Chromatin Hydrodynamics

Abstract

Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory-the two-fluid model-in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model-the Maxwell fluid-for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity.

Hydrodynamic collective effects of active protein machines in solution and lipid bilayers

“…In addition, several studies have proposed specific explanations for the importance of nonthermal random motions in living cells, whose origin lies in the forces generated by the uncorrelated activity of protein machines. (26,(42)(43)(44) Such nonthermal fluctuations may also be a consequence of the universal hydrodynamic effects, described here, that arise from active conformational changes in molecular motors and other protein machines powered by ATP.…”

“…However, thus far we have not considered collective effects due to hydrodynamic interactions on the populations of active proteins. It may be that orientation alignment leading to nematic order (26,36) and cycle synchronization also arise.…”

“…The force dipole tensor e iβ e iγ m i ðtÞ of a protein is invariant under inversion of the orientation vector e i and has properties like the tensor order parameter in nematic liquid crystals. When correlations among active proteins are taken into account it may be possible that nematically ordered active protein states could be found (26,36). We shall not consider such effects here.…”

“…Also, interactions between active hydrodynamic dipoles have been investigated theoretically (22,23) and experimentally (24,25). Effects of active dipoles on chromatin dynamics in a two-fluid model have been considered (26).…”

Response of a polymer network to the motion of a rigid sphere

“…We begin in sect. 2 by defining the problem, which is the analogue of Stokes' problem for the motion of a rigid sphere, with the viscous fluid replaced by a two-fluid medium [14,15,16,17,18,19]. An approximate treatment of the dynamics of a bead embedded in such a medium was presented by Levine and Lubensky [18].…”