First reliable recipe developed for hydrodynamical simulations in biomembranes

Since the 1960s, scientists have been able to reliably model movement in fluid suspensions in three dimensions. Taming the physics in two dimensions, surprisingly, has proven to be significantly more challenging. New research published in The Journal of Chemical Physics finally tackled the problem with an elegant mathematical framework. The results provide a useful tool in modeling diffusion of multiple proteins across biomembranes.

While the solution for three dimensions — called the Rotne-Prager-Yamakawa tensor — can be used to simulate particles moving through a fluid, it won’t allow for simulating diffusion across a membrane. In two dimensions, interactions among particles arising from mutual drag forces are particularly strong — much stronger than they are in three — and must be taken into account. Past attempts at modeling such thin film systems yielded only partial solutions that suffer from instabilities and unphysical behaviors, such as negative friction. This new method accounts properly for the drag forces and can produce physical results for any configuration of particles.

The authors proved the effectiveness of the new tensor with two cases: a pair of particles, and a circular ring of particles. In both cases of their simplistic simulation of the movement of proteins across a membrane, the tensor proved effective.

The results offer a valuable tool for biophysics. The tensor enables the proper modeling of diffusion across membranes when taking hydrodynamical interactions into account. Potential applications for this type of modeling include Brownian dynamics simulations of membrane proteins, and studies of permeability of lipids through protein “corrals” in membranes.

Source: “Many-particle mobility and diffusion tensors for objects in viscous sheets,” by Yulia Sokolov and Haim Diamant, The Journal of Chemical Physics (2018). The article can be accessed at https://doi.org/10.1063/1.5037061 .