Optimal Non-Markovian Search Strategies with n-Step Memory

Area of Science:

• Physics
• Biophysics
• Statistical Mechanics

Background:

• Stochastic search processes are common in nature.
• Memory enhances search efficiency by recalling past locations.
• Autochemotaxis, where a cell avoids its own secreted signal, is a natural example of a search with memory.

Purpose of the Study:

• To develop a general formalism for analyzing non-Markovian search processes with memory.
• To compute the mean first-passage time (MFPT) for non-Markovian random walks on a lattice.
• To investigate the efficiency of autochemotactic searchers.

Main Methods:

• Developed a general formalism for calculating MFPT in non-Markovian random walks.
• Analyzed the impact of n-step transition probabilities on search efficiency.
• Modeled autochemotactic searchers and their interaction with chemical signals.

Main Results:

• Optimal n-step transition probabilities systematically decrease MFPT with increasing steps.
• Efficient search strategies can be reduced to simple cycles, with mirror-asymmetric walks being more effective.
• Autochemotaxis, with optimal searcher-chemical coupling, reduces MFPT to one-third of that for Markovian random walks.

Conclusions:

• Memory-equipped search processes, particularly autochemotaxis, offer significant efficiency gains over memoryless processes.
• Optimal search strategies involve specific cyclic and asymmetric movements.
• The developed formalism provides a framework for understanding and optimizing complex search behaviors.