Introduction

Abstract Introduction Methods Results Discussion References

Benzodiazepines, like many drugs, often exhibit a dose-related, biphasic effect on behavior in animals. At lower doses, BZs increase response rates for operant or schedule-controlled behavior (Burke et al., 1994; File and Pellow, 1985; Griffiths and Goudie, 1987), as well as for spontaneous activity (Flaherty et al., 1996; Lopez et al., 1988); i.e., they produce a "stimulatory" effect. Conversely, at higher doses, they typically decrease these rates of responding. "Sedation" was observed as the maximum effect after high-dose BZ administration (e.g., 3 mg/kg s.c. midazolam) with animals maintaining a crouched position without movement (Lau et al., 1996). BZs exert their effects through the GABA-BZ receptor complex (Haefely et al., 1985). The behavioral endpoints observed after alprazolam administration corresponded to receptor in vivo binding of alprazolam for the respective doses; the low dose increased, and the high dose decreased the binding, although this was not observed for other BZs (Burke et al., 1994; Kaplan et al., 1990; Lopez et al., 1988; Miller et al., 1987). However, whether the stimulatory and sedative effects of BZs observed under different conditions reflect a common underlying mechanism is not clear, especially if inferences are based mainly on time-course data collapsed into a single point rather than on a complete temporal profile.

Inasmuch as pharmacological response often can be predicted from the respective PK, we chose to investigate the effects of low and high doses in light of the corresponding serum drug concentration profiles instead of the resultant receptor changes. Integrating PK and PD measures can help define and predict the drug concentration-effect relation. It may clarify the relation between the stimulatory and the sedative effects observed for BZs; for example, the sequence and the duration of these two effects as functions of BZ concentration. In humans, BZs are used widely for their therapeutic effects. But they also are associated with a variety of adverse side effects, which have been increasingly recognized in recent years, e.g., early-morning insomnia, daytime anxiety, tension or panic (Kales et al., 1983; Morgan and Oswald, 1982; Vgontzas et al., 1995; Woods et al., 1995). Although the therapeutic and adverse side effects of BZs have been described clinically, to our knowledge no explicit PK-PD model has been developed which attempts to describe these relations. In past research, we used only one measure of DRL 45-s performance, the reinforcement rate, to investigate its relation to PK (Lau and Wang, 1996; Lau et al., 1996, 1997). PK-PD-modeling BZ effects with either a single increasing function such as an EEG measure (Mandema et al., 1991, 1992) or a single decreasing function such as the reinforcement rate is a simple but perhaps an incomplete procedure. Simultaneously modeling both increasing and decreasing functions is a complicated task, however. One is required not only to use a complex behavioral paradigm but also to analyze more than one index of performance. Only then can the relation between the stimulatory and sedative effects be explored and, in turn, provide a useful model for delineating adverse BZ side effects in humans.

The present study used a DRL schedule, which produces "spaced responding" or "timing" behavior. Two distinct classes of responding are considered: reinforced and nonreinforced responses. The DRL 45-s schedule of reinforcement results in low rates of responding, because only those responses that occur after a minimum time interval (in this case, 45 s) after a previous response are reinforced. Responses that occur before 45 s have elapsed are not reinforced, and the timing interval is reset. IRT profiles and the number of responses can be recorded throughout the session without prior special physiological preparation of the subject. The DRL schedule contingency not only entails time discrimination but also requires an appropriate inhibition of responding for reinforcement to occur and involves other memory, sensory and motor capacities (Kramer and Rilling, 1970).

The effect of many drugs is to reduce the inhibition of behavior associated with signals of punishment or nonreward in DRL behavior (Gray, 1981). Drugs not only can alter the IRT distribution but also can disturb the sequential patterning of IRTs. It has been noted that the reinforcing event can be used as a discriminative stimulus for further reinforced responding and thus could function as a strategy used by animals to maximize their performance (Carter and Bruno, 1968; Farmer and Schoenfeld, 1964; Reynolds, 1964). Drug effects, such as sedation, can distort the timing behavior as displayed by the IRT profile, as well as the discriminative stimulus effects produced by the occurrence of a reinforced response. Furthermore, when performance has been disrupted by a drug, even after the drug has disappeared, a period of transition may be required for the reconditioning of base-line performance to occur. Consequently, short IRTs may dominate during this phase before reconditioning has taken place and may cascade because short IRTs are followed by further short IRTs with high probability, as described by the observed sequential dependencies (Weiss et al., 1966). The result of this increase in short IRTs is the stimulatory phenomenon reported here.

The EEG signal has been used as a pharmacodynamic measure for the evaluation of BZ effects in PK-PD analyses (Breimer et al., 1991; Mandema and Danhof, 1992; Mandema et al., 1991), because it satisfies many of the criteria desirable for such modeling (Dingemanse et al., 1988; Laurijssens and Greenblatt, 1996). DRL performance also satisfies these same criteria (Lau and Wang, 1996; Lau et al., 1996, 1997); both EEG and DRL measurement are objective, continuous, sensitive and reproducible. In addition, although "the pharmacological relevance of the EEG parameters with respect to the clinical effects of [BZs] remains to be established" (Mandema et al., 1991, p. 476), the DRL performance requires conduct that fulfills a required and objectively defined behavioral contingency instead of being limited to a passive measure of an unconditioned drug effect. Although DRL performance has been used extensively in behavioral pharmacology to study the dose-effect relation of various drugs from different classes (Richards et al., 1993; Stephens and Voet, 1994; Sanger, 1980), we do not believe this kind of behavioral measure has been used outside our laboratory for PK-PD modeling. We have found previously that the effect-time profiles of the DRL 45-s schedule correlate well with the respective serum concentration-time profiles for alprazolam, midazolam and caffeine (Lau et al., 1996, 1997). The bioavailability values derived from these profiles also mirrored those estimated from PK measures for midazolam following s.c., i.p. and p.o. routes of administration (Lau et al., 1996).

Alprazolam, a triazolobenzodiazepine, is the most widely prescribed BZ and is used as an anxiolytic, antipanic and antidepressant agent (Dawson et al., 1984; Fawcett and Kravitz, 1982). In humans, the terminal half-life of alprazolam is 6 to 16 hr (Greenblatt et al., 1983; Smith et al., 1984), whereas it is approximately 30 min in rats (Lau and Wang, 1996; Owens et al., 1991). Hence, a 3-hr session allows investigation of the onset, peak and disappearance of alprazolam effects. In a previous study, the effects of alprazolam administered s.c. on reinforcement rate were consonant with the serum alprazolam concentrations, but the relation to shorter-response rate (nonreinforced response rate or short IRT rate) was not evaluated (Lau and Wang, 1996); we use the term "shorter-response rate" instead of short IRT rate in the present study to agree with the terminology used in our previous reports (Lau et al., in press; Wang and Lau, in press). The present study investigated not only the effects of alprazolam administered s.c. on the reinforcement and shorter-response rates attained from behavioral analysis but also modeled the time course relating these changes to the respective PK. Intravenous alprazolam dosing was chosen to facilitate selecting the appropriate PD models. Thus, in this work, a comprehensive alprazolam PK-PD model was proposed to describe and predict the interplay between the shorter-response and reinforcement rates. The implications of this model for behavioral observations often reported with respect to tolerance in animals and for adverse side effects noted in humans after BZ administration will be presented under "Discussion."

	Methods

Abstract Introduction Methods Results Discussion References

Drug

Alprazolam was obtained from Upjohn Laboratories (Kalamazoo, MI). Alprazolam (5 mg) was dissolved in 50 µl of 1.2 N HCl, diluted with 0.9% NaCl and administered either subcutaneously or intravenously in an injection volume of 1 ml/kg body weight.

Pharmacokinetics of Alprazolam

Animals. Four male, albino, Sprague-Dawley rats from HSD (Indianapolis, IN) were used. They were housed individually in a temperature-regulated room with a daily cycle of illumination from 7:00 A.M. to 7:00 P.M. They were reduced to 80% of their initial, adult free-feeding body weights (mean, 386 g; 380-389 g) during a 2-week period by limiting daily food rations: 5 g for the first day, 10 g for the next 5 days and a food supplement (range, 14-16 g) to maintain their 80% body weights. Water was continuously available in the living cages. Experiments were conducted in accordance with the Guide for the Care and Use of Laboratory Animals (National Institute of Health Publ. No. 85-23, revised 1985).

Catheterization. Right jugular vein cannulation was performed under sterile conditions and was described previously (Lau et al., 1996). The proximal end of the silastic catheter was inserted into the jugular vein and the distal end of the catheter was threaded subcutaneously and exited through a small incision in the animal's back. The catheter was flushed with 0.9% saline with 50 U heparin and sealed with fishing line when not in use.

Drugs, reagents and HPLC. -Hydroxyalprazolam and 4-hydroxyalprazolam were obtained from Upjohn Laboratories. Reagents were obtained from standard commercial sources. The serum microsample HPLC method for the determination of alprazolam and its metabolites has been described previously (Jin and Lau, 1994). The capacity factors for demoxepam (internal standard), 4-hydroxyalprazolam, -hydroxyalprazolam and alprazolam were 2.08, 2.73, 3.37 and 4.43, respectively. The two metabolites were not included in the PK analysis because their concentrations were either low or not detected.

Alprazolam administration and blood sampling. Animals were allowed to recover for at least 2 days from the jugular vein catheterization before the alprazolam administration series. The animals initially received an i.v. dose of alprazolam (1.2 mg/kg) via the jugular vein catheter, followed on other days by s.c. administration into the skin on the back of the neck of 1.25, 4 and 7 mg/kg alprazolam in a random order. Drug doses were separated by 3 to 5 days. Blood samples (100 µl) from the jugular catheter were obtained after drug administration at 2, 5, 15, 30, 45, 60, 90, 120, 180, 240 and 360 min postinjection. To maintain the feeding regimen and also avoid the effect of food on drug PK, drug doses were given 6 hr before feeding time.

Pharmacodynamics of Alprazolam

Animals. Seven male rats of the same strain were used under the conditions and food-limitation regimen similar to that used in the PK study. Their mean initial, adult free-feeding body weight was 383 g (range, 380-388 g).

Apparatus. Four operant Plexiglas chambers were used as described previously (Lau and Wang, 1996). Each chamber, equipped with a response lever and a stainless steel food-pellet receptacle into which 45-mg dustless pellets (BioServ, Frenchtown, NJ) could be delivered, was enclosed in a sound-attenuating shell and was controlled by an IBM-type 486 X computer. Session contingencies were programmed and data recorded by QuickBasic.

Procedure. Animals were magazine trained initially for 15 min on a noncontingent random-time schedule. Responses on the lever were shaped by successive approximation and reinforced when IRTs were greater than 3 s. The temporal requirement was slowly increased to an IRT of 45 s during 10 to 20 sessions with a 3-hr session conducted daily. After performance had stabilized, the drug administration series began. Animals first received drug subcutaneously with administration of vehicle, 1.25, 4 and 7 mg/kg alprazolam. After completion of the s.c. administration, right jugular vein catheters were implanted as described above in four of the seven animals. These animals then received drug intravenously with administration of saline and 1.25 mg/kg alprazolam. All injections were given immediately before a session, and were separated by 3 to 5 days in a random order within a series.

Data analyses. The IRT distributions after administration of vehicle and alprazolam doses were analyzed for 3-hr sessions, omitting the first 2 min, which allowed for the transient effects of handling. Base-line IRT distributions for each session that immediately preceded each injection also were analyzed. Responses with IRTs 45 s (reinforced responses) and <45 s (shorter or nonreinforced responses) were derived from the IRT distributions. For each rat, there were four base-line day values that were averaged and treated as the mean base-line value for the s.c. injection series; there were two base-line day values for the i.v. injection series. These responses were calculated as rates (responses per min) and transformed to mean percent base-line values to compensate for individual differences in DRL performance.

Pharmacokinetic Pharmacodynamic Modeling

PK and PD data analyses were performed on mean data (PK, n = 4; PD, n = 7 and n = 4 for s.c. and i.v. routes, respectively) by the SAAM II software system (SAAM Institute, 1997). Because PK and PD data were obtained in parallel studies, individual profiles were not used. Fitting models to aggregate data with different doses (Laurijssens and Greenblatt, 1996) is frequently required to estimate one unique set of parameters (Ekblom et al., 1993; Mandema and Wada, 1995); however, this does not allow analysis of inter- or intraindividual variability. Assessment of the goodness of fit of each proposed model to experimental data was based on AIC, correlation matrix, residual and weighted residual plots, visual plots and error in parameter estimation (S.D., expressed as CV%) which is derived from the covariance matrix.

Pharmacokinetic analysis. We analyzed mean serum concentration time profiles by use of compartmental modeling. The distribution and elimination characteristics were determined after the i.v. 1.2 mg/kg alprazolam dose. Then, i.v. 1.2 mg/kg and s.c. alprazolam profiles (1.25-7 mg/kg) were analyzed simultaneously, assuming complete bioavailability of the s.c. administered drug.

Pharmacodynamic models. Shorter-response rate (IRT < 45 s): Stimulation-sedation model. A multicompartmental model, which incorporated two link compartments representing stimulation and sedation sites, was used to describe the data. This effect-link model was based on the model proposed by Sheiner and colleagues (1979). To ensure no loss of mass to the effect site, a "dummy" compartment was linked to the central compartment via a fixed rate constant k1e_st. Drug stimulation site kinetic values are defined by the loss rate constant, keo_st, and the effect site concentration (Ce_st) is defined as:

(1)

where q_e,st and Ve_st are the drug mass and the volume of stimulation site, respectively, and subscript st refers to stimulation. Assuming equilibrium conditions, i.e., dq_e/dt = 0, the fluxes between the central and the link compartments are equal, that is:

(2)

(3)

where q₁ and C₁ are the drug mass and the concentration in the central compartment, respectively, and the subscript ss denotes equilibrium conditions. At steady state, C_1ss = Ce_ss hence:

(4)

where V is the volume of the central compartment.

(5)

(6)

(7)

(8)

(9)

Integrated PK-PD model. The integrated PK-PD model incorporated the PK model (absorption and two-compartment disposition), the stimulation/sedation model describing the shorter-response rate and the indirect response model describing the reinforcement rate. Initial parameter estimates were those obtained after fitting each model separately, as described above. All data (PK and PD) after i.v. 1.25 mg/kg and s.c. 1.25-7 mg/kg were then fitted simultaneously. Only parameters resulting from the integrated model will be presented. Linear kinetics were assumed after i.v. dosing between 1.2 and 1.25 mg/kg. A diagrammatic representation of the integrated PK-PD model is shown in figure 1.

View larger version (31K): [in this window] [in a new window]   Fig. 1.   Diagrammatic representation of integrated PK-PD model used to describe both shorter-response rate (stimulation-sedation model) and the reinforcement rate in the 45-55 s bin (indirect response model) after s.c. administration of a single dose of alprazolam. Similar models were used for s.c 1.25, s.c. 4, s.c. 7 and i.v. 1.25 mg/kg.

	Results

Abstract Introduction Methods Results Discussion References

Pharmacokinetics of Alprazolam

Figure 2 shows the mean serum alprazolam concentration-time profiles after administration of i.v. 1.2 mg/kg (upper panel) and three s.c. doses of alprazolam (1.25-7 mg/kg, lower panel). A two-compartment disposition model was most suitable for describing events after i.v. administration of alprazolam; an additional absorption compartment was required to describe s.c. administration. Parameters, and associated errors, obtained with the fully integrated model are presented in table 1. The volume of the central compartment was fixed to that obtained when i.v. data were analyzed alone, 0.756 l (2.45 l/kg); this assumes no change in bioavailability. As time to peak concentration was not constant for the three s.c. doses (1.25 mg/kg = 5 min, 4 mg/kg = 12 min, 7 mg/kg = 8 min), the absorption rate constant (Ka) differed between doses with 1.25 mg/kg  7 mg/kg > 4 mg/kg, resulting in absorption half-lives of 1.9, 10.3 and 7.1 min, respectively. The intercompartmental rate constants were similar (0.03 min¹, t_1/2 25 min) and approximately twice as slow as Kel (0.06 min¹, t_1/2 11 min). The return rate constant [k(1,2)] showed the greatest interdose variation. Predicted serum concentration-time profiles are shown by solid lines in figure 2.

View larger version (23K): [in this window] [in a new window]   Fig. 2.   Mean (S.E.) measured and predicted serum concentration time profiles after i.v. (1.2 mg/kg, upper panel) and s.c. (1.25, 4 and 7 mg/kg, lower panel) administration of alprazolam (n = 4).

Pharmacodynamics of Alprazolam

After vehicle administration, response rate exhibited a function similar to a gamma distribution with the highest response rate occurring in the 40-50 s bin (fig. 3). As shown in the figure, IRTs before the first arrow (<45 s) were not reinforced and those after the first arrow were reinforced (45 s); whereas, the IRTs between the two arrows represent the reinforced IRTs in the 45-55 s bin. Alprazolam decreased the IRTs 45 s and increased the short IRTs < 45 s in a dose-related fashion. We previously found that the reinforcement rate in the 45-55 s bin not only was more sensitive to drug effects but also reached the maximum effect at a lower dose than the total-reinforcement rate (Lau and Wang, 1996). Thus, the reinforcement rate in the 45-55 s bin, rather than total-reinforcement rate, was used to characterize the effects of alprazolam. This minimized the possibility of behavioral toxicity which might occur if higher doses were necessary to perform the analysis. Figure 4, upper panel, shows the effects of s.c. doses of alprazolam (1.25-7 mg/kg) on the shorter-response rate, which increased to the maximum effect (Emax) with all doses immediately after drug administration (greatest for the 1.25 mg/kg dose), and which then decreased to near base-line levels. However, the shorter-response rate again increased in a dose-related fashion in terms of both time to and duration of the second peak. The second peak occurred at 60, 90 to 120 and 150 min for 1.25, 4 and 7 mg/kg, respectively, and peak duration progressively increased. For each dose, the second peak lasted longer, but was of a lower magnitude than the first peak. In contrast to the shorter-response rate, alprazolam decreased the reinforcement rate in the 45-55 s bin (fig. 4, lower panel). The maximum effects for the three doses of alprazolam occurred during the 15- to 45-min period, and these decrements gradually recovered to base-line level at the end of the session in a dose- and time-related fashion, although the rate remained below base line for the s.c. 7 mg/kg dose.

View larger version (24K): [in this window] [in a new window]   Fig. 3.   Mean (S.E.) effects of s.c. alprazolam on IRT distributions during the 3-hr session. All responses before and after the first arrow are nonreinforced (<45 s) and reinforced (45 s), respectively, and between the two arrows are the 45-55 s bin responses (n = 7).

View larger version (23K): [in this window] [in a new window]   Fig. 4.   Response rate-time profiles, expressed as % base line (S.E.) after s.c. administration of alprazolam (vehicle, 1.25, 4 and 7 mg/kg, n = 7). Upper panel: shorter-response rate; lower panel: reinforcement rate in the 45-55 s bin.

To further investigate the relationship between the two successive peaks for the shorter-response rate produced by s.c. doses of alprazolam, an i.v. 1.25 mg/kg alprazolam dose was chosen. Figure 5 shows the effects of i.v. 1.25 mg/kg alprazolam and vehicle on the shorter-response rate and on the reinforcement rate in the 45-55 s bin (n = 4). For comparison, the effect of s.c. 1.25 mg/kg alprazolam on the two response rates is shown for the seven animals (fig. 4). Vehicle administration by each route had negligible effects on the two rates of responding, which remained approximately at base line. The effect of i.v. 1.25 mg/kg alprazolam on the shorter-response rate closely followed that for the s.c. dose between 45 and 180 min; however, a below-base-line rate was observed during the first 30 min of the session, as opposed to an initial stimulation peak in the s.c. dose. It is interesting that the second peak produced by alprazolam was route-independent in terms of peak time, magnitude and duration of the peak (fig. 5, upper panel). After the i.v. 1.25 mg/kg dose, there was no reinforced response in the 45-55 s bin at the 5-min time point, and the reinforcement rate remained low for up to 45 min, whereas for the s.c. 1.25 mg/kg dose the reinforcement rate started to recover after 15 min (fig. 5, lower panel). Therefore, because both curves were equal at the 150-min time point, the recovery between 45 and 150 min for the i.v. dose was faster than the s.c. dose. The shorter-response rate increases produced by s.c. alprazolam occurred at the onset and immediately after the maximum effects for the reinforcement rate. Owing to the rapidity of the i.v. dose effect, the onset transition phase was lacking, and thus the first peak did not occur.

View larger version (27K): [in this window] [in a new window]   Fig. 5.   Response rate-time profiles, expressed as % baseline (S.E.) after s.c. (n = 7) and i.v. (n = 4) administration of alprazolam (vehicle and 1.25 mg/kg). Upper panel, shorter-response rate; lower panel, reinforcement rate in the 45-55 s bin.

Pharmacodynamic Models

Shorter-response rate (IRT < 45 s): Stimulation-sedation model. In the hypothetical stimulation-sedation model, the parameters k1e_st and k1e_sd were both fixed at 0.0001 min¹, numeric values that have been of no consequence (Sheiner et al., 1979). The value of E_stmax was fixed at 800%. This experimentally reasonable value was chosen so that the maximal effect observed (565%) could be accommodated. E_sdmax was set equal to E_stmax (i.e., 800%), because the sedation was capable of totally negating the stimulatory effect so that the measured effect was approximately equal to E_o (base-line value = 100%).

View larger version (41K): [in this window] [in a new window]   Fig. 6.   Measured shorter-response rate, predicted stimulatory, sedative and resultant effects versus time with the proposed model after i.v. (1.25 mg/kg, n = 4) and s.c. (1.25, 4 and 7 mg/kg; n = 7) administration of alprazolam.

Reinforcement rate (IRT 45-55 s): Indirect response model. The effects of alprazolam on the reinforcement rate were described well in terms of delay in attaining the maximum effect and the recovery of the disruptive performance to base line by the indirect response model for the three s.c. alprazolam doses (fig. 7). Table 1 shows that the parameters were all estimated with a high degree of confidence, as indicated by low estimation errors. As before, the reference concentration, IC50, remained similar across the three s.c. doses (0.022-0.028 µg/ml), whereas both the production rate (K_in) and the Hill factor (i) varied by less than 2-fold. For the i.v. 1.25 mg/kg dose, the onset and the dissipation effects of alprazolam on reinforcement rate were faster than the s.c. 1.25 mg/kg dose (i.e., large i and K_out values, table 1 and fig. 7).

View larger version (26K): [in this window] [in a new window]   Fig. 7.   Measured reinforcement rate in the 45-55 s bin and predicted effect versus time with the proposed model after i.v. (1.25 mg/kg, n = 4) and s.c. (1.25, 4 and 7 mg/kg; n = 7) administration of alprazolam.

Predicted serum alprazolam concentration and its relation to shorter-response and reinforcement rates. Both the shorter-response and reinforcement rates remained low at a predicted serum concentration of approximately 0.025 µg/ml for the i.v. 1.25 mg/kg alprazolam dose (fig. 8). As the concentration subsequently decreased, the shorter-response rate increased yielding the second peak (predicted serum concentration, 0.019 µg/ml), after which the reinforcement rate recovered rapidly to base-line level. For the shorter-response rate, an initial clockwise hysteresis was evident for the two higher doses (s.c. 4-7 mg/kg) but not for the s.c. 1.25 mg/kg dose. It is interesting that the second peak for the shorter-response rate occurred at almost the same predicted serum alprazolam concentrations: 0.037, 0.043 and 0.045 µg/ml for s.c. 1.25, 4 and 7 mg/kg doses, respectively. At these concentrations, the reinforcement rate in the 45-55 s bin was also similar and ranged from 22 to 36% of the base-line level. The decreases in reinforcement rate in the 45-55 s bin correlated well with the predicted serum alprazolam concentration, except an initial lag was observed for the three s.c. doses. It is evident that reinforcement rate generally remained low until the appearance of the second peak, after which it rapidly and progressively recovered in a dose-related fashion for both routes of administration.

View larger version (36K): [in this window] [in a new window]   Fig. 8.   Measured shorter-response and reinforcement rates (% base line, mean) versus model predicted serum concentration after i.v. (1.25 mg/kg, n = 4) and s.c. (1.25, 4 and 7 mg/kg; n = 7) administration of alprazolam. Arrows indicate the time sequence.

	Discussion

Abstract Introduction Methods Results Discussion References

The two measures of DRL 45-s performance, the shorter-response rate and the reinforcement rate in the 45-55 sec bin, exhibited time- and dose-related changes, which were readily interpretable as functions of serum alprazolam concentration during 3-hr sessions. This study presents the first attempt to characterize the effects of alprazolam by use of a steady state base-line performance of contingency-controlled behavior in PK-PD modeling. The stimulation-sedation and the indirect models presented describe and predict the shorter-response and the reinforcement rate changes, respectively. The stimulation-sedation model accounts for the two peaks in the shorter-response rate after s.c. dosing. Therefore, we propose that alprazolam produced both stimulatory and sedative effects in a continuous but sequential fashion, which were low- and high-concentration effects as reflected by their respective EC50 values, approximately 0.09 and 0.18 µg/ml. Not only did the stimulatory effect endure longer with a smaller Hill factor, but its onset preceded the sedative effect. In comparison with the i.v. dose, for the s.c. alprazolam dose series the disappearance of the first peak in the shorter-response rate resulted from the slower onset of the sedative effect, rather than from other mechanisms, e.g., acute tolerance (fig. 5). The reinforcement rate had the lowest reference concentration with an IC50 of approximately 0.02 µg/ml, and was used as an index for evaluating the timing performance on the DRL 45-s schedule. It is sensitive to both the stimulatory and sedative effects, as the rate recovered rapidly to base-line level during the disappearance phase of the two effects (figs. 6 and 8). The model dissociates the behavioral components of stimulation and sedation in the DRL performance, which might serve as a useful screening function for drug development. For example, midazolam, a BZ agonist, is similar to alprazolam in that it has both the stimulatory and sedative components (Lau et al., unpublished data). Other agents, such as novel anxiolytic or hypnotic drugs, may exhibit primarily one or the other of the two components.

We used a 3-hr session based on the serum alprazolam concentration-time profiles to evaluate the onset, peak, and disappearance of alprazolam effects (fig. 2). Figure 3 shows that alprazolam increased the IRTs < 45 s and decreased those in the 45-55 s bin in a dose-related fashion. As a result, the shorter-response rate-time and reinforcement rate-time profiles were constructed for the investigation of the effects of alprazolam on DRL 45-s performance during 3-hr sessions (figs. 4 and 5). Put in behavioral terms, the decreases in reinforcement rate and the increases in the shorter-response rate produced by alprazolam may be attributed to the disruption of the discriminative stimuli determining the reinforced behavior and the sequential dependency phenomenon (Carter and Bruno, 1968; Farmer and Schoenfeld, 1964; Reynolds, 1964; Weiss et al., 1966; see the introduction). The reinforcement rate did not start its major recovery until after the appearance of the second peak of the shorter-response rate, which can be considered a transition phase during which reconditioning was occurring. The effects of the i.v. 1.25 mg/kg alprazolam dose identified that the second peak produced by alprazolam was not only route-independent but also independent of the first peak (fig. 5, upper panel). Thus, the disappearance of the first peak was not a result of acute tolerance.

Although effect-time profiles provide a better understanding of drug action than time-course data collapsed into a single point, integrating PK and PD offers more. PK-PD modeling not only relates the time course of drug concentration to the time course of pharmacological effect but also permits the prediction of the effects for other drug doses in the linear range. Consequently, various effect measures can be plotted against the same independent variable, predicted serum or effect-site drug concentration, to investigate the interplay between these measures. Furthermore, the pharmacological effects are defined by mathematical functions, rather than by the experimenter's descriptions, which facilitates the exploration of the possible mechanism(s) of drug action involved in the complex behavioral paradigm used. Put in PK-PD terms, the PD parameters define the effects of alprazolam on the two rates of responding; the second peak occurred when the predicted serum alprazolam concentration had decreased to 0.037 to 0.045 µg/ml for each of the s.c doses, after which the reinforcement rate rapidly and progressively recovered in a dose-related fashion (fig. 8). These results suggest that reconditioning depends on serum concentration, and hence is closely linked to PK; it occurred at twice the concentration of the IC50 value (table 1). Owing to the different durations of action of the four alprazolam doses, the interplay between the reinforcement rate and shorter-response rate shown in effect-concentration profiles (fig. 8) is more apparent than that shown in effect-time profiles (figs. 4 and 5). The stimulation-sedation model further suggests the coexistence of stimulation and sedation components for alprazolam, whereas the reinforcement rate defined by the indirect response model was an index for evaluating timing performance under the DRL 45-s schedule.

Although behavioral endpoints have been used widely for studying drug dose-effect relations in behavioral pharmacology, limited attention has been given to effect-time profiles and their relation to PK. These results, as well as our previous studies, demonstrated that the effect-time profile rather than the use of data temporally collapsed into a single point is the method of choice for investigating the effects of drugs on behavior, as it describes and reflects the on-going behavior and PK (Lau and Wang, 1996; Lau et al., 1996, 1997). Taking all these rationales together, a high alprazolam dose produces predominantly a sedative effect; but when it undergoes absorption and disposition, a stimulatory effect emerges whenever the serum alprazolam concentrations reach a level similar to that produced by a low dose. In turn, both kinds of effects were detected after the administration of a high dose. Thus, it is reasonable to assume that the effects of low and high BZ doses mentioned in the introduction (Burke et al., 1994; File and Pellow, 1985; Griffiths and Goudie, 1987) resulted from the effects of the low and high concentrations, which accounted for the observed stimulatory and sedative effects, respectively. Alprazolam produces both nonspecific increases in motor activity as well as anxiolytic effects (Barbarito et al., 1996; Hascoet and Bourin, 1977; Lopez et al., 1988); whether the effect of alprazolam on increases in short IRTs in the present study was caused by either one or both effects requires further clarification.

For the three s.c. doses, the increases in the shorter-response rate occurred both before the onset and after the offset of the sedative effect; whereas, the increase occurred only in the latter phase for the i.v. 1.25 mg/kg dose. This reveals that the stimulatory effect becomes visible only at lower serum alprazolam concentrations in comparison with the higher concentrations associated with the sedative effect. This coincides with the ascending and descending limbs of the alprazolam PK profile after s.c administration. After chronic BZ administration, tolerance develops rapidly to the sedative or depressant effect of high doses but does not develop to the stimulatory effect of low doses (File and Pellow, 1985; Flaherty et al., 1996; Griffiths and Goudie, 1987). In addition, repeated low-dose administration can even enhance the stimulatory effect (Sansone, 1979). To our knowledge, no mechanism has been proposed for these observations, hence our interest in promulgating the stimulation-sedation model. If, indeed, stimulatory and sedative effects are concurrently present and both exhibit sigmoidal Emax functions but are opposed components, then stimulation would become evident and progressively enhanced as tolerance to sedation developed.

If one uses the above rationale and considers that the second peak in the DRL performance represents the transition phase for recovery from the sedative effect, then it is perhaps not surprising that adverse "rebound" side effects are observed (e.g., early-morning insomnia) as special features during chronic BZ use in humans, intruding sooner and becoming stronger. Furthermore, the violent behavior associated with flunitrazepam ("Roches") reported recently may also be attributed to the stimulatory component of the drug (Wesson et al., 1996). The rebound period in humans resembles many aspects of the second stimulation peak in DRL performance. For example, behaviorally, it is the transient rebound (i.e., stimulatory or agitated) phase for returning to base line; pharmacokinetically, it is associated with decreasing BZ concentrations. Thus, the stimulation-sedation model and DRL performance may serve as a laboratory model for studying human rebound agitated behavior and tolerance.

Although BZs commonly are prescribed for chronic use, single dosing is also used in anesthesia, and in hypnotic and anxiolytic therapies. In single-dose PD studies, a delay is often observed between drug serum concentrations and drug effect. This so-called hysteresis is generally treated by assuming an effect compartment in an effect-link model (Sheiner et al., 1979), although other models, including indirect response models, also have been applied (Dayneka et al., 1993; Jusko and Ko, 1994). The decrease in reinforcement rate produced by alprazolam was best described by an indirect response model, because the peak effect (i.e., maximum inhibition) occurred during a longer period (5-45 min); the effect-link model requires that all dose levels produce a maximum effect at the same time (Dayneka et al., 1993). During model formulation, three other models were tested, an indirect response model incorporating stimulation of K_out (adequate description but higher AIC), an effect-link model linked to the central compartment (good description for individual doses, however large variation and higher AIC value) and an effect-link model linked to the peripheral compartment (this did not optimize). In humans, the delay to the onset of the effect has been observed with alprazolam and has been attributed to a distributional delay (Smith et al., 1984). However, no hysteresis was observed between midazolam blood concentrations and EEG effect in rats (Mandema et al., 1992). For the three s.c. doses in the present study, the IC50 for the reinforcement rate ranged from 0.022 to 0.028 µg/ml, which agreed with those values reported previously by using the same behavioral paradigm (Lau and Wang, 1996; Lau et al., 1997). For the i.v. 1.25 mg/kg dose, the system was more responsive, as indicated by the lower IC50 (0.012 µg/ml), the greater Hill factor (4.03) and the faster dissipation value (K_out 2.33 min¹) than the system for the s.c. doses (table 1).

For the shorter-response rate after s.c dosing, the initial proteresis (clockwise hysteresis) observed was attributable to the onset of the sedative effect. This can be seen by comparing it with the effect after the i.v. 1.25 mg/kg dose (fig. 8); many other mechanisms have been suggested, such as acute tolerance (Ekblom et al., 1993; Laurijssens and Greenblatt, 1996; Porchet et al., 1988). Modeling the effects of alprazolam on shorter-response rate was a more complex task because no simple function can simultaneously account for the two observed peaks. The stimulation-sedation model described the shorter-response rate by using two effect-link, sigmoidal Emax models representing different hypothetical sites but having actions opposite in direction (fig.1).

It is best to determine a drug dose-response relation under conditions where a preceding dose has no residual effect on the succeeding dose for both PK and PD studies. By using the steady state performance under a DRL 45-s schedule, we have found that no mutual interference (e.g., tolerance) occurred between doses for midazolam, alprazolam and caffeine when these doses were separated by 3 to 5 days (Lau et al., 1996, 1997, in press). Therefore, learning and experience do not play a role in the observed alprazolam effects even though the sequence of the route of administration was fixed for both the PK and PD studies. Furthermore, alprazolam PK was not altered by repeated alprazolam dosing separated by 3 to 5 days even in the presence of caffeine (Lau et al., 1997).

In conclusion, we have demonstrated, by using three PD models in the context of PK-PD modeling, that the two measures of DRL performance, the reinforcement and shorter-response rates, are valid, clinically relevant PD measures for the investigation of the effects of alprazolam. There were two serum alprazolam concentration-dependent peaks in the shorter-response rate for the s.c. doses, whereas only the second peak was observed for the i.v. 1.25 mg/kg dose. This dose helps to identify the first peak as the transition phase before the onset of the sedative effect and the second peak as a transient, rebound phase in the recovery from the sedative effect. The reinforcement rate is an index for evaluating the deficit in timing performance. Although the effect of alprazolam can be described in behavioral terms, PK-PD modeling not only outlines the performance and its relation to alprazolam serum concentration but also hypothesizes the coexistence of stimulation and sedation components for alprazolam. The stimulation-sedation model may help in delineating the possible mechanisms for the adverse rebound side effects and of tolerance observed in humans.