Fig. 5: A modified motor-clutch model explains the role of HAVDI ligation in reversing YAP nuclear localization in MSCs.

a In the motor-clutch model, integrin clutches connected to RGD on ECMs with binding rate (\({k}_{{{{{{\rm{on}}}}}}}\)), and broke with ECM at force dependent unbinding rate (\({k}_{{{{{{\rm{off}}}}}}}\)). Myosin motors pulled actin filaments with traction force (\({F}_{{{{{{\rm{trac}}}}}}}\)) at velocity (\({v}_{{{{{{\rm{f}}}}}}}\)). HAVDI binding (N-cadherin based adherens junctions) disturbed integrin clustering and decreased \({k}_{{{{{{\rm{on}}}}}}}\) in integrin binding to RGD on ECMs. Decreased \({k}_{{{{{{\rm{on}}}}}}}\) reduced the \({F}_{{{{{{\rm{trac}}}}}}}\) in actin filaments, and hence deformation of the viscoelastic nucleus (spring stiffness \({E}_{{{{{{\rm{N}}}}}}}\) and viscosity \({\eta }_{{{{{{\rm{N}}}}}}}\)). b The model for variation of \({k}_{{{{{{\rm{on}}}}}}}\) with ECM stiffness (\({E}_{{{{{{\rm{sub}}}}}}}\)) on HAVDI/RGD (H/R) and Scram/RGD (S/R) substrates. c Traction on H/R or S/R substrates with different stiffness \({E}_{{{{{{\rm{sub}}}}}}}\), showing that H/R increased the stiffness threshold for generating elevated traction. Symbols are measured from experiments (mean ± s.e.m. from Supplementary Fig. 13b), while lines are modeling results. d In the force-dependent YAP redistribution model, elevated traction resulted in increased nuclear deformation, enlarged nuclear pores, increased YAP import rate, and thus higher YAP n/c ratio (\({R}_{{{{{{\rm{NC}}}}}}}\)) on HAVDI/RGD substrates than on Scram/RGD substrates. e The relationship between nuclear flattening (\({\lambda }_{{{{{{\rm{N}}}}}}}\)) and actin contraction. Symbols are measured from experiments (mean ± s.e.m. from Supplementary Fig. 14b), while lines are modeling results. f \({R}_{{{{{{\rm{NC}}}}}}}\) increased linearly with nuclear flattening for all culture conditions. The line is prediction by our model. Hollow squares are data from reference³¹. The values of solid symbols on x-axis (\({\lambda }_{{{{{{\rm{N}}}}}}}\)) are from Supplementary Fig. 14b. The values of solid symbols on y-axis (\({R}_{{{{{{\rm{NC}}}}}}}\)) are from Fig. 2f and Fig. 3c–e. The lateral and vertical error bars indicate s.e.m. Results indicated that \({R}_{{{{{{\rm{NC}}}}}}}\) is an indicator of nuclear deformation. g Validation of the model for cells cultured on substrates of different stiffness. The model reproduced the di-sigmoidal curves in data from S/R and H/R groups (3 d for culture time). The values of dots on x-axis (stiffness) are from Fig. 1c, The values of dots on y-axis (\({R}_{{{{{{\rm{NC}}}}}}}\)) are from Fig. 2f. The lateral and vertical error bars indicate s.e.m. h An explanation of mechanical memory in cells transferred from TCP (dark purple) to S/R (orange) or to H/R (blue) substrates, denoted TCP-S/R or TCP-H/R, respectively. \({R}_{{{{{{\rm{NC}}}}}}}\) increased with culture time due to plastic deformation of the nucleus. Differences between TCP-S/R and TCP-H/R groups could be attributed to the differences in elastic recovery of the nucleus modulated by N-cadherins. Source data are provided as a Source Data file.