Chromatin Compaction, Auxeticity, and the Epigenetic Landscape of Stem Cells

Abstract

When embryonic stem cells differentiate, the mechanical properties of their nuclei evolve en route to their terminal state. Measurements of the deformability of cell nuclei in the transitional state that intervenes between the embryonic stem-cell state and the differentiation primed state of mouse stem cells indicate that such nuclei are auxetic; i.e., they have a negative Poisson's ratio. We show, using a theoretical model, how this remarkable mechanical behavior results from the coupling between chromatin compaction states and nuclear shape. Our biophysical approach, which treats chromatin as an active polymer system whose mechanics is modulated by nucleosome binding and unbinding, reproduces experimental results. It provides testable predictions for changes in chromatin compaction as a function of applied force, for the correlations of chromatin compaction and nuclear shape, and for the in-phase and out-of-phase response of these quantities to an applied uniaxial oscillatory force. Our model yields a biophysical interpretation of the epigenetic landscape of stem cells, also suggesting how this landscape might be probed experimentally.