[Paper Review] Model comparison for single particle tracking in biological fluids

Martin Lysy, Natesh S. Pillai+5 more|arXiv (Cornell University)|Jul 22, 2014

Fractional Differential Equations Solutions73 references3 citations

TL;DR

This study uses Bayesian model comparison to evaluate fractional Brownian motion (fBM) and generalized Langevin equation (GLE) models for 1-µm tracer particles in human lung mucus. Data favor fBM or GLEs with long memory spectra, rejecting models with small to moderate memory, highlighting the need for viscoelastic modeling in biological fluids beyond simple Brownian motion.

ABSTRACT

State-of-the-art techniques in particle tracking microscopy provide high-resolution path trajectories for the dynamical analysis of diverse foreign particles in biological fluids. For particles on the order of one micron in diameter, these paths are not generally consistent with simple Brownian motion. Despite an abundance of data confirming these findings, stochastic modeling of the complex particle motion has received comparatively little attention. Yet, prediction beyond experimental time scales -- such as first-passage times through biological barriers -- is a fundamental scientific objective that requires a careful statistical approach. Even among existing candidate models, few attempts have been made at likelihood-based model comparisons and other quantitative evaluations. In this article, we employ a robust Bayesian methodology to address this gap. We analyze two competing models -- fractional Brownian motion (fBM) and a generalized Langevin equation (GLE) consistent with viscoelastic theory -- applied to an ensemble of 30 second paths of 1 micron diameter tracer particles in human lung mucus. We conclude that either fBM or a GLE with a long memory spectrum are favored by the data, whereas GLEs with small to moderate memory spectra are insufficient.

Motivation & Objective

• To address the lack of rigorous statistical comparison among stochastic models for particle motion in complex biological fluids.
• To evaluate whether fractional Brownian motion (fBM) or generalized Langevin equation (GLE) models better explain observed trajectories of 1-µm particles in human lung mucus.
• To determine which model structure—specifically, memory spectrum length—best fits experimental data from 30-second particle paths.
• To enable reliable prediction of long-time dynamics, such as first-passage times through biological barriers, by selecting the most appropriate stochastic model.
• To establish a robust likelihood-based framework for model evaluation in single particle tracking, filling a gap in current biophysical modeling practices.

Proposed method

• Employing a Bayesian inference framework to compute marginal likelihoods (evidence) for competing models, enabling direct model comparison.
• Applying the method to 30-second trajectories of 1-µm tracer particles in human lung mucus, collected via high-resolution particle tracking microscopy.
• Evaluating two primary models: fractional Brownian motion (fBM), characterized by a Hurst parameter H, and generalized Langevin equations (GLEs) with different memory kernel spectra.
• Using the GLE framework to test models with varying memory characteristics—specifically, long memory versus small to moderate memory spectra.
• Computing Bayes factors to quantify relative model support, favoring models with higher marginal likelihoods.
• Assessing model fit and predictive performance through posterior predictive checks and cross-validation on trajectory ensembles.

Experimental results

Research questions

• RQ1 Which stochastic model—fractional Brownian motion or generalized Langevin equation—best explains the observed motion of 1-µm particles in human lung mucus?
• RQ2 How does the memory spectrum length in GLE models affect model fit to experimental particle trajectories?
• RQ3 Is there statistical evidence favoring fBM over GLE models, or vice versa, based on likelihood-based comparison?
• RQ4 Can models with small to moderate memory spectra in the GLE framework adequately describe the dynamics of particles in viscoelastic biological fluids?
• RQ5 To what extent do the data support the use of viscoelastic models over simple Brownian motion for predicting long-time dynamics like first-passage times?

Key findings

• Fractional Brownian motion (fBM) is strongly supported by the data as a viable model for 1-µm particle motion in human lung mucus.
• Generalized Langevin equations (GLEs) with long memory spectra are also favored, indicating that viscoelastic effects with persistent memory are essential to describe the dynamics.
• GLE models with small to moderate memory spectra are statistically rejected, suggesting they fail to capture the long-range temporal correlations observed in the data.
• The Bayesian model comparison framework successfully identified the most plausible stochastic models, demonstrating the importance of likelihood-based evaluation in complex biological systems.
• The results imply that viscoelasticity plays a key role in particle transport in mucus, and models must account for long-range temporal correlations to predict long-time behavior accurately.
• The ensemble of 30-second trajectories exhibits persistent motion inconsistent with standard Brownian motion, necessitating more complex stochastic models.