DOI: 10.1073/pnas.192439099. Memory effects and oscillations in single-molecule kinetics

Memory effects and oscillations in single-molecule kinetics

10.1073/pnas.192439099

Crossref journal-article

Proceedings of the National Academy of Sciences

Proceedings of the National Academy of Sciences (341)

Abstract

An exactly solvable model for single-molecule kinetics is suggested, based on the following assumptions: ( i ) A single molecule can exist in different chemical states and the random transitions from one chemical state to another can be described by a local master equation with time-dependent transition rates. ( ii ) Because of conformational and other intramolecular fluctuations the rate coefficients in the master equation are random functions of time; their stochastic properties are represented in terms of a set of control parameters. We assume that the fluctuating rate coefficients fulfill a separability condition, that is, they are made up of the multiplicative contributions of two factors: ( a ) a universal factor, which depends on the vector of control parameters and is the same for all chemical transformation processes and ( b ) process-dependent factors, which depend on the initial and final chemical states of the molecule but are independent of the control parameters. For systems with two chemical states the condition of separability is automatically fulfilled. We introduce an intrinsic time scale, which makes it possible to compute theoretically various experimental observables, such as the correlation functions of the fluorescent signal. We analyze the connections between the condition of separability and detailed balance, and discuss the possible cause of chemical oscillations in single molecule kinetics. We show that the intrinsic dynamics of the molecule, expressed by the fluctuations of the control parameters, may lead to damped oscillations of the correlation functions of the fluorescent signal. The influence of the random fluctuations on the control parameters may be described by a renormalized master equation with nonfluctuating apparent rate coefficients. The apparent rate coefficients do not have to obey a condition of detailed balance, even though the real rate coefficients do obey such a condition. It follows that the renormalized master equation may have damped oscillatory solutions.

Bibliography

Vlad, M. O., Moran, F., Schneider, F. W., & Ross, J. (2002). Memory effects and oscillations in single-molecule kinetics. Proceedings of the National Academy of Sciences, 99(20), 12548â12555.

Authors 4

Marcel O. Vlad (first)
Federico Moran (additional)
Friedemann W. Schneider (additional)
John Ross (additional)

References 16 Referenced 23

10.1021/jp9634518
10.1021/jp971915b
10.1021/jp992324j
10.1063/1.478369
10.1126/science.283.5408.1670
10.1021/jp012992g
10.1126/science.283.5408.1689
10.1073/pnas.130589397
10.1103/PhysRevE.50.798
10.1063/1.531415
R Bellman Matrix Analysis (McGraw–Hill, 2nd Ed., New York, 1970). / Matrix Analysis by Bellman R (1970)
J P Boon, S Yip Molecular Hydrodynamics (McGraw–Hill, New York, 1980). / Molecular Hydrodynamics by Boon J P (1980)
B L Clarke Adv Chem Phys 43, 1–216 (1980). / Adv Chem Phys by Clarke B L (1980)
N G Van Kampen Stochastic Processes in Physics and Chemistry (North Holland, 2nd Ed., Amsterdam), pp. 383–421 (1992). / Stochastic Processes in Physics and Chemistry by Van Kampen N G (1992)
10.1038/41048
10.1021/jp991968o

Dates

Type	When
Created	22 years, 11 months ago (Oct. 1, 2002, 12:58 p.m.)
Deposited	3 years, 4 months ago (April 13, 2022, 5:15 a.m.)
Indexed	1 year, 7 months ago (Jan. 9, 2024, 10:21 p.m.)
Issued	22 years, 11 months ago (Sept. 12, 2002)
Published	22 years, 11 months ago (Sept. 12, 2002)
Published Online	22 years, 11 months ago (Sept. 12, 2002)
Published Print	22 years, 11 months ago (Oct. 1, 2002)

Funders 0

None

BibTeX

@article{Vlad_2002, title={Memory effects and oscillations in single-molecule kinetics}, volume={99}, ISSN={1091-6490}, url={http://dx.doi.org/10.1073/pnas.192439099}, DOI={10.1073/pnas.192439099}, number={20}, journal={Proceedings of the National Academy of Sciences}, publisher={Proceedings of the National Academy of Sciences}, author={Vlad, Marcel O. and Moran, Federico and Schneider, Friedemann W. and Ross, John}, year={2002}, month=sep, pages={12548–12555} }

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