A non-dimensional, two-parameter mechanical model for nuclear morphology

Morphology of the nucleus is an important regulator of gene-expression and therefore of cell function. Aberrations in nuclear morphology are an indicator of cellular dysfunction and have been used to diagnose various diseases such as cancer and laminopathies. From a biochemical perspective, changes in nuclear morphology are due to differences in the expression of proteins such as lamins and cytoskeleton. To obtain the molecular mechanism, these proteins are systematically probed by various experimental techniques. On the other hand, from a mechanical perspective, the shape of the nucleus is a result of the forces acting on the nuclear envelope and its mechanical properties. Hence, information regarding these mechanical factors is contained in the morphology of the nucleus. Here we present a mechanical model to decompose the contributions of the forces and mechanical properties from the nuclear morphology and thereby indicate the molecular mechanism responsible for changes in the shape of the nucleus.

We assumed a simplified, axisymmetric model wherein two forces act on the nuclear envelope; (i) an inflating pressure and (ii) a compressive force from cortical actin akin to a flat plate pushing down on the nucleus. The governing equations of mechanical equilibrium revealed that the resulting nuclear morphology depended only on two non-dimensional parameters; (i) the ratio between the inflating pressure and the elastic modulus of the nuclear envelope and (ii) the ratio between the compressive force and the inflating pressure. By simulating nuclear morphologies for a range of values of these non-dimensional parameters we predicted a relationship among nuclear shape parameters such as projected area, surface area and volume. Individual nuclei of Huh7 and HeLa cells were in close agreement (< 5% error) with this prediction. The aforementioned non-dimensional parameters corresponding to individual nuclei could be obtained by fitting our model to its nuclear shape parameters. By comparing these non-dimensional parameters between control and treated cells, we can discern the molecular mechanism responsible for changes in nuclear morphology.

We present a case study wherein changes in nuclear mechanics due to Hepatitis C Virus (HCV) were studied using our model. The model predicted a decrease in the elastic modulus of the nuclear envelope and an increase in compression force from cortical actin due to HCV. These mechanical predictions further suggested down-regulation of lamin-A,C, the major structural member of the nuclear envelope and an up-regulation of actin. Both these predictions were experimentally verified.

In summary, we propose a novel method for obtaining the molecular mechanism responsible for changes in nuclear mechanics by merely analysing the nuclear morphology using a quantitative model. The procedure is as follows:

1. Obtain the three dimensional morphology of the nuclei of control and treated cells using confocal microscopy.
2. Calculate the projected area, surface area and volume of each nuclei.
3. Estimate the non-dimensional parameters from these nuclear shape parameters using our model.
4. Analyse the differences in non-dimensional parameters between control and treated cells to obtain the molecular mechanism.

Publication of this work is available here.