A critical re-evaluation of the slope factor of the operational model of agonism: When to exponentiate operational efficacy

Elucidating the link between binding statistics and Shannon information in biological networks

The response of a biological network to ligand binding is of crucial importance for regulatory control in various cellular biophysical processes that is achieved with information transmission through the different ligand-bound states of such networks. In this work, we address a vital issue regarding the link between the information content of such network states and the experimentally measurable binding statistics. Several fundamental networks of cooperative ligand binding, with the bound states being adjacent in time only and in both space and time, are considered for this purpose using the chemical master equation approach. To express the binding characteristics in the language of information, a quantity denoted as differential information index is employed based on the Shannon information. The index, determined for the whole network, follows a linear relationship with (logarithmic) ligand concentration with a slope equal to the size of the system. On the other hand, the variation of Shannon information associated with the individual network states and the logarithmic sensitivity of its slope are shown to have generic forms related to the average binding number and variance, respectively, the latter yielding the Hill slope, the phenomenological measure of cooperativity. Furthermore, the variation of Shannon information entropy, the average of Shannon information, is also shown to be related to the average binding.

Distinct roles of the extracellular surface residues of glucagon-like peptide-1 receptor in β-arrestin 1/2 signaling

Glucagon-like peptide-1 receptor (GLP-1R) is a prime drug target for type 2 diabetes and obesity. The ligand initiated GLP-1R interaction with G protein has been well studied, but not with β-arrestin 1/2. Therefore, bioluminescence resonance energy transfer (BRET), mutagenesis and an operational model were used to evaluate the roles of 85 extracellular surface residues on GLP-1R in β-arrestin 1/2 recruitment triggered by three representative GLP-1R agonists (GLP-1, exendin-4 and oxyntomodulin). Residues selectively regulated β-arrestin 1/2 recruitment for diverse ligands, and β-arrestin isoforms were identified. Mutation of residues K130-S136, L142 and Y145 on the transmembrane helix 1 (TM1)-extracellular domain (ECD) linker decreased β-arrestin 1 recruitment but increased β-arrestin 2 recruitment. Other extracellular loop (ECL) mutations, including P137A, Q211A, D222A and M303A selectively affected β-arrestin 1 recruitment while D215A, L217A, Q221A, S223A, Y289A, S301A, F381A and I382A involved more in β-arrestin 2 recruitment for the ligands. Oxyntomodulin engaged more broadly with GLP-1R extracellular surface to drive β-arrestin 1/2 recruitment than GLP-1 and exendin-4; I147, W214 and L218 involved in β-arrestin 1 recruitment, while L141, D215, L218, D293 and F381 in β-arrestin 2 recruitment for oxyntomodulin particularly. Additionally, the non-conserved residues on β-arrestin 1/2 C-domains contributed to interaction with GLP-1R. Further proteomic profiling of GLP-1R stably expressed cell line upon ligand stimulation with or without β-arrestin 1/2 overexpression demonstrated both commonly and biasedly regulated proteins and pathways associated with cognate ligands and β-arrestins. Our study offers valuable information about ligand induced β-arrestin recruitment mediated by GLP-1R and consequent intracellular signaling events.