Minimal models of multi-site ligand-binding kinetics

Mathematical models based on the current understanding of co-operativity in ligand binding to the (macro) molecule and relating the dose-response (saturation) curve of the (macro) molecule ligation to intrinsic dissociation constants characterizing the affinities of ligand for binding sites of both unliganded and partly liganded (macro) molecule have been developed. The simplified models disregarding the structural properties and considerations concerning conformational changes of the (macro) molecule retain the ability to yield sigmoid curves of ligand binding and reflect the co-operativity. Model 1 contains only three parameters, parameter κ (a multiplier characterising the change in the affinity) reflects also the existence and type of co-operativity of ligand binding: κ<1 corresponds to positive co-operativity, κ>1 to the negative and κ=1 to the absence of any co-operativity. Model 2 contains an extra parameter, ω, equilibrium constant for the T₀↔R₀ transition but fails to produce dose-response, which would suggest negative co-operativity. For any fixed n>1, the deviation of the dose-response (saturation) curve from the Henri hyperbola depends either solely on parameter κ (Model 1) or also on parameter ω (Model 2). The (macro) molecule being a receptor, both models yield a diversity of dose-response curves due to possible variety of efficacies of the (macro) molecule. The models may be considered as extensions of the Henri model: in case the dissociation constants remain unchanged, the proposed models are reduced to the latter.     

A computer simulation of aggregated phytochrome photoconversion

In order to check the relevance of possible phytochrome aggregation forms for the diversity of action spectra and dose-response curves for light sensing by plants, a model for phytochrome photoconversion was produced for different aggregates. Under saturating light treatments, a computer simulation of dimer and aggregated dimer (tetramers and hexamers) photoconversion provided similar compositions of various aggregates in red and green light, which differed from blue and far-red light. These aggregates could account for the variable action spectra only if the nature of the primary transducing components is taken into account. The initial kinetics of aggregated phytochrome appear to be slower in comparison to the monomeric form, and there were transient peaks of certain aggregates in red and green light. A single peak occurred under blue light, but not in far-red, only if dimers are aggregated into tetramers and hexamers. This finding suggests that the initial kinetics of aggregated phytochrome are not sufficient to account for the variable dose-response curves in light-mediated responses by plants, so again the feature of signal transduction components may play a decisive role.     

The dependence of enzyme activity on temperature: determination and validation of parameters

Traditionally, the dependence of enzyme activity on temperature has been described by a model consisting of two processes: the catalytic reaction defined by DeltaG(Dagger)(cat), and irreversible inactivation defined by DeltaG(Dagger)(inact). However, such a model does not account for the observed temperature-dependent behaviour of enzymes, and a new model has been developed and validated. This model (the Equilibrium Model) describes a new mechanism by which enzymes lose activity at high temperatures, by including an inactive form of the enzyme (E(inact)) that is in reversible equilibrium with the active form (E(act)); it is the inactive form that undergoes irreversible thermal inactivation to the thermally denatured state. This equilibrium is described by an equilibrium constant whose temperature-dependence is characterized in terms of the enthalpy of the equilibrium, DeltaH(eq), and a new thermal parameter, T(eq), which is the temperature at which the concentrations of E(act) and E(inact) are equal; T(eq) may therefore be regarded as the thermal equivalent of K(m). Characterization of an enzyme with respect to its temperature-dependent behaviour must therefore include a determination of these intrinsic properties. The Equilibrium Model has major implications for enzymology, biotechnology and understanding the evolution of enzymes. The present study presents a new direct data-fitting method based on fitting progress curves directly to the Equilibrium Model, and assesses the robustness of this procedure and the effect of assay data on the accurate determination of T(eq) and its associated parameters. It also describes simpler experimental methods for their determination than have been previously available, including those required for the application of the Equilibrium Model to non-ideal enzyme reactions.     

Receptor-agonist interactions in service-theoretic perspective, effects of molecular timing on the shape of dose-response curves

Service-theoretic concepts and methods, widely used in other fields (e.g., telecommunication and operations research), are useful also in a biochemical setting because the treatment of biocatalysts (enzymes, receptors) as servers and their ligands as customers, based on the established formal methods of service or queuing theory, may lead to insights and results unobtainable by conventional, mass-action-law-based theories. In this article, we apply the service-theoretic approach to receptor-agonist systems and show how by changing the stochastic time pattern of "operationally relevant" point events (e.g., instants of agonist arrival, instants of post-climax agonist departure) a great variety of dose-response curves may be generated, even in very simple reaction schemes, which, according to mass action kinetics, invariably lead to hyperbolic r(A) curves (r and A stand for response and agonist concentration, respectively). The molecular timing inherent to a hyperbolic response system is not optimal: for instance, at the agonist concentration A(50), half of the agonist molecules are rejected ("lost") because of unfortunate timing of the arrival events. The fraction of lost arrivers can be diminished considerably if the arrivals are better timed: "sub-Poisson" arrivals improve the timing and, thus, convert hyperbolic r(A) curves into "lifted" nonhyperbolic ones. Conversely, "super-Poisson" arrivals make the non-optimal timing in hyperbolic response systems even worse and, thus, convert hyperbolic r(A) curves into "depressed" nonhyperbolic ones. Furthermore, under special timing conditions, nonhyperbolic r(A) curves can be generated, which are partly lifted, partly depressed relative to the reference hyperbola, and which resemble in shape well-known nonhyperbolic forms of enzyme and receptor kinetics (negatively cooperative, positively cooperative, and sigmoidal kinetics). In addition unusual (undulatory and sawtooth-like) r(A) curves can be generated solely by changing the temporal pattern of arrival and service completion instants. Virtually any shape of dose-response curves may be obtained by allowing for probability distributions whose characteristic shape varies with their mean; we call such distributions "variomorphic" and apply them to the arrival process of agonist molecules.     

Flux detectors versus concentration detectors: two types of chemoreceptors

Dose-response curves relating the external stimulus concentration to receptor occupancy differ in two types of chemoreceptor organs. In 'concentration detectors' the receptor molecules at the receptor cell membrane are directly exposed to the external stimulus concentration; these organs exhibit the well-known hyperbolic dose-response relationship reflecting the association-dissociation of stimulus and receptor molecules. In contrast, 'flux detectors' accumulate the stimulus molecules in a perireceptor compartment. In flux detectors, deactivation of stimulus molecules may be in balance with arrival, as a prerequisite for producing a constant effective stimulus concentration at constant adsorptive flux of stimulus molecules. In a simple model of a flux detector in which receptor molecules themselves catalyze the deactivation, the dose-response relationship is linear. It reflects the rate of stimulus deactivation. If the deactivation is catalyzed by a separate enzyme, the dose-response relationship can be close to hyperbolic, or linear. In all cases, the receptor molecules are maximally occupied if the adsorptive flux equals or exceeds the maximum rate of stimulus deactivation. The time course of the receptor potential recorded from moths' pheromone receptors depends on the odor compound, which suggests that a peripheral process, possibly the stimulus deactivation, is the slowest, rate-limiting process of the transduction cascade. Further evidence comes from experiments with stimuli oversaturating the mechanism responsible for the decline of the receptor potential.      

A cometabolic kinetics model incoroporating enzyme inhibition, inactivation, and recovery: II. Trichloroethylene degradaation experiments

A Cometabolism enzyme kinetics model has been presented which takes into account changes in bacterial activity associated with enzyme inhibitiion, inactivation, inactivation of enzyme resulting from product toxicty, and respondent synthesis of new enzyme. Although this process is inherently unsteady-state, the model assumes that cometabolic degradation of a compound exhibiting product toxicity can be modeled as pseudo-steady-staate under certain conditions. In its simplified from, the model also assumes that enzyme inactivation is directly propoertional to nongrawth substrate oxidation, and that recovery is directly proportionla to growth substrate oxidation. In part 1, model drivation, simplification, and analyses were described. In this articles, model assuptiions are tested by analyzing data from experiments exmining trichloroethylene (TCE) degradation by the ammoniaoxidizing baceterium Nitrosomonas europaea in a quasisteady-state bioreactor. Model solution results showed steady-state bioreactor. Model solution results showed TCE to be a competitive inhibitoer of ammonia oxidation, with TCE affinity for ammonia monooxygenase (AMO) being about four times greater than that of ammonia for the enzyme. Inhibition was independent fo TCE oxidation and occurred essentially instantly upon exposure to TCE. In contrast, inactivation of AMO occurred more gradually and was proportional to the rate and amount of TCE oxidized. Evaluation of other O(2)-dependent enzymes and electron transport proteins suggested that TCE-related damage was predominantly confined to AMO. In response to inhibition and/or inactivation, bacterial recovery was initiated, even in the presence of TCE, implying that membranes adn protein synthesis systems were functioning. Analysis of data and comparison of model results showed the inhibition/inactivation/recovery concept to provide a reasonable basis for understandign the effects fo TCE on AMO function and bacterial response. The model assumptions were verified except tht questions remain regarding the factores controlling recovery and its role in the long term. (c) 1995 John Wiley & Sons, Inc.     

A cometabilic kinetics model incorporating enzyme inhbition, inactivation, and recovery: I. Model development, analysis, and testing

Cometabolic biodegradation prcesses are important for bioremediation of hazardous waste sites. However, these proceeses are not well understood and have not been modeled thoroughly. Traditional Michaelis-Menten kinetics models often are used, but toxic effects and bacterial responses to toxicity may cause changes in enzyme levels, rendering such models inappropriate. In this article, a conceptual and mathematical model of cometabolic enzyme kinetics i described. Model derivation is based on enzyme/growth-substrate/nongrowth-substrate interaction and incorporates enzyme inhibition (caused by the presence of a cometabolic compound), inactivation (resulting from toxicity of a cometabolic product), and recovery (associated with bacterial synthesis of new enbzyme in response to inactivation). The mathematical model consists of a system of two, nonlinear ordinary differential equations that can be solved implicitly using numerical methods, providing estimates of model parameters. Model analysis shows that growth substraate adn nongrowth substrate oxidation rates are related by a dimensionless constant. Reliability of tehy model solution prcedure is verifiedl by abnalyzing data ses, containing random error, from simulated experimentss with trichhloroethyylene (TCE) degradation by ammonia-oxidizing bacterialunder various conditions. Estimation of the recovery rate contant is deterimined to be sensitive to intial TCE concentration. Model assumptions are evaluated in a companion article using data from TCE degradation experiments with amoniaoxidizing bacteria. (c) 1995 John Wiley & Sons, Inc.     

A dose-response model incorporating nonlinear kinetics

This paper introduces a dose-response model for toxic quantal response data based on hit theory applied to the dose unit as transformed by a nonlinear kinetic equation. When spontaneous background response is included in the model, the resulting dose-response model has four parameters. The maximum likelihood estimators and their large-sample properties are given. Likelihood ratio tests of interest are developed, including one for whether the model is one-hit in the transformed dose and one to check whether nonlinear kinetics is operative. The use of the model for low-dose extrapolation is presented. Finally, the procedures developed are illustrated on data from three animal carcinogenicity bioassays that show, respectively, concave, linear, and convex dose-response curves in the observed data.     

Chemotaxis receptor complexes: from signaling to assembly

Complexes of chemoreceptors in the bacterial cytoplasmic membrane allow for the sensing of ligands with remarkable sensitivity. Despite the excellent characterization of the chemotaxis signaling network, very little is known about what controls receptor complex size. Here we use in vitro signaling data to model the distribution of complex sizes. In particular, we model Tar receptors in membranes as an ensemble of different sized oligomer complexes, i.e., receptor dimers, dimers of dimers, and trimers of dimers, where the relative free energies, including receptor modification, ligand binding, and interaction with the kinase CheA determine the size distribution. Our model compares favorably with a variety of signaling data, including dose-response curves of receptor activity and the dependence of activity on receptor density in the membrane. We propose that the kinetics of complex assembly can be measured in vitro from the temporal response to a perturbation of the complex free energies, e.g., by addition of ligand.     

The muscarinic receptor of chick embryo cells: correlation between ligand binding and calcium mobilization

In this report we characterize muscarinic cholinergic receptor on embryonic cells. We established dose-response curves by fluorometric measurement of Ca2+ mobilization in cell suspensions of whole chick embryos stage 23/24. Ca2+ mobilization was quantitated by standardization of chlorotetracycline (CTC) fluorescence changes after stimulation with muscarinic agonists. We determined ED50 values for the agonists acetylcholine and carbachol as 3.4 X 10(-6) and 2.7 X 10(-5) M, respectively. Pilocarpine and oxotremorine were found to act as reversible competitive antagonists with inhibition constants (Kl) of 5.0 X 10(-6) and 1.4 X 10(-6) M, respectively. Bethanechol, which induced only 23% of the maximal effect obtained by acetylcholine, was a partial agonist with an ED50 of 4.8 X 10(-4) M. Its antagonistic component is expressed by an inhibition constant of 1.9 X 10(-4) M. In parallel, binding studies were performed in a competition assay with [3H]-quinuclidinylbenzilate. For the agonists acetylcholine and carbachol, binding parameters were best fitted by a "two binding-sites model." Comparison with dose-response curves indicated that Ca2+ mobilization was triggered via the high-affinity binding site. The inhibition constants of antagonists derived from the shift of dose-response curves corresponded to the fitted KD values of the binding studies when a "one binding-site model" was applied. Combination of dose-response and binding data showed close proportionality between receptor occupancy and calcium mobilization. No spare receptors were present.     

Kinetic manifestations of slow conformation rearrangements of lactate dehydrogenase. An experiment and a mathematical model

Non-steady-state kinetics of lactate dehydrogenase (LDH) catalyzed reaction was investigated for a wide time interval (from 100 msec to 1-3 min) by using stopped-flow methods. A two-stage character of LDH reaction, slow changes like a lag-period on kinetic curves at pH 8.0, flexions on kinetic curves after pre-mixing LDH with NAD+ and pyruvate have been revealed. The graph theory for mathematical analysis of experimental data was applied, which has been developed for the non-steady-state kinetics. An enzyme model of the two-conformer LDH structure was used. The reaction scheme with a preferential inhibition of one of the conformers (pH 8.0) is suggested. The obtained values of kinetic constants prove that transitions between LDH conformers must be slow.     

Use of a receptor competition assay to explore the interaction of the T cell antigen-specific receptor with its ligands

The observation has previously been made that receptor-bearing cells in culture compete with each other for their ligand. As a result, at a fixed concentration of ligand, the fractional occupancy of the receptor will tend to fall as the number of cells is increased. We have demonstrated that T cells in culture also compete for their ligand, the combination of foreign antigen and the Ia molecule (antigen-Ia), and that this manifests itself as shifts in the antigen dose-response curves as the number of responding T cells is increased. Because of the complexity of T cell activation, modifications to the antigen that affected its stimulatory capacity (i.e., its potency) could come about by altering its interaction with either the T cell receptor or the Ia molecule. We could distinguish between these two possibilities by studying the extent to which the antigen dose-response curves shifted as the T cell number was increased. Amino acid substitutions in the antigen that affected the interaction with the T cell receptor caused changes in the dose-response curve shifts, whereas substitutions that decreased potency by other means did not cause such changes. Finally, two allelic forms of the Ia molecule that differed only slightly in their amino-terminal domain were used to present a single antigen to a T cell clone. Despite a difference in antigenic potency in the presence of these two Ia molecules, no difference was demonstrated in the avidity of the T cell receptor for either antigen-Ia combination. These results suggest that the antigen and the Ia molecule make physical contact during the process of antigen recognition, and that the potency of an antigen can vary as a result of its interaction with either the T cell receptor or the Ia molecule.     

Kinetic models for association of 2,3,7,8-tetrachlorodibenzo-p-dioxin with the Ah receptor

Saturation binding studies of the interaction between 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and the Ah receptor obtained from the hepatic cytosol of Wistar rats have been carried out. The conventional Scatchard analysis for determination of the equilibrium constant for ligand-receptor binding has been shown to be inappropriate due to thermal inactivation of the unoccupied receptor. Simulation models of the receptor-ligand binding kinetics which take into account receptor degradation have been developed and the results are consistent with two alternative kinetic models. In Model 1, reversible 2,3,7,8-TCDD-receptor binding occurs in parallel with inactivation of the unbound receptor; analysis of the observed data using this model suggests that the previously determined equilibrium constants (Kass) for association of the ligand with the receptor are orders of magnitude too low and the total initial receptor concentrations are somewhat underestimated. In Model 2, the unbound receptor is converted unimolecularly to an activated state which then undergoes competitive degradation or entrapment by ligand. Experiments have been carried out over the temperature range 4-37 degrees C, enabling activation parameters to be obtained. According to Scheme 1, the activation enthalpies for association of receptor with ligand and for thermal inactivation of the unoccupied receptor are high, and numerically almost identical (delta H++ ca 125 kJ mol-1). These reactions are strongly entropically driven and this is consistent with association being accompanied by a conformational change in the receptor protein, and the previously postulated binding of the ligand to a hydrophobic pocket. According to Scheme 2, there is only one enthalpy of activation because both inactivation and entrapment by 2,3,7,8-TCDD are fast processes which follow the same slow activation step. On the basis of this latter model, a 10(-9) M concentration of 2,3,7,8-TCDD is sufficient to trap roughly two-thirds of the activated receptors.     

Steroid binding to hepatoma tissue culture cell glucocorticoid receptors involves at least two sulfhydryl groups

The presence of a thiol in the steroid binding cavity of glucocorticoid receptors has recently been proved by our affinity labeling of Cys-656 in the steroid binding domain of rat receptors (Simons, S. S., Jr., Pumphrey, J. G., Rudikoff, S., and Eisen, H. J. (1987) J. Biol. Chem. 262, 9676-9680). Studies with the sterically small, thiol-specific reagent methyl methanethiolsulfonate (MMTS) now reveal the involvement of at least two sulfhydryl groups in steroid binding. While the dose-response curves for [3H]dexamethasone binding versus thiol reagent are normally sigmoidal, an unusual bimodal curve is obtained with MMTS in which dexamethasone binding is eliminated at low, but maintained at intermediate, MMTS concentrations. This bimodal dose-response curve demands the involvement of two (or more) thiol groups. Those receptors pretreated with intermediate concentrations of MMTS retain approximately 70% of the initial binding capacity and one-fifth the affinity for dexamethasone. Solutions of this low affinity form of receptor contain essentially no accessible -SH groups, and all of the usual covalent labeling by dexamethasone 21-mesylate of various proteins, including the receptor, is blocked. The facts, that this low affinity form of the receptor is not affected by added iodoacetamide, cannot be produced from the nonsteroid binding form of receptor simply by adding more MMTS, and displays different kinetics of formation than does the nonsteroid binding form of receptor all argue that reaction of the receptor with intermediate and low MMTS, concentrations occurs via different pathways. Nevertheless, the effects of both concentrations of MMTS on the receptor are fully reversible with added dithiothreitol. The kinetics of inhibition of [3H]dexamethasone binding at low MMTS concentrations are independent of receptor concentration, indicating an intramolecular reaction. Collectively these data suggest a model of steroid binding involving two thiols, one of which appears to be Cys-656. Low concentrations of MMTS induce the formation of an intramolecular disulfide, which prevents steroid binding, while the intermediate MMTS concentrations convert both thiols directly to mixed disulfides, and steroid binding persists. Thus, reduced thiols do not appear to be required for steroid binding if the steric bulk of the oxidized thiols is small.     

A Model for Single-Substrate Trimolecular Enzymatic Kinetics

We developed a kinetic model for a single-substrate trimolecular enzymatic system, where a receptor binds and stretches a substrate to expose its cleavage site, allowing an enzyme to bind and cleave it into product. We demonstrated that the general kinetics of the trimolecular enzymatic system is more complex than the Michaelis-Menten kinetics. Under a limiting condition when the enzyme-substrate binding is in fast equilibrium, the enzymatic kinetics of the trimolecular system reduces to the Michaelis-Menten kinetics. In another limiting case when the receptor dissociates negligibly slowly from the substrate, the trimolecular system is simplified to a bimolecular system, which follows the Michaelis-Menten equation if and only if there is no enzyme-substrate complex initially. We applied this model to a particular trimolecular system important to hemostasis and thrombosis, consisting of von Willebrand factor (substrate), platelet glycoprotein Ibα (receptor), and ADAMTS13 (enzyme). Using parameters from independent experiments, our model successfully predicted published data from two single-molecule experiments and fitted/predicted published data from an ensemble experiment.     

Insulin receptor binding kinetics: modeling and simulation studies

Biological actions of insulin regulate glucose metabolism and other essential physiological functions. Binding of insulin to its cell surface receptor initiates signal transduction pathways that mediate cellular responses. Thus, it is of great interest to understand the mechanisms underlying insulin receptor binding kinetics. Interestingly, negative cooperative interactions are observed at high insulin concentrations while positive cooperativity may be present at low insulin concentrations. Clearly, insulin receptor binding kinetics cannot be simply explained by a classical bimolecular reaction. Mature insulin receptors have a dimeric structure capable of binding two molecules of insulin. The binding affinity of the receptor for the second insulin molecule is significantly lower than for the first bound insulin molecule. In addition, insulin receptor aggregation occurs in response to ligand binding and aggregation may also influence binding kinetics. In this study, we develop a mathematical model for insulin receptor binding kinetics that explicitly represents the divalent nature of the insulin receptor and incorporates receptor aggregation into the kinetic model. Model parameters are based upon published data where available. Computer simulations with our model are capable of reproducing both negative and positive cooperativity at the appropriate insulin concentrations. This model may be a useful tool for helping to understand the mechanisms underlying insulin receptor binding and the coupling of receptor binding to downstream signaling events.     

Kinetics of glucose transport and sequestration in lactating bovine mammary glands measured in vivo with a paired indicator/nutrient dilution technique.

To quantify kinetics of mammary glucose utilization in vivo, 24 paired glucose and extracellular indicator (p-aminohippuric acid) dilution curves across intact bovine mammary glands were obtained after bolus injections into the external iliac artery. Dilution curves were analyzed using a compartmental capillary, convolution integration model. Four candidate submodels of glucose transport and metabolism in capillary supply zones were fit to the glucose dilution curves and evaluated. Model I, with one extracellular compartment for glucose and first-order unidirectional uptake, failed, indicating that efflux of glucose from the intracellular space could not be ignored. Model II, with first-order exchanges between extracellular and intracellular compartments and sequestration from the latter, was overdefined because unidirectional clearance of glucose was at least five times the blood flow rate and 20 times the net clearance rate. Model III, combining extracellular and intracellular space into one compartment, was superior in its goodness-of-fit to curves and identifiability of parameters. Michaelis-Menten parameters of sequestration were not identifiable. Parameters of the optimal compartmental capillary, convolution integration model were applicable to both the dynamics of injected glucose dilution and the steady-state background arteriovenous difference of glucose. Glucose sequestration followed first-order kinetics between 0 and 7 mM extracellular glucose with an average rate constant of 0.006 s(-1) or a clearance of 44 ml/s. The ratio of intracellular to extracellular glucose distribution space was 0.34, which is considerably lower than the expected intracellular volume and suggests an intracellular occlusion compartment with which extracellular glucose rapidly exchanges.     

Cometabolism of chlorinated solvents by nitrifying bacteria: kinetics, substrate interactions, toxicity effects, and bacterial response

Pure cultures of ammonia-oxidizing bacteria, Nitrosomonas europaea, were exposed to trichloroethylene (TCE), 1,1-dichloroethylene (1,1-DCE), chloroform (CF), 1,2-dichloroethane (1,2-DCA), or carbon tetrachloride (CT), in the presence of ammonia, in a quasi-steady-state bioreactor. Estimates of enzyme kinetics constants, solvent inactivation constants, and culture recovery constants were obtained by simultaneously fitting three model curves to experimental data using nonlinear optimization techniques and an enzyme kinetics model, referred to as the inhibition, inactivation, and recovery (IIR) model, that accounts for inhibition of ammonia oxidation by the solvent, enzyme inactivation by solvent product toxicity, and respondent synthesis of new enzyme (recovery). Results showed relative enzyme affinities for ammonia monooxygenase (AMO) of 1,1-DCE approximately TCE > CT > NH(3) > CF > 1,2-DCA. Relative maximum specific substrate transformation rates were NH(3) > 1,2-DCA > CF > TCE approximately 1,1-DCE > CT (=0). The TCE, CF, and 1,1-DCE inactivated the cells, with 1,1-DCE being about three times more potent than TCE or CF. Under the conditions of these experiments, inactivating injuries caused by TCE and 1,1-DCE appeared limited primarily to the AMO enzyme, but injuries caused by CF appeared to be more generalized. The CT was not oxidized by N. europaea while 1,2-DCA was oxidized quite readily and showed no inactivation effects. Recovery capabilities were demonstrated with all solvents except CF. A method for estimating protein yield, the relationship between the transformation capacity model and the IIR model, and a condition necessary for sustainable cometabolic treatment of inactivating substrates are presented. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 520-534, 1997.     

Receptor-Agonist Interactions in Service-Theoretic Perspective,Effects of Molecular Timing on the Shape of Dose-Response Curves

Service-theoretic concepts and methods, widely used in other fields (e.g., telecommunication and operations research), are useful also in a biochemical setting because the treatment of biocatalysts (enzymes, receptors) as servers and their ligands as customers, based on the established formal methods of service or queuing theory, may lead to insights and results unobtainable by conventional, mass-action-law-based theories. In this article, we apply the service-theoretic approach to receptor-agonist systems and show how by changing the stochastic time pattern of “operationally relevant” point events (e.g., instants of agonist arrival, instants of postclimax agonist departure) a great variety of dose-response curves may be generated, even in very simple reaction schemes, which, according to mass action kinetics, invariably lead to hyperbolic r(A) curves (r and A stand for response and agonist concentration, respectively). The molecular timing inherent to a hyperbolic response system is not optimal: for instance, at the agonist concentration A₅₀, half of the agonist molecules are rejected (“lost”) because of unfortunate timing of the arrival events. The fraction of lost arrivers can be diminished considerably if the arrivals are better timed: “sub-Poisson” arrivals improve the timing and, thus, convert hyperbolic r(A) curves into “lifted” nonhyperbolic ones. Conversely, “super-Poisson” arrivals make the nonoptimal timing in hyperbolic response systems even worse and, thus, convert hyperbolic r(A) curves into “depressed” nonhyperbolic ones. Furthermore, under special timing conditions, nonhyperbolic r(A) curves can be generated, which are partly lifted, partly depressed relative to the reference hyperbola, and which resemble in shape well-known nonhyperbolic forms of enzyme and receptor kinetics (negatively cooperative, positively cooperative, and sigmoidal kinetics). In addition unusual (undulatory and sawtooth-like) r(A) curves can be generated solely by changing the temporal pattern of arrival and service completion instants. Virtually any shape of dose-response curves may be obtained by allowing for probability distributions whose characteristic shape varies with their mean; we call such distributions “variomorphic” and apply them to the arrival process of agonist molecules.