Correcting for Bias of Molecular Confinement Parameters Induced by Small Time Series Sample Sizes in Single-Molecule Trajectories Containing Measurement Noise

TL;DR

This paper develops a bias correction method for estimating molecular confinement parameters from single-molecule trajectories, accounting for finite sample sizes and measurement noise, improving accuracy in diffusion studies.

Contribution

It extends existing bias correction techniques to handle measurement noise and finite sample sizes, enabling more accurate confinement parameter estimation in single-molecule tracking.

Findings

Accurately estimates corral radius with only hundreds of observations.

Corrects bias in confinement parameters caused by finite sampling and measurement noise.

Outperforms MSD and Bayesian methods in challenging noisy, limited data scenarios.

Abstract

Several single-molecule studies aim to reliably extract parameters characterizing molecular confinement or transient kinetic trapping from experimental observations. Pioneering works from single particle tracking in membrane diffusion studies [Kusumi et al., Biophysical J., 1993] appealed to Mean Square Displacement tools for extracting diffusivity and other parameters quantifying the degree of confinement. More recently, the practical utility of systematically treating multiple noise sources (including noise induced by random photon counts) through likelihood techniques have been more broadly realized in the SPT community. However, bias induced by finite time series sample sizes has not received great attention. Mitigating parameter bias induced by finite sampling is important to any scientific endeavor aiming for high accuracy, but correcting for bias is also often an important step in the construction of optimal parameter estimates. In this article, it is demonstrated how a popular model of confinement can be corrected for finite sample bias in situations where the underlying data exhibits Brownian diffusion and observations are measured with non-negligible experimental noise (e.g., noise induced by finite photon counts). The work of Tang and Chen [J. Econometrics, 2009] is extended to correct for bias in the estimated corral radius (a parameter commonly used to quantify confinement in SPT studies) in the presence of measurement noise. It is shown that the approach presented is capable of reliably extracting the corral radius using only hundreds of discretely sampled observations in situations where other methods (including MSD and Bayesian techniques) would encounter serious difficulties. The ability to accurately statistically characterize transient confinement suggests new techniques for quantifying confined and/or hop diffusion in complex environments.