High-Resolution Models of Motion of Macromolecules in Cell Membranes

The path of a macromolecule on a cell membrane is modeled by a sum of independent identically distributed random variables. Random variables with simple discrete distribution functions capture some important aspects of the jump or hop diffusion reported from single particle tracking experiments that measure the motion of single molecules on a cell membrane. The detail provided by the distribution function for the random variables is critical for accurate simulations of the motion and interactions of macromolecules on the cell membrane. Additionally, the probability distribution for the random variables is easily estimated from single-particle tracking data. The diffusion constant is given by the second moment of the probability distribution, which agrees with the diffusion constant estimated from the mean-square displacement, and thus represents far less information than the distribution function.