Estimating the Rate Constant from Biosensor Data via an Adaptive Variational Bayesian Approach
Abstract
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 illposed 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.03795
 Bibcode:
 2019arXiv190203795Z
 Keywords:

 Mathematics  Statistics Theory