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A comprehensive mathematical model for three-body binding equilibria.

ABSTRACT: Three-component systems are often more complex than their two-component counterparts. Although the reversible association of three components in solution is critical for a vast array of chemical and biological processes, no general physical picture of such systems has emerged. Here we have developed a general, comprehensive framework for understanding ternary complex equilibria, which relates directly to familiar concepts such as EC50 and IC50 from simpler (binary complex) equilibria. Importantly, application of our model to data from the published literature has enabled us to achieve new insights into complex systems ranging from coagulation to therapeutic dosing regimens for monoclonal antibodies. We also provide an Excel spreadsheet to assist readers in both conceptualizing and applying our models. Overall, our analysis has the potential to render complex three-component systems--which have previously been characterized as "analytically intractable"--readily comprehensible to theoreticians and experimentalists alike.

SUBMITTER: Douglass EF

PROVIDER: S-EPMC3717292 | biostudies-literature | 2013 Apr

REPOSITORIES: biostudies-literature

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A comprehensive mathematical model for three-body binding equilibria.

Douglass Eugene F EF Miller Chad J CJ Sparer Gerson G Shapiro Harold H Spiegel David A DA

Journal of the American Chemical Society 20130416 16

Three-component systems are often more complex than their two-component counterparts. Although the reversible association of three components in solution is critical for a vast array of chemical and biological processes, no general physical picture of such systems has emerged. Here we have developed a general, comprehensive framework for understanding ternary complex equilibria, which relates directly to familiar concepts such as EC50 and IC50 from simpler (binary complex) equilibria. Importantl ...[more]

PMID: 23544844

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Project description:Neuromuscular physiology is a vibrant research field that has recently seen exciting advances. Previous publications have focused on thorough analyses of particular aspects of neuromuscular physiology, yet an integration of the various novel findings into a single, comprehensive model is missing. In this article, we provide a unified description of a comprehensive mathematical model of surface electromyographic (EMG) measurements and the corresponding force signal in skeletal muscles, both consolidating and extending the results of previous studies regarding various components of the neuromuscular system. The model comprises motor unit (MU) pool organization, recruitment and rate coding, intracellular action potential generation and the resulting EMG measurements, as well as the generated muscular force during voluntary isometric contractions. Mathematically, it consists of a large number of linear PDEs, ODEs, and various stochastic nonlinear relationships, some of which are solved analytically, others numerically. A parameterization of the electrical and mechanical components of the model is proposed that ensures a physiologically meaningful EMG-force relation in the simulated signals, in particular taking the continuous, size-dependent distribution of MU parameters into account. Moreover, a novel nonlinear transformation of the common drive model input is proposed, which ensures that the model force output equals the desired target force. On a physiological level, this corresponds to adjusting the rate coding model to the force generating capabilities of the simulated muscle, while from a control theoretic point of view, this step is equivalent to an exact linearizing transformation of the controlled neuromuscular system. Finally, an alternative analytical formulation of the EMG model is proposed, which renders the physiological meaning of the model more clear and facilitates a mathematical proof that muscle fibers in this model at no point in time represent a net current source or sink. A consistent description of a complete physiological model as presented here, including thorough justification of model component choices, will facilitate the use of these advanced models in future research. Results of a numerical simulation highlight the model's capability to reproduce many physiological effects observed in experimental measurements, and to produce realistic synthetic data that are useful for the validation of signal processing algorithms.

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A comprehensive mathematical model for three-body binding equilibria.

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A comprehensive mathematical model for three-body binding equilibria.

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