Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach

Area of Science:

• Microfluidics
• Biophysics
• Biotechnology

Background:

• Bacterial flagella possess helical geometry and autonomously change shape based on fluid properties.
• This unique characteristic enables their potential use in microscale chemical transport and regulation.
• While flagellar phase synchronization is studied, flagellar tilt synchronization for pumping is less understood.

Purpose of the Study:

• To investigate the impact of helical geometry and tilt on pumping flows generated by individual rotating flagella.
• To explore a mean-field model for an array of flagella to understand collective tilt and its influence on pumping.
• To identify conditions for self-consistent pumping solutions in engineered flagellar arrays.

Main Methods:

• Analysis of pumping flows from single rotating flagella with varying helical geometry and tilt.
• Development and application of a mean-field model for an infinite array of helical flagella.
• Time-averaging procedures to account for phase differences in the mean-field model.

Main Results:

• Identified specific array separation distances, magnetic field strengths, and rotation frequencies yielding self-consistent pumping solutions.
• Observed that individual flagellar pumping reverses with helicity or rotation reversal.
• Found that collective effects lead to tilted pumping solutions becoming untilted and nonpumping upon reversal of helicity or rotation.

Conclusions:

• Collective flagellar tilt synchronization is crucial for effective microscale pumping.
• Engineered flagellar arrays can achieve self-consistent pumping under specific conditions.
• The behavior of flagellar arrays differs significantly from individual flagella regarding pumping directionality.