An Algorithmic Barrier to Neural Circuit Understanding

Abstract

Neuroscience is witnessing extraordinary progress in experimental techniques, especially at the neural circuit level. These advances are largely aimed at enabling us to understand how neural circuit computations mechanistically cause behavior. Here, using techniques from Theoretical Computer Science, we examine how many experiments are needed to obtain such an empirical understanding. It is proved, mathematically, that establishing the most extensive notions of understanding need exponentially-many experiments in the number of neurons, in general, unless a widely-posited hypothesis about computation is false. Worse still, the feasible experimental regime is one where the number of experiments scales sub-linearly in the number of neurons, suggesting a fundamental impediment to such an understanding. Determining which notions of understanding are algorithmically tractable, thus, becomes an important new endeavor in Neuroscience.Neuroscience is making remarkable ongoing progress in experimental techniques, at the present time. At the neuronal and network level, advances include the ability to both image activity in (1, 2), as well as activate/silence subsets (3-5) of neurons in-vivo, all-optically (6), in awake, behaving animals. Already, such techniques are being deployed to study (nearly) whole-brain neural activity at cellular resolution in C. elegans (7), hydra (8) & adult Drosophila (9) and to combine imaging of whole-brain neural activity with optogenetic perturbations of arbitrary subsets of neurons in larval zebrafish (10). Likewise, connectomes of the nematode C. elegans (11) and the larval tadpole C. intestinalis (12) have been fully reconstructed, as have significant portions of the larval fruitfly D. melanogaster (13).Indeed, ongoing national initiatives in the United States (14), Japan (15), China (16) and Korea (17) have endeavored to accelerate the development of these (and other) neurotechnologies. The general premise has been that such technologies will ultimately enable us to reach the goal of understanding how networks of neurons mechanistically perform computations that lead to specific behaviors.Understanding how the activity of neurons in circuits mechanistically causes behavior will require 1 perturbational experiments at high spatial and temporal resolution that contemporary techniques are allowing us to approach. Efficient algorithms are needed that will seek to prescribe the smallest number of experiments necessary (that scale as a function of the number of neurons in the network) to establish such an understanding. An experiment, for example, might entail perturbing activity of a chosen subset of neurons, while concurrently imaging neural circuit activity and attempting to elicit behavior. The specifics of the next experiment prescribed by the algorithm could depend on the outcome of the current experiment. We are thus treating the problem of experiment design as an algorithmic problem 2 , invoking tools from Computer 1 Imaging of neural circuit activity alone, will only tell us which neur...

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