INTRODUCTION

TOP ABSTRACT INTRODUCTION SET-POINT MODEL FOR 5-HT1A... EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX REFERENCES

IT IS WELL ESTABLISHED that the 5-hydroxytryptamine (HT)_1A receptor plays a role in the physiological regulation of body temperature (40, 54). Consequently, the 5-HT_1A agonists, which are used therapeutically as antidepressants and antianxiety drugs (16), cause hypothermia (4, 20, 27, 50). For the prototype 5-HT_1A agonists it has been demonstrated that this hypothermic response is indeed mediated specifically through the 5-HT_1A receptor because it can be blocked in a dose-dependent manner by the selective, competitive 5-HT_1A receptor antagonist WAY-100,635 (14, 17) and not by antagonists for other G protein-coupled receptors (34).

In a number of investigations, the time course of the hypothermic response after administration of 5-HT_1A receptor agonists has been studied in detail. In these studies, complex effect vs. time patterns have been observed, suggesting the involvement of homeostatic control mechanisms (51, 54). So far, however, no mathematical models have been developed to characterize these complex time profiles of the hypothermic response in a strict quantitative manner. Specifically, there have been no attempts to link existing temperature regulation models (25, 49) to pharmacokinetic models describing the time course of the drug concentration in the body.

In recent years important progress has been made in the area of integrated pharmacokinetic-pharmacodynamic (PK-PD) modeling (11). PK-PD modeling has even allowed estimation of the in vivo affinity and intrinsic efficacy of drugs (43-46). Specifically, models have been proposed that allow for a delay between drug concentration and the pharmacological response (15, 19, 30). So far, however, very few of these models incorporate complex regulatory behavior (7, 18, 48). In this report we propose a new physiological PK-PD model, in which 5-HT_1A receptor agonists exert their effect on body temperature by lowering of the set-point temperature. The model was applied to characterize hypothermic response vs. time profiles after administration of different doses of the reference 5-HT_1A receptor agonists R- and S-8-OH-DPAT. It is shown that differences in the observed hypothermic response profiles can be explained by differences in in vivo intrinsic efficacy between the two compounds.

Glossary

a	Rate of change in the set-point signal (min1 · °C1)
AIC	Akaike Information Criterion
C	Drug concentration in the central compartment (ng/ml)
CL	Clearance of the drug from the body (ml/min)
CL2, CL3	Intercompartmental clearance (ml/min)
	Residual error
	Interindividual variation
	Amplification of the set-point signal
I	Identity matrix
kin	Zeroth-order rate constant associated with the production of body heat (°C/min)
kout	First-order rate constant associated with the cooling of the body (min1)
	Eigenvalue
M	Jacobian matrix
n	Slope factor
P	Population parameter
Pi	Individual's parameter
R-7-OH-DPAT	R-(+)-7-hydroxy-2-(di-n-propylamino) tetralin
R-8-OH-DPAT	R-(+)-8-hydroxy-2-(di-n-propylamino) tetralin
S-8-OH-DPAT	S-()-8-hydroxy-2-(di-n-propylamino) tetralin
SC50	Concentration at 50% of maximum stimulation
Smax	Maximum stimulation the drug can produce
T	Core body temperature (°C)
	Fixed effect
min	Population-averaged minimal temperature (°C)
TSP	Individual's set-point temperature (°C)
V1	Volume of distribution of the central compartment (ml)
V2, V3	Volume of distribution of the peripheral compartments (ml)
WAY-100,635	N-[2-[4-(2-methoxyphenyl)-1-piperazinyl] ethyl]-N-2-pyridinyl-cyclohexanecarboxamide
X	Set-point signal

	SET-POINT MODEL FOR 5-HT1A AGONIST-INDUCED HYPOTHERMIA

TOP ABSTRACT INTRODUCTION SET-POINT MODEL FOR 5-HT1A... EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The proposed set-point model for the effect of 5-HT_1A agonists on body temperature is shown in Fig. 1. As the agonist binds to its receptor, a stimulus is generated. This stimulus in turn drives physiological processes that lower the temperature. This stimulus, which is determined by the drug-receptor interaction and hence the drug's affinity and efficacy, can be described by a sigmoidal function f(C)

(1)

where S_max represents the maximum stimulus the drug can produce, C is the drug concentration, SC₅₀ is the concentration required to produce 50% of the maximum stimulus, and n is a slope factor, which determines the steepness of the curve. As the drug concentration changes with time, the stimulus changes as well. As the stimulus S is assumed to be inhibitory, it is defined as S = 1  f(C). The behavior of the concentration C and the corresponding stimulus S is shown in Fig. 2, A and B. This stimulus induces the hypothermic response. The changing drug concentrations therefore govern the first time scale of the model.

View larger version (11K): [in this window] [in a new window]   Fig. 1.   Proposed full model for describing 5-HT1A-receptor mediated hypothermia. The model is based on the concepts of the indirect physiological response model (15) and takes into account rate constants associated with the warming of the body (kin) and cooling of the body (kout). The indirect physiological response model is combined with the thermostat-like regulation of body temperature, in which body temperature (T) is compared with a fixed reference or set-point temperature (TSP) at rate a, generating a set-point signal X. The extent to which the set-point value decreases is a function of drug concentration f(C), which decreases X by the amplification factor .

View larger version (18K): [in this window] [in a new window]   Fig. 2.   Graphic representation of the behavior of the models applied for a low dose (solid line) and a high dose (dashed line). A: profile of the 3-compartment pharmacokinetic model (Eq. 1). B: behavior of the stimulus equation in time [1  f(C); Eq. 1] for the concentration vs. time profiles as shown in A. C: phase plot of the set-point model, clearly showing an oscillation for the low dose and not for the high dose. D: time-effect profiles of the set-point model (Eq. 6) following the input from C. Note that the temperature has been rescaled. The inputs used were CL, 22.8 ml/min; CL2, 13.9 ml/min, CL3, 69.2 ml/min, V1, 126 ml; V2, 2,090 ml; V3, 603 ml; kin, 0.5°C/min; TSP, 38°C; A, 0.01 min1; , 10; SC50, 25 ng/ml; Smax, 1; n, 1. For other definitions, see Glossary.

The second time scale on which the model operates is governed by physiological principles. The model that describes the hypothermic response utilizes the concepts of the indirect physiological response model as proposed by Dayneka et al. (15) and Gabrielsson et al. (19). In this model the change in temperature (T) is described as an indirect response to either the inhibition of the production of body heat or the stimulation of its loss (Eq. 2)

(2)

Here k_in represents the zeroth-order rate constant associated with the warming of the body and k_out represents a first-order rate constant associated with the cooling of the body.

The indirect physiological response model is combined with the thermostat-like regulation of body temperature. This regulation is implemented as a continuous process in which the body temperature is compared with a reference or set-point temperature (T_SP) (Fig. 1). It is accepted that 5-HT_1A agonists elicit hypothermia by decreasing the value of T_SP, and hence T_SP depends on the drug concentration C: T_SP = T_SP(C). It is assumed that T_SP is controlled by the drug concentration C through Eq. 3

(3)

where T₀ is the set-point value in the absence of any drug: T₀ = T_SP(0). Combining the indirect physiological response model with the thermostat-like regulation therefore yields

(4)

in which X denotes the thermostat signal. In the model as described in Eq. 4, the change in X is driven by the difference between the body temperature T and T_SP on a time scale that is governed by a. Hence, when the set-point value is lowered, the body temperature is perceived as too high and X is lowered. To relate this decreasing signal to the drop in body temperature, an effector function X was designed, in which  determines the amplification. Raising this function to the loss term k_out · T therefore facilitates the loss of heat. In Eq. 4, body temperature and set-point temperature are interdependent, and a feedback loop is created that can give rise to oscillatory behavior, as will be shown later. When the body temperature is at its initial set point, the no-drug situation, the equilibrium set-point signal X₀ can be defined in terms of k_in, k_out, , and T₀ (see APPENDIX).

With four system parameters to be estimated, the degree of parameterization in Eq. 4 is high and thus may lead to parameter unidentifiability. It can be shown that one parameter can be eliminated by combining parameters into dimensionless quantities. Thus, we set

(5)

where X₀ is the reference signal of X when no drug is present and T₀ has been defined in Eq. 3. For these dimensionless variables, we obtain the system

(6)

where

(7)

are the new dimensionless parameters. For the derivation of the new system, refer to APPENDIX. After reparameterization, the number of physiological parameters has been reduced from four (a, k_in, k_out, and ) in Eq. 4 to three (A, B, and ) in Eq. 6, and as a result, parameter unidentifiability has been abolished.

Under certain conditions, Eqs. 4 and 6 produce damped oscillations, around the equilibrium point (, ), defined by

(8)

The local behavior near this point can be characterized by the eigenvalues of the Jacobian matrix M, fromwhich the discriminant D can be determined (see APPENDIX). For Eq. 6 the discriminant becomes

(9)

When D < 0, the eigenvalues are complex, and the system of differential equations will exhibit oscillatory behavior. When D  0, which is the case for a relatively large stimulus, the eigenvalues are real and the system of differential equations will be "overdamped." In both cases the eigenvalues have a negative real part, so that (, ) is asymptotically stable. The behavior of the model is depicted in a phase plot (Fig. 2C) for low and high doses. In this picture, as the temperature starts to drop, the curves are transversed from the point (x, y) = (1,1) in a clockwise fashion to the slowly moving equilibrium points (, ). This behavior results in temperature-time profiles as depicted in Fig. 2D. The complex behavior of the model is further depicted in a three-dimensional graph in Fig. 3.

View larger version (15K): [in this window] [in a new window]   Fig. 3.   Three-dimensional representation of the behavior of the models applied for a low dose (solid line) and a high dose (dashed line) in the temperature-set point-time scene. Inputs used were the same as for Fig. 2. The drop lines or curtain is added for clarity. The model predicts oscillatory behavior particularly for the low-dose administrations.

As the drug concentrations will be known as time progresses, substituting the expressions of Eq. 8 into Eq. 6 gives a relationship that predicts the qualitative behavior of the model at different parameter combinations. Initial estimates of the model were further obtained with the use of simulations using different parameter values, an overview of which can be found in Fig. 4. It turns out that the model predicts the behavior as described above when S_max approaches or equals 1, whereas it predicts an oscillation at all doses for S_max between 0 and 1, i.e., partial agonist. This concept was implemented in Eq. 6 by defining the ranges of S_max and the dependent variable y. In the model the S_max value of a full agonist equals 1 and that of an antagonist equals 0. The procedure for calculating the redefined y values on the basis of the observed temperatures is represented in Eq. 10

(10)

In Eq. 10, T is the temperature at time t, T_SP is the average temperature from the hour before drug administration, and _min is the average minimal temperature of the individuals receiving a high dose of the full agonists.

View larger version (21K): [in this window] [in a new window]   Fig. 4.   Behavior of the model for different values of the model parameters. The middle line is simulated with the same pharmacokinetics as the low dose in Fig. 1 and kin = 1°C/min, A = 0.02 min1,  = 2, SC50 = 50 ng/ml, Smax = 1, and n = 1. The lines beside the middle line are simulated with the values as represented in the graph, where the greatest decrease is caused by the greatest value, except for kin, where it is the lowest value.

	EXPERIMENTAL METHODS

TOP ABSTRACT INTRODUCTION SET-POINT MODEL FOR 5-HT1A... EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Experiments were preformed on male Wistar rats (Broekman BV, Someren, The Netherlands) weighing 297 ± 3.4 g (mean ± SE, n = 68) and were approved by the Leiden University Ethics Committee. The animals were housed in standard plastic cages (6 per cage before surgery and individually after surgery). They were kept in a room with a normal 12:12-h light-dark cycle (lights on at 7:00 AM and lights off at 7:00 PM) and a temperature of 21°C. During the light period, a radio was on for background noise. Acidified water and food (laboratory chow, Hope Farms, Woerden, The Netherlands) was provided ad libitum before the experiment.

Surgical Procedure

Experimental Protocol

Dosage regimen. Eight days after surgery, the experiments were performed. Rats received different doses in different infusion rates of R-8-OH-DPAT or S-8-OH-DPAT. For R-8-OH-DPAT, bolus infusions of 1 mg/kg in 15 min (n = 7), 3 mg/kg in 5 min (n = 7), 3 mg/kg in 15 min (n = 5), and 3 mg/kg in 30 min (n = 6) were given. In addition, a computer-controlled infusion was administered over 6 h, by which a stable concentration of 160 ng/ml was maintained in blood (n = 6). For S-8-OH-DPAT, infusions of 5 mg/kg (n = 6) and 15 mg/kg (n = 6) in 15 min were administered. Twenty-four rats received vehicle treatments, in which an equivalent amount of saline was infused.

Blood sampling. Approximately 15-18 serial blood samples of 50 µl were taken according to a fixed time schedule to determine the concentration vs. time profile of the drug. The exact amount was measured with a capillary (Servoprax, Wesel, Germany) and transferred into a glass centrifuge tube containing 400 µl of purified water for hemolysis. During the experiment the samples were kept on ice. After the experiment, samples were stored at 20°C pending analysis.

Data Acquisition

Temperature measurements. To measure the body temperature of the rat, a telemetric system (Physiotel Telemetry System, DSI) was used. The transmitter measured the body temperature every 30 s for a 2-s period and signaled it to a receiver (Physiotel Receiver, model RPC-1, DSI). The receiver was connected to the computer through a BCM 100 consolidation matrix (DSI). The computer processed the data and visualized the temperature profiles [Dataquest LabPro software (DSI) running under OS/2 Warp, IBM] as it did for room temperature (C10T temperature adapter, DSI).

HPLC analysis of R- and S-8-OH-DPAT. The blood concentrations of R- and S-8-OH-DPAT were assayed by an enantioselective HPLC method as described previously (55). Briefly, detection with the HPLC system was obtained using an electrochemical detector (DECADE, Antec Leyden, Zoeterwoude, The Netherlands) operating in DC mode at 0.63 V, at a temperature of 30°C. Chromatography was performed on a Chiralcel OD-R (Diacel Chemical Industries, Tokyo, Japan). The mobile phase was a mixture of 50 mM phosphate buffer (pH 5.5)-acetonitrile (80/20, vol/vol) and contained a total concentration of 5 mM KCl and 20 mg/l of EDTA. The analytes were extracted from blood using a liquid-liquid cleanup step and isolated on Bakerbond solid phase extraction NARC-2 columns (Baker, Phillipsburg, NJ). Calibration curves in the concentration range of 0.1-5000 ng/ml were analyzed with each run, and peak area ratios of analyte over internal standard [R-(+)-7-hydroxy-2-(di-n-propylamino)tetralin (R-7-OH-DPAT)] were calculated. Using 50 µl of blood, the limit of detection was 0.5 ng/ml.

Chemicals. R-8-OH-DPAT, S-8-OH-DPAT, and R-7-OH-DPAT were purchased from Research Biochemicals International. All other chemicals used were of analytical grade (Baker, Deventer, The Netherlands).

Data Analysis

(11)

(12)

(13)

	RESULTS

TOP ABSTRACT INTRODUCTION SET-POINT MODEL FOR 5-HT1A... EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The average effect-time profiles for the hypothermic response after administration of vehicle, R-8-OH-DPAT, and S-8-OH-DPAT are represented in Fig. 5. In the control group (Fig. 5A), rats received the amount of saline equivalent to the drug infusions used and were subjected to blood sampling. They showed no hypothermic response. The administration of R-8-OH-DPAT resulted in a maximum decrease in temperature of 4 ± 0.3°C at 40 to 60 min (Fig. 5, B and D). After an infusion of R-8-OH-DPAT of 1 mg/kg in 5 min, a complex effect vs. time profile was observed. The body temperature quickly rose after reaching its minimum; subsequently, a plateau phase was observed, after which temperature returned to baseline. For the higher doses (3 mg/kg in 5, 15, and 30 min) the plateau phase was not observed, and the body temperature returned to baseline more gradually. In the experiments in which the R-8-OH-DPAT concentration was maintained at a concentration of 160 ng/ml for 6 h, a similar plateau phase was observed, and as the infusion was turned off, the body temperature returned to baseline in a similar fashion.

View larger version (27K): [in this window] [in a new window]   Fig. 5.   Average temperature-time profiles (±SE) for vehicle treatments (A; n = 24); for R-8-OH-DPAT regular infusions [B: infusion 1, 1 mg/kg in 5 min (n = 7); infusion 2, 3 mg/kg in 5 min (n = 7); infusion 3, 3 mg/kg in 15 min (n = 5), and infusion 4, 3 mg/kg in 30 min (n = 6)]; for S-8-OH-DPAT infusions [C: infusion 1, 5 mg/kg in 15 min (n = 6) and infusion 2, 15 mg/kg in 15 min (n = 6)]; and for computer-controlled infusions of R-8-OH-DPAT (D), where the concentration was clamped at 160 ng/ml in blood (n = 6). All infusions started at t = 0; horizontal bars represent duration of the infusion.

On administration of S-8-OH-DPAT, a maximum decrease in body temperature of 3.2 ± 0.2°C was observed within 40-60 min (Fig. 5C). For S-8-OH-DPAT a plateau phase was observed, such as with the low dose of R-8-OH-DPAT, before returning to baseline for both infusions (5 and 15 mg/kg in 15 min).

Pharmacokinetics

View larger version (30K): [in this window] [in a new window]   Fig. 6.   Pharmacokinetic profiles for R-8-OH-DPAT regular infusions [1 mg/kg in 5 min (n = 7), 3 mg/kg in 5 min (n = 7), 3 mg/kg in 15 min (n = 5), and 3 mg/kg in 30 min (n = 6)] and the profiles (n = 6) of the computer-controlled infusion (160 ng/ml for 6 h). Both the individually measured profiles (dashed lines with markers) and the population prediction (thick line) are represented. Horizontal bars represent duration of infusion.

View larger version (22K): [in this window] [in a new window]   Fig. 7.   Pharmacokinetic profiles for S-8-OH-DPAT regular infusions: 15 mg/kg in 15 min (A; n = 6) and 5 mg/kg in 15 min (B; n = 6). Both the individually measured profiles (thin lines with markers) and the population prediction (thick line) are represented.

Fitting the Set-Point Model

View larger version (38K): [in this window] [in a new window]   Fig. 8.   Selected representative fits of different doses and infusions of R- and S-8-OH-DPAT. Open circles represent measured body temperature, solid line represents individual prediction, and dashed line represents population prediction. Infusions started at t = 60.

	DISCUSSION

TOP ABSTRACT INTRODUCTION SET-POINT MODEL FOR 5-HT1A... EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Development of the Set-Point Model

To characterize 5-HT_1A-agonist-induced hypothermia, we have developed a mathematical model that describes the hypothermic effect on the basis of the concept of a set point (8, 12, 54) and a general physiological response model (15, 19, 30). The model developed is able to reproduce the observed complex effect vs. time profile with regard to both the delay relative to the maximal drug concentration and the plateau phase. It appears that the plateau phase originates from damped oscillations that occur around the equilibrium point on returning to baseline, when the model is not fully "pushed" into the maximal effect. When the model is fully pushed into its maximal effect, such as is the case for a relatively high dose of a full agonist, the system becomes overdamped, thereby losing its oscillatory behavior. Hence, the observed plateau phase is an intrinsic part of the regulatory mechanism related to the oscillatory behavior found in many regulatory systems (22, 31).

Because the model as represented by Eq. 4 is overparameterized, the model was simplified by introducing dimensionless quantities. Such operation does not change the behavior of the model but merely reduces the parameters that are correlated. One major drawback of this approach is, however, that the parameters become difficult to interpret. On the other hand, a major advantage is that it becomes possible to estimate the parameters with a higher degree of certainty. To fully utilize the properties of the model, the temperature data were rescaled as well. This was done under the assumption that R-8-OH-DPAT is the fullest agonist and that the maximal temperature decrease observed was indeed the maximum. Despite the fact that it is well known that temperature is regulated within a narrow range, it has been shown that when the body temperature does drop below approximately 4-4.5°C below its homeostatic temperature, either very long recovery times are observed (>10 h) or the animals die. Examples of such experiments include administration of the adenosine agonist 5'-(N-ethylcarboxamido)adenosine and high but nonlethal doses of pentobarbital or clozapine (unpublished results). It is therefore reasonable to assume that the absolute drop as observed with R-8-OH-DPAT is the absolute maximum for the range in which the set-point system operates.

Because it is known from both in vitro and in vivo data that R- and S-8-OH-DPAT are, respectively, full and partial agonists for the hypothalamic 5-HT_1A receptor (14) and behave as such for the hypothermic response (24), we were interested in estimating the intrinsic activity and potency of these compounds on the basis of our model. Despite the fact that it has been suggested that the hypothermic effect of S-8-OH-DPAT is mediated via the dopamine D₂ receptor (52), we have not been able to reproduce this result and were able to block the S-8-OH-DPAT-mediated hypothermic effect using the selective 5-HT_1A receptor antagonist WAY-100,635 (results not shown). Furthermore, we could not block the S-8-OH-DPAT-mediated response using the a-selective dopamine receptor antagonist haloperidol (results not shown). Finally, we were unable to block an effective dose of the selective dopamine D₃ receptor agonist R-7-OH-DPAT, which does induce a hypothermic response in our studies (results not shown). These findings show that the observed hypothermic response after S-8-OH-DPAT is mediated exclusively through the 5-HT_1A receptor.

Fitting the Set-Point Model

General Conclusions

View larger version (23K): [in this window] [in a new window]   Fig. 9.   Concentration-effect curve for R-8-OH-DPAT (full agonist; A) and S-8-OH-DPAT (partial agonist; B). The curves are based on the pharmacodynamic parameters obtained (thin lines represent individually predicted curves). Error bars refer to the interindividual variance, ±[(%interindividual variation/100) × SC50 or Smax.

Perspectives