Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory
Tóm tắt
Several approaches, including metabolic control analysis (MCA), flux balance analysis (FBA), correlation metric construction (CMC), and biochemical circuit theory (BCT), have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS) biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SR
T
where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of R
T
BS and S
T
BS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix e
A
t
plays a central role in CMC. One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA).
Tài liệu tham khảo
Fell DA, Sauro HM: Metabolic control and its analysis. Eur J Biochem. 1985, 148: 555-561. 10.1111/j.1432-1033.1985.tb08876.x
Kholodenko BN, Westerhoff HV: The macroworld versus the microworld of biochemical regulation and control. TIBS. 1995, 20: 52-54.
Edwards JS, Palsson BØ: The E. Coli MG1655 in silico metabolic geotype: its definition, characteristics, and capabilities. Proc Natl Acad Sci USA. 2000, 97: 5528-5533. 10.1073/pnas.97.10.5528
Schilling CH, Palsson BØ: The underlying pathway structure of biochemical reaction networks. Proc Natl Acad Sci USA. 1998, 95: 4193-4198. 10.1073/pnas.95.8.4193
Arkin A, Ross J: Statistical construction of chemical reaction mechanisms from measured time-series. J Phys Chem. 1995, 99: 970-979. 10.1021/j100003a020.
Samoilov M, Arkin A, Ross J: On the deduction of chemical reaction pathways from measurements of time series of concentrations. Chaos. 2001, 11: 108-114. 10.1063/1.1336499
Qian H: Phosphorylation energy hypothesis: open chemical systems and their biological functions. Ann Rev Phys Chem. 2007, 58: 113-142. 10.1146/annurev.physchem.58.032806.104550.
Qian H: Open-system nonequilibrium steady-state: statistical thermodynamics, fluctuations and chemical oscillations. J Phys Chem B. 2006, 110: 15063-15074. 10.1021/jp061858z
Wyman J: The turning wheel: a study in steady state. Proc Natl Acad Sci USA. 1975, 72: 3983-3987. 10.1073/pnas.72.10.3983
Hill TL: Free Energy Transduction in Biology: The Steady-State Kinetic and Thermodynamic Formalism. 1977, New York: Academic Press
Hill TL: Free Energy Transduction and Biochemical Cycle Kinetics. 1989, New York: Springer-Verlag
Qian H: The Mathematical theory of molecular motor movement and chemomechanical energy transduction. J Math Chem. 2000, 27: 219-234. 10.1023/A:1026428320489.
Qian H: Cycle kinetics, steady-state thermodynamics and motors – a paradigm for living matter physics. J Phys: Condens Matter. 2005, 17: S3783-S3794. 10.1088/0953-8984/17/47/010.
Murray JD: Mathematical Biology. 1991, New York: Springer, 2
Beard DA, Liang SD, Qian H: Energy balance for analysis of complex metabolic networks. Biophys J. 2002, 83: 79-86.
Qian H, Beard DA, Liang SD: Stoichiometric network theory for nonequilibrium biochemical systems. Eur J Biochem. 2003, 270: 415-421. 10.1046/j.1432-1033.2003.03357.x
Beard DA, Qian H: Chapter 6: Biochemical Reaction Networks. Chemical Biophysics: Quantitative Analysis of Cellular Systems. 2008, Cambridge, UK: Cambridge University Press
Segel IH: Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-state Enzyme Systems. 1975, New York: John Wiley & Sons
Alberty RA: Degrees of freedom in biochemical reaction systems at specific pH and pMg. J Phys Chem. 1992, 96: 9614-9621. 10.1021/j100203a012.
Poland D: On the stability of mass action reactions in open systems. J Chem Phys. 1991, 94: 4427-4439. 10.1063/1.460633.
Savageau MA: Biochemical system analysis I. J Theor Biol. 1969, 25: 365-369. 10.1016/S0022-5193(69)80026-3
Savageau MA: Biochemical system analysis II. J Theor Biol. 1969, 25: 370-379. 10.1016/S0022-5193(69)80027-5
Heinrich R, Schuster S: The Regulation of Cellular Systems. 1996, New York: Chapman & Hall
Westerhoff HV, Chen YD: How do enzyme activities control metabolite concentrations?. Eur J Biochem. 1984, 142: 425-430. 10.1111/j.1432-1033.1984.tb08304.x
Westerhoff HV, van Dam K: Thermodynamics and control of biological free-energy transduction. 1987, Amsterdam: Elsevier
Giersch C: Control analysis and metabolic networks. Eur J Biochem. 1988, 174: 509-519. 10.1111/j.1432-1033.1988.tb14128.x
Reder C: Metabolic control theory: a structural approach. J Theor Biol. 1988, 135: 175-201. 10.1016/S0022-5193(88)80073-0
Beard DA, Qian H: Relationship between thermodynamic driving force and one-way fluxes in reversible processes. PLoS One. 2007, 2: e144- 10.1371/journal.pone.0000144
Heuett WJ, Qian H: Grand canonical Markov model: a stochastic theory for open nonequilibrium biochemical networks. J Chem Phys. 2006, 124: 044110- 10.1063/1.2165193
Fell DA: Increasing the flux in metabolic pathways: a metabolic control analysis perspective. Biotechnol Bioeng. 1998, 58: 121-124. 10.1002/(SICI)1097-0290(19980420)58:2/3<121::AID-BIT2>3.0.CO;2-N
Derrida B: Velocity and diffusion constant of a periodic one-dimensional hopping model. J Stat Phys. 1983, 31: 433-450. 10.1007/BF01019492.
Fisher ME, Kolomeisky AB: The force exerted by a molecular motor. Proc Natl Acad Sci USA. 1999, 96: 6597-6602. 10.1073/pnas.96.12.6597
Oster G, Wang HY: Reverse engineering a protein: the mechanochemistry of ATP synthase. Biochim Biophys Acta. 2000, 1458: 482-510. 10.1016/S0005-2728(00)00096-7
Beard DA, Qian H, Bassingthwaighte JB: Stoichiometric foundation of large-scale biochemical system analysis. Modelling in Molecular Biology. Edited by: Ciobanu G, Rozenberg G. 2004, 1-19. [Natural Computing Series]., New York: Springer
Bender CM, Orszag SA: Advanced Mathematical Methods for Scientists and Engineers. 1999, New York: Springer-Verlag