Calculation of the force field required for nucleus deformation during cell migration through constrictions.

During cell migration in confinement, the nucleus has to deform for a cell to pass through small constrictions. Such nuclear deformations require significant forces. A direct experimental measure of the deformation force field is extremely challenging. However, experimental images of nuclear shape are relatively easy to obtain. Therefore, here we present a method to calculate predictions of the deformation force field based purely on analysis of experimental images of nuclei before and after deformation. Such an inverse calculation is technically non-trivial and relies on a mechanical model for the nucleus. Here we compare two simple continuum elastic models of a cell nucleus undergoing deformation. In the first, we treat the nucleus as a homogeneous elastic solid and, in the second, as an elastic shell. For each of these models we calculate the force field required to produce the deformation given by experimental images of nuclei in dendritic cells migrating in microchannels with constrictions of controlled dimensions. These microfabricated channels provide a simplified confined environment mimicking that experienced by cells in tissues. Our calculations predict the forces felt by a deforming nucleus as a migrating cell encounters a constriction. Since a direct experimental measure of the deformation force field is very challenging and has not yet been achieved, our numerical approaches can make important predictions motivating further experiments, even though all the parameters are not yet available. We demonstrate the power of our method by showing how it predicts lateral forces corresponding to actin polymerisation around the nucleus, providing evidence for actin generated forces squeezing the sides of the nucleus as it enters a constriction. In addition, the algorithm we have developed could be adapted to analyse experimental images of deformation in other situations.

Regulation of cellular contractile force, shape and migration of fibroblasts by oncogenes and Histone deacetylase 6.

The capacity of cells to adhere to, exert forces upon and migrate through their surrounding environment governs tissue regeneration and cancer metastasis. The role of the physical contractile forces that cells exert in this process, and the underlying molecular mechanisms are not fully understood. We, therefore, aimed to clarify if the extracellular forces that cells exert on their environment and/or the intracellular forces that deform the cell nucleus, and the link between these forces, are defective in transformed and invasive fibroblasts, and to indicate the underlying molecular mechanism of control. Confocal, Epifluorescence and Traction force microscopy, followed by computational analysis, showed an increased maximum contractile force that cells apply on their environment and a decreased intracellular force on the cell nucleus in the invasive fibroblasts, as compared to normal control cells. Loss of HDAC6 activity by tubacin-treatment and siRNA-mediated HDAC6 knockdown also reversed the reduced size and more circular shape and defective migration of the transformed and invasive cells to normal. However, only tubacin-mediated, and not siRNA knockdown reversed the increased force of the invasive cells on their surrounding environment to normal, with no effects on nuclear forces. We observed that the forces on the environment and the nucleus were weakly positively correlated, with the exception of HDAC6 siRNA-treated cells, in which the correlation was weakly negative. The transformed and invasive fibroblasts showed an increased number and smaller cell-matrix adhesions than control, and neither tubacin-treatment, nor HDAC6 knockdown reversed this phenotype to normal, but instead increased it further. This highlights the possibility that the control of contractile force requires separate functions of HDAC6, than the control of cell adhesions, spreading and shape. These data are consistent with the possibility that defective force-transduction from the extracellular environment to the nucleus contributes to metastasis, via a mechanism that depends upon HDAC6. To our knowledge, our findings present the first correlation between the cellular forces that deforms the surrounding environment and the nucleus in fibroblasts, and it expands our understanding of how cells generate contractile forces that contribute to cell invasion and metastasis.

Modelling cytoskeletal transport by clusters of non-processive molecular motors with limited binding sites.

Molecular motors are responsible for intracellular transport of a variety of biological cargo. We consider the collective behaviour of a finite number of motors attached on a cargo. We extend previous analytical work on processive motors to the case of non-processive motors, which stochastically bind on and off cytoskeletal filaments with a limited number of binding sites available. Physically, motors attached to a cargo cannot bind anywhere along the filaments, so the number of accessible binding sites on the filament should be limited. Thus, we analytically study the distribution and the velocity of a cluster of non-processive motors with limited number of binding sites. To validate our analytical results and to go beyond the level of detail possible analytically, we perform Monte Carlo latticed based stochastic simulations. In particular, in our simulations, we include sequence preservation of motors performing stepping and binding obeying a simple exclusion process. We find that limiting the number of binding sites reduces the probability of non-processive motors binding but has a relatively small effect on force-velocity relations. Our analytical and stochastic simulation results compare well to published data from in vitro and in vivo experiments.