The brain's topographical organization shapes dynamic interaction patterns that support flexible behaviour based on rules and long term knowledge.

Adaptive behavior relies both on specific rules that vary across situations and stable long-term knowledge gained from experience. The frontoparietal control network (FPCN) is implicated in the brain's ability to balance these different influences on action. Here, we investigate how the topographical organization of the cortex supports behavioral flexibility within the FPCN. Functional properties of this network might reflect its juxtaposition between the dorsal attention network (DAN) and the default mode network (DMN), two large-scale systems implicated in top-down attention and memory-guided cognition, respectively. Our study tests whether subnetworks of FPCN are topographically proximal to the DAN and the DMN, respectively, and how these topographical differences relate to functional differences: the proximity of each subnetwork is anticipated to play a pivotal role in generating distinct cognitive modes relevant to working memory and long-term memory. We show that FPCN subsystems share multiple anatomical and functional similarities with their neighboring systems (DAN and DMN) and that this topographic architecture supports distinct interaction patterns that give rise to different patterns of functional behavior. The FPCN acts as a unified system when long-term knowledge supports behavior but becomes segregated into discrete subsystems with different patterns of interaction when long term memory is less relevant. In this way, our study suggests that the topographic organization of the FPCN, as well as the connections it forms with distant regions of cortex, are important influences on how this system supports flexible behavior. Significance Statement Adaptive behavior depends on adjudicating between specific rules that vary across situations. The frontoparietal control network (FPCN) helps guide this process through its interactions with other brain regions. We examined how local topographical features support this function of the FPCN. Subnetworks within the FPCN share key anatomical and functional features with adjacent systems linked to external attention and long-term knowledge. This topographic architecture supports the emergence of distinct interaction patterns: FPCN subnetworks act cohesively when long-term memory can support behavior, but segregate when long-term memory is not aligned with current goals. Our study shows that, in addition to dynamic interaction with spatially distant cortical regions, local topographical features of the FPCN play a significant role in flexible behavior.