Mean square displacement for a discrete centroid model of cell motion

Area of Science:

• Biophysics
• Statistical Mechanics
• Computational Biology

Background:

• The mean square displacement (MSD) is a crucial metric for analyzing stochastic processes and trajectories.
• In cell biology, MSD quantifies overall drift and indicates transport mechanisms.
• Existing models often require complex calculations for accurate MSD determination.

Purpose of the Study:

• To develop an approximation for the mean square displacement (MSD) in a discrete-time jump process model of cell motion.
• To provide insights into the effectiveness of using a subset of the state space for MSD approximation.
• To establish bounds for the MSD in this cell motion model.

Main Methods:

• Developed a discrete-time jump process model approximating a force-based cell motion model.
• Calculated the MSD for a subset of the state space.
• Utilized this subset MSD as an approximation for the entire state space.
• Derived lower and upper bounds for the MSD.

Main Results:

• The MSD approximation using a state space subset proved unexpectedly accurate for cell motion.
• Provided intuitive explanations for the efficacy of the subset approximation method.
• Established theoretical lower and upper bounds for the MSD.
• Demonstrated that while the upper bound is loose, it captures rare, large displacement events.

Conclusions:

• The proposed discrete-time jump process model offers an efficient method for approximating cell motion MSD.
• Approximating MSD using a subset of the state space is a viable and effective strategy.
• The derived bounds provide a theoretical framework for understanding displacement variations in cell motility.