1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Physical Chemistry
  4. Volume 71, 2020
  5. Article

Annual Review of Physical Chemistry

Volume 71, 2020

The Maximum Caliber Variational Principle for Nonequilibria

Abstract

Abstract

Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.

Keyword(s): biological dynamics, caliber, entropy, inference, network models, nonequilibrium, variational principles
Loading

Article metrics loading...

/content/journals/10.1146/annurev-physchem-071119-040206
2020-04-20
2024-04-16
Loading full text...

Full text loading...

/deliver/fulltext/physchem/71/1/annurev-physchem-071119-040206.html?itemId=/content/journals/10.1146/annurev-physchem-071119-040206&mimeType=html&fmt=ahah

Literature Cited

  1. 1. 
    Broder A 2000. Graph structure in the web. Comput. Netw. 33:309–20
     [Google Scholar]
  2. 2. 
    Zipf GK 1949. Human Behavior and the Principle of Least Effort Cambridge, MA: Addison-Wesley
  3. 3. 
    Marsili M, Maslov S, Zhang YC 1998. Dynamical optimization theory of a diversified portfolio. Phys. A Stat. Mech. Appl. 253:403–18
     [Google Scholar]
  4. 4. 
    Cavagna A, Queirós SD, Giardina I, Stefanini F, Viale M 2013. Diffusion of individual birds in starling flocks. Proc. R. Soc. B Biol. Sci. 280:20122484
     [Google Scholar]
  5. 5. 
    Peterson J, Dixit P, Dill KA 2013. A maximum entropy framework for nonexponential distributions. PNAS 110:20380–85
     [Google Scholar]
  6. 6. 
    Zeldovich K, Chen P, Shakhnovich E 2007. Protein stability imposes limits on organism complexity and speed of molecular evolution. PNAS 104:16152–57
     [Google Scholar]
  7. 7. 
    Zou T, Williams N, Ozkan S, Ghosh K 2014. Proteome folding kinetics is limited by protein halflife. PLOS ONE 9:e112701
     [Google Scholar]
  8. 8. 
    Dixit PD, Maslov S 2013. Evolutionary capacitance and control of protein stability in protein-protein interaction networks. PLOS Comput. Biol. 9:e1003023
     [Google Scholar]
  9. 9. 
    Dixit PD, Pang TY, Maslov S 2017. Recombination-driven genome evolution and stability of bacterial species. Genetics 207:281–95
     [Google Scholar]
  10. 10. 
    Mora T, Deny S, Marre O 2015. Dynamical criticality in the collective activity of a population of retinal neurons. Phys. Rev. Lett. 114:078105
     [Google Scholar]
  11. 11. 
    Onsager L 1931. Reciprocal relations in irreversible processes. Phys. Rev. 37:405
     [Google Scholar]
  12. 12. 
    Prigogine I, Kondepudi D 1998. Modern Thermodynamics: From Heat Engines to Dissipative Structures New York: John Wiley
  13. 13. 
    Martyushev LM, Seleznev VD 2006. Maximum entropy production principle in physics, chemistry and biology. Phys. Rep. 426:1–45
     [Google Scholar]
  14. 14. 
    Jaynes ET 1980. The minimum entropy production principle. Annu. Rev. Phys. Chem. 31:579–601
     [Google Scholar]
  15. 15. 
    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
     [Google Scholar]
  16. 16. 
    Wu D, Ghosh K, Inamdar M, Lee H, Fraser S et al. 2009. Trajectory approach to two-state kinetics of single particles on sculpted energy landscapes. Phys. Rev. Lett. 103:050603
     [Google Scholar]
  17. 17. 
    Pressé S, Ghosh K, Phillips R, Dill KA 2010. Dynamical fluctuations in biochemical reactions and cycles. Phys. Rev. E 82:031905
     [Google Scholar]
  18. 18. 
    Ghosh K, Dill K, Inamdar M, Seitaridou E, Phillips R 2006. Teaching the principles of statistical dynamics. Am. J. Phys. 74:123–33
     [Google Scholar]
  19. 19. 
    Seitaridou E, Inamdar M, Phillips R, Ghosh K, Dill K 2007. Measuring flux distributions for diffusion in the small-numbers limit. J. Phys. Chem. B 111:2288–92
     [Google Scholar]
  20. 20. 
    Firman T, Balazsi G, Ghosh K 2017. Building predictive models of genetic circuits using the principle of maximum caliber. Biophys. J. 113:2121–30
     [Google Scholar]
  21. 21. 
    Nevozhay D, Adams R, Itallie EV, Bennett M, Balázsi G 2012. Mapping the environmental fitness landscape of a synthetic gene circuit. PLOS Comput. Biol. 8:e1002480
     [Google Scholar]
  22. 22. 
    Firman T, Wedekind S, McMorrow TJ, Ghosh K 2018. Maximum caliber can characterize genetic switches with multiple hidden species. J. Phys. Chem. B 122:5666–77
     [Google Scholar]
  23. 23. 
    Gardner T, Cantor C, Collins J 2000. Construction of a genetic toggle switch in Escherichia coli. Nature 403:339–42
     [Google Scholar]
  24. 24. 
    Pressé S, Ghosh K, Dill K 2011. Modeling stochastic dynamics in biochemical systems with feedback using maximum caliber. J. Phys. Chem. B 115:6202–12
     [Google Scholar]
  25. 25. 
    Elowitz M, Leibler S 2000. A synthetic oscillatory network of transcriptional regulators. Nature 403:335–38
     [Google Scholar]
  26. 26. 
    Firman T, Amgalan A, Ghosh K 2019. Maximum caliber can build and infer models of oscillation in a three-gene feedback network. J. Phys. Chem. B 123:343–55
     [Google Scholar]
  27. 27. 
    Van Kampen NG 1992. Stochastic Processes in Physics and Chemistry 1: Amsterdam: Elsevier
  28. 28. 
    Gillespie D 1992. A rigorous derivation of the chemical master equation. Phys. A Stat. Mech. Appl. 188:404–25
     [Google Scholar]
  29. 29. 
    Munsky B, Khammash M 2006. The finite state projection algorithm for the solution of the chemical master equation. J. Chem. Phys. 124:044104
     [Google Scholar]
  30. 30. 
    Frigola D, Casanellas L, Sancho J, Ibanes M 2012. Asymmetric stochastic switching driven by intrinsic molecular noise. PLOS ONE 7:e31407
     [Google Scholar]
  31. 31. 
    Llamosi A, Gonzalez-Vargas AM, Versari C, Cinquemani E, Ferrari-Trecate G et al. 2016. What population reveals about individual cell identity: single-cell parameter estimation of models of gene expression in yeast. PLOS Comput. Biol. 12:e1004706
     [Google Scholar]
  32. 32. 
    Raj A, van Oudenaarden A 2008. Nature, nurture, or chance: stochastic gene expression and its consequences. Cell 135:216–26
     [Google Scholar]
  33. 33. 
    Wu M, Singh AK 2012. Single-cell protein analysis. Curr. Opin. Biotechnol. 23:83–88
     [Google Scholar]
  34. 34. 
    Saliba AE, Westermann AJ, Gorski SA, Vogel J 2014. Single-cell RNA-seq: advances and future challenges. Nucleic Acids Res. 42:8845–60
     [Google Scholar]
  35. 35. 
    Dixit PD, Lyashenko E, Niepel M, Vitkup D 2019. Maximum entropy framework for predictive inference of cell population heterogeneity and responses in signaling networks. Cell Syst https://doi.org/10.1016/j.cels.2019.11.010
     [Crossref] [Google Scholar]
  36. 36. 
    Dixit PD 2013. Quantifying extrinsic noise in gene expression using the maximum entropy framework. Biophys. J. 104:2743–50
     [Google Scholar]
  37. 37. 
    Dixit PD, Dill KA 2014. Inferring microscopic kinetic rates from stationary state distributions. J. Chem. Theory Comput. 10:3002–5
     [Google Scholar]
  38. 38. 
    Wan H, Zhou G, Voelz VA 2016. A maximum-caliber approach to predicting perturbed folding kinetics due to mutations. J. Chem. Theory Comput. 12:5768–76
     [Google Scholar]
  39. 39. 
    Zhou G, Pantelopulos GA, Mukherjee S, Voelz VA 2017. Bridging microscopic and macroscopic mechanisms of p53-MDM2 binding with kinetic network models. Biophys. J. 113:785–93
     [Google Scholar]
  40. 40. 
    Dixit PD, Jain A, Stock G, Dill KA 2015. Inferring transition rates of networks from populations in continuous-time Markov processes. J. Chem. Theory Comput. 11:5464–72
     [Google Scholar]
  41. 41. 
    Tiwary P, Berne B 2016. How wet should be the reaction coordinate for ligand unbinding?. J. Chem. Phys. 145:054113
     [Google Scholar]
  42. 42. 
    Tiwary P, Berne B 2016. Spectral gap optimization of order parameters for sampling complex molecular systems. PNAS 113:2839–44
     [Google Scholar]
  43. 43. 
    Tiwary P 2017. Molecular determinants and bottlenecks in the dissociation dynamics of biotin–streptavidin. J. Phys. Chem. B 121:10841–49
     [Google Scholar]
  44. 44. 
    Hovan L, Comitani F, Gervasio FL 2018. Defining an optimal metric for the path collective variables. J. Chem. Theory Comput. 15:25–32
     [Google Scholar]
  45. 45. 
    Smith Z, Pramanik D, Tsai ST, Tiwary P 2018. Multi-dimensional spectral gap optimization of order parameters (SGOOP) through conditional probability factorization. J. Chem. Phys. 149:234105
     [Google Scholar]
  46. 46. 
    Dixit PD, Dill KA 2019. Building Markov state models using optimal transport theory. J. Chem. Phys. 150:054105
     [Google Scholar]
  47. 47. 
    Dixit PD 2018. Communication: Introducing prescribed biases in out-of-equilibrium Markov models. J. Chem. Phys. 148:091101
     [Google Scholar]
  48. 48. 
    Dixit PD 2018. Entropy production rate as a criterion for inconsistency in decision theory. J. Stat. Mech. Theory Exp. 2018:053408
     [Google Scholar]
  49. 49. 
    Dixit PD 2019. Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reduction. Neural Comput. 31:980–97
     [Google Scholar]
  50. 50. 
    Meral D, Provasi D, Filizola M 2018. An efficient strategy to estimate thermodynamics and kinetics of G protein-coupled receptor activation using metadynamics and maximum caliber. J. Chem. Phys. 149:224101
     [Google Scholar]
  51. 51. 
    Tiwary P, Parrinello M 2014. A time-independent free energy estimator for metadynamics. J. Phys. Chem. B 119:736–42
     [Google Scholar]
  52. 52. 
    Sawle L, Ghosh K 2016. Convergence of molecular dynamics simulation of protein native states: feasibility versus self-consistency dilemma. J. Chem. Theory Comput. 12:861–69
     [Google Scholar]
  53. 53. 
    Dixit PD, Dill KA 2018. Caliber corrected Markov modeling (C2M2): correcting equilibrium Markov models. J. Chem. Theory Comput. 14:1111–19
     [Google Scholar]
  54. 54. 
    Herbst RS 2004. Review of epidermal growth factor receptor biology. Int. J. Radiat. Oncol. Biol. Phys. 59:S21–26
     [Google Scholar]
  55. 55. 
    Huang HJS, Nagane M, Klingbeil CK, Lin H, Nishikawa R et al. 1997. The enhanced tumorigenic activity of a mutant epidermal growth factor receptor common in human cancers is mediated by threshold levels of constitutive tyrosine phosphorylation and unattenuated signaling. J. Biol. Chem. 272:2927–35
     [Google Scholar]
  56. 56. 
    Cavagna A, Giardina I, Ginelli F, Mora T, Piovanni D et al. 2014. Dynamical maximum entropy approach to flocking. Phys. Rev. E 89:042707
     [Google Scholar]
  57. 57. 
    Tweedy L, Witzel P, Heinrich D, Insall RH, Endres RG 2019. Screening by changes in stereotypical behavior during cell motility. Sci. Rep. 9:8784
     [Google Scholar]
  58. 58. 
    Vasquez JC, Marre O, Palacios AG, Berry MJ II, Cessac B 2012. Gibbs distribution analysis of temporal correlations structure in retina ganglion cells. J. Physiol. Paris 106:120–27
     [Google Scholar]
  59. 59. 
    Tkačik G, Mora T, Marre O, Amodei D, Palmer SE et al. 2015. Thermodynamics and signatures of criticality in a network of neurons. PNAS 112:11508–13
     [Google Scholar]
  60. 60. 
    Stock G, Ghosh K, Dill K 2008. Maximum caliber: a variational approach applied to two-state dynamics. J. Chem. Phys. 128:194102
     [Google Scholar]
  61. 61. 
    Ge H, Pressé S, Ghosh K, Dill K 2012. Markov processes follow from the principle of maximum caliber. J. Chem. Phys. 134:064108
     [Google Scholar]
  62. 62. 
    Lee J, Pressé S 2012. A derivation of the master equation from path entropy maximization. J. Chem. Phys. 137:074103
     [Google Scholar]
  63. 63. 
    Pressé S, Ghosh K, Lee J, Dill K 2013. Principle of maximum entropy and maximum caliber in statistical physics. Rev. Mod. Phys. 85:1115–41
     [Google Scholar]
  64. 64. 
    Hazoglou MJ, Walther V, Dixit PD, Dill KA 2015. Communication: Maximum caliber is a general variational principle for nonequilibrium statistical mechanics. J. Chem. Phys. 143:051104
     [Google Scholar]
  65. 65. 
    Seifert U 2012. Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys. 75:126001
     [Google Scholar]
  66. 66. 
    Touchette H 2009. The large deviation approach to statistical mechanics. Phys. Rep. 478:1–69
     [Google Scholar]
  67. 67. 
    Jack RL, Evans R 2016. Absence of dissipation in trajectory ensembles biased by currents. J. Stat. Mech. Theory Exp. 2016:093305
     [Google Scholar]
  68. 68. 
    Maes C 2018. Non-Dissipative Effects in Nonequilibrium Systems Cham, Switz.: Springer
  69. 69. 
    Agozzino L, Dill KA 2019. Minimal constraints for maximum caliber analysis of dissipative steady-state systems. Phys. Rev. E 100:010105
     [Google Scholar]
  70. 70. 
    Tkacik G, Schneidman E, Berry I, Michael J, Bialek W 2006. Ising models for networks of real neurons. arXiv:q-bio/0611072 [q-bio.NC]
    [Google Scholar]
  71. 71. 
    Broderick T, Dudik M, Tkacik G, Schapire RE, Bialek W 2007. Faster solutions of the inverse pairwise Ising problem. arXiv:0712.2437 [q-bio.QM]
    [Google Scholar]
  72. 72. 
    Sgouralis I, Pressé S 2017. An introduction to infinite HMMs for single-molecule data analysis. Biophys. J. 112:2021–29
     [Google Scholar]
  73. 73. 
    Sgouralis I, Pressé S 2017. ICON: an adaptation of infinite HMMs for time traces with drift. Biophys. J. 112:2117–26
     [Google Scholar]
  74. 74. 
    Jaynes ET 1957. Information theory and statistical mechanics. Phys. Rev. 106:620
     [Google Scholar]
  75. 75. 
    Dixit PD, Wagoner J, Weistuch C, Pressé S, Ghosh K, Dill KA 2018. Perspective: Maximum caliber is a general variational principle for dynamical systems. J. Chem. Phys. 148:010901
     [Google Scholar]
  76. 76. 
    Attard P 2008. The second entropy: a variational principle for time-dependent systems. Entropy 10:380–90
     [Google Scholar]
/content/journals/10.1146/annurev-physchem-071119-040206
Loading
The Maximum Caliber Variational Principle for Nonequilibria
Annual Review of Physical Chemistry 71, 213 (2020); https://doi.org/10.1146/annurev-physchem-071119-040206
/content/journals/10.1146/annurev-physchem-071119-040206
/content/journals/10.1146/annurev-physchem-071119-040206
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error