We study a segmentally active Rouse chain in which activity is confined to a single contiguous segment of tunable length and position along the contour. Employing analytical normal-mode theory together with Brownian-dynamics simulations, we quantify how localized activity governs conformation and dynamics. Using global conformational measures such as the mean square radius of gyration and end-to-end distance, we observe an unusual swelling pattern: for a fixed length of the active segment, placing the segment near a chain end results in enhanced swelling than positioning the same segment at midchain, reflecting efficient coupling to long-wavelength modes when activity is end-driven. In contrast, fluctuations within a prescribed observation window depend not only on the location and size of the active segment but also on how much the window overlaps the active region. We further examine the dynamics of a tagged point on the chain, which exhibits distinct signatures in the form of a characteristic sequence of diffusive-subdiffusive-superdiffusive crossovers when the tag lies within the active region, while the response is progressively attenuated as the tag is moved away from it. Our results present a minimal, analytically tractable framework for heterogeneous activity in block polymers, providing a basis for extending and interpreting experimental measurements on active biopolymers.
Goswami et al. (Sat,) studied this question.