Topological constraints and finite-size effects in quantitative polymer models of chromatin organization

Polymer physics simulations have provided a versatile framework to quantitatively explore the complex mechanisms driving chromosome organization. However, simulating whole chromosomes over biologically-relevant timescales at high resolution often constitutes a computationally-intensive task — while genes or other regions of biological interest may typically only span a small fraction of the full chromosome length. Conversely, only simulating the sub-chromosomal region of interest might provide an over-simplistic or even wrong description of the mechanism controlling the 3D organization. In this work, we characterize what should be the minimal length of chromosome to be simulated in order to correctly capture the properties of a given restricted region. In particular, since the physics of long, topologically-constrained polymers may significantly deviate from those of shorter chains, we theoretically investigate how chromosomes being a long polymer quantitatively affects the structure and dynamics of its sub-segments. We show that increasing the total polymer length impacts on the topological constraints acting on the system and thus affects the compaction and mobility of sub-chains. Depending on the entanglement properties of the system, we derive a phenomenological relation defining the minimal total length to account for to maintain a correct topological regime. We finally detail the implications of these conclusions in the case of several specific biological systems. Abstract Figure