Inferring diffusion in single live cells at the single-molecule level

Abstract

The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single-molecule and single-cell level can add significant insight into understanding molecular architectures of diffusing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell membrane under relatively physiological conditions compared with competing single-molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the molecular level owing to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles; however, this generally requires more data points than is typical for single FP tracks owing to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes to discriminate multiple complex modes probabilistically. It is a computational approach that biologists can use to understand single-molecule features in live cells.

Analytical tools for single-molecule fluorescence imaging in cellulo

“…Tracking fluorescent particles in a cell membrane is complicated because the trajectories may be interpreted based on different biological phenomena and particle diffusion models, such as Brownian or normal diffusion via a two-dimensional random walk, directed motion, confined diffusion, or anomalous or sub-diffusion. 46 Similarly, photophysics of the fluorescent reporter tag on the particle being tracked may add complications resulting in, for example, particle blinking manifest as truncated particle trajectories. Nearest-neighbour methods are simple to implement but very sensitive to noise.…”

“…To counter this, my laboratory has developed a novel method called Bayesian Analysis to Ranking Diffusion (BARD) that uses propagator functions of diffusive processes directly to discriminate different modes that is capable of working on short fluorescent tracks . 46 Brownian motion represents 'normal' diffusion characterized by a linear relation between time interval in the molecular trajectory and MSD. However, a tracked protein trajectory for which the MSD plateaus at large values of time interval indicates confinement suggesting that the protein is trapped by its local environment; such corrals may be important to forming nano-chambers for reactions thereby greatly enhancing the physical chemical efficiency.…”

Imaging Live Cells at the Nanometer-Scale with Single-Molecule Microscopy: Obstacles and Achievements in Experiment Optimization for Microbiology

“…For MSD analysis, only points in the first 50%–60% of time-lags are plotted because MSD values at larger values are averages drawn from few points and therefore have large errors [129,138]. This commonly used threshold is somewhat arbitrary [139], however.…”

Towards physiological complexity with in vitro single-molecule biophysics

“…The above discussion intimates that non-ergodicity arises only from pronounced static disorder, a persistent heterogeneity in a population of biological macromolecules. However, in the case of diffusion, on a cell surface for example, certain physical processes can disrupt molecular movement and cause anomalous diffusion that is either faster or slower than that expected for a strictly Brownian particle [35,[38][39][40]. In some cases, anomalous diffusion also betrays non-ergodicity.…”