Motor-driven bacterial flagella and buckling instabilities.

Area of Science:

• Biophysics
• Microbiology
• Fluid Dynamics

Background:

• Bacteria utilize rotating flagella for motility.
• Flagellar rotation generates thrust for cell propulsion.
• The flexible hook transmits torque from the motor to the flagellum.

Purpose of the Study:

• To model and analyze the buckling behavior of bacterial flagella under motor-induced torque and thrust.
• To investigate the relationship between motor torque, thrust force, and flagellar buckling.
• To explore the implications of flagellar buckling on bacterial locomotion and stability.

Main Methods:

• Discretization of Kirchhoff's elastic-rod theory for modeling.
• Development of a coarse-grained approach for helical filament simulation.
• Analysis of buckling transitions via supercritical Hopf bifurcation.
• Integration of a spherical cell body model to simulate locomotion.

Main Results:

• Flagella buckle at critical motor torques due to generated thrust.
• Buckling manifests as a supercritical Hopf bifurcation in thrust force.
• A second buckling transition occurs at higher motor torques.
• Locomotion simulations show buckling during cell body movement.
• A quantitative model accurately predicts the critical force-torque relationship.

Conclusions:

• Bacterial flagellar buckling is predicted to occur under physiological conditions.
• The orientation of flagella relative to torque is crucial for stability.
• Findings have biological relevance for marine bacteria motility and stability.