Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic...

Area of Science:

• Cell biology
• Biophysics
• Mathematical modeling

Background:

• Actin patterns (waves, peaks) are observed in cells.
• Existing models focus on filamentous actin (F-actin) and nucleation promoting factors (NPFs).
• Small GTPases are known NPFs with distinct active/inactive states.

Purpose of the Study:

• To present a new, biologically-motivated model for F-actin-NPF interactions.
• To investigate the role of GTPase properties in actin pattern formation.
• To explore the relationship between NPF kinetics, negative feedback, and emergent actin dynamics.

Main Methods:

• Developed a simplified mathematical model of F-actin and GTPase-based NPFs.
• Incorporated negative feedback of F-actin to localize activity.
• Utilized nonlinear bifurcation analysis and simulations to explore parameter space.

Main Results:

• The model reproduces diverse actin patterns: static polarization, single pulses, waves, wave trains, and oscillations.
• Weak actin feedback leads to static patterns.
• Moderate feedback generates traveling waves, while strong feedback results in wave trains or pattern suppression.
• Identified distinct pattern initiation mechanisms and parameter regimes.

Conclusions:

• The model successfully explains various actin pattern formations based on NPF-actin interactions and feedback.
• GTPase properties and feedback strength are key determinants of cellular actin dynamics.
• The study provides insights into mechanisms underlying cell polarization and pattern generation.