Learning Diffusion Coefficients, Kinetic Parameters, and the Number of Underlying States from a Multistate Diffusion Process: Robustness Results and Application to PDK1/PKC α $$\upalpha $$ Dynamics

Lewis R. Baker (), Moshe T. Gordon (), Brian P. Ziemba (), Victoria Gershuny (), Joseph J. Falke () and David M. Bortz ()
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Lewis R. Baker: University of Colorado, Department of Applied Mathematics
Moshe T. Gordon: University of Colorado, Department of Biochemistry
Brian P. Ziemba: University of Colorado, Department of Biochemistry
Victoria Gershuny: University of Colorado, Department of Applied Mathematics
Joseph J. Falke: University of Colorado, Department of Biochemistry
David M. Bortz: University of Colorado, Department of Applied Mathematics

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 1603-1638 from Springer

Abstract: Abstract Systems driven by Brownian motion are ubiquitous. A prevailing challenge is inferring, from data, the diffusion and kinetic parameters that describe these stochastic processes. This work involves an investigation into multistate diffusion process that arises in the context of single-particle tracking (SPT), wherein the motion of a particle is governed by a discrete set of diffusive states, and the tendency of the particle to switch between these states is modeled as a random process. Two models for this behavior are considered: a mixture model and a hidden Markov model (HMM). For both, a Bayesian approach is adopted to sample the distributions of the underlying parameters and implement a Markov chain Monte Carlo (MCMC) scheme to compute the posterior distributions. The primary contribution of this work is a study of the robustness of this method to infer parameters of a three-state HMM and a discussion of the challenges and degeneracies that arise from considering three states. Finally, the problem of determining the number of diffusive states using model selection criteria is investigated. The results are presented from simulated data that demonstrate proof of concept, as well as apply the method to experimentally measured single-molecule diffusion trajectories of monomeric phosphoinositide-dependent kinase-1 (PDK1) on a synthetic target membrane where it can associate with its binding partner protein kinase C alpha isoform (PKC α $$\upalpha $$ ) to form a heterodimer detected by its significantly lower diffusivity.

Keywords: Diffusion coefficient inference; Multistate diffusion; PDK1/PKC α $$\upalpha $$ dynamics; MCMC (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_50

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