J Comput Neurosci (2012) 33:435–447 DOI 10.1007/s10827-012-0394-8 Synaptic conditions for auto-associative memory storage and pattern completion in Jensen et al.’s model of hippocampal area CA3 Eng Yeow Cheu · Jiali Yu · Chin Hiong Tan · Huajin Tang Received: 18 November 2011 / Revised: 28 March 2012 / Accepted: 30 March 2012 / Published online: 30 May 2012 © Springer Science+Business Media, LLC 2012 Abstract Jensen et al. (Learn Memory 3(2–3):243–256, 1996b) proposed an auto-associative memory model us- ing an integrated short-term memory (STM) and long- term memory (LTM) spiking neural network. Their model requires that distinct pyramidal cells encoding different STM patterns are fired in different high- frequency gamma subcycles within each low-frequency theta oscillation. Auto-associative LTM is formed by modifying the recurrent synaptic efficacy between pyra- midal cells. In order to store auto-associative LTM cor- rectly, the recurrent synaptic efficacy must be bounded. The synaptic efficacy must be upper bounded to pre- vent re-firing of pyramidal cells in subsequent gamma subcycles. If cells encoding one memory item were to re-fire synchronously with other cells encoding another item in subsequent gamma subcycle, LTM stored via modifiable recurrent synapses would be corrupted. The synaptic efficacy must also be lower bounded so that memory pattern completion can be performed cor- rectly. This paper uses the original model by Jensen et al. as the basis to illustrate the following points. Firstly, the importance of coordinated long-term mem- ory (LTM) synaptic modification. Secondly, the use of a generic mathematical formulation (spiking response model) that can theoretically extend the results to other spiking network utilizing threshold-fire spiking neuron model. Thirdly, the interaction of long-term and short-term memory networks that possibly explains the Action Editor: Alessandro Treves E. Y. Cheu · J. Yu · C. H. Tan · H. Tang (B ) Institute for Infocomm Research, Agency for Science Technology and Research (A*STAR), Singapore e-mail: htang@i2r.a-star.edu.sg asymmetric distribution of spike density in theta cycle through the merger of STM patterns with interaction of LTM network. Keywords CA3 · Auto-associative · Pattern completion · Synaptic condition · Short-term memory · Long-term memory 1 Introduction A key functional role of the hippocampus is the stor- age and recall of associative memories (Rolls 2008; Cutsuridis and Wennekers 2009). Auto-association refers to the retrieval or completing of a memory from a partial or noisy sample of itself. Hetero-association refers to the recall of a memory from one category as a result of a cue from another category. The CA1 region of the hippocampus has been proposed to be hetero-associator (Rolls 2010). Depending on the ki- netics of NDMA channels, CA3 region of hippocampus can function as either hetero-associator (Jensen and Lisman 1996c) or auto-associator (Jensen et al. 1996b) for the storage of declarative memories. Dual oscillations have been recorded in hippo- campus in which a low frequency theta oscillation is subdivided into about seven subcycles of high fre- quency gamma oscillation (Bragin et al. 1995). The theta rhythm in the hippocampus refers to the regu- lar oscillations of the local field potential at frequen- cies of 4–12 Hz which has been observed in rodents (Vanderwolf 1969). In humans, the theta rhythm typ- ically refers to oscillations in the frequencies of 4–7 Hz (Cantero et al. 2003), while gamma rhythm typically refers to oscillations in the frequencies of 25–100 Hz