Errors in energy landscapes measured with particle tracking

TL;DR

This paper investigates how localization errors in particle tracking distort measured energy landscapes, deriving formulas to correct biases caused by static and dynamic errors in biological and soft matter studies.

Contribution

It provides a theoretical framework and correction methods for biases in energy landscape measurements caused by localization errors in particle tracking.

Findings

Static errors decrease measured potential depth.

Dynamic errors increase apparent spring stiffness.

Corrective formulas enable more accurate energy landscape reconstructions.

Abstract

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet, video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame acquisition time. We show that these errors result in systematic and non-trivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials, by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors, but decreased by static errors. Our formula allows for the development of efficient corrections schemes, which we also present in this paper.