Abstract
The effect of fluctuations in rate constants on the kinetic behavior of cyclic reacting systems, caused by a fluctuating external parameter, is studied. It is shown (i) that the stochastic properties of the system can be analyzed analytically by using the usual master equation approach when the external parameter is fluctuating with discrete square pulses and (ii) that the system is equivalent to an expanded chemical kinetic system with no fluctuation in rate constants. When applied to a linear four-state cyclic enzyme system, the formalism can be used to prove analytically the finding that an enzyme can extract the free energy from an externally applied fluctuating membrane potential and perform active free energy transduction. The formalism also can be used to assess the asymmetry constraints imposed on the values of the rate constants in order for the model to work.
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Selected References
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- Astumian R. D., Chock P. B., Tsong T. Y., Chen Y. D., Westerhoff H. V. Can free energy be transduced from electric noise? Proc Natl Acad Sci U S A. 1987 Jan;84(2):434–438. doi: 10.1073/pnas.84.2.434. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hahn H. S., Nitzan A., Ortoleva P., Ross J. Threshold excitations, relaxation oscillations, and effect of noise in an enzyme reaction. Proc Natl Acad Sci U S A. 1974 Oct;71(10):4067–4071. doi: 10.1073/pnas.71.10.4067. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Horsthemke W., Lefever R. Voltage-noise-induced transitions in electrically excitable membranes. Biophys J. 1981 Aug;35(2):415–432. doi: 10.1016/S0006-3495(81)84799-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Lefever R., Horsthemke W. Bistability in fluctuating environments. Implications in tumor immunology. Bull Math Biol. 1979;41(4):469–490. doi: 10.1007/BF02458325. [DOI] [PubMed] [Google Scholar]
- Lefever R., Horsthemke W. Multiple transitions induced by light intensity fluctuations in illuminated chemical systems. Proc Natl Acad Sci U S A. 1979 Jun;76(6):2490–2494. doi: 10.1073/pnas.76.6.2490. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Westerhoff H. V., Tsong T. Y., Chock P. B., Chen Y. D., Astumian R. D. How enzymes can capture and transmit free energy from an oscillating electric field. Proc Natl Acad Sci U S A. 1986 Jul;83(13):4734–4738. doi: 10.1073/pnas.83.13.4734. [DOI] [PMC free article] [PubMed] [Google Scholar]