A mathematical model of pattern formation by swimming microorganisms

Area of Science:

• Microbiology
• Fluid Dynamics
• Pattern Formation

Background:

• Bioconvection, the collective movement of microorganisms, is influenced by environmental factors.
• Tetrahymena pyriformis and Crypthecodinium cohnii exhibit complex behaviors in liquid suspensions.
• Understanding bioconvection patterns is crucial for microbial ecology and biophysics.

Purpose of the Study:

• To describe bioconvection patterns in Tetrahymena pyriformis and Crypthecodinium cohnii suspensions.
• To report novel bioconvection patterns: toroid and cat's-eye, observed in Crypthecodinium cohnii.
• To develop a mathematical model for predicting critical conditions for bioconvection onset.

Main Methods:

• Observation and documentation of bioconvection patterns in microbial suspensions.
• Development of a mathematical model for the hydrodynamics of negatively geotactic microorganisms.
• Analysis of critical depths and concentrations influencing pattern formation.

Main Results:

• Identified critical depth and concentration thresholds for bioconvection initiation.
• Discovered and described two new bioconvection patterns: toroid and cat's-eye in C. cohnii.
• The mathematical model predicts critical values and explains observed 'polka-dot' patterns.

Conclusions:

• Bioconvection onset is dependent on critical suspension depths and microorganism concentrations.
• Novel toroid and cat's-eye patterns emerge under specific shallow suspension conditions.
• The developed mathematical model accurately predicts bioconvection phenomena in dilute suspensions.