Universal center-of-mass scaling shapes segment fluctuations and chromatin dynamics

We show that cancellation of internal forces together with spatially uncorrelated noise generically enforces a universal <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mi>s</a:mi> </a:mrow> </a:math> scaling of the center-of-mass (COM) diffusivity for polymer segments of contour length <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>s</b:mi> </b:math> , independent of model details. Within an active generalized Rouse-Langevin (A-GRLE) framework for fractal polymers in a viscoelastic bath with weak activity, we derive closed-form links between segment COM motion and the short-time behavior of two-point fluctuations. The same COM law predicts transient <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msup> <c:mi>s</c:mi> <c:mrow> <c:mo>−</c:mo> <c:mn>3</c:mn> </c:mrow> </c:msup> </c:math> tangent-tangent correlations along the contour following a temperature quench. Reanalyzing recent two-locus chromatin tracking, we extract a dynamic COM exponent <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>ξ</d:mi> <d:mo>=</d:mo> <d:mn>0.77</d:mn> <d:mo>±</d:mo> <d:mn>0.16</d:mn> </d:mrow> </d:math> , suggesting topological constraints. These results identify model-independent signatures of collective polymer dynamics and clarify that the observed Rouse-like scaling of chromatin loci reflects transient, unentangled dynamics with an inevitable crossover to an entangled regime at longer times.