Geometric phase predicts locomotion performance in undulating living systems across scales

Area of Science:

• Biomechanics
• Comparative Physiology
• Mathematical Biology

Background:

• Self-propelling organisms use self-deformation for locomotion.
• Limbess vertebrates and invertebrates often employ traveling waves of axial body bending.
• Understanding how deformation parameters influence locomotor performance is challenging.

Purpose of the Study:

• To develop a geometric framework for analyzing and comparing wave dynamics in organismal locomotion.
• To investigate the universality of locomotion patterns across different taxa and body sizes.
• To propose hypotheses for neuromechanical control schemes.

Main Methods:

• Application of a geometric framework to analyze self-deformation patterns.
• Focus on highly damped environments applicable to viscous and frictional media.
• Description of traveling wave dynamics using time series of weights for two principal modes.

Main Results:

• Locomotion of nematode worms and desert snakes/lizards can be described by two principal modes.
• Mode weight trajectories form closed paths enclosing near-maximal geometric phase.
• This geometric approach applies to organisms spanning two decades in body length.

Conclusions:

• The geometric framework provides a unified description of locomotion across diverse taxa.
• Identified "serpenoid templates" as potential targets of neuromechanical control.
• Complex behaviors like turning and sidewinding can be explained as modulations of these templates.