Many-body forces between membrane inclusions: A new pattern-formation mechanism

The elastic interaction of membrane inclusions provides a unique physical realization of multibody forces. We derive an expression for the multibody curvature interaction between membrane proteins, and show that this interaction cannot be approximated by a pairwise additive theory. However, the interaction can be decomposed into a repulsive pairwise part and a non-pairwise part of similar magnitude which is anisotropic and can be attractive. This non-pairwise interaction can create stable spatial patterns which arise from an interplay between thermal fluctuations and competing pairwise repulsive and non-pairwise attractive interactions. We present numerical simulations which show how aggregates can assemble into ordered patterns from a random initial distribution at room temperature.