Anomalous diffusion in the interphase cell nucleus: The effect of spatial correlations of chromatin

Abstract

The metabolism of a living cell requires a permanent transfer of molecules throughout the cell and beyond its bounds. Within cell nuclei, molecules are predominantly driven by diffusion, which is influenced by the chromatin network. We propose a quantity related to the pair correlation function to measure the diffusion-relevant clumpiness of chromatin. Using Monte Carlo lattice simulations, we investigate to what extent diffusion can be anomalous due to obstruction by the chromatin network. Chromatin is simulated by a wormlike chain on a lattice, which exhibits different types of loop-induced compartmentalization on a subchromosomal level. Our simulation results show that the proposed measure of clumpiness is suitable to quantify the compartmentalization of chromatin and to connect it to diffusion anomaly parameters, critical molecule sizes for trapping and the transition lengths at which diffusion becomes normal at long times.

Chromosome dynamics, molecular crowding, and diffusion in the interphase cell nucleus: a Monte Carlo lattice simulation study

“…Recent simulation studies suggest that the diffusion behavior of small molecules with radii up to 10 nm does not differ between a dynamic and a static chromatin network (Wedemeier et al 2009) and also that the influence of different network topologies cannot be resolved (Fritsch and Langowski 2010). Nuclear dynamics can only be probed with tracer molecules that are significantly influenced by the macromolecular network in the nucleus.…”

“…The persistence length L p of the chain is the characteristic length over which the chain behaves approximately like a rigid rod and is directly related to g (for a detailed derivation of the connection between the persistence length and the internal bending rigidity on the Cartesian lattice, see Fritsch and Langowski 2010). To account for steric volume exclusion (self-avoidance), the occupation of a lattice site by two or more distinct chain bonds is prohibited.…”

“…For this equilibration, a Metropolis Monte Carlo (MC) procedure is performed during which single MC steps randomly alter the positions of chain bonds on the lattice (Carmesin and Kremer 1988;Metropolis et al 1953). In this procedure, the internal bending rigidity is explicitly accounted for, and after a sufficiently large number of steps, the initial condensed chromatin conformation has transformed into a statistically more favorable decondensed interphase conformation (see also Fritsch and Langowski 2010).…”

“…where N and g denote the number of chain bonds and the bending rigidity constant in units of k B T (Fritsch and Langowski 2010;Wedemeier et al 2007). The persistence length L p of the chain is the characteristic length over which the chain behaves approximately like a rigid rod and is directly related to g (for a detailed derivation of the connection between the persistence length and the internal bending rigidity on the Cartesian lattice, see Fritsch and Langowski 2010).…”

“…It offers the advantage that physically consistent chain conformations can be generated in a computationally inexpensive way, since only local interactions have to be considered. In previous work on the effect of specific folding topologies on diffusion (Fritsch and Langowski 2010), we concentrated on the purely geometric obstruction effect of chromatin, assuming the simulated chromatin chain immobile and affecting diffusion only via steric volume exclusion. There we succeeded in developing a theory for the spatial arrangement of a heterogeneous polymer network in terms of correlations and derived a measure for its "clumpiness" and how this affects macromolecular transport.…”