Calculation of the force field required for nucleus deformation during cell migration through constrictions
Fig 4
Deformation (left) and traction force (right) fields for the solid model.
The axes show pixel numbers where each pixel is 0.215μm and scale bars show 1μm. The black outline is the initial shape and the green outline is the target deformed shape. Blue arrows represent the final deformation field found between the images and red arrows represent the traction force direction and magnitude, with each arrow scaled such that one unit of length on the axes represents a traction force of 250 Pa. The traction force is calculated using a Young’s modulus of E = 5 kPa and assuming that the nucleus behaves as an incompressible elastic solid with a Poisson ratio ν = 0.5. A. Initial shape is the average of 71 nuclei before the constriction and the target shape is the average of 56 nuclei beginning to enter the constriction. B. Initial shape is the average of 56 nuclei entering the constriction and the target shape is the average of 71 nuclei within the constriction. C. Initial shape is the average of 71 nuclei within the constriction and the target shape is the average of 55 nuclei as they begin exiting the constriction. D Initial shape is the average of 55 nuclei exiting the constriction, to the average shape of 71 nuclei after they have fully exited the constriction. Since the shapes are averages they do not correlate directly to any single nucleus, however experimental images of a typical nucleus are shown for comparison in Fig 1. The target shape is moved −1.7, −7.3, 0.15, 0.0 pixels along the x direction, from the centroid aligned position for A-D respectively (see Appendix D in S1 Text).