Learning diffusion coefficients, kinetic parameters, and the number of underlying states from a multi-state diffusion process: robustness results and application to PDK1/PKC$\alpha$, dynamics

TL;DR

This paper develops a Bayesian MCMC method to infer diffusion and kinetic parameters, including the number of states, from multi-state diffusion data, with robustness analysis and application to single molecule trajectories of PDK1/PKCα.

Contribution

It introduces a robust Bayesian approach for parameter inference and model selection in multi-state diffusion processes, addressing challenges in state degeneracy and model complexity.

Findings

Method accurately infers parameters from simulated data.

Successfully applied to real single molecule diffusion trajectories.

Demonstrates the ability to determine the number of diffusive states.

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. In this work, we investigate a multi-state 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. We consider two models for this behavior: a mixture model and a hidden Markov model (HMM). For both, we adopt a Bayesian approach to sample the distributions of the underlying parameters and implement a Markov Chain Monte Carlo (MCMC) scheme to compute the posterior distributions, as in Das, Cairo, Coombs (2009). 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, we investigate the problem of determining the number of diffusive states using model selection criteria. We present results from simulated data that demonstrate proof of concept, as well as apply our 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$\alpha$) to form a heterodimer detected by its significantly lower diffusivity. All matlab software is available here: \url{https://github.com/MathBioCU/SingleMolecule}