Receptor binding kinetics equations: Derivation using the Laplace transform method

Tailoring electrode surface charge to achieve discrimination and quantification of chemically similar small molecules with electrochemical aptamers

Electrochemical biosensors based on structure-switching aptamers offer many advantages because they can operate directly in complex samples and offer the potential to integrate with miniaturized electronics. Unfortunately, these biosensors often suffer from cross-reactivity problems when measuring a target in samples containing other chemically similar molecules, such as precursors or metabolites. While some progress has been made in selecting highly specific aptamers, the discovery of these reagents remains slow and costly. In this work, we demonstrate a novel strategy to distinguish molecules with miniscule difference in chemical composition (such as a single hydroxyl group) - with cross reactive aptamer probes - by tuning the charge state of the surface on which the aptamer probes are immobilized. As an exemplar, we show that our strategy can distinguish between DOX and many structurally similar analytes, including its primary metabolite doxorubicinol (DOXol). We then demonstrate the ability to accurately quantify mixtures of these two molecules based on their differential response to sensors with different surface-charge properties. We believe this methodology is general and can be extended to a broad range of applications.

Mathematical approaches in estimating aptamer-target binding affinity

The performance of aptamers as versatile tools in numerous analytical applications is critically dependent on their high target binding specificity and selectivity. However, only the technical or methodological aspects of measuring aptamer-target binding affinities are focused, ignoring the equally important mathematical components that play pivotal roles in affinity measurements. In this study, we aim to provide a comprehensive review regarding the utilization of different mathematical models and equations, along with a detailed description of the computational steps involved in mathematically deriving the binding affinity of aptamers against their specific target molecules. Mathematical models ranging from one-site binding to multiple aptameric binding site-based models are explained in detail. Models applied in several different approaches of affinity measurements such as thermodynamics and kinetic analysis, including cooperativity and competitive-assay based mathematical models have been elaborately discussed. Mathematical models incorporating factors that could potentially affect affinity measurements are also further scrutinized.

Considerations for improved performance of competition association assays analysed with the Motulsky-Mahan's "kinetics of competitive binding" model

Background and Purpose

Target engagement dynamics can influence drugs' pharmacological effects. Kinetic parameters for drug:target interactions are often quantified by evaluating competition association experiments—measuring simultaneous protein binding of labelled tracers and unlabelled test compounds over time—with Motulsky–Mahan's “kinetics of competitive binding” model. Despite recent technical improvements, the current assay formats impose practical limitations to this approach. This study aims at the characterisation, understanding and prevention of these experimental constraints, and associated analytical challenges.

Experimental Approach

Monte Carlo simulations were used to run virtual kinetic and equilibrium tracer binding and competition experiments in both normal and perturbed assay conditions. Data were fitted to standard equations derived from the mass action law (including Motulsky–Mahan's) and to extended versions aiming to cope with frequently observed deviations of the canonical traces. Results were compared to assess the precision and accuracy of these models and identify experimental factors influencing their performance.

Key Results

Key factors influencing the precision and accuracy of the Motulsky–Mahan model are the interplay between compound dissociation rates, measurement time and interval frequency, tracer concentration and binding kinetics and the relative abundance of equilibrium complexes in vehicle controls. Experimental results produced recommendations for better design of tracer characterisation experiments and new strategies to deal with systematic signal decay.

Conclusions and Implications

Our data advances our comprehension of the Motulsky–Mahan kinetics of competitive binding models and provides experimental design recommendations, data analysis tools, and general guidelines for its practical application to in vitro pharmacology and drug screening.

Kinetic operational models of agonism for G-protein-coupled receptors

The application of kinetics to research and therapeutic development of G-protein-coupled receptors has become increasingly valuable. Pharmacological models provide the foundation of pharmacology, providing concepts and measurable parameters such as efficacy and potency that have underlain decades of successful drug discovery. Currently there are few pharmacological models that incorporate kinetic activity in such a way as to yield experimentally-accessible drug parameters. In this study, a kinetic model of pharmacological response was developed that provides a kinetic descriptor of efficacy (the transduction rate constant, k_τ) and allows measurement of receptor-ligand binding kinetics from functional data. The model assumes: (1) receptor interacts with a precursor of the response ("Transduction potential") and converts it to the response. (2) The response can decay. Familiar response vs time plots emerge, depending on whether transduction potential is depleted and/or response decays. These are the straight line, the "association" exponential curve, and the rise-and-fall curve. Convenient, familiar methods are described for measuring the model parameters and files are provided for the curve-fitting program Prism (GraphPad Software) that can be used as a guide. The efficacy parameter k_τ is straightforward to measure and accounts for receptor reserve; all that is required is measurement of response over time at a maximally-stimulating concentration of agonist. The modular nature of the model framework allows it to be extended. Here this is done to incorporate antagonist-receptor binding kinetics and slow agonist-receptor equilibration. In principle, the modular framework can incorporate other cellular processes, such as receptor desensitization. The kinetic response model described here can be applied to measure kinetic pharmacological parameters than can be used to advance the understanding of GPCR pharmacology and optimize new and improved therapeutics.