2000 character limit reached
Probabilistic and Maximum Entropy Modeling of Chemical Reaction Systems: Characteristics and Comparisons to Mass Action Kinetic Models
Published 9 Oct 2023 in physics.chem-ph and q-bio.MN | (2310.06135v2)
Abstract: We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between the entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Subsequent implementation of an maximum free energy dissipation model for systems of coupled reactions is accomplished by using an approximation to the Marcelin equation for mass action kinetics that maximizes the entropy production. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy production model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy production model is characterized by a high probability of free energy dissipation rate, and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy production predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.
- R. C. Dewar, “Maximum entropy production and plant optimization theories,” Philosophical Transactions of the Royal Society B-Biological Sciences 365, 1429–1435 (2010).
- A. J. Lotka, “Contribution to the energetics of evolution,” Proceedings of the National Academy of Sciences of the United States of America 8, 147–51 (1922).
- H. T. Odum and R. T. Pinkerton, “Time’s speed regulator: The optimum efficiency for maximum power output in physical and biological systems,” American Scientist 43 (1955).
- J. Dyke and A. Kleidon, “The maximum entropy production principle: Its theoretical foundations and applications to the earth system,” Entropy 12, 613–630 (2010).
- A. Kleidon, Y. Malhi, and P. M. Cox, “Maximum entropy production in environmental and ecological systems,” Philos Trans R Soc Lond B Biol Sci 365, 1297–302 (2010).
- F. J. R. Meysman and S. Bruers, “Ecosystem functioning and maximum entropy production: a quantitative test of hypotheses,” Phil. Trans. R. Soc. B 365, 1405–1416 (2009).
- P. Unrean and F. Srienc, “Metabolic networks evolve towards states of maximum entropy production,” Metab Eng 13, 666–73 (2011).
- J. J. Vallino, “Ecosystem biogeochemistry considered as a distributed metabolic network ordered by maximum entropy production.” Phil. Trans. R. Soc. B 365, 1417–1427 (2009).
- H. Ge and H. Qian, “Physical origins of entropy production, free energy dissipation, and their mathematical representations,” Physical Review E 81, 051133 (2010).
- E. T. Jaynes, “Macroscopic prediction,” in Complex Systems Operational Approaches in Neurobiology, Physics and Computers, Vol. 31, edited by H. Haken (Springer-Verlag, Berlin Heidelberg, 1985) pp. 254–269.
- R. C. Dewar, “Maximum entropy production as an inference algorithm that translates physical assumptions into macroscopic predictions: Don’t shoot the messenger,” Entropy 11, 931–944 (2009).
- L. Agozzino and K. Dill, “Minimal constraints for maximum caliber analysis of dissipative steady-state systems,” Phys. Rev. E 100, 010105 (2019).
- K. Sharp and F. Matschinsky, “Translation of ludwig boltzmann’s paper "on the relationship between the second fundamental theorem of the mechanical theory of heat and probability calculations regarding the conditions for thermal equilibrium" sitzungberichte der kaiserlichen akademie der wissenschaften. mathematisch-naturwissen classe. abt. ii, lxxvi 1877, pp 373-435 (wien. ber. 1877, 76:373-435). reprinted in wiss. abhandlungen, vol. ii, reprint 42, p. 164-223, barth, leipzig, 1909,” Entropy 17, 1971–2009 (2015).
- J. W. Gibbs, Elementary principles in statistical mechanics (Charles Scribner’s Sons, New York, 1902).
- N. Davidson, Statistical mechanics, McGraw-Hill series in advanced chemistry (McGraw, New York,, 1962) p. 540 p.
- A. Radzicka and R. Wolfenden, “A proficient enzyme,” Science 267, 90–3 (1995).
- I. Schomburg, A. Chang, S. Placzek, C. Sohngen, M. Rother, M. Lang, C. Munaretto, S. Ulas, M. Stelzer, A. Grote, M. Scheer, and D. Schomburg, “Brenda in 2013: integrated reactions, kinetic data, enzyme function data, improved disease classification: new options and contents in brenda,” Nucleic Acids Res 41, D764–72 (2013).
- S. Britton, M. Alber, and W. R. Cannon, “Enzyme activities predicted by metabolite concentrations and solvent capacity in the cell,” bioRxiv (2020), 10.1101/2020.04.06.028035.
- W. R. Cannon, J. D. Zucker, D. J. Baxter, N. Kumar, J. M. Hurley, and J. C. Dunlap, “Prediction of metabolite concentrations, rate constants and post-translational regulation using maximum entropy-based simulations with application to central metabolism of neurospora crassa,” Processes 6 (2018), https://doi.org/10.3390/pr6060063.
- D. E. Atkinson, “Limitation of metabolite concentrations and the conservation of solvent capacity in the living cell,” in Current Topics in Cellular Regulation, Vol. 1, edited by B. L. Horecker and E. R. Stadtman (Academic Press, 1969) pp. 29–43.
- W. F. K. Wynne-Jones and H. Eyring, “The absolute rate of reactions in condensed phases,” Journal of Chemical Physics 3, 492–502 (1935).
- K. J. Laidler and M. C. King, “The development of transition-state theory,” Journal of Physical Chemistry 87, 2657–2664 (1983).
- R. Marcelin, “The mechanics of irreversible phenomenon.” Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences 151, 1052–1055 (1910).
- R. Dewar, “Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states,” Journal of Physics a-Mathematical and General 36, 631–641 (2003).
- W. R. Cannon, “Simulating metabolism with statistical thermodynamics,” PLoS One 9, e103582 (2014).
- A. Flamholz, E. Noor, A. Bar-Even, and R. Milo, “equilibrator–the biochemical thermodynamics calculator,” Nucleic Acids Res 40, D770–5 (2012).
- E. Noor, A. Bar-Even, A. Flamholz, E. Reznik, W. Liebermeister, and R. Milo, “Pathway thermodynamics highlights kinetic obstacles in central metabolism,” Plos Computational Biology 10 (2014).
- H. Qian, D. A. Beard, and S. D. Liang, “Stoichiometric network theory for nonequilibrium biochemical systems,” Eur J Biochem 270, 415–21 (2003).
- A. Fersht, Structure and mechanism in protein science : a guide to enzyme catalysis and protein folding (W.H. Freeman, New York, 1999) pp. xxi, 631 pages.
- M. D. Mckay, R. J. Beckman, and W. J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics 21, 239–245 (1979).
- S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology,” Journal of Theoretical Biology 254, 178–196 (2008).
- J. O. Park, S. A. Rubin, Y. F. Xu, D. Amador-Noguez, J. Fan, T. Shlomi, and J. D. Rabinowitz, “Metabolite concentrations, fluxes and free energies imply efficient enzyme usage,” Nat Chem Biol 12, 482–9 (2016).
- B. D. Bennett, E. H. Kimball, M. Gao, R. Osterhout, S. J. Van Dien, and J. D. Rabinowitz, “Absolute metabolite concentrations and implied enzyme active site occupancy in escherichia coli,” Nature chemical biology 5, 593–9 (2009).
- D. A. Sivak and M. Thomson, “Environmental statistics and optimal regulation,” PLoS Comput Biol 10, e1003826 (2014).
- T. Firman, G. Balazsi, and K. Ghosh, “Building predictive models of genetic circuits using the principle of maximum caliber,” Biophysical Journal 113, 2121–2130 (2017).
- E. J. Bylaska, “Estimating the thermodynamics and kinetics of chlorinated hydrocarbon degradation,” Theoretical Chemistry Accounts 116, 281–296 (2006).
- A. Jinich, D. Rappoport, I. Dunn, B. Sanchez-Lengeling, R. Olivares-Amaya, E. Noor, A. Bar Even, and A. Aspuru-Guzik, “Quantum chemical approach to estimating the thermodynamics of metabolic reactions,” Scientific Reports 4 (2014).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.