Feedback between motion and sensation provides nonlinear boost in run-and-tumble navigation

Area of Science:

• Biophysics
• Cellular Biology
• Systems Biology

Background:

• Organisms navigate chemical gradients using a strategy of alternating straight movements (runs) and random reorientations (tumbles).
• Tumbling probability is modulated by the organism's internal state, which depends on past signal levels, creating a link between movement and sensation.
• While negative feedback typically maintains adaptation, positive feedback can emerge, enhancing movement up gradients.

Purpose of the Study:

• To investigate the role of positive feedback in run-and-tumble navigation, particularly in physiologically relevant parameter spaces.
• To explain the emergence of large transients and asymmetric movement patterns during gradient climbing.
• To demonstrate how non-normal dynamics and nonlinearity contribute to efficient chemotaxis.

Main Methods:

• Analysis of movement and sensation coupling in a run-and-tumble model.
• Investigation of positive feedback dominance in shallow gradients.
• Identification of non-normal dynamics and nonlinear amplification effects.

Main Results:

• Positive feedback can dominate navigation dynamics even in shallow gradients, contrary to previous assumptions.
• Non-normal dynamics, characterized by non-orthogonal eigenvectors, lead to significant transient behaviors.
• A fundamental nonlinearity amplifies these transients asymmetrically, elongating runs in favorable directions.
• This results in a "ratchet-like" gradient climbing with drift speeds approaching half the maximum run speed.

Conclusions:

• The study reveals that positive feedback and non-normal dynamics are crucial for efficient gradient climbing in run-and-tumble navigation.
• Asymmetric amplification of transients provides a "ratchet" mechanism that mitigates wasteful runs.
• This strategy enhances chemotaxis efficiency, overcoming limitations of classical models.