Run-and-tumble bacteria slowly approaching the diffusive regime.

Area of Science:

• Statistical Physics
• Biophysics
• Soft Matter Physics

Background:

• Bacterial swimmers exhibit run-and-tumble (RT) dynamics, transitioning from ballistic motion to diffusive behavior.
• Characterizing this transition requires more than just mean-squared displacement (MSD), necessitating analysis of displacement distribution.

Purpose of the Study:

• To determine the time scale for dilute bacterial swimmer suspensions to reach the diffusive regime.
• To quantify deviations from diffusive dynamics, focusing on excess kurtosis and non-Gaussian behavior.
• To investigate four distinct bacterial swimming strategies: conventional RT, partial reorientation, run-and-reverse, and protein-concentration-dependent RT.

Main Methods:

• Analysis of kinetic equations for the probability density function.
• Computer simulations of the four swimming models.
• Theoretical approach using eigenvalue and angular Fourier expansions of the van Hove function.

Main Results:

• Models with partial reorientation, run-and-reverse, and protein-dependent tumbling show prolonged relaxation to diffusion, with large displacement tails.
• Significant positive excess kurtosis values were observed, indicating non-Gaussian displacement distributions.
• Linear MSD was achieved in some partial reorientation and low rotational diffusivity run-and-reverse models, yet dynamics remained non-Gaussian.

Conclusions:

• The transition to diffusion in bacterial swimming is complex and can be significantly delayed in modified RT models.
• Excess kurtosis is a crucial metric for identifying non-Gaussian dynamics, even when MSD appears linear.
• Theoretical predictions align well with simulation results, validating the analytical approach for understanding bacterial motility.