Intermittent Adaptation: A Theory of Drug Tolerance, Dependence and Addiction


Abraham Peper

University of Amsterdam
Department of Medical Physics
Academic Medical Centre
Amsterdam
The Netherlands






Papers


Journal of Theoretical Biology (1987):
An approach to the modelling of the tolerance mechanism in the drug effect. Part I: The drug effect as a disturbance of regulations.

It is argued that the disturbing effects of drugs upon regulations in the organism are an important factor in the total drug effect and it is made plausible that the decrease of the drug effect after prolonged or repeated administration of the drug is caused by the adaptation of the involved regulations to the presence of the drug, the adaptive process being selective for the drug in question. A mathematical model based on these assumptions is developed taking into account the specific behaviour of regulated processes. The functioning of the model is investigated by means of computer simulations. The behaviour of the model appears to be well in accordance with the phenomenon of drug tolerance as described in the literature.


Journal of Theoretical Biology (1988):
An approach to the modelling of the tolerance mechanism in the drug effect. Part II: On the implications of compensatory regulations.

The behaviour of a previously published mathematical model of drug tolerance was studied with respect to the dose-response relation, the drug effect in dependent and non-dependent subjects and withdrawal symptoms. Simulations with the model demonstrate the model to be highly sensitive to sudden changes in drug dose. Dependent on the open loop gain of the adaptive mechanism, a decrease in drug dose might result in an effect opposite to the common drug effect. The behaviour of the model suggests the degree of drug dependence in an addicted subject to depend on the extent to which non-somatic factors are involved in the process of initiation of the adaptive mechanisms.
 

International Journal of Hyperthermia (1998):

A mathematical model of the hsp70 regulation in the cell

A mathematical model of the regulation process of the heat shock protein hsp70 in the cell is presented. The model describes the damaging effect of elevated temperature on proteins; the interaction of free hsp70 with injured proteins and its chaperone role in nascent protein translation; the relation between the amount of free hsp70 and the formation of the activated trimer form of the heat shock factor protein (HSF); the binding of activated HSF with the heat shock elements on the DNA; the transcription of mRNA of hsp70 and the synthesis of hsp70. The reaction of the model to a temporal rise in temperature shows an initial decline and a subsequent sharp rise to an ultimately increased level of free hsp70 in the cell. The response of the model to both a single and two consecutive heat shocks appears to closely resemble experimental data on hsp70 synthesis. This general agreement demonstrates the structure of the model to be sound and suitable as a basis for further modelling the complex tolerance mechanism of the cell.


Journal of Theoretical Biology (1999):

Preliminary results of simulations with an improved mathematical model of drug tolerance.

Simulations with a mathematical model of drug tolerance of different ways withdrawal in addiction can be achieved are presented. The outcome of the simulations suggest that there are several ways in which drug withdrawal can be made considerably less demanding for the patient than the usual abrupt withdrawal or the slow tapering off of the drug dose.


Journal of Theoretical Biology (2004):
A Theory of Drug Tolerance and Dependence I: A conceptual analysis.

A mathematical model of drug tolerance and its underlying theory is presented. The model extends a first approach, published previously. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural—oral—route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model’s behavior to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes. In addition, it establishes a relation between the drug dose at any moment, and the resulting drug effect and relates the magnitude of the reactions following withdrawal to the rate of tolerance and other parameters involved in the tolerance process. The present paper analyses the concept behind the model. The next paper discusses the mathematical model.


Journal of Theoretical Biology (2004):
A Theory of Drug Tolerance and Dependence II: The mathematical model.

The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural—oral—route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model’s behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus—the drug intake—and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.


Dose-Response (2009):
Aspects of the Relationship Between Drug Dose and Drug Effect

It is generally assumed that there exists a well-defined relationship between drug dose and drug effect and that this can be expressed by a dose-response curve. This paper argues that there is no such clear relation and that the dose-response curve provides only limited information about the drug effect. It is demonstrated that tolerance development during the measurement of the dose-response curve may cause major distortion of the curve and it is argued that the curve may only be used to indicate the response to the first administration of a drug, before tolerance has developed. The precise effect of a drug on an individual depends on the dynamic relation between several variables, particularly the level of tolerance, the dose anticipated by the organism and the actual drug dose. It is shown that when tolerance has developed a small change in drug dose can produce a large change in magnitude of the drug effect. Simulations with the mathematical model demonstrate that a small dose of a drug may generate symptoms opposite to the action of the drug in high doses, verifying the hypothesis underlying homeopathy and hormesis.


Pharmacopsychiatry - Review article (2009):
Intermittent adaptation. A theory of drug tolerance, dependence and addiction

A mathematical model of drug tolerance and its underlying theory is presented. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of endogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural - oral - route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model’ behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. Simulations of different ways withdrawal can be accomplished, demonstrate the practical applicability of the model.


Intermittent Adaptation; A Mathematical model of Drug Tolerance, dependence and addiction In: Computational Neuroscience of Drug Addiction (Springer Series in Computational Neuroscience); Boris Gutkin and Serge H. Ahmed (eds). New York: Springer, 2011.

A model of drug tolerance, dependence and addiction is discussed. The model is essentially much more complex than the commonly used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a process of intermittently developing adaptation. The oral detection and analysis of endogenous substances is proposed to be the primary stimulus triggering the adaptation process. Anticipation and environmental cues are considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural - oral - route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomously functioning adaptation processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. It is demonstrated that tolerance development during the measurement of the dose-response curve may cause major distortion of the curve and it is argued that the curve may only be used to indicate the response to the first administration of a drug, before tolerance has developed. It is shown that when tolerance has developed a small change in drug dose can produce a large change in magnitude of the drug effect. Simulations with the mathematical model demonstrate that a small dose of a drug may generate symptoms opposite to the action of the drug in high doses, verifying the hypothesis underlying hormesis and homeopathy. Simulations of different ways withdrawal can be accomplished, demonstrate the practical applicability of the model.

 

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