Hong-pyo Lee^1,*, Ryan Stowers^1,* & Ovijit Chaudhuri<sup>1

1</sup> Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA.

^*These authors contributed equally: Hong-pyo Lee, Ryan Stowers

Correspondence and requests for materials should be addressed to O.C.

For mesenchymal stem cells (MSCs) cultured in three dimensional matrices, matrix remodeling is associated with enhanced osteogenic differentiation. However, the mechanism linking matrix remodeling in 3D to osteogenesis of MSCs remains unclear. Here, we find that MSCs in viscoelastic hydrogels exhibit volume expansion during cell spreading, and greater volume expansion is associated with enhanced osteogenesis. Restriction of expansion by either hydrogels with slow stress relaxation or increased osmotic pressure diminishes osteogenesis, independent of cell morphology. Conversely, induced expansion by hypoosmotic pressure accelerates osteogenesis. Volume expansion is mediated by activation of TRPV4 ion channels, and reciprocal feedback between TRPV4 activation and volume expansion controls nuclear localization of RUNX2, but not YAP, to promote osteogenesis. This work demonstrates the role of cell volume in regulating cell fate in 3D culture, and identifies TRPV4 as a molecular sensor of matrix viscoelasticity that regulates osteogenic differentiation.