Flexible neural connectivity under constraints on total connection strength

Neural computation is determined by neuron dynamics and circuit connectivity. Uncertain and dynamic environments may require neural hardware to adapt to different computational tasks, each requiring different connectivity configurations. At the same time, connectivity is subject to a variety of constraints, placing limits on the possible computations a given neural circuit can perform. It is desirable that constraints permit the circuit to be flexible in the sense that it be capable of learning to perform many different computations, so that the circuit can adapt to or develop towards the demands of its environment. Here we examine the hypothesis that neural circuitry is organized such that physiological constraints permit the highest possible degree of computational flexibility, i.e. that they allow for the largest possible number of computational solutions available to the circuit. From this hypothesis, we develop models of the degree distributions of connectivity based on constraints on a neuron’s total synaptic weight. To test these models, we examine reconstructions of the mushroom bodies from the first instar larva and the adult Drosophila melanogaster. We perform a Bayesian model comparison for two constraint models and a random wiring null model. Overall, we find that flexibility under a homeostatically fixed total synaptic weight describes Kenyon cell connectivity better than other models, suggesting a principle shaping the apparently random structure of Kenyon cell wiring. Furthermore, we find evidence that larval Kenyon cells are more flexible earlier in development, suggesting a mechanism whereby neural circuits begin as flexible system that develop into specialized computational circuits. Author summary The structure of neural circuits provides a backbone for circuit function. Physiological constraints restrict the possible circuit configurations, so that healthy neural circuits must satisfy demands of both their constraints and their computational tasks. A desirable property of neural circuits is that they be able to perform a variety of computations. Here we examine simple models of constraints on total synaptic weights, and calculate the number of configurations they allow: their computational flexibility. We propose probabilistic models of connectivity that weight the number of synaptic partners according to computational flexibility. High-throughput electron microscopic anatomical experiments have begun to yield detailed connectivity maps at the resolution of individual synapses. We test our hypothesis using recent wiring diagrams from a learning center, the mushroom body, in the brain of the fly Drosophila melanogaster. We compare constraints that fix or that bound a neuron’s total connection strength, and compare them to a simple random wiring null model. Of these models, the fixed total connection strength matched the overall connectivity best in mushroom bodies from both larval and adult flies. We provide evidence that neural circuits are more flexible in early stages of development and lose this flexibility as they grow towards specialized function.