On the validity and errors of the pseudo-first-order kinetics in ligand-receptor binding. (English) Zbl 1377.92040
Summary: The simple bimolecular ligand-receptor binding interaction is often linearized by assuming pseudo-first-order kinetics when one species is present in excess. Here, a phase-plane analysis allows the derivation of a new condition for the validity of pseudo-first-order kinetics that is independent of the initial receptor concentration. The validity of the derived condition is analyzed from two viewpoints. In the first, time courses of the exact and approximate solutions to the ligand-receptor rate equations are compared when all rate constants are known. The second viewpoint assesses the validity through the error induced when the approximate equation is used to estimate kinetic constants from data. Although these two interpretations of validity are often assumed to coincide, we show that they are distinct, and that large errors are possible in estimated kinetic constants, even when the linearized and exact rate equations provide nearly identical solutions.
MSC:
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 92C40 | Biochemistry, molecular biology |
Keywords:
pseudo-first-order kinetics; ligand-receptor binding; experimental design; approximation validity; rate constant estimation; fitting procedureReferences:
| [1] | Griffiths, J., Reduced kinetic models and their application to practical combustion systems, Prog. Energy Combust. Sci., 21, 1, 25-107 (1995) |
| [2] | Okino, M. S.; Mavrovouniotis, M. L., Simplification of mathematical models of chemical reaction systems, Chem. Rev., 98, 2, 391-408 (1998) |
| [3] | Gutfreund, H., Kinetics for the Life Sciences: Receptors, Transmitters, and Catalysts (1995), Cambridge University Press: Cambridge University Press Cambridge, UK |
| [4] | Fersht, A., Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding (1999), Freeman: Freeman New York |
| [5] | Espenson, J. H., Chemical Kinetics and Reaction Mechanisms (2002), McGraw-Hill: McGraw-Hill New York |
| [6] | Heineken, F. G.; Tsuchiya, H. M.; Aris, R., On the accuracy of determining rate constants in enzymatic reactions, Math. Biosci., 1, 1, 115-141 (1967) |
| [7] | Segel, L. A., On the validity of the steady state assumption of enzyme kinetics, Bull. Math. Biol., 50, 6, 579-593 (1988) · Zbl 0653.92006 |
| [8] | Hall, D. R.; Gorgani, N. N.; Altin, J. G.; Winzor, D. J., Theoretical and experimental considerations of the pseudo-first-order approximation in conventional kinetic analysis of IAsys biosensor data, Anal. Biochem., 253, 2, 145-155 (1997) |
| [9] | Schnell, S.; Maini, P. K., Enzyme kinetics at high enzyme concentration, Bull. Math. Biol., 62, 3, 483-499 (2000) · Zbl 1323.92099 |
| [10] | Schnell, S.; Mendoza, C., The condition for pseudo-first-order kinetics in enzymatic reactions is independent of the initial enzyme concentration, Biophys. Chem., 107, 2, 165-174 (2004) |
| [11] | Schnell, S., Validity of the Michaelis-Menten equation—steady-state or reactant stationary assumption: that is the question, FEBS J., 281, 2 (2014) |
| [12] | Schnell, S.; Hanson, S. M., A test for measuring the effects of enzyme inactivation, Biophys. Chem., 125, 2-3, 269-274 (2007) |
| [13] | Hanson, S. M.; Schnell, S., Reactant stationary approximation in enzyme kinetics, J. Phys. Chem. A, 112, 37, 8654-8658 (2008) |
| [14] | Whidden, M.; Ho, A.; Ivanova, M. I.; Schnell, S., Competitive inhibition reaction mechanisms for the two-step model of protein aggregation, Biophys. Chem., 193-194, 9-19 (2014) |
| [15] | Lauffenburger, D. A.; Linderman, J., Receptors: Models for Binding, Trafficking, and Signaling (1995), Oxford University Press: Oxford University Press New York |
| [16] | (Hulme, E. C. (1992), IRL Press at Oxford University Press: IRL Press at Oxford University Press New York) |
| [17] | Kahn, C. R., Membrane receptors for hormones and neurotransmitters, J. Cell Biol., 70, 2, 261-286 (1976) |
| [18] | Weiland, G. A.; Molinoff, P. B., Quantitative analysis of drug-receptor interactions: I. Determination of kinetic and equilibrium properties, Life Sci., 29, 4, 313-330 (1981) |
| [19] | Hollenberg, M. D.; Goren, H. J., Ligand-receptor interactions at the cell surface, (Poste, G.; Crooke, S. T., Mechanisms of Receptor Regulation (1985), Plenum Press: Plenum Press New York), 323-373 |
| [20] | Pettersson, G., The transient-state kinetics of two-substrate enzyme systems operating by an ordered ternary-complex mechanism, Eur. J. Biochem., 69, 1, 273-278 (1976) |
| [21] | Pettersson, G., A generalized theoretical treatment of the transient-state kinetics of enzymic reaction systems far from equilibrium, Acta Chem. Scand. B, 32, 6, 437-446 (1978) |
| [22] | Sicilio, F.; Peterson, M. D., Ratio errors in pseudo first order reactions, J. Chem. Educ., 38, 11, 576-577 (1961) |
| [23] | Moore, J. W.; Pearson, R. G., Kinetics and Mechanism (1981), John Wiley & Sons: John Wiley & Sons News York |
| [24] | Corbett, J. F., Pseudo first-order kinetics, J. Chem. Educ., 49, 10, 663 (1972) |
| [25] | Lowry, T. M.; John, W. T., CCLXIX.—Studies of dynamic isomerism. Part XII. The equations for two consecutive unimolecular changes, J. Chem. Soc. Trans., 97, 2634-2645 (1910) |
| [26] | Castillo-Chavez, C.; Song, B., Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1, 2, 361-404 (2004) · Zbl 1060.92041 |
| [27] | Laidler, K. J., Theory of the transient phase in kinetics, with special reference to enzyme systems, Can. J. Chem., 33, 10, 1614-1624 (1955) |
| [28] | Borghans, J. A.M.; de Boer, R. J.; Segel, L. A., Extending the quasi-steady state approximation by changing variables, Bull. Math. Biol., 58, 1, 43-63 (1996) · Zbl 0866.92010 |
| [29] | Tzafriri, A. R., Michaelis-Menten kinetics at high enzyme concentrations, Bull. Math. Biol., 65, 6, 1111-1129 (2003) · Zbl 1334.92185 |
| [30] | Pollard, T. D.; De La Cruz, E. M., Take advantage of time in your experiments: a guide to simple, informative kinetics assays, Mol. Biol. Cell., 24, 8, 1103-1110 (2013) |
| [31] | Segel, L. A.; Slemrod, M., The quasi-steady state assumption: a case study in perturbation, SIAM Rev., 31, 3, 446-477 (1989) · Zbl 0679.34066 |
| [32] | Pollard, T. D., A guide to simple and informative binding assays, Mol. Biol. Cell., 21, 23, 4061-4067 (2010) |
| [33] | Pedersen, M. G.; Bersani, A. M.; Bersani, E.; Cortese, G., The total quasi-steady-state approximation for complex enzyme reactions, Math. Comput. Simul., 79, 4, 1010-1019 (2008) · Zbl 1157.92019 |
| [34] | Jacquez, J. A., The inverse problem for compartmental systems, Math. Comput. Simul., 24, 6, 452-459 (1982) · Zbl 0562.93018 |
| [35] | Kennedy, M. C.; O’Hagan, A., Bayesian calibration of computer models, J. R. Stat. Soc. B., 63, 3, 425-464 (2001) · Zbl 1007.62021 |
| [36] | Engl, H. W.; Flamm, C.; Kügler, P.; Lu, J.; Müller, S.; Schuster, P., Inverse problems in systems biology, Inverse Probl., 25, 12, 123014 (2009) · Zbl 1193.34001 |
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