., Szurmant, H., Hoch, J.A., Hwa, T., Identification of direct residue contacts in protein–protein interaction by message passing. Proc Natl Acad Sci U S A 106 (2009), 67–72, 10.1073/pnas.0805923106.
14. 14 Marks, D.S., Colwell, L.J., Sheridan, R., Hopf, T.A., Pagnani, A., Zecchina, R., Sander, C., Protein 3D structure computed from evolutionary sequence variation. PLoS ONE, 6, 2011, e28766EP, 10.1371/journal.pone.0028766.
15. 15 Marks, D.S., Hopf, T.A., Sander, C., Protein structure prediction from sequence variation. Nat Biotechnol 30 (2012), 1072–1080, 10.1038/nbt.2419.
16. 16 Ovchinnikov, S., Kamisetty, H., Baker, D., Roux, B., Robust and accurate prediction of residue–residue interactions across protein interfaces using evolutionary information. eLife, 3, 2014, e02030, 10.7554/eLife.02030.
17. 17 Sukowska, J.I., Morcos, F., Weigt, M., Hwa, T., Onuchic, J.N., Genomics-aided structure prediction. Proc Natl Acad Sci U S A 109 (2012), 10340–10345, 10.1073/pnas.1207864109.
18. 18 Ovchinnikov, S., Kinch, L., Park, H., Liao, Y., Pei, J., Kim, D.E., Kamisetty, H., Grishin, N.V., Baker, D., Shan, Y., Large-scale determination of previously unsolved protein structures using evolutionary information. eLife, 4, 2015, e09248, 10.7554/eLife.09248.
19. 19• Morcos, F., Jana, B., Hwa, T., Onuchic, J.N., Coevolutionary signals across protein lineages help capture multiple protein conformations. Proc Natl Acad Sci U S A 110 (2013), 20533–20538, 10.1073/pnas.1315625110 Uses Potts model constraints in structure-based models to explore conformational landscapes of three proteins, revealing multi-welled landscapes which capture previously-proposed intermediates in addition to known functional states.
20. 20• Sutto, L., Marsili, S., Valencia, A., Gervasio, F.L., From residue coevolution to protein conformational ensembles and functional dynamics. Proc Natl Acad Sci U S A 112 (2015), 13567–13572, 10.1073/pnas.1508584112 This study uses Monte Carlo methods to infer a Potts model. Using the predicted contacts as constraints in a coarse-grained simulation, the conformational landscape between two end-states is mapped, and conformational dynamics of subsets of the protein are examined.
21. 21 dos Santos, R.N., Morcos, F., Jana, B., Andricopulo, A.D., Onuchic, J.N., Dimeric interactions and complex formation using direct coevolutionary couplings. Sci Rep, 5, 2015, 13652, 10.1038/srep13652.
22. 22 Malinverni, D., Marsili, S., Barducci, A., Rios, P.D.L., Large-scale conformational transitions and dimerization are encoded in the amino-acid sequences of Hsp70 chaperones. PLoS Comput Biol, 11, 2015, e1004262, 10.1371/journal.pcbi.1004262.
23. 23 Feinauer, C., Szurmant, H., Weigt, M., Pagnani, A., Inter-protein sequence co-evolution predicts known physical interactions in bacterial ribosomes and the Trp operon. PLOS ONE, 11, 2016, e0149166, 10.1371/journal.pone.0149166.
24. 24 Espada, R., Parra, R.G., Mora, T., Walczak, A.M., Ferreiro, D.U., Capturing coevolutionary signals inrepeat proteins. BMC Bioinform 16 (2015), 1–10.
25. 25 Jeong, C.-S., Kim, D., Structure-based Markov random field model for representing evolutionary constraints on functional sites. BMC Bioinform 17 (2016), 1–11, 10.1186/s12859-016-0948-2.
26. 26 Tang, Y., Huang, Y.J., Hopf, T.A., Sander, C., Marks, D.S., Montelione, G.T., Protein structure determination by combining sparse NMR data with evolutionary couplings. Nat Methods 12 (2015), 751–754, 10.1038/nmeth.3455.
27. 27 Hayat, S., Sander, C., Marks, D.S., Elofsson, A., All-atom 3D structure prediction of transmembrane-barrel proteins from sequences. Proc Natl Acad Sci U S A 112 (2015), 5413–5418, 10.1073/pnas.1419956112.
28. 28 Cheng, R.R., Raghunathan, M., Noel, J.K., Onuchic, J.N., Constructing sequence-dependent protein models using coevolutionary information. Protein Sci 25 (2015), 111–122, 10.1002/pro.2758.
29. 29• Haldane, A., Flynn, W.F., He, P., Vijayan, R., Levy, R.M., Structural propensities of kinase family proteins from a Potts model of residue co-variation. Protein Sci 25 (2016), 1378–1384, 10.1002/pro.2954 This study demonstrates how sequence-dependent conformational preferences can be predicted using the Potts model, for many sequences in the studied family.
30. 30•• Figliuzzi, M., Jacquier, H., Schug, A., Tenaillon, O., Weigt, M., Coevolutionary landscape inference and the context-dependence of mutations in beta-lactamase TEM-1. Mol Biol Evol 33 (2015), 268–280, 10.1093/molbev/msv211 A comparison of several thousand experimental fitness measurements of beta lactamase TEM-1 with statistical energies from a Potts model parameterized via mean-field DCA, an independent model, and other state-of-the-art structure-based and sequence-based methodologies used to predict effects of mutations. Results show that the Potts model and independent model outperform other methods, especially structure based methods, at predicting fitness of individual sequences, and that residues up to 20 away in conformation space contribute to the fitness upon mutation.
31. 31•• Morcos, F., Schafer, N.P., Cheng, R.R., Onuchic, J.N., Wolynes, P.G., Coevolutionary information, protein folding landscapes, and the thermodynamics of natural selection. Proc Natl Acad Sci U S A 111 (2014), 12408–12413, 10.1073/pnas.1413575111 A study interpreting the Potts model in light of energy landscape theory, showing how the Potts Hamiltonian may be related to the free energy of folding, and how parameters in energy landscape theory such as the glass temperature can be deduced from a Potts analysis.
32. 32 Contini, A., Tiana, G., A many-body term improves the accuracy of effective potentials based on protein coevolutionary data. J Chem Phys, 143, 2015, 025103, 10.1063/1.4926665.
33. 33 Lapedes, A., Giraud, B., Jarzynski, C., Using sequence alignments to predict protein structure and stability with high accuracy. 2002 arXiv:1207.2484.
34. 34 Hopf, T.A., Ingraham, J.B., Poelwijk, F.J., Springer, M., Sander, C., Marks, D.S., Quantification of the effect of mutations using a global probability model of natural sequence variation. 2015 arXiv:1510.04612.
35. 35 Onuchic, J.N., Luthey-Schulten, Z., Wolynes, P.G., Theory of protein folding: the energy landscape perspective. Annu Rev Phys Chem 48 (1997), 545–600, 10.1146/annurev.physchem.48.1.545.
36. 36 Bryngelson, J.D., Wolynes, P.G., Spin glasses and the statistical mechanics of protein folding. Proc Natl Acad Sci U S A 84 (1987), 7524–7528.
37. 37• Haq, O., Andrec, M., Morozov, A.V., Levy, R.M., Correlated electrostatic mutations provide a reservoir of stability in HIV protease. PLoS Comput Biol, 8, 2012, e1002675EP, 10.1371/journal.pcbi.1002675 Parameterizes a Potts model on the charged residues of HIV-1 protease using message-passing and demonstrates that the model can predict sequence probabilities in a separate database. This is one of the first studies to show that the Potts model captures higher order statistics up to those of full sequences.
38. 38 Jacquin, H., Gilson, A., Shakhnovich, E., Cocco, S., Monasson, R., Benchmarking inverse statistical approaches for protein structure and design with exactly solvable models. PLoS Comput Biol, 12, 2016, e1004889, 10.1371/journal.pcbi.1004889.
39. 39 Boucher, J.I., Bolon, D.N.A., Tawfik, D.S., Quantifying and understanding the fitness effects of protein mutations: laboratory versus nature. Protein Sci 25 (2016), 1219–1226, 10.1002/pro.2928 ISSN: 1469896X.
40. 40 Butler, T.C., Barton, J.P., Kardar, M., Chakraborty, A.K., Identification of drug resistance mutations in HIV from constraints on natural evolution. Phys Rev E, 93, 2016, 022412, 10.1103/PhysRevE.93.022412.
41. 41 Shekhar, K., Ruberman, C.F., Ferguson, A.L., Barton, J.P., Kardar, M., Chakraborty, A.K., Spin models inferred from patient data faithfully describe HIV fitness landscapes and enable rational vaccine design. Phys Rev E 88 (2013), 1539–3755, 10.1103/PhysRevE.88.062705.
42. 42•• Ferguson, A.L., Mann, J.K., Omarjee, S., Ndung'u, T., Walker, B.D., Chakraborty, A.K., Translating HIV sequences into quantitative fitness landscapes predicts viral vulnerabilities for rational immunogen design. Immunity 38 (2013), 606–617, 10.1016/j.immuni.2012.11.022 Using Ising models of the 4 principal structural proteins of HIV-1, this manuscript shows that experimental measurements of replicative fitness is proportional to the Ising statistical energy for these proteins. Further, clinically observed sequence fragments that lead to immune escape are computed to be highly fit in the model. They leverage the results to design a Gag sequence fragment which their model suggests will allow the host immune system to recognize the most vulnerable Gag epitopes.
43. 43•• Barton, J.P., Goonetilleke, N., Butler, T.C., Walker, B.D., McMichael, A.J., Chakraborty, A.K., Relative rate and location of intra-host HIV evolution to evade cellular immunity are predictable. Nat Commun, 7, 2016, 10.1038/ncomms11660 A concise study which shows escape from immune pressure in HIV is dependent on the sequence background; identical HLA epitopes targeted by the immune system in some patients are primed for escape by compensatory mutations in the background sequence. This study also demonstrates that equilibrium predictions of in vivo protein fitness using Potts model can be improved by incorporating the Potts Hamiltonian into dynamic Wright-Fisher evolutionary simulations.
44. 44 Mann, J.K., Barton, J.P., Ferguson, A.L., Omarjee, S., Walker, B.D., Chakraborty, A., Ndung'u, T., The fitness landscape of HIV-1 Gag: advanced modeling approaches and validation of model predictions by in vitro testing. PLoS Comput Biol, 10, 2014, e1003776EP, 10.1371/journal.pcbi.1003776.
45. 45• Flynn, W.F., Haldane, A., Torbett, B.E., Levy, R.M., Inference of epistatic effects leading to entrenchment and drug resistance in HIV-1 protease. bioRxiv, 2016, 10.1101/063750 A forthcoming study using Potts models to demonstrate the context-dependent effects promoting resistance mutations in drug-experienced HIV-1 protease, emphasizing that deleterious primary resistance mutations become stabilizing for the sequence as background mutations accumulate. Experimental and computational validation of the Potts model is also shown.
46. 46 Grenfell, B.T., Pybus, O.G., Gog, J.R., Wood, J.L.N., Daly, J.M., Mumford, J.A., Holmes, E.C., Unifying the epidemiological and evolutionary dynamics of pathogens. Science 303 (2004), 327–332, 10.1126/science.1090727 ISSN: 1095-9203.
47. 47 Nowak, M.A., Evolutionary dynamics: exploring the equations of life. 2006, Harvard University Press.
48. 48 Sella, G., Hirsh, A.E., The application of statistical physics to evolutionary biology. Proc Natl Acad Sci U S A 102 (2005), 9541–9546, 10.1073/pnas.0501865102.
49. 49 Fowler, D.M., Fields, S., Deep mutational scanning: a new style of protein science. Nat Methods 11 (2014), 801–807, 10.1038/nmeth.3027.
50. 50 Olson, C.A., Wu, N.C., Sun, R., A comprehensive biophysical description of pairwise epistasis throughout an entire protein domain. Curr Biol 24 (2014), 2643–2651, 10.1016/j.cub.2014.09.072.
51. 51 Wu, N.C., Olson, C.A., Sun, R., High-throughput identification of protein mutant stability computed from a double mutant fitness landscape. Protein Sci 25 (2016), 530–539, 10.1002/pro.2840.
52. 52 Bank, C., Hietpas, R.T., Jensen, J.D., Bolon, D.N.A., A systematic survey of an intragenic epistatic landscape. Mol Biol Evol 32 (2015), 229–238, 10.1093/molbev/msu301 ISSN: 1537-1719.
53. 53 Schneidman, E., Berry, M.J., Segev, R., Bialek, W., Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440 (2006), 1007–1012, 10.1038/nature04701.
54. 54 Pollock, D.D., Thiltgen, G., Goldstein, R.A., Amino acid coevolution induces an evolutionary Stokes shift. Proc Natl Acad Sci U S A 109 (2012), E1352–E1359, 10.1073/pnas.1120084109.
55. 55 Gong, L.I., Suchard, M.A., Bloom, J.D., Pascual, M., Stability-mediated epistasis constrains the evolution of an influenza protein. eLife, 2, 2013, e00631, 10.7554/eLife.00631.
56. 56 Shah, P., McCandlish, D.M., Plotkin, J.B., Contingency and entrenchment in protein evolution under purifying selection. Proc Natl Acad Sci U S A 112 (2015), E3226–E3235, 10.1073/pnas.1412933112.
57. 57 Barton, J.P., Leonardis, E.D., Coucke, A., Cocco, S., ACE: adaptive cluster expansion for maximum entropy graphical model inference. Bioinformatics, 2016, 10.1093/bioinformatics/btw328.
58. 58 Jones, D.T., Buchan, D.W.A., Cozzetto, D., Pontil, M., PSICOV: precise structural contact prediction using sparse inverse covariance estimation on large multiple sequence alignments. Bioinformatics 28 (2012), 184–190, 10.1093/bioinformatics/btr638.
59. 59 Lövkvist, C., Lan, Y., Weigt, M., Aurell, E., Ekeberg, M., Improved contact prediction in proteins: using pseudolikelihoods to infer Potts models. Phys Rev E, 87, 2013, 012707, 10.1103/PhysRevE.87.012707.
60. 60 Kamisetty, H., Ovchinnikov, S., Baker, D., Assessing the utility of coevolution-based residue-residue contact predictions in a sequence- and structure-rich era. Proc Natl Acad Sci U S A, 2013, 10.1073/pnas.1314045110.
61. 61 Morcos, F., Pagnani, A., Lunt, B., Bertolino, A., Marks, D.S., Sander, C., Zecchina, R., Onuchic, J.N., Hwa, T., Weigt, M., Direct-coupling analysis of residue coevolution captures native contacts across many protein families. Proc Natl Acad Sci U S A 108 (2011), E1293–E1301, 10.1073/pnas.1111471108.
62. 62 Ekeberg, M., Hartonen, T., Aurell, E., Fast pseudolikelihood maximization for direct-coupling analysis of protein structure from many homologous amino-acid sequences. J Comput Phys 276 (2014), 341–356.
63. 63 Avila-Herrera, A., Pollard, K.S., Coevolutionary analyses require phylogenetically deep alignments and better null models to accurately detect inter-protein contacts within and between species. BMC Bioinform 16 (2015), 1–18, 10.1186/s12859-015-0677-y.
64. 64 Gupta, A., Adami, C., Strong selection significantly increases epistatic interactions in the long-term evolution of a protein. PLoS Genet, 12, 2016, e1005960, 10.1371/journal.pgen.1005960 ISSN: 1553-7404.
65. 65 Feinauer, C., Skwark, M.J., Pagnani, A., Aurell, E., Improving contact prediction along three dimensions. PLoS Comput Biol, 10, 2014, e1003847EP, 10.1371/journal.pcbi.1003847.
66. 66 Haq, O., Levy, R.M., Morozov, A.V., Andrec, M., Pairwise and higher-order correlations among drug-resistance mutations in HIV-1 subtype B protease. BMC Bioinform 14 (2009), 1–14, 10.1186/1471-2105-10-S8-S10.
67. 67 Obermayer, B., Levine, E., Inverse Ising inference with correlated samples. New J Phys, 16, 2014, 123017, 10.1088/1367-2630/16/12/123017.
68. 68 Ma, J., Wang, S., Wang, Z., Xu, J., Protein contact prediction by integrating joint evolutionary coupling analysis and supervised learning. Bioinformatics 31 (2015), 3506–3513.
69. 69 Jones, D.T., Singh, T., Kosciolek, T., Tetchner, S., MetaPSICOV: combining coevolution methods for accurate prediction of contacts and long range hydrogen bonding in proteins. Bioinformatics 31 (2015), 999–1006, 10.1093/bioinformatics/btu791.