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December 2019 Estimating the rate constant from biosensor data via an adaptive variational Bayesian approach
Ye Zhang, Zhigang Yao, Patrik Forssén, Torgny Fornstedt
Ann. Appl. Stat. 13(4): 2011-2042 (December 2019). DOI: 10.1214/19-AOAS1263


The means to obtain the rate constants of a chemical reaction is a fundamental open problem in both science and the industry. Traditional techniques for finding rate constants require either chemical modifications of the reactants or indirect measurements. The rate constant map method is a modern technique to study binding equilibrium and kinetics in chemical reactions. Finding a rate constant map from biosensor data is an ill-posed inverse problem that is usually solved by regularization. In this work, rather than finding a deterministic regularized rate constant map that does not provide uncertainty quantification of the solution, we develop an adaptive variational Bayesian approach to estimate the distribution of the rate constant map, from which some intrinsic properties of a chemical reaction can be explored, including information about rate constants. Our new approach is more realistic than the existing approaches used for biosensors and allows us to estimate the dynamics of the interactions, which are usually hidden in a deterministic approximate solution. We verify the performance of the new proposed method by numerical simulations, and compare it with the Markov chain Monte Carlo algorithm. The results illustrate that the variational method can reliably capture the posterior distribution in a computationally efficient way. Finally, the developed method is also tested on the real biosensor data (parathyroid hormone), where we provide two novel analysis tools—the thresholding contour map and the high order moment map—to estimate the number of interactions as well as their rate constants.


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Ye Zhang. Zhigang Yao. Patrik Forssén. Torgny Fornstedt. "Estimating the rate constant from biosensor data via an adaptive variational Bayesian approach." Ann. Appl. Stat. 13 (4) 2011 - 2042, December 2019.


Received: 1 September 2018; Revised: 1 April 2019; Published: December 2019
First available in Project Euclid: 28 November 2019

zbMATH: 07160929
MathSciNet: MR4037420
Digital Object Identifier: 10.1214/19-AOAS1263

Keywords: adaptive discretization algorithm , Bayesian , biosensor , integral equation , Rate constant , variational method

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.13 • No. 4 • December 2019
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