On the Minimal Model of Kinetic Cooperativity

Authors

  • L.N. Christophorov Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe68.10.684

Keywords:

monomeric enzymes, kinetic cooperativity, conformational regulation, nonMichaelis schemes, kinetic resonance, glucokinase

Abstract

The minimal 3-state scheme of kinetic cooperativity of monomeric enzymes is subjected to a detailed analysis. The rigorous criteria of the positive cooperativity and its sigmoidal version are established in terms of the system parameters (rate constants). It is shown that the cooperativity extent is especially sensitive to the rates and direction of the exchange between conformational states of the free enzyme. However, no necessity of the “kinetic resonance” (or, moreover, its generality claimed recently) for enhancing the cooperativity is revealed. Overall, while the minimal 3-state model serves well for the qualitative understanding of the origin of kinetic cooperativity, it is hardly suitable for the quantitative description of reactions of real enzymes, as it is shown with the case of glucokinase.

Author Biography

L.N. Christophorov, Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine

Bogolyubov Institute
for Theoretical Physics
14-b Metrolohichna str. Kiev
Ukraine 03143

References

L. Michaelis, M.L. Menten. Die Kinetik der Invertinwirkung. Biochem. Zeitschrift 49, 333 (1913).

A Century of Michaelis-Menten Kinetics (Special issue. Edited by A. Cornish-Bowden, C.P. Whitham). FEBS Lett. 587, 2711 (2013).

https://doi.org/10.1016/j.febslet.2013.07.035

A. Cornish-Bowden. One hundred years of Michaelis-Menten kinetics. Perspective in Science 4, 3 (2015).

https://doi.org/10.1016/j.pisc.2014.12.002

J. Monod, Wyman, J.-P. Changeux. On the nature of allosteric transitions: A plausible model. J. Mol. Biol. 12, 88 (1965).

https://doi.org/10.1016/S0022-2836(65)80285-6

D.E. Koshland, Jr, G. Nemethy, D. Filmer. Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry 5, 365 (1966).

https://doi.org/10.1021/bi00865a047

A. Cornish-Bowden, M.L. C'ardenas. Cooperativity in monomeric enzymes. J. Theor. Biol. 124, 1 (1987).

https://doi.org/10.1016/S0022-5193(87)80248-5

B.R. Rabin. Co-operative effects in enzyme catalysis: A possible kinetic mode based in substrate-induced conformational isomerization. Biochem. J. 102, 22c (1967).

https://doi.org/10.1042/bj1020022C

E. Whitehead. The regulation of enzyme activity and allosteric transition. Progr. Biophys. Mol. Biol. 21, 321 (1970).

https://doi.org/10.1016/0079-6107(70)90028-3

C. Frieden. Kinetic aspects of regulation of metabolic processes: The hysteretic enzyme concept. J. Biol. Chem. 245, 5788 (1970).

https://doi.org/10.1016/S0021-9258(18)62721-8

G.R. Ainslie, J.P. Shill, K.E. Neet. Transient and cooperativity. A slow transition model for relating transients and cooperative kinetics of enzymes. J. Biol. Chem. 247, 7088 (1980).

https://doi.org/10.1016/S0021-9258(19)44697-8

J. Ricard, J.-C. Meunier, J. Buc. Regulatory behavior of monomeric enzymes. 1. The mnemonical enzyme concept. Eur. J. Biochem. 49, 105 (1974).

https://doi.org/10.1111/j.1432-1033.1974.tb03825.x

J. Ricard, A. Cornish-Bowden. Co-operative and allosteric enzymes: 20 years on. Eur. J. Biochem. 166, 255 (1987).

https://doi.org/10.1111/j.1432-1033.1987.tb13510.x

C.M. Porter, B.G. Miller. Cooperativity in monomeric enzymes with single ligand-binding sites (minireview). Bioorg. Chem. 43, 44 (2012).

https://doi.org/10.1016/j.bioorg.2011.11.001

D. Michel. Conformational selection or induced fit? New insights from old principles. Biochimie, 128-129, 48 (2016).

https://doi.org/10.1016/j.biochi.2016.06.012

D.E. Piephoff, J. Wu, J. Cao. Conformational nonequilibrium enzyme kinetics: Generalized Michaelis-Menten equation. J. Phys. Chem. Lett. 8, 3619 (2017).

https://doi.org/10.1021/acs.jpclett.7b01210

H. Niemeyer, M. Luz Cardenas, E. Rabajille, T. Ureta, L. Clark-Turri, J. Penaranda. Sigmoidal kinetics of glucokinase. Enzyme 20, 321 (1975).

https://doi.org/10.1159/000458957

M.L. C'ardenas. Comparative biochemistry of glucokinase. Front. Diabetes 16, 31 (2004).

https://doi.org/10.1159/000079005

A. Cornish-Bowden, M.L. C'ardenas. Glucokinase: A monomeric enzyme with positive cooperativity. Front. Diabetes 16, 125 (2004).

https://doi.org/10.1159/000079011

M. Larion, A.L. Hansen, F. Zhang, L. Bruschweiler-Li, V. Tugarinov, B.G. Miller, R. Bruschweiler. Kinetic cooperativity in human pancreatic glucokinase originates from millisecond dynamics of the small domain. Angew. Chem. 54, 8129 (2015).

https://doi.org/10.1002/anie.201501204

A.C. Whittington, M. Larion, J.M. Bowler, K.M. Ramsey, R. Bruschweiler, B.G. Miller. Dual allosteric activation mechanisms in monomeric human glucokinase. Proc. Natl. Acad. Sci. U.S.A. 112, 11553 (2015).

https://doi.org/10.1073/pnas.1506664112

V.J. Hilser, J.A. Anderson, H.N. Motlagh. Allostery vs. allokairy. Proc. Natl. Acad. Sci. U.S.A. 112, 11430 (2015).

https://doi.org/10.1073/pnas.1515239112

W. Mu, J. Kong, J. Cao. Understanding the optimal cooperativity of human glucokinase: Kinetic resonance in nonequilibrium conformational fluctuations. J. Phys. Chem. Lett. 12, 2900 (2021).

https://doi.org/10.1021/acs.jpclett.1c00438

H. Qian. Cooperativity and specificity in enzyme kinetics: A single-molecule time-based perspective. Biohys. J. 95, 10 (2008).

https://doi.org/10.1529/biophysj.108.131771

M. Panigrahy, S. Garani, A. Dua. Molecular memory and dynamic cooperativity in monomeric enzymes. J. Indian Chem. Soc. 96, 817 (2019).

L.N. Christophorov, V.N. Kharkyanen. Synergetic mechanisms of structural regulation of the electron-transfer and other reactions of biological macromolecules. Chem. Phys. 319, 330 (2005).

https://doi.org/10.1016/j.chemphys.2005.06.029

L.N. Christophorov. On the velocity of enzymatic reactions in Michaelis-Menten-like schemes (ensemble and singlemolecule versions). Ukr. J. Phys. 65, 412 (2020).

https://doi.org/10.15407/ujpe65.5.412

J.H. Choi, A.H. Laurent, V.J. Hilser, M. Ostermeier. Design of protein switches based on an ensemble model of allostery. Nat. Comm. 6, 6968 (2015).

https://doi.org/10.1038/ncomms7968

Yu.M. Barabash, N.M. Berezetskaya, L.N. Christophorov, A.O. Goushcha, V.N. Kharkyanen. Effects of structural memory in protein reactions. J. Chem. Phys. 116, 4339 (2002).

https://doi.org/10.1063/1.1447906

L.N. Christophorov. Enzyme functioning: Along the lines of nonequilibrium phase transitions. AIP Advances 8, 125326 (2018).

https://doi.org/10.1063/1.5055354

Downloads

Published

2023-11-29

How to Cite

Christophorov, L. (2023). On the Minimal Model of Kinetic Cooperativity. Ukrainian Journal of Physics, 68(10), 684. https://doi.org/10.15407/ujpe68.10.684

Issue

Section

Physics of liquids and liquid systems, biophysics and medical physics