Fig 1.
a- Spherical configuration of the cell in which sensing forces are exerted at each membrane node towards the cell centroid (mechano-sensing process). b- Calculation of the cell internal deformation due to cell mechano-sensing. Deformed cell due to mechano-sensing. epol stands for polarisation direction of the reoriented cell while , Fprot and Fdrag represent the net traction force, protrusion force and drag force, respectively.
Fig 2.
Interaction of two cells in contact.
For the assumed cell configuration, two cells can have four common nodes (n1:n4). xi and xj are position vectors of the ith and the jth cells, respectively, while xij is a vector passing by the centroids of the ith and jth cells. The distance between their centroids (Oi and Oj) is equal to or greater than the proposed cell diameter, ‖xij‖ ≥ 2r.
Fig 3.
Computational algorithm of cell mechano-sensing and consequent cell fate due to mechanotaxis.
Table 1.
General parameters employed in the model.
General parameters employed in the model except where other values are specified.
Fig 4.
MSC proliferation and differentiation within a substrate of 45 kPa stiffness after 5.5 days.
MSC proliferation (see also S1 Video).
Fig 5.
MSC proliferation and differentiation within a substrate of 45 kPa stiffness after 32 days.
The first commitment of a mature mother MSC to osteogenic lineage specification (see also S1 Video)
Fig 6.
MSC proliferation and differentiation within a substrate of 45 kPa stiffness after 50 days.
Continuing differentiation and proliferation of MSCs and osteoblasts (see also S1 Video).
Fig 7.
MI of MSCs within substrates of different uniform stiffnesses.
E represents substrate elasticity modulus.
Fig 8.
Average cell traction force within a hard substrate of 45 kPa stiffness.
Average cell traction force, , versus time within a hard substrate of 45 kPa stiffness during MSC proliferation and differentiation. Point A represents the instant of MSC proliferation which causes a considerable jump in the average net traction force while point B is the initial instant of MSC differentiation to osteoblast leading to an enhancement of the average net traction force.
Fig 9.
Osteoblast proliferation in hard substrates.
a- 30 kPa and b- 45 kPa stiffness (see also S2 Video).
Fig 10.
Average cell traction force within a hard substrate of 30 kPa and 45 kPa stiffness.
Average cell traction force, , versus time within hard substrates during MSC differentiation and osteoblast proliferation. Points A represent the instant of MSC differentiation to osteoblast which instantly causes a traction force increase while points B are the initial instant of osteoblast proliferation causing a jump in the average net traction force.
Fig 11.
Normalized density of each cell phenotype.
Normalized density of each cell phenotype versus substrate stiffness during identical times as a consequence of MSC differentiation and proliferation of each cell phenotype. The error bars represent mean standard deviation of different runs.
Fig 12.
Chondrocyte proliferation in intermediate substrates.
a- 20 kPa and b- 25 kPa stiffness (see also S3 Video).
Fig 13.
Average cell traction force within intermediate substrates of 20 kPa and 25 kPa stiffness.
Average cell traction force, , versus time within intermediate substrates during MSC differentiation and chondrocyte proliferation. Point A represents the moment of MSC differentiation to chondrocyte which instantly causes the traction force to increase while point B is the initial moment of chondrocyte proliferation causing a jump in the average net traction force.
Fig 14.
Neuroblast proliferation in soft substrates.
a- 0.1 kPa and b- 1 kPa stiffness (see also S4 Video).
Fig 15.
Average cell traction force within soft substrates of 0.1 kPa and 1 kPa stiffness.
Average cell traction force, , versus time within soft substrates during MSC differentiation and neuroblast proliferation. Points A represent the instant of MSC differentiation to neuroblast which instantly causes the traction force to decrease while points B are the initial instant of neuroblast proliferation causing a jump in the average net traction force.