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The transport of macromolecules, such as DNA, through the cytoskeleton is critical to wide-ranging cellular processes from cytoplasmic streaming to transcription. The rigidity and steric hindrances imparted by the network of filaments comprising the cytoskeleton often leads to anomalous subdiffusion, while active processes such as motor-driven restructuring can induce athermal superdiffusion. Understanding the interplay between these seemingly antagonistic contributions to intracellular dynamics remains a grand challenge. Here, we use single-molecule tracking to show that the transport of large linear and relaxed circular DNA through motor-driven microtubule networks can be non-Gaussian and multimodal, with the degree and spatiotemporal scales over which these features manifest depending nontrivially on the state of activity and DNA topology. For example, active network restructuring increases caging and non-Gaussian transport modes of linear DNA, while dampening these mechanisms for circular DNA. We further discover that circular DNA molecules exhibit either markedly enhanced subdiffusion or superdiffusion compared to their linear counterparts, in the absence or presence of kinesin activity, indicative of microtubules threading circular DNA. This strong coupling leads to both stalling and directed transport, providing a direct route towards parsing distinct contributions to transport and determining the impact of coupling on the transport signatures. More generally, leveraging macromolecular topology as a route to programming molecular interactions and transport dynamics is an elegant yet largely overlooked mechanism that cells may exploit for intracellular trafficking, streaming, and compartmentalization. This mechanism could be harnessed for the design of self-regulating, sensing, and reconfigurable biomimetic matter. Published by the American Physical Society2025