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Mean field and dynamics of multi-stable states during ongoing and evoked cortical activity
Luca Mazzucato1, Alfredo Fontanini1,2 and Giancarlo La Camera1,2
1Department of Neurobiology and Behavior and 2Program in Neuroscience, Stony Brook University

The dynamics of simultaneously recorded spike trains in alert animals have been shown to evolve through temporal sequences of metastable states. Very little is known about the network mechanisms responsible for the genesis of such sequences. It is often assumed that their onset is triggered by an external stimulus. We have recently shown that, in multi-electrode recordings from the gustatory cortex of alert rats, state sequences can be observed also in the absence of overt sensory stimulation [1]. Unlike some previously described patterns of ongoing activity, where all or no neurons fire at high or low firing rate (as in UP and DOWN states), we found only a partial degree of coordination among neurons, and also found that about half of the neurons are multi-stable, i.e., they express three or more different firing rates in different states.

This single neuron multi-stability represents a challenge to existing spiking network models, where typically each neuron is at most bi-stable. We present a recurrent spiking network model that accounts for both the spontaneous generation of state sequences and the (network-generated) multi-stability in single neuron firing rates. Each network state results from the activation of neural clusters with potentiated intra-cluster connections [2,3]. A mean field solution of the model shows a large number of stable states and saddle points, each characterized by a subset of simultaneously active clusters. The firing rate in each cluster during persistent activity depends on the number of active clusters, so that the same neuron can have different firing rates depending on the state of the network. The firing rate distributions qualitatively match the empirical distributions. This is, to our knowledge, the first characterization of a network-generated multi stability in single neurons during ongoing activity.

Because of dense intra-cluster connectivity and the balanced excitatory-inhibitory regime of the network [4], in finite networks the stable states lose stability due to finite size effects. Simulations of the dynamics show that the model's ensemble activity continuously hops among the different states, reproducing the ongoing dynamics observed in the data. Moreover, when probed with external stimuli, the model predicts the quenching of single neuron multi-stability into bi-stability and the reduction of trial-by-trial variability (as e.g. measured via the mean-matched Fano Factor [5]). Both predictions were confirmed in the data.

The model also makes clear predictions on the dimensionality of the neural representation, defined as the smallest number of coordinate axes that account for most of the variance of the neural population activity. In alert monkeys, the dimensionality of evoked activity has been found to predict the ability to perform correctly a task [6]. We compared the dimensionality of the neural representation between periods of ongoing and stimulus-evoked activity and found that stimulus presentation quenches dimensionality. During ongoing activity, the dimensionality is proportional to the ensemble size (i.e., the number of simultaneously recorded neurons); however, this dependence on ensemble size is highly reduced during stimulus-evoked activity. The model predicts the existence of an upper bound on ensemble size, given by the number of clusters, beyond which recording from larger ensembles would not increase the dimensionality, differently from what predicted from an ensemble of Poisson spike trains with the same degree of cross-correlations found in the data. An experimental validation of such upper bound during ongoing activity would provide independent evidence for a cortical organization in neural clusters.

Altogether, our results provide a unified mechanistic model of the essential features of both ongoing and evoked cortical dynamics.

[1] L. Mazzucato, A. Fontanini and G. La Camera, J. Neurosci. in press (2015).
[2] D.J. Amit and N. Brunel, Cereb. Cortex 7:237-252 (1997).
[3] A. Litwin-Kumar and B. Doiron, Nat. Neurosci. 15:1498-1505 (2012).
[4] C. van Vreeswijk and H. Sompolinsky, Neural Comp. 10:1321-1371 (1998).
[5] M.M. Churchland et al., Nat. Neurosci. 13:369-378 (2010).
[6] M. Rigotti, O. Barak, M.R. Warden, X.J. Wang, N.D. Daw, E.K. Miller and S. Fusi, Nature 497:585-590 (2013).