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NJIT Mathematical Biology Seminar

Tuesday, October 16, 2007, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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Retrieving noise-based memories by reading heterogeneous neurons

Daniel Ben Dayan Rubin

Center for Theoretical Neuroscience, Columbia University

Biologically plausible synaptic models have synaptic efficacies which are restricted to vary in a limited range. For these models old memories are continuously overwritten by new ones, and typical memory lifetimes grow only logarithmically with the number of synapses (see e.g. Fusi Abbott, Nat Neurosc 2007). Memories can be retrieved when the correlation between a synaptic configuration of weights and the memorized pattern of neural activity (signal) is significantly larger than the noise generated by the interference of other stored memories. This noise is composed of two parts: if the signal is normalized in such a way that it increases linearly with the number N of synapses, then one part of the noise scales as the square root of N, and the other, due to correlations between synapses, scales linearly with N. The arousal of correlation is a general consequence of the fact that synapses on the same dendritic tree share the same post-synaptic neurons. These correlations are present also for random uncorrelated patterns of neural activity.

Here we investigate whether the correlated part of the noise can be harnessed to retrieve more efficiently old memories. We show that the memory lifetime of the mnemonic trace contained in the signal and in the correlated part of the noise are the same. In order to read out the noise, we need a neural mechanism that can compute both the first and the second order statistics of the synaptic currents. We propose to exploit the non linearities and the diversity of the response functions of cortical neurons: different neurons, when injected with the same synaptic current, operate in different regimes, which can be linear (e.g. for relatively large synaptic currents) or non-linear (e.g. around the rheobase current). We show that it is possible to read out the second order statistics of the synaptic currents if we use a population of realistic fast spiking interneurons and pyramidal cells. The response curves of real neurons was reconstructed from the data recorded in L5 and L2/3 of rat somatosensory cortex (Rauch et al., J. Neurophysiol. 2003, 2006).