Abstract
The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.
Highlights
One of the characteristics that distinguishes living things from non-living things is motility
The starred values are only valid for sequential attachments. (For the purposes of finding an estimate for the mean square displacement (MSD), the probabilities on the table are for the entire state space even though the random variables for a detach event are only valid for a sequential configuration.)
MSD is a measure of the overall drift of a particle and can be a useful tool for understanding cell motion because it indicates mode of transport
Summary
OPEN ACCESS Citation: Rosen ME, Grant CP, Dallon JC (2021) Mean square displacement for a discrete centroid model of cell motion. The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. The mean square displacement gives a measure of overall drift, but it is an indicator of mode of transport. A lower bound and upper bound for the mean square displacement are given. The upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached
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