Ligand binding dynamics for pre-dimerised G protein-coupled receptor homodimers: Linear models and analytical solutions

White, Carla; Bridge, Lloyd

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 labeled 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 does 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.

• Journal Article Type: Article
• Acceptance Date: Dec 21, 2017
• Online Publication Date: Jan 18, 2018
• Publication Date: 2019-09
• Deposit Date: Jan 23, 2018
• Publicly Available Date: Jan 23, 2018
• Journal: Bulletin of Mathematical Biology
• Print ISSN: 0092-8240
• Electronic ISSN: 1522-9602
• Publisher: Springer (part of Springer Nature)
• Peer Reviewed: Peer Reviewed
• Volume: 81
• Issue: 9
• Pages: 3542-3574
• DOI: https://doi.org/10.1007/s11538-017-0387-x
• Keywords: mathematical pharmacology, receptor theory, G protein-coupled receptors, ordinary differential equations
• Public URL: https://uwe-repository.worktribe.com/output/876493
• Publisher URL: https://doi.org/10.1007/s11538-017-0387-x
• Contract Date: Jan 23, 2018