Diffusion through complex confining environments: Motion in fluctuating porous membrane structures

The transport of individual entities through interconnected structures is a process of practical relevance in both biology and technology. Examples are given by diffusive dynamics of molecules in porous structures. In soft environments, this transport can be strongly influenced by fluctuations of the porous structure itself. Here, we focus on triply periodic membrane structures found in both cell organelles and synthetic amphiphilic systems. We theoretically study the effect of a complex three-dimensional fluctuating environment on the diffusive motion of a test object using a phase-field approach. The rigid spherical test object is energetically forced not to penetrate the membrane. Generally, the pores of the membrane structure can be smaller than the diffusing object. Yet fluctuations in the membrane can intermittently widen its pores, still allowing for the larger particles to move through them. Thus, the object stays trapped for a while inside one cavity formed by the membrane, before an appropriate fluctuation event widens a membrane pore at the right moment, allowing the object to jump into the next cavity. The process is reflected by a pronounced plateau in the time evolution of the mean squared displacement. We think that the described scenario should be directly observable, for instance, in protein diffusion through biological environments.