Low-dimensional network models for recordings from the prefrontal cortex
Christian Machens1, Ranulfo Romo2, and Carlos Brody3
1University of Munich, 2UNAM Mexico, 3Princeton

During short-term memory maintenance, different neurons in prefrontal cortex (PFC), recorded under identical conditions, show a wide variety of temporal dynamics and response properties [1]. These data are a specific example of the more general finding that neural recordings from frontal cortices often reveal that different neurons have very different response characteristics. Modeling this complexity of responses has been difficult. Most commonly, some features of the responses are focused on, and models that fit those reduced features are built. But can the full complexity of responses be easily captured? Here we attack the problem by fitting simple recurrent neural network models to the data.

Following the traditional approach, we first group neurons into different classes. When selecting neurons from a single class, the estimation procedure yields a connectivity matrix with two populations of neurons coupled by mutual inhibition and self-excitation. The connectivity matrix has rank one and approximately agrees with a model we proposed earlier [2]. When selecting neurons from two classes, a connectivity matrix similar to that of the ring attractor network emerges, with a rank of two. The full complexity and richness of the observed neural dynamics, however, can only be captured when estimating a network architecture from the full set of neurons. In this case, the resulting connectivity matrix has rank four to five and its structure is dominated by randomness. Simulations of the resulting network reproduce most of the diversity and richness of neural responses found in the data. We show that several of the eigenvalues of the connectivity matrix are close zero, so that the network dynamics has either a constant or integrating flow along the respective dimensions. Finally, we discuss the consistency of the estimated connectivity matrices with the measured noise correlations.

[1] Timing and Neural Encoding of Somatosensory Parametric Working Memory in Macaque Prefrontal Cortex. C.D. Brody, A. Hernandez, A. Zainos, and R. Romo, Cereb. Cortex 13:1196-1207, 2003.
[2] Flexible control of mutual inhibition: a neural model of two- interval discrimination. C.K. Machens, R. Romo, and C.D. Brody, Science, 307:1121-1124, 2005.