# Fast crystallization of rotating membrane proteins

## TL;DR

This paper demonstrates that actively rotating membrane proteins can self-assemble into stable, rotating hexagonal lattices driven by hydrodynamic and repulsive interactions, revealing a novel mechanism for membrane protein crystallization.

## Contribution

The study introduces a new understanding of how rotational hydrodynamic interactions facilitate the crystallization of membrane proteins into stable lattices.

## Key findings

- Rotating membrane proteins can form hexagonal lattices.
- The crystal rotation speed depends on protein density and lattice size.
- Rotational interactions act as a bounded, stabilizing 'temperature' for order.

## Abstract

We examine the interactions between actively rotating proteins moving in a membrane. Experimental evidence suggests that such rotor proteins, like the ATP synthases of the inner mitochondrial membrane, can arrange themselves into lattices. We show that crystallization is possible through a combination of hydrodynamic and repulsive interactions between the rotor proteins. In particular, hydrodynamic interactions induce rotational motion of the rotor protein assembly that, in the presence of repulsion, drives the system into a hexagonal lattice. The entire crystal rotates with an angular velocity which increases with motor density and decreases with lattice diameter - larger and sparser arrays rotate at a slower pace. The rotational interactions allow ensembles of proteins to sample configurations and reach an ordered steady state, which are inaccessible to the quenched nonrotational system. Rotational interactions thus act as a sort of temperature that removes disorder, except that actual thermal diffusion leads to expansion and loss of order. In contrast, the rotational interactions are bounded in space. Hence, once an ordered state is reached, it is maintained at all times.