Modeling and simulation of active fluids

Abstract

Within cells, the cytoskeleton organizes into polymer networks with unique properties. At short time-scales, they behave elastically. However, due to molecular turnover, at longer time-scales they behave like viscous fluids in low Reynold limit. In addition to this, they are capable of actively developing tension, thanks to molecular motors using chemical energy . At the tissue scale, epithelial cell formed by monolayers can exhibit, in some regimes, a similar active fluid behavior. Contractile forces plays a key role in tissue, for example, in organ development, wound healing, remodeling of the newly synthesized connective tissue, and in sub-cellular level like cell elongation, contraction, rearrangements, cell adhesion, division, cell migration and furrow construction in cytokinesis. Furthermore, as a part of optogenetic technnique, the doped epithelial tissues experience contractility upon illumination. Motivated by this, in the present work we considered a monolayer of cells with illumination as an external power input defined as an tension pattern in space and time to engineer contractility patterns to transport material from one part of the tissue to another or to engineer morphogensis. Altogether, for the system at low Reynold’s limit, governing equations of this compressible active visco-elastic model are developed using traditional continuum approach and Onsager’s variational principle and solved using linear finite elements. The system is non-dimensionalized and the effect of each independent parameter on the system is analyzed. Finally, this model helps in examining the principles that govern the ability to remodel the material by applying space-time patterns of activity.