Stochastic modeling of protein motions within cell membranes

A simple model in which immobilizing events are imposed onto otherwise free Brownian diffusion [R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000) and a recent adaptation due to S. Khan and A. M. Reynolds, Physica A 350, 183 (2005)] is shown to encapsulate the peculiar transport characteristics of individual cell receptors within plasma membranes observed in single-particle tracking (SPT) experiments. These characteristics include the occurrence of normal diffusion; non-Gaussian subdiffusion; confined diffusion; a superdiffusive mode of transport that is not due to flow of the membrane or molecular motor attachment; and the occurrence of transitions between these transport modes. Model predictions are shown to be in close agreement with a reanalysis of existing SPT data.

Figure 1

(a) Ln-ln plot of the time evolution (in seconds) of the MSD (in pixels, using a scale of $0.205\mu \mathrm{m}∕\text{pixel}$) of MHC class II Fab-phycoerythrin on a fibroblast. Linear regression fits (dashed lines) to the short and long time behaviors are also shown. (b) Histogram of the incremental displacements in the $x$ direction in pixels that occur within the $20\mathrm{s}$ intervals between successive observations. The ensemble is taken over the entire measurement time and over all trajectories within the data set. Gaussian (dotted line) and Fox function (solid line) PDFs with equivalent mean and variance are shown for comparison.

Figure 2

(a) Ln-ln plot of the time-evolution (in seconds) of the MSD (in pixels, using a scale of $0.205\mu \mathrm{m}∕\text{pixel}$) of MHC class I. Linear regression fits (dashed lines) to the short and long time behaviors are also shown. (b) Histogram of the incremental displacements in the $x$ direction in pixels that occur within the $60\mathrm{s}$ intervals between successive observations. The ensemble is taken over the entire measurement time and over all trajectories within the data set. Gaussian (dotted line) and Fox function (solid line) PDFs with equivalent mean and variance are shown for comparison.

Figure 3

(a) Ln-ln plot of the time evolution (in seconds) of the MSD (in pixels, using a scale of $0.205\mu \mathrm{m}∕\text{pixel}$) of MHC class II Fab-phycoerythrin on a fibroblast. Linear regression fits (dashed lines) to the short and long time behaviors are also shown. (b) Histogram of observed incremental displacements in the $x$ direction in pixels that occur within the $20\mathrm{s}$ interval between successive observations. The ensemble is taken over the entire measurement time and over all trajectories within the data set. Gaussian (dotted line) and Fox function (solid line) PDFs with equivalent mean and variance are shown for comparison.

Figure 4

Distribution of the diffusion exponents found when using simulated normal diffusion data.