Many-body interactions between curvature-inducing membrane inclusions with arbitrary cross-sections

Area of Science:

• Membrane biophysics
• Soft matter physics
• Computational physics

Background:

• Membrane inclusions induce curvature, affecting membrane properties.
• Understanding multi-body interactions is crucial for biological and material systems.

Purpose of the Study:

• To analytically and numerically investigate interactions between multiple identical membrane inclusions.
• To determine how inclusion shape and arrangement influence interaction forces.

Main Methods:

• Analytical multipolar expansion for tensionless membranes.
• Numerical computation of multi-body interaction contributions.
• Analysis of inclusions with arbitrary cross-sections and regular polygonal arrangements.

Main Results:

• Analytical expressions for total asymptotic interaction up to N=6 circular inclusions.
• Multi-body contributions are comparable to pairwise interactions.
• For N=5, interaction scales as d^-6; for N!=5, it scales as d^-4.
• Non-circular inclusions exhibit attractive (d^-2) or repulsive (d^-4) interactions depending on lobe number and amplitude.

Conclusions:

• Analytical and numerical results show good agreement, confirming repulsive interactions for circular inclusions.
• Inclusion shape and arrangement significantly alter interaction behavior, including attraction at large distances for specific non-circular shapes.
• Interaction dependence on in-plane rotation angles is characterized.