Abstract
A direct nonlinear least squares method is described that obtains the true kinetic rate constants and the temperature-independent spectra of n intermediates from spectroscopic data taken in the visible at three or more temperatures. A theoretical analysis, which is independent of implementation of the direct method, proves that well determined local solutions are not possible for fewer than three temperatures. This analysis also proves that measurements at more than n wavelengths are redundant, although the direct method indicates that convergence is faster if n + m wavelengths are measured, where m is of order one. This suggests that measurements should concentrate on high precision for a few measuring wavelengths, rather than lower precision for many wavelengths. Globally, false solutions occur, and the ability to reject these depends upon the precision of the data, as shown by explicit example. An optimized way to analyze vibrational spectroscopic data is also presented. Such data yield unique results, which are comparably accurate to those obtained from data taken in the visible with comparable noise. It is discussed how use of both kinds of data is advantageous if the data taken in the visible are significantly less noisy.
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- Ames J. B., Mathies R. A. The role of back-reactions and proton uptake during the N----O transition in bacteriorhodopsin's photocycle: a kinetic resonance Raman study. Biochemistry. 1990 Aug 7;29(31):7181–7190. doi: 10.1021/bi00483a005. [DOI] [PubMed] [Google Scholar]
- Groma G. I., Dancshazy Z. How Many M Forms are there in the Bacteriorhodopsin Photocycle? Biophys J. 1986 Aug;50(2):357–366. doi: 10.1016/S0006-3495(86)83469-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hofrichter J., Henry E. R., Lozier R. H. Photocycles of bacteriorhodopsin in light- and dark-adapted purple membrane studied by time-resolved absorption spectroscopy. Biophys J. 1989 Oct;56(4):693–706. doi: 10.1016/S0006-3495(89)82716-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Kouyama T., Nasuda-Kouyama A., Ikegami A., Mathew M. K., Stoeckenius W. Bacteriorhodopsin photoreaction: identification of a long-lived intermediate N (P,R350) at high pH and its M-like photoproduct. Biochemistry. 1988 Aug 9;27(16):5855–5863. doi: 10.1021/bi00416a006. [DOI] [PubMed] [Google Scholar]
- Lozier R. H., Bogomolni R. A., Stoeckenius W. Bacteriorhodopsin: a light-driven proton pump in Halobacterium Halobium. Biophys J. 1975 Sep;15(9):955–962. doi: 10.1016/S0006-3495(75)85875-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Nagle J. F., Parodi L. A., Lozier R. H. Procedure for testing kinetic models of the photocycle of bacteriorhodopsin. Biophys J. 1982 May;38(2):161–174. doi: 10.1016/S0006-3495(82)84543-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Parodi L. A., Lozier R. H., Bhattacharjee S. M., Nagle J. F. Testing kinetic models for the bacteriorhodopsin photocycle--II. Inclusion of an O to M backreaction. Photochem Photobiol. 1984 Oct;40(4):501–506. doi: 10.1111/j.1751-1097.1984.tb04624.x. [DOI] [PubMed] [Google Scholar]
- Rayfield G. W. Events in proton pumping by bacteriorhodopsin. Biophys J. 1983 Feb;41(2):109–117. doi: 10.1016/S0006-3495(83)84413-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Roepe P., Ahl P. L., Das Gupta S. K., Herzfeld J., Rothschild K. J. Tyrosine and carboxyl protonation changes in the bacteriorhodopsin photocycle. 1. M412 and L550 intermediates. Biochemistry. 1987 Oct 20;26(21):6696–6707. doi: 10.1021/bi00395a020. [DOI] [PubMed] [Google Scholar]
- Váró G., Duschl A., Lanyi J. K. Interconversions of the M, N, and O intermediates in the bacteriorhodopsin photocycle. Biochemistry. 1990 Apr 17;29(15):3798–3804. doi: 10.1021/bi00467a029. [DOI] [PubMed] [Google Scholar]
- Xie A. H., Nagle J. F., Lozier R. H. Flash spectroscopy of purple membrane. Biophys J. 1987 Apr;51(4):627–635. doi: 10.1016/S0006-3495(87)83387-8. [DOI] [PMC free article] [PubMed] [Google Scholar]