Active Brownian particles with energy depots modeling animal mobility

Area of Science:

• Physics
• Biophysics
• Statistical Mechanics

Background:

• Brownian particles exhibit random motion influenced by environmental factors.
• Active biological motion requires energy intake, storage, and conversion into kinetic energy.
• Understanding energy dynamics is crucial for modeling self-propelled biological systems.

Purpose of the Study:

• To develop a simplified model for active biological motion.
• To investigate how different energy uptake mechanisms affect particle dynamics.
• To analyze the efficiency of energy conversion in active motion.

Main Methods:

• Formulation of a simplified model for active motion incorporating energy storage and conversion.
• Description of particle motion using a Langevin equation with an acceleration term.
• Analysis of energy uptake from homogeneous and localized sources.
• Application of analytic approximations for stationary motion and critical parameter calculation.

Main Results:

• Identified different forms of periodic motion (limit cycles) dependent on energy source distribution.
• Developed an analytic approximation to describe stationary motion.
• Calculated critical parameters governing energy uptake.
• Derived an analytic expression for the energy conversion efficiency ratio.

Conclusions:

• The model successfully captures key aspects of active biological motion, including energy dynamics and resulting movement patterns.
• Spatially localized energy sources can induce specific periodic behaviors, such as movement between 'nest' and 'food' locations.
• The derived efficiency ratio provides a quantitative measure for energy conversion in these active systems.