Ligand Binding Dynamics for Pre-dimerised G Protein-Coupled Receptor Homodimers: Linear Models and Analytical Solutions

Computational modelling of dynamic cAMP responses to GPCR agonists for exploration of GLP-1R ligand effects in pancreatic β-cells and neurons

The glucagon-like peptide-1 receptor (GLP-1R) is a class B G protein-coupled receptor (GPCR) which plays important physiological roles in insulin release and promoting fullness. GLP-1R agonists initiate cellular responses by cyclic AMP (cAMP) pathway signal transduction. Understanding of the potential of GLP-1R agonists in the treatment of type 2 diabetes may be advanced by considering the cAMP dynamics for agonists at GLP-1R in both pancreatic β-cells (important in insulin release) and neurons (important in appetite regulation). Receptor desensitisation in the cAMP pathway is known to be an important regulatory mechanism, with different ligands differentially promoting G protein activation and desensitisation. Here, we use mathematical modelling to quantify and understand experimentally obtained cAMP timecourses for two GLP-1R agonists, exendin-F1 (ExF1) and exendin-D3 (ExD3), which give markedly different signals in β-cells and neurons. We formulate an ordinary differential equation (ODE) model for the dynamics of cAMP signalling in response to G protein-coupled receptor (GPCR) ligands, encompassing ligand binding, receptor activation, G protein activation, desensitisation and second messenger generation. We validate our model initially by fitting to timecourse data for HEK293 cells, then proceed to parameterise the model for β-cells and neurons. Through numerical simulation and sensitivity studies, our analysis adds support to the hypothesis that ExF1 offers more potential glucose regulation benefit than ExD3 over long timescales via signalling in pancreatic β-cells, but that there is little difference between the two ligands in the potential appetite suppression effects offered via long-time signalling in neurons on the same timescales.

Time-dependent ligand-receptor binding kinetics and functionality in a heterodimeric receptor model

GPCRs heteromerize both in CNS and non-CNS regions. The cell uses receptor heteromerization to modulate receptor functionality and to provide fine tuning of receptor signaling. In order for pharmacologists to explore these mechanisms for therapeutic purposes, quantitative receptor models are needed. We have developed a time-dependent model of the binding kinetics and functionality of a preformed heterodimeric receptor involving two drugs. Two cases were considered: both or only one of the drugs are in excess with respect to the total concentration of the receptor. The latter case can be applied to those situations in which a drug causes unwanted side effects that need to be reduced by decreasing its concentration. The required efficacy can be maintained by the allosteric effects mutually exerted by the two drugs in the two-drug combination system. We discuss this concept assuming that the drug causing unwanted side effects is an opioid and that analgesia is the therapeutic effect. As additional points, allosteric modulation by endogenous compounds and synthetic bivalent ligands was included in the study. Receptor heteromerization offers a mechanistic understanding and quantification of the pharmacological effects elicited by combinations of two drugs at different doses and with different efficacies and cooperativity effects, thus providing a conceptual framework for drug combination therapy.

Classical structural identifiability methodology applied to low-dimensional dynamic systems in receptor theory

Mathematical modelling has become a key tool in pharmacological analysis, towards understanding dynamics of cell signalling and quantifying ligand-receptor interactions. Ordinary differential equation (ODE) models in receptor theory may be used to parameterise such interactions using timecourse data, but attention needs to be paid to the theoretical identifiability of the parameters of interest. Identifiability analysis is an often overlooked step in many bio-modelling works. In this paper we introduce structural identifiability analysis (SIA) to the field of receptor theory by applying three classical SIA methods (transfer function, Taylor Series and similarity transformation) to ligand-receptor binding models of biological importance (single ligand and Motulsky-Mahan competition binding at monomers, and a recently presented model of a single ligand binding at receptor dimers). New results are obtained which indicate the identifiable parameters for a single timecourse for Motulsky-Mahan binding and dimerised receptor binding. Importantly, we further consider combinations of experiments which may be performed to overcome issues of non-identifiability, to ensure the practical applicability of the work. The three SIA methods are demonstrated through a tutorial-style approach, using detailed calculations, which show the methods to be tractable for the low-dimensional ODE models.

Allosteric binding cooperativity in a kinetic context

Allosteric modulators are of prime interest in drug discovery. These drugs regulate the binding and function of endogenous ligands, with some advantages over orthosteric ligands. A typical pharmacological parameter in allosteric modulation is binding cooperativity. This property can yield unexpected but illuminating results when decomposed into its kinetic parameters. Using two reference models (the allosteric ternary complex receptor model and a heterodimer receptor model), a relationship has been derived for the cooperativity rate constant parameters. This relationship allows many combinations of the cooperativity kinetic parameters for a single binding cooperativity value obtained under equilibrium conditions. This assessment may help understand striking experimental results involving allosteric modulation and suggest further investigations in the field.

Experimental validation of computerised models of clustering of platelet glycoprotein receptors that signal via tandem SH2 domain proteins

The clustering of platelet glycoprotein receptors with cytosolic YxxL and YxxM motifs, including GPVI, CLEC-2 and PEAR1, triggers activation via phosphorylation of the conserved tyrosine residues and recruitment of the tandem SH2 (Src homology 2) domain effector proteins, Syk and PI 3-kinase. We have modelled the clustering of these receptors with monovalent, divalent and tetravalent soluble ligands and with transmembrane ligands based on the law of mass action using ordinary differential equations and agent-based modelling. The models were experimentally evaluated in platelets and transfected cell lines using monovalent and multivalent ligands, including novel nanobody-based divalent and tetravalent ligands, by fluorescence correlation spectroscopy. Ligand valency, receptor number, receptor dimerisation, receptor phosphorylation and a cytosolic tandem SH2 domain protein act in synergy to drive receptor clustering. Threshold concentrations of a CLEC-2-blocking antibody and Syk inhibitor act in synergy to block platelet aggregation. This offers a strategy for countering the effect of avidity of multivalent ligands and in limiting off-target effects.