Flow & Transport in Poroelastic Biological Networks

Biphasic materials composed of deformable solid-like structures, permeated by an interstitial fluid-like phase are found everywhere in cell biology. Examples include tissues, the cell cytoskeleton, and the cell nucleus. In many processes the mechanical deformations coincide with volumetric contraction and expansion of the skeleton. The poroelastic relaxation time associated with the relaxation of fluid pressure and network stresses increase with the distance from the applied stress. Recent studies suggests that poroelastic relaxation may be very consequential to some cellular functions, such as setting a constraint on the rate of swelling and mechanical response of plant cells, contraction of muscle fibers, and blebbing of the plasma membrane. Yet, the effect of these volumetric flows on the mechanics and transport of proteins and organelles within the network remains unexplored. We focus on three aspects of this problem:

• Mathematical aspects: We extend the framework of Stokes flow microhydrodynamics to biphasic systems to develop highly efficient pseudo-analytical and numerical methods for studying transport in poroelastic media.

• Physics in model-systems: Using these tools we study the transport of a single or a collection of rigid or deformable inclusions in simple and idealized geometries.

• Applying the tools and physics to biology: The interior structure of the cell nucleus is a heterogenous poroelastic medium. In collaboration with Superfine (Applied Physical Sciences, UNC-CH) and Bloom (Biology, UNC-CH) Labs we aim to combine modeling and experiment to study the interplay between structural heterogeneity and nuclear mechanics and transport and how that mediates gene transcription through active (advective) and passive (diffusion) processes.