Arousal dynamics: diverse measurements of a universal manifold

Recent findings from awake, behaving animals lead us to hypothesize the existence of an underlying dynamical process whose manifestations are observed across diverse neural, physiological and behavioral measurements. Our ability to construct nonlinear mappings between such measurements (here, pupillometry and widefield calcium imaging) from a latent, low-rank representation of their dynamics provides strong support for this hypothesis. Specifically, we introduce an integrative theoretical framework that casts arousal as a dynamical process unfolding along a low-dimensional manifold that segregates different physiological regimes (i.e., brain and body states), each of which has a high-dimensional expression in the space of measurements. This motivates a data-driven approach to parsimoniously link observables that evolve according to a common but unknown dynamical mechanism. Our approach exploits Takens’ embedding theorem from dynamical systems theory, which permits the (topology-preserving) reconstruction of a full-state attractor manifold from a single observable and its time history. Takens’ theorem enables a strong prediction – and thus, a challenging test – of our framework: in theory, a single arousal-related observable (e.g., pupil size) should suffice to reconstruct high-dimensional observables, to the extent that a dynamical mechanism is shared. We test this prediction by performing simultaneous pupillometry and widefield calcium imaging in awake mice. The latter reports the large-scale spatial structure of cortical activity, which we hypothesize to be tightly regulated in accordance with arousal dynamics. We train neural networks to approximate the hypothesized mapping from delay-embedded pupil time series to widefield measurements. This procedure enables us to reconstruct a surprising extent of cortex-wide spatiotemporal dynamics in awake mice (i.e., 74 ± 8% of variance < 0.2 Hz in held-out data, vs. 13 ± 10% without delay embedding (mean ± std, n=7 mice)). Our framework and findings thus elucidate an arousal-related dynamical mechanism that is both richer and substantially further-reaching than presently recognized.