Abnormalities in nuclear morphology are predictors of cellular dysfunction and diseases such as cancer, laminopathy and cardiomyopathy. Molecular mechanisms responsible for the changes in nuclear geometry due a stimulus are typically obtained by systematically probing the various structural proteins in the cell using biochemical experiments. In this work, we have shown that the molecular mechanisms responsible for changes in nuclear geometry can be inferred by modelling the nucleus as a mechanical structure under equilibrium. From the existing literature, we modelled the nucleus as an inflated spherical membrane compressed between two rigid plates. The parameters of this model were related to the amount of the structural proteins relevant to nuclear mechanics. The equations for the mechanical equilibrium of the membrane revealed that its deformed shape was a function of two nondimensional parameters, namely, the ratio between the inflating pressure to the modulus of the membrane and the ratio between the compressive force to the pressure. By fitting the model to experimentally measured nuclear morphologies, we could estimate the nondimensional parameters of individual nuclei. The changes in these nondimensional parameters due to a stimulus revealed aberrations in the mechanical parameters and thereby in the structural proteins. We used this model to predict the molecular mechanisms responsible for changes in nuclear mechanics due to Hepatitis C Virus replication in liver cells and further verified them experimentally.
Proposed method for predicting molecular mechanisms from nuclear geometry. Clockwise from top left – Obtain three-dimensional morphology of nuclei from confocal images. From these morphologies, calculate nuclear shape parameters such as projected area, surface area and volume of individual nuclei. By fitting the model to these shape parameters, estimate both the nondimensional parameters. The differences in the nondimensional parameters due to a stimulus suggest molecular mechanisms causing changes in nuclear mechanics
Since the nuclear morphology was described by two non-dimensional parameters, there should be a relationship among any three shape parameters of the nucleus. We estimated the relationship among nuclear volume, surface area and projected area; and found that the relationship was followed by individual nuclei of multiple cell types. This shows that there are underlying patterns in the variability between individual nuclei, which can be revealed by mechanical modelling. The relationship and the fact that individual nuclei follow this relationship were artistically portrayed by plotting the nuclear morphologies on a surface.
Balakrishnan, S., S.S. Mathad, G. Sharma, S.R. Raju, U.B. Reddy, S. Das, and G.K. Ananthasuresh. 2019. A Nondimensional Model Reveals Alterations in Nuclear Mechanics upon Hepatitis C Virus Replication. Biophys. J. 116: 1328–1339.