AM  Vol.12 No.1 , January 2021
A Mathematical Model for the Effect of Enzymes on Metabolism of Pharmacologically Active Substances
Abstract: Addiction is a societal issue with many negative effects. Substances that cause addictive reactions are easily ingested and interact with some part of the neural pathway. This paper describes a mathematical model for the systemic level of a substance subject to degradation (via metabolism) and reversible binding to psychoactive sites. The model allows the determination of bound substance levels during the processing of a dose, and how the maximum level depends on system parameters. The model also allows the study of a particular periodic repetitive dosing described by a rapid ingestion if a dose is at constant intervals.
Cite this paper: Drew, D. (2021) A Mathematical Model for the Effect of Enzymes on Metabolism of Pharmacologically Active Substances. Applied Mathematics, 12, 1-17. doi: 10.4236/am.2021.121001.

[1]   Nestler, E.J. and Luescher, C. (2019) The Molecular Basis of Drug Addiction: Linking Epigenetic to Synaptic and Circuit Mechanisms. Neuron, 102, 48-59.

[2]   Pascoli, V., Hiver, A., Van Zessen, R., et al. (2018) Stochastic Synaptic Plasticity Underlying Compulsion in a Model of Addiction. Nature, 564, 366-371.

[3]   Luescher, C. and Ungless, M.A. (2006) The Mechanistic Classification of Addictive Drugs. PLoS Medicine, 3, e437.

[4]   Tabakoff, B., Cornell, N. and Hoffman, P.L. (1986) Alcohol Tolerance. Annals of Emergency Medicine, 15, 1005-1012.

[5]   Grace, A.A. (2000) The Tonic/Phasic Model of Dopamine System Regulation and Its Implications for Understanding Alcohol and Psychostimulant Craving. Addiction, 95, S119-S128.

[6]   Drew, D.A. (2018) A Mathematical Model for Nutrient Metabolic Chemistry. Applied Mathematics, 9, 647-671.

[7]   Cederbaum, A.I. (2012) Alcohol Metabolism. Clinics in Liver Disease, 16, 667-685.

[8]   Berg, J.L., Tymoczko, J.L. and Stryer, L. (2007) Biochemistry. Fifth Edition, W. H. Freeman, NY.

[9]   Hoffman, P.L. and Tabakoff, B. (1989) Mechanisms 0f Alcohol Tolerance. Alcohol and Alcoholism, 24, 251-252.

[10]   Michaelis, L. and Menten, M. (1913) Die kinetik der invertinwirkung. Biochemistry Zeitung, 49, 333-369.

[11]   Lin, C.C. and Segel, L.A. (1988) Mathematics Applied to Deterministic Problems in the Natural Sciences. SIAM Classics in Applied Mathematics, New York.