A Chemical Reaction Network to Generate Random, Power-Law-Distributed Time Intervals

Area of Science:

• Biophysics
• Systems Biology
• Biochemical Engineering

Background:

• Lévy walks (LWs) are movement patterns with power-law distributed waiting times, considered efficient for foraging and search.
• While complex organisms utilize LWs, the mechanism for single-cell organisms to generate these correlated behaviors remains unclear.

Purpose of the Study:

• To construct a biochemical reaction system enabling single-cell organisms to perform Lévy walks.
• To demonstrate the generation of long-time correlated concentration fluctuations for signaling.

Main Methods:

• Designed a biochemical reaction network using established modules.
• Analyzed the system's ability to produce tunable, power-law distributed time intervals.
• Investigated the autocorrelation function of signaling substance concentration fluctuations.

Main Results:

• Successfully constructed a biochemical system that generates long-time correlated concentration fluctuations.
• The system allows for tunable control over the fractional exponent of the autocorrelation function.
• The core functionality of the network demonstrates robustness across various parameter settings.

Conclusions:

• This biochemical system provides a plausible mechanism for single-cell organisms to exhibit Lévy walk behavior.
• The findings offer insights into the biophysical basis of efficient search strategies in microorganisms.
• The robust and tunable nature of the network has implications for synthetic biology and understanding biological movement.