First passage times, ergodicity and ageing for single-particle tracking in biological membranes
Diego Krapf
Department of Electrical and Computer Engineering and School of Biomedical Engineering, Colorado State University, Fort Collins CO, USA
Single-molecule tracking of proteins in the cell membrane offers the possibility of directly studying the molecule dynamics. Detection at the single-molecule level allows for the localization of individual proteins with nanometer resolution and discrimination of inhomogeneous molecular distributions, providing access to the underlying mechanisms that govern protein mobility. We employ simultaneous labeling of proteins with different reporters such as fluorescent proteins (e.g. green fluorescent protein, GFP), fluorescently conjugated antibodies, and quantum dots. Each of these probes has its own advantages and disadvantages regarding stability, size, and optical properties.
Tracking individual proteins on the surface of mammalian cells reveals strikingly complex dynamics involving anomalous diffusion, transient confinement, clustering, and immobilization, to name a few examples. Theoretical models show that anomalous subdiffusion can be caused by vastly different processes. By performing time series and ensemble analysis of extensive single-molecule tracking we find that different anomalous subdiffusion processes coexist in live cells. Furthermore, the time-averaged mean square displacements (MSD) are different from the ensemble-averaged MSD, an indication of ergodicity breaking. Non-ergodic dynamics are found to be caused by immobilization events that take place when the proteins are captured within specific macromolecular complexes. This process can be accurately modeled as a continuous time random walk (CTRW) with a heavy tail distribution of waiting times. One of the most interesting phenomena of heavy-tailed CTRWs is that they can exhibit aging, that is, the MSD depends on the time that passed since the onset of the process, i.e., it depends on the age of the system. In agreement with a CTRW our data show aging in the diffusion properties of membrane proteins both in human embryonic kidney cells and in hippocampal neurons.
A very different diffusion process is observed for peripheral proteins, where protein-membrane interactions are transient. Thus, these proteins alternate between periods of two-dimensional diffusion on the membrane and three-dimensional diffusion in the bulk. When proteins dissociate from the membrane, they exert a three-dimensional random walk until they find the membrane again and are able to rebind, i.e., the process is governed by the distribution of first return times. These bulk excursions have broad implications on protein dynamics. Again, we study bulk-mediated diffusion using single-molecule tracking methods. The experimental observations are explained in terms of bulk excursions that introduce jumps with a heavy-tail distribution, rapidly increasing the explored area.
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