Although Dews and others showed that the rate-dependency theory described the actions of many drugs on schedule-controlled operant responding, a question remained about whether the rate of the ongoing behavior could account for drug effects on other behaviors (nonoper-ant). Looking at a wide range of behavioral effects of amphetamine in rats, Dews and Wenger (1977) could not show any separation between operant studies and non-operant studies (e.g., locomotor activity or rearing). For the most part, data from operant and nonoperant studies fell on the same log-log regression line. Similarly, if one examined very low rates of behavior, although the variance was very high, there was no obvious break in the loglog relationship. However, there were a couple of notable exceptions for the rate-dependency of amphetamines. Control rates of behavior that were very low as a result of the presentation of an aversive event upon a response (punishment) did not appear to be increased to the same extent as equally low rates of responding in the absence of a punishment procedure. These low punished rates may, however, have their own parallel relationship between drug effect and control rate of responding. Interestingly, barbiturates, benzodiazepines, and other drugs with clinical antianxiety properties do not share this attenuated capacity of amphetamines to increase low rates under punishment situations. The barbiturates and benzodiaze-pines, for example, may produce an even larger increase in low rates maintained by punishment procedures compared to their effect on equally low rates maintained by procedures not involving punishment. In nonoperant experiments, there was one notable exception to the rate-dependent effects of amphetamine. The rate of licking by rats appeared to be relatively resistant to change by amphetamines. The resistance to change of licking responses has been reported for several other drug classes.
In addition to the punishment situations discussed earlier for amphetamines, there are a couple of other situations where the rate of ongoing behavior is not the sole determinant of the drug effect (for review see: McKearney 1981). As with the effect of amphetamines on low rates of behavior that have been suppressed by punishment, the ability of barbiturates to increase low rates of responding that are under strong discriminative control has been shown to be less than predicted based solely upon the rate of responding. Nevertheless, the effect of the barbiturates in this situation seemed to be strongly influenced by the control rate of responding. A third situation of note is where the rate of responding directly influences the rate of reinforcement. In many situations, the rate of responding can vary widely with minimal effect on reinforcement rate. However, in situations where an increase in rate decreases reinforcement frequency, these low rates are relatively resistant to increases by drug. Finally, although under most situations the drug effects are independent of the event maintaining the behavior, there are a few known examples where similar rates of responding are altered differently depending upon the reinforcing event. For example, the effect of ► morphine has been shown to alter rates of responding differentially depending upon whether the reinforcing event used to maintain the behavior is food or electric shock presentation.
Although a vast body of literature shows that drugs obey the rate-dependency theory of drug action as proposed by Dews, there have been several challenges and alternative theories proposed. The most significant challenge was, in part, a mathematical issue versus a biological issue, but it also raised questions about the nature of drug effects. Gonzalez and Byrd (1977) stated that the log-log linear relationship proposed by Dews (1964) can be summarized by eqn. 1. By rearranging eqn. 1 to yield eqn. 2, it can be seen that when the slope of the rate-dependency plot equals —1, then the rate following drug administration becomes independent of the control rate and all rates are equal. They further stated that, in order to make it easier to see when the rate after drug administration becomes independent of the control rate, the data should be plotted as shown in Fig. 2. As can be seen with increasing dose and increasing effect, the slope becomes less and less positive and potentially approaches zero. Furthermore, they argued that both the control rate and the rate after
Control rate (Rc), log scale
Rate-Dependency Theory. Fig. 2. Rate-dependency plot according to Gonzalez and Byrd (1977). Abscissa: rate of responding under control conditions (Rc); Ordinate: rate of responding following drug (Rd). X dose administered.
drug administration are dependent upon the maximum possible response rate. Thus, Gonzalez and Byrd stated that the effect of a drug on the rate of responding is best considered independent of the control rate, and it is necessary to know the maximum possible rate of responding before the drug effect can be interpreted.
Rearrangement yields the following:
where, R<j - rate after drug administration Rc - control rate k - Y-intercept j - slope of the regression line
In defense of Dews' position (Dews 1964), it must be remembered that drugs do not create behavior, they only modify existing behavior. Thus, the drug effect cannot be considered in the absence of a comparison to the control behavior. With respect to the contribution played by the maximum possible response rate, such a rate can only be determined experimentally, and it never will be possible to establish the true maximum rate of responding. Furthermore, there is no experimental evidence to support the need to know the maximum rate of responding (see Dews 1978).
The second major challenge to the theory was published in 1981 (Ksir 1981). Ksir's challenge can be summarized by saying that drugs tend to make the rate of responding a constant independent of the control rate of responding. Thus, with increasing doses of drug, the rate of responding approaches some constant value. If this were the case, such a nonspecific effect of a drug would be of little interest. Furthermore, few pharmacologists would accept such a conclusion. Thus, like the Gonzalez and Byrd (1977) challenge, the arguments maybe mathematically correct, but they may not be correct from a biological standpoint.
In summary, a question that arises is how strongly can the theory be stated? Based upon the literature, Dews and Wenger (1977) stated that it is probably true that with all other variables unchanged, a change in the rate of responding may change the behavioral effect of a drug. It is probably also true that not only may differences in the rate of responding lead to differences in the effects of drugs, but in general, such differences will be determined by the control rate, and there will be a systematic relationship between the rate of responding and drug effect. Although there are some exceptions as noted earlier, the control rate of responding relates to the drug effect in such a manner that in most cases the log of the effect is a linear function of the log of the control rate of the behavior. However, probably it is a mistake to conclude that the control rate of responding is the sole determinant of the effect of a drug and that other factors are only important to the extent that they modify the control rate of responding.
The rate-dependency theory describes a relationship between the control rate of behavior and the rate of responding after drug administration. It was never intended to be an absolute relationship, but rather it was a way of showing order and predictability in drug effects. McKearney (1981) summarized the concept by saying rate-dependency is more of a theoretical law than it is a theory or hypothesis. It describes a predictable relationship between the control behavior and the effects of drugs. Viewed in this manner, it is not unlike the way the temperature of a tissue bath influences the response of a tissue to a drug. The temperature of the bath does not explain the action of the drug, but to consider the action of the drug without considering the bath temperature will lead to something that makes little sense. Thus, the rate of responding should be viewed not as the sole determinant of drug action, but, under the right conditions, it can assume a prime role in the determination of the response.
Although the issues and theories of the 1950s seem of little consequence today, the lessons learned need not be forgotten. For example, as we explore the role of genetics in the control of behavior and the response to drugs in newly developed animal strains, it must be remembered that ignoring the role of the control behavior in influencing drug effects is done at ones own peril.
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