Both Ligand- and Cell-Specific Parameters Control Ligand Agonism in a Kinetic Model of G Protein–Coupled Receptor Signaling (original) (raw)
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Journal of Theoretical Biology, 1999
Signaling through G-protein coupled receptors is one of the most prevalent and important methods of transmitting information to the inside of cells. Many mathematical models have been proposed to describe this type of signal transduction, and the ternary complex (ligand/receptor/G-protein) model and its derivatives are among the most widely accepted. Current versions of these equilibrium models include both active (i.e. signaling) and inactive conformations of the receptor, but do not include the dynamics of G-protein activation or receptor desensitization. Yet understanding how these dynamic events e!ect response behavior is crucial to determining ligand e$cacy. We developed a mathematical model for G-protein coupled receptor signaling that includes G-protein activation and receptor desensitization, and used it to predict how activation and desensitization would change if either the conformational selectivity (the e!ect of ligand binding on the distribution of active and inactive receptor states) or the desensitization rate constant was ligand-speci"c. In addition, the model was used to explore the implications of measuring responses far downstream from G-protein activation. By comparing the experimental data from the -adrenergic, -opioid, D dopamine, and neutrophil N-formyl peptide receptors with the predictions of our model, we found that the conformational selectivity is the predominant factor in determining the amounts of activation and desensitization caused by a particular ligand.
Pharmacological responses are modulated over time by regulation of signaling mechanisms. The canonical short-term regulation mechanisms are receptor desensitization and degradation of the response. Here for the first time a pharmacological model for measuring drug parameters is developed that incorporates short-term mechanisms of regulation of signaling. The model is formulated in a manner that enables measurement of drug parameters using familiar curve fitting methods. The efficacy parameter is kTau, which is simply the initial rate of signaling before it becomes limited by regulation mechanisms. The regulation parameters are rate constants, kDES for receptor desensitization and kD for response degradation. Efficacy and regulation are separate parameters, meaning these properties can be optimized independently of one another in drug discovery. The parameters can be applied to translate in vitro findings to in vivo efficacy in terms of the magnitude and duration of drug effect. When...
Analyzing kinetic signaling data for G-protein-coupled receptors
In classical pharmacology, bioassay data are fit to general equations (e.g. the dose response equation) to determine empirical drug parameters (e.g. EC50 and Emax), which are then used to calculate chemical parameters such as affinity and efficacy. Here we used a similar approach for kinetic, time course signaling data, to allow empirical and chemical definition of signaling by G-protein-coupled receptors in kinetic terms. Experimental data are analyzed using general time course equations (model-free approach) and mechanistic model equations (mechanistic approach) in the commonly-used curve-fitting program, GraphPad Prism. A literature survey indicated signaling time course data usually conform to one of four curve shapes: the straight line, association exponential curve, rise-and-fall to zero curve, and rise-and-fall to steady-state curve. In the model-free approach, the initial rate of signaling is quantified and this is done by curve-fitting to the whole time course, avoiding the...
Untangling Ligand Induced Activation and Desensitization of G-Protein–Coupled Receptors
Biophysical Journal, 2003
Long-term treatment with a drug to a G-protein-coupled receptor (GPCR) often leads to receptor-mediated desensitization, limiting the therapeutic lifetime of the drug. To better understand how this therapeutic window might be controlled, we created a mechanistic Monte Carlo model of the early steps in GPCR signaling and desensitization. Using this model we found that the rates of G-protein activation and receptor phosphorylation can be partially decoupled by varying the drug-receptor dissociation rate constant, k off , and the drug's efficacy, a. The maximum ratio of G-protein activation to receptor phosphorylation (GARP) was found for drugs with an intermediate k off value and small a-value. Changes to the cellular environment, such as changes in the diffusivity of membrane molecules and the G-protein inactivation rate constant, affected the GARP value of a drug but did not change the characteristic shape of the GARP curve. These model results are examined in light of experimental data for a number of GPCRs and are found to be in good agreement, lending support to the idea that the desensitization properties of a drug might be tailored to suit a specific application.
On the analysis of ligand-directed signaling at G protein-coupled receptors
Naunyn-Schmiedeberg's Archives of Pharmacology, 2008
The phenomenon of "ligand-directed signaling" is often considered to be inconsistent with the traditional receptor theory. In this review, I show how the mathematics of the receptor theory can be used to measure the observed affinity and relative efficacy of protean ligands at G protein-coupled receptors. The basis of this analysis rests on the assumption that the fraction of agonist bound in the form of the active receptor-G protein-guanine nucleotide complex is the biochemical equivalent of the pharmacological stimulus. Consequently, this stimulus function is analogous to the current response of a ligand-gated ion channel. Because guanosine triphosphate (GTP) greatly inhibits the formation of the active quaternary complex, even the most efficacious agonists probably only elicit partial receptor activation, and it seems likely that the ceiling of 100% receptor activation is not reached in the intact cell with high intracellular concentrations of GTP. Under these conditions, the maximum of the stimulus function is proportional to the ratio of microscopic affinity constants of the agonist for ground and active states. Ligand-directed signaling depends on the existence of different active states of the receptor with different selectivities for different G proteins or other effectors. This phenomenon can be characterized using classic pharmacological methods. Although not widely appreciated, it is possible to estimate the product of observed affinity and intrinsic efficacy expressed relative to that of another agonist (intrinsic relative activity) through the analysis of the concentration-response curves. No other information is required. This approach should be useful in quantifying agonist activity and in converting the two disparate parameters of potency and maximal response into a single parameter dependent only on the agonist-receptor-effector complex.
Modelling the activation of G-protein coupled receptors by a single drug
Mathematical Biosciences, 2009
In this paper, the most popular proposed mechanism for activation of G-protein coupled receptors (GPCRs)-the shuttling mechanism-is modelled mathematically. An asymptotic analysis of this model clarifies the dynamics of the system in the presence of a drug, in particular identifying which reactions dominate during the different timescales. The modelling also reveals challenging behaviour in the form of a peak response. This new mechanism gives simple explanations for complex, possibly misunderstood, behaviour.
Mathematical Biosciences, 2010
A new mathematical model of cell signalling for a two-ligand G-protein coupled receptor (GPCR) system is presented. This model extends the single-ligand cubic ternary complex to account for the possibility of an agonist and an antagonist competing for receptor sites. The G-protein cycle is included, and signalling as far as the dissociated G a subunit is considered. Numerical simulations are performed, and the effects on the system dynamics, such as peak and plateau behaviour, of antagonist ''stickiness", and of the doses of agonist and antagonist, are discussed. Under certain parameter regimes, the plateau response is subject to surmountable antagonism, while the peak response is subject to insurmountable antagonism. The numerical results reveal responses evolving over a number of timescales. An asymptotic analysis is presented which identifies dominant reactions and gives leading order solutions over these various timescales, for a number of parameter regimes.
European Journal of Pharmacology, 1997
A thermodynamic model of signal transduction that incorporates the possibility of multiple conformational states between the inactive and the active forms of the receptor was developed. The obtained equilibrium model is equivalent to the extended ternary complex of Samama et al. (J. Biol. Chem. 268 (1993) 4625-4636) if only two states of the receptor exist. These multiple equilibria between receptor states are modeled by two sets of equilibrium constants: K(piAR) and K(sigma piAR), in the presence of the ligand; and K(piR) and K(sigma piR), in the absence of the ligand. The higher the value of these constants, the more efficiently the active form of the receptor is generated. Intrinsic efficacy of the agonist is defined in the present formulation as the molecular processes induced by ligands in the receptor that lead to the active form of the receptor. Both the energetics (associated to K[piAR]) and mechanism of the process of receptor activation (associated to K[sigma piAR]) are important in eliciting the maximum response. Moreover, analytical expressions of basal activity, potency and maximum response were obtained. These definitions were used to classify the extra cellular ligand as agonists (K[sigma piAR] > K[sigma piR]), inverse agonists (K[sigma piR] > K[sigma piAR] > 0), neutral antagonists (K[sigma piAR] = K[sigma piR]), and pure antagonists.