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

Abstract

Evidence suggests that many G protein-coupled receptors (GPCRs) are bound together forming dimers. The implications of dimerisation for cellular signalling outcomes, and ultimately drug discovery and therapeutics, remain unclear. Consideration of ligand binding and signalling via receptor dimers is therefore required as an addition to classical receptor theory, which is largely built on assumptions of monomeric receptors. A key factor in developing theoretical models of dimer signalling is cooperativity across the dimer, whereby binding of a ligand to one protomer affects the binding of a ligand to the other protomer. Here, we present and analyse linear models for one-ligand and two-ligand binding dynamics at homodimerised receptors, as an essential building block in the development of dimerised receptor theory. For systems at equilibrium, we compute analytical solutions for total bound labelled ligand and derive conditions on the cooperativity factors under which multiphasic log dose-response curves are expected. This could help explain data extracted from pharmacological experiments that do not fit to the standard Hill curves that are often used in this type of analysis. For the time-dependent problems, we also obtain analytical solutions. For the single-ligand case, the construction of the analytical solution is straightforward; it is bi-exponential in time, sharing a similar structure to the well-known monomeric competition dynamics of Motulsky-Mahan. We suggest that this model is therefore practically usable by the pharmacologist towards developing insights into the potential dynamics and consequences of dimerised receptors.B Lloyd J. Bridge

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

“…The ratio of α + and α − can be defined as a single variable, α, a cooperativity coefficient with a value of >1, equal to 1 and <1 denoting positive, neutral and negative cooperativity, respectively [ 21 ]: …”

Allosteric binding cooperativity in a kinetic context

“…We see that a homodimeric receptor is a particular case of a heterodimeric receptor with R 1 = R 2 = R or, in other words, a homodimeric receptor is a limit- ing case of a heterodimeric receptor in which the two protomers progressively resemble each other until finally they are the same. 11 If, in addition, only one ligand species (say A) is included, then the previous relationship between cooperativity rate constants is simplified (a + = b + and a À = b À ) and only two cooperativity rate constants (a + and a À ) contribute to the homodimer receptor system 12 (Fig. 4).…”

What Can Mathematics Do for Drug Development?

“…The authors apply maximum likelihood statistical methods to improve the quantification of PET image binding data with the goal of minimizing bias and variance and show results for both simulated and real data. White and Bridge (2018) formulate and analytically solve differential equation models for drugs with one- and two-ligand binding kinetics. Their dynamical systems analysis provides conditions that indicate when the dose–response curves will be multiphasic.…”