Multistability in neural systems with random cross-connections.

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems using a firing rate model framework, in which clusters of similarly responsive neurons are represented as single units, which interact with each other through independent random connections. We explore the range of conditions in which multistability arises via recurrent input from other units while individual units, typically with some degree of self-excitation, lack sufficient self-excitation to become bistable on their own. We find many cases of multistability-defined as the system possessing more than one stable fixed point-in which stable states arise via a network effect, allowing subsets of units to maintain each others' activity because their net input to each other when active is sufficiently positive. In terms of the strength of within-unit self-excitation and standard deviation of random cross-connections, the region of multistability depends on the response function of units. Indeed, multistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the response function rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which produces Zipf's Law when enumerating the proportion of trials within which random initial conditions lead to a particular stable state of the system.

Intrinsic dynamics of randomly clustered networks generate place fields and preplay of novel environments.

During both sleep and awake immobility, hippocampal place cells reactivate time-compressed versions of sequences representing recently experienced trajectories in a phenomenon known as replay. Intriguingly, spontaneous sequences can also correspond to forthcoming trajectories in novel environments experienced later, in a phenomenon known as preplay. Here, we present a model showing that sequences of spikes correlated with the place fields underlying spatial trajectories in both previously experienced and future novel environments can arise spontaneously in neural circuits with random, clustered connectivity rather than pre-configured spatial maps. Moreover, the realistic place fields themselves arise in the circuit from minimal, landmark-based inputs. We find that preplay quality depends on the network's balance of cluster isolation and overlap, with optimal preplay occurring in small-world regimes of high clustering yet short path lengths. We validate the results of our model by applying the same place field and preplay analyses to previously published rat hippocampal place cell data. Our results show that clustered recurrent connectivity can generate spontaneous preplay and immediate replay of novel environments. These findings support a framework whereby novel sensory experiences become associated with preexisting "pluripotent" internal neural activity patterns.

Multistability in neural systems with random cross-connections.

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems, using a firing-rate model framework, in which clusters of neurons with net self-excitation are represented as units, which interact with each other through random connections. We focus on conditions in which individual units lack sufficient self-excitation to become bistable on their own. Rather, multistability can arise via recurrent input from other units as a network effect for subsets of units, whose net input to each other when active is sufficiently positive to maintain such activity. In terms of the strength of within-unit self-excitation and standard-deviation of random cross-connections, the region of multistability depends on the firing-rate curve of units. Indeed, bistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the firing-rate curve rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which can appear as Zipf's Law when sampled as the proportion of trials within which random initial conditions lead to a particular stable state of the system.

An early phase of instructive plasticity before the typical onset of sensory experience.

While early experience with moving stimuli is necessary for the development of direction selectivity in visual cortex of carnivores, it is unclear whether experience exerts a permissive or instructive influence. To test if the specific parameters of the experienced stimuli could instructively sculpt the emergent responses, visually naive ferrets were exposed to several hours of experience with unusual spatiotemporal patterns. In the most immature ferrets, cortical neurons developed selectivity to these patterns, indicating an instructive influence. In animals that were 1-10 days more mature, exposure to the same patterns led to a developmentally-typical increase in direction selectivity. We conclude that visual development progresses via an early phase of instructive plasticity, when the specific patterns of neural activity shape the specific parameters of the emerging response properties, followed by a late phase of permissive maturation, when sensory-driven activity merely serves to enhance the response properties already seeded in cortical circuits.