Bacterial chemotaxis considering memory effects: Derivation of the reaction-diffusion equations

Area of Science:

• Microbiology
• Biophysics
• Theoretical Biology

Background:

• Bacterial chemotaxis, exemplified by Escherichia coli, relies on chemoreceptor methylation to regulate CheY-P protein levels and control tumbling.
• This methylation process is slow, leading to a memory effect in the bacterial response to chemical gradients.
• Existing Keller-Segel equations, assuming local responses, do not fully capture this memory-dependent, nonlocal behavior.

Purpose of the Study:

• To develop new macroscopic equations that accurately describe bacterial chemotaxis, incorporating the memory effect.
• To derive these equations from a kinetic approach, considering the dynamics of protein concentration alongside bacterial density.
• To analyze the resulting reaction-diffusion equations and their implications for bacterial transport.

Main Methods:

• A kinetic theory approach was employed to model bacterial transport, accounting for protein concentration dynamics.
• The Chapman-Enskog method was utilized to derive macroscopic equations from the kinetic model.
• The derived equations were solved for inhomogeneous chemical signals to analyze bacterial response and transport coefficients.

Main Results:

• New reaction-diffusion equations were obtained, with flux and source terms dependent on chemical signal gradients.
• Transport coefficients were derived from microscopic dynamics, revealing symmetry properties and specific values for E. coli.
• Nonlocal responses were observed, with a smoothing length up to 170µm for E. coli in inhomogeneous signals.

Conclusions:

• The study provides a more accurate model for bacterial chemotaxis by incorporating memory effects, leading to nonlocal responses.
• The derived equations offer explicit expressions for transport coefficients and capture phenomena beyond the scope of traditional Keller-Segel models.
• The findings highlight the importance of considering internal cellular dynamics in macroscopic descriptions of bacterial behavior.