Small-angle neutron scattering (SANS) on nuclei of chicken erythrocytes demonstrates the cubic dependence of the scattering intensity $Q^{-3}$ in the range of momentum transfer $Q\in {10}^{-3}–{10}^{-2}{\mathrm{nm}}^{-1}$. Independent spin-echo SANS measurements give the spin-echo function, which is well described by the exponential law in a range of sizes $(3\times {10}^2)–(3\times {10}^4)$ nm. Both experimental dependences reflect the nature of the structural organization of chromatin in the nucleus of a living cell, which corresponds to the correlation function $\gamma \left(r\right)=ln(\xi /r)$ for $r<\xi$, where $\xi =(3.69\pm 0.07)\times {10}^3$ nm, the size of the nucleus. It has the specific scaling property of the logarithmic fractal $\gamma (r/a)=\gamma \left(r\right)+ln\left(a\right),$ i.e., the scaling down by $a$ gives an additive constant to the correlation function, which distinguishes it from the mass fractal, which is characterized by multiplicative constant.

• Received 19 January 2017

DOI:https://doi.org/10.1103/PhysRevE.96.012411