The complete computational CA1 microcircuit model of Cutsuridis et al. [17] is depicted in Fig. 1. The complete model consisted of 100 PCs, one axoaxonic cell (AAC), two basket cells (BCs), one BSC, and one oriens lacunosummoleculare (OLM) cell. An entorhinal cortical (EC) excitatory input excited the distal dendrites of PCs, AAC, and BC, whereas an excitatory Schaffer collateral CA3 input excited the proximal dendrites of PCs, AAC, BCs, and BSC. A medial septum (MS) inhibitory input inhibited all inhibitory cells in the network and caused them to fire at specific phases of a theta rhythm.
In this study where only the recall ability of the microcircuit was tested when a growing number of memory patterns were stored in its synapses without examining the exact details of the learning (storage) process, a subnetwork of the complete microcircuit model was utilized. The subnetwork consisted of N PCs (N = 100 or 300), one BSC, and one OLM cell (see Fig. 2). Simplified morphologies including the soma, apical and basal dendrites and a portion of the axon, were used for each cell type. The biophysical properties of each cell were adapted from cell types reported in the literature, which were extensively validated against experimental data in [24,25,26,27]. BCs and AAC although present in the network were disconnected from it and they were inactive during the retrieval cycle due to strong MS inhibition and hence had no effect on the network dynamics. EC input although present also had no effect on the network cells, because it was also disconnected. The only excitation to the network was from CA3 which excited the dendrites of BSC and PCs. All simulations were performed using NEURON [28] running on a PC with 4 CPUs under Windows 8. Voltage traces of all connected (PCs, BSC, OLM) and disconnected (AAC, BCs) cells to the network with respect to a single theta cycle are depicted in Fig. 3.
To assist the readers of this work and increase the readability of our manuscript, we provide below brief descriptions of each network’s components. Interested readers should refer to [17, 29] studies for more details of the microcircuit model and its components including the dimensions of their cells’ somatic, axonic, and dendritic compartments and distributions of passive and active conductances, synaptic waveforms, and synaptic conductances along these compartments. The complete mathematical formalism of the model can be found in the supplementary online materials document of [29].
Pyramidal cells
Each PC had 15 compartments. Each compartment contained a calcium pump and buffering mechanisms, calcium activated slow afterhyperpolarized (AHP) and medium AHP K^{+} currents, a highvoltage activated (HVA) Ltype Ca^{2+} current, an HVA Rtype Ca^{2+} current, a lowvoltage activated (LVA) Ttype Ca^{2+} current, an h current, a fast sodium and a delayed rectifier K^{+} current, a slowly inactivating Mtype K^{+} current, and a fast inactivating Atype K^{+} current [24, 25].
Each PC received middendritic excitation from Schaffer collaterals (CA3PCs), proximal excitation from around 1% of other CA1 PCs in the network (recurrent collaterals) [30], spatially distributed (six contacts) proximal dendritic synaptic inhibition from the BSC, and distal synaptic inhibition on each distal [stratum lacunosummoleculare (SLM)] dendritic branch from the OLM cell.
Bistratified cell
The BSC had 13 compartments. Each compartment contained a leak conductance, a sodium current, a fast delayed rectifier K^{+} current, an Atype K^{+} current, L and Ntype Ca^{2+} currents, a Ca^{2+}dependent K^{+} current, and a Ca^{2+} and voltagedependent K^{+} current [26]. It received excitation from the CA3 Schaffer collaterals in its medial dendritic compartments, excitation from active CA1 PCs in its basal dendrites, and inhibition from MS in its basal dendritic compartments.
OLM cell
The OLM cell had four compartments. Each compartment had a sodium (Na^{+}) current, a delayed rectifier K^{+} current, an Atype K^{+} current, and an h current [27]. It received excitation from the PCs in its basal dendrites and inhibition from MS in the soma.
Model inputs
An excitatory input originating from CA3 Schaffer collateral pyramidal cell axons and an inhibitory input originating from MS drove the network’s cells during recall (see Fig. 4). The CA3 input was modelled as the firing of M (M = 5, 10 or 20) out of N (N = 100 or 300) CA3 pyramidal cells at an average gamma frequency of 40 Hz (spike trains only modelled and not the explicit cells). PCs and BSC received CA3 excitatory input in their medial dendrites. MS inhibition was modelled as the rhythmic firing of two populations of ten septal cells (MS_{1} and MS_{2}) each modulated at opposite phases of a theta cycle (180 ° out of phase) [31] (see Fig. 4). Each septal cell output was modelled as bursts of action potentials using a presynaptic spike generator. Each spike train consisted of bursts of action potentials at a mean frequency of 8 Hz for a halftheta cycle (70 ms) followed by a halftheta cycle of silence. Due to 8% noise in the interspike intervals, the ten spike trains in each septal population were asynchronous. During recall, MS_{1} cells inhibited the MS_{2} cells, which disinhibited the BSC and OLM cells in the network.
Synaptic properties
AMPA, NMDA, GABAA, and GABAB synapses were considered. GABAA were present in somatic and dendritic compartments, whereas GABAB were present only in medial and distal dendrites. AMPA and NMDA synapses were present only in medial dendrites.
Network testing
The goal of this research work was to test the recall performance of the model when the network had already stored patterns without examining the exact details of the learning process. To test the recall performance of the model, the methodology described in [17] was adopted. A memory pattern was stored by generating a weight matrix based on a clipped Hebbian learning rule. This weight matrix was used to prespecify the CA3–CA1 PC connection weights. Without loss of generality, the input (CA3) and output (CA1) patterns were assumed to be the same, with each pattern consisting of M (M = 5, 10 or 20) randomly chosen PCs (active cells) out of the population of N (N = 100 or 300) PCs. The N × N (N × N = 100 × 100 or 300 × 300)dimensional weight matrix was created by setting matrix entry (i, j), w_{ij} = 1 if input PC i and output PC j are both active in the same pattern pair; otherwise, weights are 0. Any number of pattern pairs could be stored to create this binary weight matrix. The matrix was applied to our network model by connecting a CA3 input to a CA1 PC with a high AMPA conductance (gAMPA = 1.5 nS) if their connection weight was 1, or with a low conductance (gAMPA = 0.5 nS) if their connection was 0. This approach is supported by experimental evidence favouring twostate synapses [32].
Memory patterns
Sets of memory patterns at different sizes (1, 5, 10, 20), pattern overlaps (0%, 10%, 20%, 40%), and number of active cells per pattern (5, 10, 20) were created. A 0% overlap between for example five patterns in a set meant no overlap between patterns 1 and 2, 1 and 3, 1 and 4, 1 and 5, 2 and 3, 2 and 4, 2 and 5, 3 and 4, 3 and 5, and 4 and 5. Similarly, a 40% overlap between five patterns in a set meant that 0.4 × Μ cells were shared between patterns 1 and 2, a different 0.4 × Μ cells were shared between patterns 2 and 3, a different 0.4 × Μ cells between patterns 3 and 4, a different 0.4 × Μ cells between patterns 4 and 5, and a different 0.4 × Μ cells between patterns 5 and 1 (see Fig. 5). For 20 active cells per pattern, a maximum of five patterns could be stored by a network of 100 PCs. For ten active cells per pattern, a maximum of ten patterns could be stored, and for five active cells per pattern, a maximum of 20 patterns could be stored. Similar maximum number of patterns could be stored for 10%, 20%, and 40% overlap and 5, 10, and 20 active cells per pattern, respectively.
Recall performance
To measure the recall performance of our network, the normalized dot product metric was used which measured the distance between the recalled output pattern, A, from the required output pattern, A^{*}:
$$C=\frac{A\cdot {A}^{*}}{\left({\sum }_{i=1}^{{N}_{A}}{A}_{i}\cdot {\sum }_{j=1}^{{N}_{A}}{A}_{j}^{*}\right)},$$
(1)
where N_{A} is the number of output units. Correlation between the recalled and required output patterns took value from 0 (no correlation between output pattern A = [1 0 1 0 1 0] and output pattern A^{*} = [0 1 0 1 0 1]) to 1 (output pattern A = [1 0 1 0 1 0] and output pattern A^{*} = [1 0 1 0 1 0] are identical). The higher the correlation value, the better the recall performance.
Mean recall quality
We defined mean recall quality of our network model as the mean value of all recall qualities estimated from each pattern presentation when a P number of patterns were already stored in the network:
$$\mathrm{MC}=\frac{\sum_{i=1}^{{N}_{p}}{C}_{i}}{{N}_{p}},$$
(2)
where C_{i} is the recall quality of pattern i and N_{p} is total number of recalled patterns. For example, when ten patterns (N_{p} = 10) were initially stored in the network and pattern 1 was presented to the network during recall, then a recall quality value for pattern 1 (C1) was calculated. Repeating this process for each of the other patterns [pattern 2 (C2), pattern 3 (C3), …, pattern 10 (C10)], a recall quality value was calculated. The mean recall quality (MC) of the network was then the mean value of these individual recall qualities.
Model selection
In [17], BSC inhibition to PC dendrites acted as a global nonspecific threshold machine capable of removing spurious activities at the network level during recall. BSC inhibition was held constant as more patterns loaded onto the PC dendritic synapses. The recall quality of the model in [17] decreased as more and more memories were stored (see Fig. 14 in [17]).
To improve the recall performance of [17], we artificially modulated the synaptic strength of selective excitatory and inhibitory pathways to BSC and PC dendrites as more and more patterns were stored in the network:

1.
Model 1: strengthening of CA3 feedforward excitatory synaptic drive to BSC dendrites (Fig. 6a) increased BSC’s firing rate. As a result, more IPSPs were generated in the PC dendrites producing a very strong inhibitory environment, which eliminated all spurious activity.

2.
Model 2: strengthening of BSC feedforward inhibitory synaptic drive to PC dendrites (Fig. 6b) produced fewer IPSPs, but with greater amplitude.

3.
Model 3: strengthening of PC feedback excitatory synaptic drive to BSC basal dendrites (Fig. 6c) had a similar effect as model 1, but with smaller potency.