A strain-dependent diffusivity model to study the nuclear import of mechanobiological transcription factors

Nuclear spreading plays a crucial role in stem cell fate determination. In previous works, we reported evidence of multipotency maintenance of mesenchymal stromal cells cultured on three-dimensional engineered niche substrates fabricated via two-photon laser polymerization (2PP). We correlated multipotency maintenance to a more roundish nuclear morphology of cells cultured in the 2PP-fabricated niches, with respect to those on flat substrates. To interpret these findings, here we present a multiphysics model coupling nuclear strains induced by cell adhesion to diffusive transport across the cell nucleus. We reconstructed the cell nuclear geometry from confocal Z-stack images of 2PP-cultured cells, and we estimated the volume, surface and shape factors. The levels of nuclear spreading significantly varied depending on the cell localization within the niche architecture. We assumed the cell diffusivity as a function of the local volumetric strain. The computational model also indicate that the larger the nuclear deformation (e.g. in spread nuclei), the higher the nuclear flux of small solutes such as transcription factors through the nuclear membrane. Our results point towards nuclear deformation as a primary mechanism by which the stem cell translates its shape into a fate decision, i.e. through a strain-dependent amplification of the diffusive flow of signaling molecules into the nucleus.