Maximum likelihood estimation for single particle, passive microrheology data with drift

Abstract

SynopsisVolume limitations and low yield thresholds of biological fluids have led to widespread use of passive microparticle rheology. The mean-squared-displacement (MSD) statistics of bead position time series (bead paths) are either applied directly to determine the creep compliance [1] or transformed to determine dynamic storage and loss moduli [2]. A prevalent hurdle arises when there is a non-diffusive experimental drift in the data. Commensurate with the magnitude of drift relative to diffusive mobility, quantified by a Péclet number, the MSD statistics are distorted, and thus the path data must be "corrected" for drift. The standard approach is to estimate and subtract the drift from particle paths, and then calculate MSD statistics. We present an alternative, parametric approach using maximum likelihood estimation that simultaneously fits drift and diffusive model parameters from the path data; the MSD statistics (and consequently the compliance and dynamic moduli) then follow directly from the best-fit model. We illustrate and compare both methods on simulated path data over a range of Péclet numbers, where exact answers are known. We choose fractional Brownian motion as the numerical model because it affords tunable, sub-diffusive MSD statistics consistent with typical 30 second long, experimental observations of microbeads in several biological fluids. Finally, we apply and compare both methods on data from human bronchial epithelial cell culture mucus.

Technological strategies to estimate and control diffusive passage times through the mucus barrier in mucosal drug delivery

“…boldΘ^=argmaxboldΘp(X∣Θ), along with its error bars, can be calculated efficiently via the methods in [46, 47, 80]. In particular, [47] show that the generalized Rouse-GLE model provides a much better fit than fBM to tracer particles in 2.5% wt human bronchial epithelial (HBE) mucus, reliably detecting t min , the transition time from ordinary to sub-diffusive MSD scaling.…”

“…Second, correlations in the increments of a path can be influenced by a host of factors, and often several completely different mechanisms can have the same effect on the “shape” (i.e., scaling) of the MSD locally and globally versus lag time (time between increments). Third, standard methods for calculating the MSD (e.g., using overlapping lag times to get enough data for longer lag times, and estimating particle by a non-zero mean of the increments, then subtraction of drift from the increments) impose correlations that skew the MSD estimate [46, 47].…”

“…Such a strategy requires sophisticated modeling of transient, sub-diffusive processes together with significant experimental and theoretical challenges to identify the timescales of memory due to elasticity of the network (cf. [46–51]).…”

Estimation of microscope drift using fluorescent nanodiamonds as fiducial markers

“…MLE has been widely used in single molecule tracking (Mortensen et al, 2010;El Beheiry et al, 2016;Yu, 2016), microrheology (Mellnik et al, 2016), electron microscopy (Van Aert et al, 2005) and drift estimation (Kleinhans & Friedrich, 2007). If the tracks of fiducial markers contain only Gaussian noise, averaging multiple tracks is sufficient for drift estimation.…”

Decorrelation correction for nanoparticle tracking analysis of dilute polydisperse suspensions in bulk flow

“…These optimally accurate estimators are generally derived from parametric models of non-Brownian motion or other errors [17][18][19]. For example, random motion overlayed by uniform, constant directed motion leads to first-and second-order terms for mean-squared displacement (MSD), which can be determined simultaneously using maximum likelihood estimation [20]. Orthogonal experiments that reduce the dimension of the parametric model are also effective, such as using immobile beads to estimate localization error [21,22].…”