AUTHOR=Soudry Daniel , Meir Ron TITLE=The neuronal response at extended timescales: long-term correlations without long-term memory JOURNAL=Frontiers in Computational Neuroscience VOLUME=8 YEAR=2014 URL=https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2014.00035 DOI=10.3389/fncom.2014.00035 ISSN=1662-5188 ABSTRACT=

Long term temporal correlations frequently appear at many levels of neural activity. We show that when such correlations appear in isolated neurons, they indicate the existence of slow underlying processes and lead to explicit conditions on the dynamics of these processes. Moreover, although these slow processes can potentially store information for long times, we demonstrate that this does not imply that the neuron possesses a long memory of its input, even if these processes are bidirectionally coupled with neuronal response. We derive these results for a broad class of biophysical neuron models, and then fit a specific model to recent experiments. The model reproduces the experimental results, exhibiting long term (days-long) correlations due to the interaction between slow variables and internal fluctuations. However, its memory of the input decays on a timescale of minutes. We suggest experiments to test these predictions directly.