Cell nucleus as a mcirorheological probe to study the rheology of the cytoskeleton

Mechanical properties of the cell are important biomarkers for probing its pathological changes, and are increasingly used for cancer diagnosis and detecting rare cells. Yet, determining the time-dependent contributions of different cellular components --including the cell membrane, the cell cytoskeleton and the nucleus-- to the mechanical response of the whole cell has remained challenging. We propose a novel method to decouple the mechanics of membrane and cytoskeleton, by analyzing the correlation between the membrane deformations that are induced by external microfluidic flows and nucleus displacements induced by those membrane deformations i.e. we use the nucleus as a microrheological probe to study the rheology of the interior cytoskeleton, independent of membrane rheology. To demonstrate the applicability of this method, we consider a proof of concept model consisting of a rigid spherical nucleus centered in a spherical membrane. We obtain analytical expressions for time-dependent nucleus velocity as a function of membrane deformations, when the interior cytoskeleton is modelled as a viscoelastic and a poroelastic material, and demonstrate how the nucleus velocity can be used to characterize the rheology of the cytoskeleton over a wide range of forces and time-scales.