Emergence of asymmetry in evolution.

We investigate symmetry-breaking bifurcation patterns in evolution in the framework of adaptive dynamics (AD). We define weak and strong symmetry. The former applies for populations where only the simultaneous reflection of all individuals is an invariant transformation. The symmetry is strong in populations where reflection of some, but not all, individuals leaves the situation unchanged. We show that in case of weak symmetry evolutionary branching can lead to the emergence of two asymmetric variants, which are mirror images of each other, and the loss of the symmetric ancestor. We also show that in case of strong symmetry, evolutionary branching can occur into a symmetric and an asymmetric variant, both of which survive. The latter, asymmetric branching differs from the generic branching patterns of AD, which is always symmetric. We discuss biological examples for weak and strong symmetries and a specific model producing the new kind of branching.

Physiologically based pharmacokinetic model useful in prediction of the influence of species, dose, and exposure route on perchloroethylene pharmacokinetics.

The ability of a physiologically based pharmacokinetic (PBPK) model to predict the uptake and elimination of perchloroethylene (PCE) in venous blood was evaluated by comparison of model simulations with experimental data for two species, two routes of exposure, and three dosage levels. Unanesthetized male Sprague-Dawley rats and beagle dogs were administered 1, 3, or 10 mg PCE/kg body weight in polyethylene glycol 400 as a single bolus, either by gavage or by intraarterial (ia) injection. Serial blood samples were obtained from a jugular vein cannula for up to 96 h following dosing. The PCE concentrations were analyzed by headspace gas chromatography. For each dose and route of administration, terminal elimination half-lives in rats were shorter than in dogs, and areas under the blood concentration-time curve were smaller in rats than in dogs. Over a 10-fold range of doses, PCE blood levels in the rat were well predicted by the PBPK model following ia administration, and slightly underpredicted following oral administration. The PCE concentrations in dog blood were generally overpredicted, except for fairly precise predictions for the 3 mg/kg oral dose. These studies provide experimental evidence of the utility of the PBPK model for PCE in interspecies, route-to-route, and dose extrapolations.

Use of tissue disposition data from rats and dogs to determine species differences in input parameters for a physiological model for perchloroethylene.

Tissue disposition of perchloroethylene (PCE) was determined experimentally in two mammalian species of markedly different size in order to derive input parameters for the development of a physiologically based pharmacokinetic (PBPK) model, which could forecast the disposition of PCE in each species. Male Sprague-Dawley rats and male beagle dogs received a single bolus of 10 mg PCE/kg body wt in polyethylene glycol 400 by gavage. Serial samples of brain, liver, kidney, lung, heart, skeletal muscle, perirenal fat, and blood were taken for up to 72 hr following PCE administration. Blood and tissue PCE concentrations were analyzed using a gas chromatography headspace technique. Dogs exhibited considerably longer tissue and blood half-lives than did rats. The dogs also exhibited larger area under tissue concentration versus time curves for all tissues except the liver. Whole body clearance of PCE in the rat was greater than that in the dog. Model simulations indicated this could be attributed to more rapid and extensive PCE exhalation and metabolism by the rat. The in vivo blood:air partition coefficient determined for rats was similar to an in vitro value previously reported. In vivo tissue: blood partition coefficients, however, were 1.4 to 2.8 times greater than published in vitro values. The PCE in vivo blood:air partition coefficient for the dog was twice that of the rat, but tissue:blood partition coefficients were 1.5 to 3.0 times greater in the rat than in the dog. These results demonstrated the existence of significant differences in partition coefficients in two species commonly used in toxicity testing. The PBPK model was shown to have utility in predicting the impact of metabolism and exhalation on pharmacokinetics of PCE in different species of widely differing size.

Development of a physiologically based pharmacokinetic model for perchloroethylene using tissue concentration-time data.

The tissue disposition of perchloroethylene (PCE) was characterized experimentally in rats in order to (1) obtain input parameters from in vivo data for the development of a physiologically based pharmacokinetic (PBPK) model, and (2) use the PBPK model to predict the deposition of PCE in a variety of tissues following inhalation exposure. For the derivation of model input parameters, male Sprague-Dawley rats received a single bolus of 10 mg PCE/kg body wt in polyethylene glycol 400 by ia injection through an indwelling carotid arterial cannula. Other male Sprague-Dawley rats inhaled 500 ppm PCE for 2 hr in dynamic exposure inhalation chambers. Serial samples of brain, liver, kidney, lung, heart, skeletal muscle, perirenal fat, and blood were taken for up to 72 hr following ia injection, during the 2-hr inhalation exposure, and for up to 72 hr postexposure. Blood and tissue PCE concentrations were analyzed using a gas chromatography headspace technique. Following ia administration, the tissues exhibited similar terminal elimination half-lives (t1/2). As comparable tissue t1/2 are consistent with a blood-flow-limited model, tissue:blood partition coefficients were calculated for noneliminating compartments by division of the area under the tissue concentration-time curve (AUC) by the blood AUC. Liver PCE concentration versus time data were employed in the calculation of in vivo metabolic rate constants. A PBPK model was developed using these parameters derived from the ia data set and used to predict tissue PCE concentrations during and following PCE inhalation. Predicted tissue levels were in close agreement with the levels measured over time in the seven tissues and in blood. Tissue concentration-time data can thus provide valuable input for parameter estimation and for validation of PBPK model simulations, as long as independent in vivo data sets are used for each step.

Use of a physiologically based model to predict systemic uptake and respiratory elimination of perchloroethylene.

The pharmacokinetics of inhaled perchloroethylene (PCE) were studied in male Sprague-Dawley rats to characterize the pulmonary absorption and elimination of the volatile organic chemical (VOC). The direct measurements of the time course of PCE in the blood and breath were used to evaluate the ability of a physiologically based pharmacokinetic (PBPK) model to predict systemic uptake and elimination of PCE. Fifty or 500 ppm PCE was inhaled for 2 hr through a miniaturized one-way breathing valve by unanesthetized male Sprague-Dawley rats of 325-375 g. Serial samples of the inhaled and exhaled breath streams, as well as arterial blood, were collected during and following PCE inhalation and analyzed by headspace gas chromatography. PCE-exhaled breath concentrations increased rapidly to near steady state (i.e., within 20 min) and were directly proportional to the inhaled concentration. Uptake of PCE into the blood was also rapid, but blood levels continued to increase progressively over the course of the 2-hr exposure at both exposure levels. Cumulative uptake, or total absorbed dose, was not proportional to the exposure level. A PBPK model was developed from in vivo parameters determined from tissue concentration-time data in a companion ia study (Dallas et al., 1994, Toxicol. Appl. Pharmacol. 128, 50-59). PCE concentrations in the blood and exhaled breath during and following PCE inhalation were well predicted by the PBPK model. Despite species differences in blood:air and lung:air partition coefficients, the model was used to account for similar levels of PCE and other VOCs in the expired air of rats and humans. The model also accurately simulated percentage uptake and cumulative uptake of PCE over time. The model's ability to predict systemically absorbed doses of PCE under a variety of exposure scenarios should be useful in assessment of risks in occupational and environmental settings.

Targeting anticancer drugs to the brain: II. Physiological pharmacokinetic model of oxantrazole following intraarterial administration to rat glioma-2 (RG-2) bearing rats.

The disposition of the anticancer drug oxantrazole (OX) was characterized in rats bearing the rat glioma-2 (RG-2) brain tumor. Following intraarterial administration of 3 mg/kg of OX, serial sacrifices were completed from 5 min to 5 hr after administration. Blood and tissue samples collected at the time of sacrifice were processed and measured for OX concentrations by HPLC. The kidney had the greatest affinity for OX with the Cmax being 40.6 micrograms/ml at 15 min after administration. OX concentrations in brain tumor were higher than in normal right and left brain hemispheres, and consistent with enhanced drug blood-tumor barrier (BTB) permeability seen in experimental models for brain tumors. Observed heart, liver, lung, and spleen OX concentrations were similar, ranging from approximately 2 micrograms/ml to 20 micrograms/ml. A unique technique was used to develop a global physiological pharmacokinetic model for OX. A hybrid or forcing function method was used to estimate individual tissue compartment biochemical parameters (i.e., partition and mass transfer coefficients). A log likelihood optimization scheme was used to determine the best model structure and parameter sets for each tissue. Most tissues required a 3-subcompartment structure to adequately describe the observed data. The global model was then reconstructed with an arterial blood and rest of body compartments that provided predicted OX concentrations in agreement with the data. The model development strategy provides a systematic approach to physiological pharmacokinetic model development.

Phenomenological kinetics of pharmacological response.

The evaluation and quantitative analysis of the time course of drug response are difficult tasks even in uncomplicated fields of pharmacology. In an attempt to assist the analysis of the pharmacological effect, a procedure is presented which incorporates widely used intuitive-experimental practices of evaluation, and descriptive kinetic functions. The aim is to find a simple function which can approximate the time course of the response curves at different doses. Having estimated the values of parameters for each curve, valuable information can be drawn by examining the dose-parameter relationships. The method is illustrated by one possible evaluation and interpretation of the blood pressure-time curves of a drug.

Mathematical description of the interaction between prostaglandins and calcium.

The interpretation of the biological action of prostaglandins is very difficult because the shape of the dose-response curves in different assays is often unusual. Horrobin has attempted to explain these unusual curves by supposing special interactions between Ca and the prostaglandin receptors. This paper gives a mathematical description of his theoretical models. The results of computer simulation based on these models were in good agreement with the reported experimental observations.

An extended hypothetical theory of the dose-response relations in pharmacology.

The authors present an extended version of Clark's and Ariëns's classical theory that enables the interpretation and quantitative characterization of dose-response curves which are not in accordance with classical theory. Being supported by the chemical receptor theory, the new model expands its applicability to two or multi-receptor and multi-effect systems. Mathematical interpretation of the model is given in this paper.

The fate of drotaverine-acephyllinate in rat and man. II. Human pharmacokinetics of drotaverine-14C-acephyllinate.

Pharmacokinetics of Drotaverine-Acephyllinate, Chinoin was investigated in seven male volunteers using 14C labelled drug. Drotaverine-Acephyllinate was administered at a 100 mg single oral dose. Measurements of total radioactivity showed that the drug was absorbed completely and was eliminated by renal and biliary routes. Within 72 hours 39.9 +/- 9.9% and 47.1 +/- 4.9% of the dose were recovered in the urine and faeces respectively. Experimental results were interpreted on the basis of a complex linear compartment model. The structural identifiability of the model was proved by computer analysis, and the pharmacokinetic parameters were determined.

A calculator package for pharmacokinetic application.

A calculator program package is given for the computation of the parameters of two different pharmacokinetic models: the 'one compartment open model' with first order absorption, and the 'two compartment open model' with rapid intravenous injection, using the peeling method. If parameters are known, simulation of these systems can be done for single and repetitive doses. The package includes an area under curve (AUC) program for the evaluation of clearance. The algorithms were applied for TI 58,59 and HP 97 calculators and they can be widely used in clinical practice.

A computer program for the analysis of structural identifiability and equivalence of linear compartmental models.

A FORTRAN program based on the sufficient and necessary algebraic condition for structural identifiability is presented. In the case of an unidentifiable model the program generates all identifiable submodels that are structurally equivalent to the original model in the given input--output experiment. The parametrization vector of the model may include first-order and zero-order transport rate coefficients, unknown distribution volumes and initial conditions, as well as unknown elements of input and output matrices. Any a priori constraint imposed upon the parameters may be taken into account. An attempt is made to reduce input data requirements preserving generality of the program.