Scale-free models of chromosome structure, dynamics, and mechanics

The nucleus of a cell contains its genetic information in the form of chromatin: polymers of DNA and associated proteins. The physical nature of this polymer system is yet to be understood. Orthogonal experimental approaches probing chromosome structure, dynamics, and mechanics typically suggest the existence of scaling relationships, leading to the widespread use of scale-free, or fractal, models to represent interphase chromosomes. However, currently, there is no single physical model consistent with all reported scaling exponents. Here, we consider the space of possible scale-free models of chromosome structure, dynamics, and mechanics, and examine the fundamental connections between these physical properties. We demonstrate the existence of two algebraic relationships between the scaling exponents-connecting structure with dynamics, and dynamics with mechanics, respectively-outlining the necessary physical conditions for a model to match specific exponent values. Applied to values reported in metazoans, our theory identifies the family of models consistent with all observed scalings, which notably excludes the classical Rouse, Zimm, and fractal globule polymer models. Our theory highlights dynamic correlations between distal genomic loci as necessary to reconnect seemingly contradictory measurements. Consequently, we propose new experiments to narrow down the space of possible models. We expect this framework to serve as a guide for understanding past and future measurements, and for building new physical models of interphase chromosomes.