Independence and coherence in temporal sequence computation across the fronto-parietal network

Time processing requires distributed and coordinated cortical dynamics. Flexible yet robust temporal representations can arise from two distinct computational modes: a coherence mode, where multiple cortical areas hold the same elapsed-time estimate, and an independence mode, where each area maintains its own local estimate. However, how the brain switches between these modes has remained unknown. Using mesoscale two-photon calcium imaging, we simultaneously recorded neuronal populations in the secondary motor cortex (M2) and posterior parietal cortex (PPC) of mice performing a novel alternating-interval timing task. Both areas encoded elapsed time through similar high-dimensional sequential activity. Decoding analyses revealed that the fronto-parietal network has both independent and coherent temporal codes. Communication-subspace analysis showed that temporal information was distributed across multiple low-variance subspaces, whereas the largest subspace preferentially encoded behaviour. A twin recurrent neural network (RNN) model with sparse inter-RNN connections and shared high-variance noise reproduced these experimental findings. Moreover, perturbations applied along the dominant shared subspace paradoxically enhanced independence between the two networks. Through a mathematical formalization based on the local Lyapunov exponents, we uncovered how perturbations along different subspaces selectively evoke either independent or coherent communication mode. Together, these results reveal a principle by which fronto-parietal circuits achieve robust yet flexible computation through the interplay of sparse coupling and shared global fluctuations.