Computational modelling of dynamic cAMP responses to GPCR agonists for exploration of GLP-1R ligand effects in pancreatic ß-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 ß-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 ß-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 ß-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 ß-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.

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.

NanoBiT- and NanoBiT/BRET-based assays allow the analysis of binding kinetics of Wnt-3a to endogenous Frizzled 7 in a colorectal cancer model.

BACKGROUND AND PURPOSE: Wnt binding to Frizzleds (FZD) is a crucial step that leads to the initiation of signalling cascades governing multiple processes during embryonic development, stem cell regulation and adult tissue homeostasis. Recent efforts have enabled us to shed light on Wnt-FZD pharmacology using overexpressed HEK293 cells. However, assessing ligand binding at endogenous receptor expression levels is important due to differential binding behaviour in a native environment. Here, we study FZD paralogue, FZD7 , and analyse its interactions with Wnt-3a in live CRISPR-Cas9-edited SW480 cells typifying colorectal cancer. EXPERIMENTAL APPROACH: SW480 cells were CRISPR-Cas9-edited to insert a HiBiT tag on the N-terminus of FZD7 , preserving the native signal peptide. These cells were used to study eGFP-Wnt-3a association with endogenous and overexpressed HiBiT-FZD7 using NanoBiT/bioluminescence resonance energy transfer (BRET) and NanoBiT to measure ligand binding and receptor internalization. KEY RESULTS: With this new assay the binding of eGFP-Wnt-3a to endogenous HiBiT-FZD7 was compared with overexpressed receptors. Receptor overexpression results in increased membrane dynamics, leading to an apparent decrease in binding on-rate and consequently in higher, up to 10 times, calculated Kd . Thus, measurements of binding affinities to FZD7 obtained in overexpressed cells are suboptimal compared with the measurements from endogenously expressing cells. CONCLUSIONS AND IMPLICATIONS: Binding affinity measurements in the overexpressing cells fail to replicate ligand binding affinities assessed in a (patho)physiologically relevant context where receptor expression is lower. Therefore, future studies on Wnt-FZD7 binding should be performed using receptors expressed under endogenous promotion.

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.

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 need to select the linear part of the curve. It is shown that the four shapes are consistent with a mechanistic model of signaling, based on enzyme kinetics, with the shape defined by the regulation of signaling mechanisms (e.g. receptor desensitization, signal degradation). Signaling efficacy is the initial rate of signaling by agonist-occupied receptor (kτ), simply the rate of signal generation before it becomes affected by regulation mechanisms, measurable using the model-free analysis. Regulation of signaling parameters such as the receptor desensitization rate constant can be estimated if the mechanism is known. This study extends the empirical and mechanistic approach used in classical pharmacology to kinetic signaling data, facilitating optimization of new therapeutics in kinetic terms.

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

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.

A two-state model for the kinetics of competitive radioligand binding.

BACKGROUND AND PURPOSE: Ligand-receptor binding kinetics is receiving increasing attention in the drug research community. The Motulsky and Mahan model, a one-state model, offers a method for measuring the binding kinetics of an unlabelled ligand, with the assumption that the labelled ligand has no preference while binding to distinct states or conformations of a drug target. As such, the one-state model is not applicable if the radioligand displays biphasic binding kinetics to the receptor. EXPERIMENTAL APPROACH: We extended the Motulsky and Mahan model to a two-state model, in which the kinetics of the unlabelled competitor binding to different receptor states (R1 and R2 ) can be measured. With this extended model, we determined the binding kinetics of unlabelled N-5'-ethylcarboxamidoadenosine (NECA), a representative agonist for the adenosine A1 receptor. Subsequently, an application of the model was exemplified by measuring the binding kinetics of other A1 receptor ligands. In addition, limitations of the model were investigated as well. KEY RESULTS: The kinetic rate constants of unlabelled NECA were comparable with the results of kinetic radioligand binding assays in which [3 H]-NECA was used. The model was further validated by good correlation between simulated results and the experimental data. CONCLUSION: The two-state model is sufficient to analyse the binding kinetics of an unlabelled ligand, when a radioligand shows biphasic association characteristics. We expect this two-state model to have general applicability for other targets as well.

Dynamic NF-κB and E2F interactions control the priority and timing of inflammatory signalling and cell proliferation.

Dynamic cellular systems reprogram gene expression to ensure appropriate cellular fate responses to specific extracellular cues. Here we demonstrate that the dynamics of Nuclear Factor kappa B (NF-κB) signalling and the cell cycle are prioritised differently depending on the timing of an inflammatory signal. Using iterative experimental and computational analyses, we show physical and functional interactions between NF-κB and the E2 Factor 1 (E2F-1) and E2 Factor 4 (E2F-4) cell cycle regulators. These interactions modulate the NF-κB response. In S-phase, the NF-κB response was delayed or repressed, while cell cycle progression was unimpeded. By contrast, activation of NF-κB at the G1/S boundary resulted in a longer cell cycle and more synchronous initial NF-κB responses between cells. These data identify new mechanisms by which the cellular response to stress is differentially controlled at different stages of the cell cycle.

A method of 'speed coefficients' for biochemical model reduction applied to the NF-κB system.

The relationship between components of biochemical network and the resulting dynamics of the overall system is a key focus of computational biology. However, as these networks and resulting mathematical models are inherently complex and non-linear, the understanding of this relationship becomes challenging. Among many approaches, model reduction methods provide an avenue to extract components responsible for the key dynamical features of the system. Unfortunately, these approaches often require intuition to apply. In this manuscript we propose a practical algorithm for the reduction of biochemical reaction systems using fast-slow asymptotics. This method allows the ranking of system variables according to how quickly they approach their momentary steady state, thus selecting the fastest for a steady state approximation. We applied this method to derive models of the Nuclear Factor kappa B network, a key regulator of the immune response that exhibits oscillatory dynamics. Analyses with respect to two specific solutions, which corresponded to different experimental conditions identified different components of the system that were responsible for the respective dynamics. This is an important demonstration of how reduction methods that provide approximations around a specific steady state, could be utilised in order to gain a better understanding of network topology in a broader context.

Allosteric interactions across native adenosine-A3 receptor homodimers: quantification using single-cell ligand-binding kinetics.

A growing awareness indicates that many G-protein-coupled receptors (GPCRs) exist as homodimers, but the extent of the cooperativity across the dimer interface has been largely unexplored. Here, measurement of the dissociation kinetics of a fluorescent agonist (ABA-X-BY630) from the human A(1) or A(3) adenosine receptors expressed in CHO-K1 cells has provided evidence for highly cooperative interactions between protomers of the A(3)-receptor dimer in single living cells. In the absence of competitive ligands, the dissociation rate constants of ABA-X-BY630 from A(1) and A(3) receptors were 1.45 ± 0.05 and 0.57 ± 0.07 min(-1), respectively. At the A(3) receptor, this could be markedly increased by both orthosteric agonists and antagonists [15-, 9-, and 19-fold for xanthine amine congener (XAC), 5'-(N-ethyl carboxamido)adenosine (NECA), and adenosine, respectively] and reduced by coexpression of a nonbinding (N250A) A(3)-receptor mutant. The changes in ABA-X-BY630 dissociation were much lower at the A(1) receptor (1.5-, 1.4-, and 1.5-fold). Analysis of the pEC(50) values of XAC, NECA, and adenosine for the ABA-X-BY630-occupied A(3)-receptor dimer yielded values of 6.0 ± 0.1, 5.9 ± 0.1, and 5.2 ± 0.1, respectively. This study provides new insight into the spatial and temporal specificity of drug action that can be provided by allosteric modulation across a GPCR homodimeric interface.