Bio-inspired models of memory capacity, recall performance and theta phase precession
ABSTRACT The hippocampus plays an important role in the encoding and retrieval of spatial and non-spatial memories. Much is known about the anatomical, physiological and molecular characteristics as well as the connectivity and synaptic properties of various cell types in the hippocampal circuits , but how these detailed properties of individual neurons give rise to the encoding and retrieval of memories remains unclear. Computational models play an instrumental role in providing clues on how these processes may take place. Here, we present three computational models of the region CA1 of the hippocampus at various levels of detail. Issues such as retrieval of memories as a function of cue loading, presentation frequency and learning paradigm, memory capacity, recall performance, and theta phase precession in the presence of dopamine neuromodulation and various types of inhibitory interneurons are addressed. The models lead to a number of experimentally testable predictions that may lead to a better understanding of the biophysical computations in the hippocampus.
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ABSTRACT: Successful spatial exploration requires gating, storage, and retrieval of spatial memories in the correct order. The hippocampus is known to play an important role in the temporal organization of spatial information. Temporally ordered spatial memories are encoded and retrieved by the firing rate and phase of hippocampal pyramidal cells and inhibitory interneurons with respect to ongoing network theta oscillations paced by intra- and extrahippocampal areas. Much is known about the anatomical, physiological, and molecular characteristics as well as the connectivity and synaptic properties of various cell types in the hippocampal microcircuits, but how these detailed properties of individual neurons give rise to temporal organization of spatial memories remains unclear. We present a model of the hippocampal CA1 microcircuit based on observed biophysical properties of pyramidal cells and six types of inhibitory interneurons: axo-axonic, basket, bistratistified, neurogliaform, ivy, and oriens lacunosum-moleculare cells. The model simulates a virtual rat running on a linear track. Excitatory transient inputs come from the entorhinal cortex (EC) and the CA3 Schaffer collaterals and impinge on both the pyramidal cells and inhibitory interneurons, whereas inhibitory inputs from the medial septum impinge only on the inhibitory interneurons. Dopamine operates as a gate-keeper modulating the spatial memory flow to the PC distal dendrites in a frequency-dependent manner. A mechanism for spike-timing-dependent plasticity in distal and proximal PC dendrites consisting of three calcium detectors, which responds to the instantaneous calcium level and its time course in the dendrite, is used to model the plasticity effects. The model simulates the timing of firing of different hippocampal cell types relative to theta oscillations, and proposes functional roles for the different classes of the hippocampal and septal inhibitory interneurons in the correct ordering of spatial memories as well as in the generation and maintenance of theta phase precession of pyramidal cells (place cells) in CA1. The model leads to a number of experimentally testable predictions that may lead to a better understanding of the biophysical computations in the hippocampus and medial septum.Hippocampus 01/2012; 22(7):1597-621. · 4.30 Impact Factor
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ABSTRACT: Sharp wave-ripples (SWRs) are population oscillatory patterns in hippocampal LFPs during deep sleep and immobility, involved in the replay of memories acquired during wakefulness. SWRs have been extensively studied, but their exact generation mechanism is still unknown. A computational model has suggested that fast perisomatic inhibition may generate the high frequency ripples (~200 Hz). Another model showed how replay of memories can be controlled by various classes of inhibitory interneurons targeting specific parts of pyramidal cells (PC) and firing at particular SWR phases. Optogenetic studies revealed new roles for interneuronal classes and rich dynamic interplays between them, shedding new light in their potential role in SWRs. Here, we integrate these findings in a conceptual model of how dendritic and somatic inhibition may collectively contribute to the SWR generation. We suggest that sharp wave excitation and basket cell (BC) recurrent inhibition synchronises BC spiking in ripple frequencies. This rhythm is imposed on bistratified cells which prevent pyramidal bursting. Axo-axonic and stratum lacunosum/moleculare interneurons are silenced by inhibitory inputs originating in the medial septum. PCs receiving rippling inhibition in both dendritic and perisomatic areas and excitation in their apical dendrites, exhibit sparse ripple phase-locked spiking.Frontiers in Systems Neuroscience 01/2013; 7:13.
Abstract— The hippocampus plays an important role in the
encoding and retrieval of spatial and non-spatial memories.
Much is known about the anatomical, physiological and
molecular characteristics as well as the connectivity and
synaptic properties of various cell types in the hippocampal
circuits , but how these detailed properties of individual
neurons give rise to the encoding and retrieval of memories
remains unclear. Computational models play an instrumental
role in providing clues on how these processes may take place.
Here, we present three computational models of the region CA1
of the hippocampus at various levels of detail. Issues such as
retrieval of memories as a function of cue loading, presentation
frequency and learning paradigm, memory capacity, recall
performance, and theta phase precession in the presence of
dopamine neuromodulation and various types of inhibitory
interneurons are addressed. The models lead to a number of
experimentally testable predictions that may lead to a better
understanding of the biophysical computations in the
The hippocampus is a key brain structure known to play a
role in the encoding and retrieval of spatial (e.g. landmark)
and non-spatial (e.g. object) memories. The principal
excitatory cells (pyramidal cells (PCs)) exhibit firing
patterns which code for spatial features (e.g. places) of the
external world. The firing rate and phase of the pyramidal
cells that code for place change with respect to theta
oscillations . Theta oscillations (4-10 Hz) are observed
in rats during navigation and rapid eye movement (REM)
sleep . During exploration hippocampal place cells shift
their phase of firing to earlier phases of the theta oscillation
as the animal transverses the place field (a phenomenon
known as theta phase precession) [35-36].
Network oscillations (theta, gamma, ripples) in the
hippocampus are either internally generated  or are
paced by extrahippocampal areas (e.g. medial septum (MS))
. Theta oscillations have been suggested to contribute to
memory formation  by separating the encoding of new
Manuscript received February 28, 2011. This work was supported by the
EPSRC project grant EP/D04281X/1 and the NSF Science for Learning
Center CELEST grant SMA 0835976.
V. Cutsuridis is with the Center for Memory and Brain, Boston
University, Boston, MA 02215, USA (corresponding author; phone: 617-
353-2840; fax: 617-358-3296; e-mail: firstname.lastname@example.org).
B.P. Graham is with the Institute of Computing Science and
Mathematics, University of Stirling, U.K. (e-mail: email@example.com).
S. Cobb is with the Institute of Neuroscience and Psychology, University
of Glasgow, U.K. (e-mail: firstname.lastname@example.org).
M.E. Hasselmo is with the Center for Memory and Brain, Department of
Psychology, and Graduate Program in Neuroscience, Boston University,
Boston, MA 02215, USA (e-mail: email@example.com).
information and the recall of old information in separate
functional sub-cycles of theta. Gamma oscillations have
been proposed to be an internal clock . Ripples play a
role in the replay of memories in a temporally compressed
In recent years a zoo of inhibitory interneurons has been
identified in the hippocampus [24-28]. These cells are
categorised based on their anatomical, morphological,
pharmacological and physiological properties . These
include the axo-axonic cells (AAC), the perisomatic basket
cells (BC) and the dendritic bistratified (BSC), ivy (IVY),
neurogliaform (NGL) and oriens lacunosum-moleculare
(OLM) cells , [26-27]. AACs target exclusively the axon
of the CA1 PC, whereas BCs inhibit their cell bodies and
proximal dendrites . BSCs and IVYs inhibit the PC basal
and oblique dendrites, whereas OLM and NGL cells target
the apical dendritic tuft of PCs , [26-27].
Recent experimental studies have shown that the CA1
excitatory and inhibitory neurons fire at different phases of
the theta oscillations [12-14, 41]. During theta, AACs, BCs
and NGLs fire almost in phase with respect to the peak
phases of theta, whereas BSCs, PCs, IVYs and OLM cells
fire during the trough phases of theta [12-14, 41].
Similarly, medial septal (MS) GABAergic neurons
differentially phase their activities with respect to theta
oscillations , . During theta, some MS GABAergic
cells increase their firing during the peak of theta (MS180),
whereas others during the trough of theta (MS360) .
As we speak further biological evidence is gathered from
labs around the world on the properties of hippocampal cells
with respect to theta, gamma and ripple oscillations. What
we are trying to convey in this paper is that experimental
evidence and detailed computational modeling have
complementary roles in understanding the biophysical
mechanisms and computations in the hippocampus. We
show how such a marriage of theory and experiment within
the context of encoding and retrieval of memory patterns in
the hippocampus is possible in the next three sections.
II. ENCODING AND RETRIEVAL OF MEMORIES AS A FUNCTION
OF CUE LOADING AND PRESENTATION FREQUENCY
A. The Model
We’ve constructed a neural network model (see Fig. 1) of
the region CA1 of the hippocampus consisting of 100 PCs, 2
BCs, 1 AAC, 1 BSC and 1 OLM cell [3-4], . The cell
numbers, morphology, ionic and synaptic properties,
connectivity and spatial distribution followed closely the
experimental evidence of the hippocampus . All model
Bio-inspired Models of Memory Capacity, Recall Performance and
Theta Phase Precession in the Hippocampus
Vassilis Cutsuridis, Bruce P. Graham, Stuart Cobb, and Michael E. Hasselmo
Proceedings of International Joint Conference on Neural Networks, San Jose, California, USA, July 31 – August 5, 2011
978-1-4244-9636-5/11/$26.00 ©2011 IEEE
cell morphologies included a soma, an axon, and dendrites
(proximal, distal and basal). The biophysical properties of
each cell were adapted from cell types reported in the
literature [16-19]. Dimensions of the somatic, axonic and
dendritic compartments of the model cells were adapted
from [37-38]. All passive and active ionic conductances,
synaptic waveform parameters and synaptic conductances
have been published elsewhere . The complete Hodgkin-
Huxley mathematical formalism of the model has been
described in the appendix of  (see also ).
In the model, PCs were inhibited in the axon by the AAC,
in the soma by the BCs, in the proximal dendrites by the
BSC and the distal dendrites by the OLM cell, and in turn
they excited all network INs in their basal dendrites. BC and
BSC mutually inhibited each other, whereas the BC also
inhibited the neighboring BC in the network. The OLM cell
was excited by all PCs. All network INs were inhibited by
GABAergic MS cells (MS180).
AMPA, NMDA, GABA-A and GABA-B synapses
were considered. GABA-A were present in soma, axon,
proximal, distal and basal dendrites of cells, whereas AMPA
and GABA-B were present only in the proximal and distal
dendrites. NMDA synapses were present only in the
proximal dendrites of the network PCs.
The strength of the CA3 Schaffer collateral input to the
proximal PC dendrites was modulated by presynaptic
GABA-B inhibition, which was active during the first half-
cycle of theta and inactive during the second half-cycle of it.
PCs, BCs and AAC were excited in their distal dendrites
by the entorhinal cortical (EC) input and in their proximal
dendrites by the CA3 Schaffer collateral input. The BSC was
only excited by the CA3 input.
Model EC and CA3 inputs were modeled as the firing of
20 entorhinal cortical cells and 20 out of 100 CA3 pyramidal
cells. EC and CA3 inputs were presented every Δτ during
the theta oscillation. Δτ was set to either 5ms, or 7ms, or
8ms or 10 ms or 11ms. EC inputs preceded the CA3 inputs
by 9ms in accordance with experimental evidence that
showed the conduction latency of the EC-layer III input to
CA1 distal dendrites to range between 5 and 8 ms, whereas
the conduction latency of the EC-layer II input to CA1
proximal dendrite via the trisynaptic loop to range between
12 and 18 ms [20-21].
A phenomenological spike timing-dependent plasticity
(STDP) rule was used to modify the synaptic strength of the
PC proximal AMPA synapses by comparing the CA3 input
with the proximal postsynaptic voltage response. During
recall, the PC proximal AMPA synaptic conductance was
fixed and equated to the conductance value at the end of the
encoding cycle plus a constant term, which represented the
lift-off of the presynaptic GABA-B inhibition.
B. Simulation Results and Model Predictions
The model demonstrated the biological feasibility of the
separation of encoding and retrieval processes into separate
theta sub-cycles . On the assumption that EC input
always precedes the CA3 input by 9ms [20-21], the model
predicted that the only way the EC and CA3 input patterns
could be hetero-associated in the PC proximal dendrites is
by maintaining an amplified postsynaptic voltage response
for a sufficiently long period of time. The model predicted
that such amplification of the PC proximal postsynaptic
response may be due to the activation of, by the strong
hyperpolarization from the BC and AAC inhibition of the
soma and axon, non-specific cationic h-channels, which
allowed the influx of Na+ ions in the PC soma and proximal
dendrites and hence the ``boosting'' of the proximal
postsynaptic voltage response.
The model further predicted that the only way such
careful timing can take place is if inhibitory cells are
switched on and switched off in certain phase relationships
with respect to the theta oscillation, as demonstrated by
recent experimental data [12-14]. So, in the model, during
storage the AACs and BCs were switched on and operated
to: (1) exert tight inhibitory control on the axons and somas
of the PCs, thus preventing them from firing during the
storage cycle , (2) exert powerful inhibitory control to
neighboring BCs and BSCs, preventing the latter from firing
 during the encoding phase and disrupting the learning
process, and (3) maintain the environment necessary for the
activation of non-specific Na+ -based cation h-channels and
subsequently the amplification of the proximal postsynaptic
response. During the retrieval phase, the septal inhibition
was switched on, which in turn inhibited the AACs and BCs,
which dis-inhibited the BSCs and allowed the PCs to fire
action potentials and hence recall the information. BSCs
provided a general broadcasting inhibitory signal to all PCs,
which silenced all spurious cells in the network and allowed
cells that have learnt the pattern to retrieve it. Finally, OLM
cells were switched on during recall by the PC excitation
[12-14] and inhibited the PC distal dendrites, thus preventing
unwanted or similar memories from being retrieved.
The recall performance of the model (see Fig. 2) for a
memory pattern was tested for different input pattern
Fig. 1. Hippocampal CA1 microcircuit showing major cell types and
their connectivity (adapted from  with permission). Black filled
triangles: pyramidal cells. Dark gray filled circles: CA1 inhibitory
interneurons. Light gray filled circles: Septal GABA inhibition. EC:
entorhinal cortical input; CA3: CA3 Schaffer collateral input; AA: axo-
axonic cell; B: basket cell; BS: bistratified cell; OLM: oriens lacunosum-
moleculare cell; SLM: stratum lacunosum-moleculare; SR: stratum
radiatum; SO: stratum oriens.
presentation periods (Δτ = 5 ms, 7 ms, 8 ms, 10 ms and 11
ms), levels of cue (EC input) loading (10%, 50% and 75% of
the cue was presented to PC) and learning paradigms (one-
trial vs. many-trials). To estimate the recall performance, we
counted the number of active cells in the pattern during a
retrieval cycle and divided this number by the actual number
of cells that ought to be active (pattern cells). If the active
cells were equal to the pattern cells, then the recall fraction
was 1 (i.e. perfect recall). At 75% cue loading, the recall
performance for the “many-trials” case was nearly perfect
(100%) regardless of the presentation period. At 50% and
10% cue loading in the “many-trials'' case, the recall
performance dropped by 5% and 20% respectively when the
input presentation period was 5 ms. At larger input
presentation periods, the recall performance degraded
progressively for both 50% and 10% cue loading reaching a
minimum of 45% and 70% respectively at 11 ms.
In the ``one-trial'' case at 75% cue loading, the recall
performance across input presentation periods varied slightly
between 60% and 80%. At 50% and 10% cue loading, the
recall performance dropped at 65% and 55% respectively at
5 ms. Across input presentation periods, the recall
performance at 50% cue loading varied between 45% and
65%, whereas at 10% cue loading varied between 20% and
55%. Across learning case at 75% cue loading and 5ms time
input presentation period, a drop of 20% in recall
performance was observed between the “many-trial'' and
“one-trial'' learning cases. Across all other presentation
periods, the recall performance drop varied from 20% (7 ms)
to 40% (8 ms) between the two cases. A constant 30% drop
was observed across all presentation periods at 50% cue
loading between the two cases with the exception of a 10%
increase at 11 ms during the one-trial learning case. At 10%
cue loading, the recall performance drop between the
“many-trials'' and the “one-trial” cases varied from 25% (5
ms) to 50% (8 ms and 11 ms).
III. TESTING MEMORY CAPACITY AND RECALL
A. The Model
We used the model of region CA1 of the hippocampus
described in the previous section and changed it in the
following ways in order to test its memory capacity and
recall performance in the presence of various types of
inhibitory interneurons. In contrast to the model described in
the previous section, this model’s EC and CA3 inputs were
modeled as the firing of 20 entorhinal cortical cells and 20
out of 100 CA3 pyramidal cells, respectively, at an average
gamma frequency of 40Hz. EC inputs preceded the CA3
inputs by 9ms in accordance with experimental evidence that
showed the conduction latency of the EC-layer III input to
CA1 apical dendrites to range between 5 and 8 ms, whereas
the conduction latency of the EC-layer II input to CA1 basal
dendrite via the trisynaptic loop to range between 12 and 18
All other parameters such as cell numbers, cell
morphologies, passive and active ionic conductances,
synaptic waveform parameters and synaptic conductances
were left unchanged. The same phenomenological STDP
rule as before was used here to modify the synaptic strength
of the PC proximal AMPA synapses by comparing the
relative timing between the CA3 input and the postsynaptic
voltage response. During storage, the weights were
initialized according to the predefined weight matrix and
were allowed to change according to a clipped STDP rule.
The low conductance state (gAMPA = 0.5 nS) was the
minimum weight that could be achieved by long-term
depression (LTD), whereas the high conductance state
(gAMPA = 1.5 nS) was the saturated value that could be
achieved by long-term potentiation (LTP). During each
retrieval cycle the STDP learning rule was switched off. The
conductance values from the last gamma cycle of the storage
sub-cycle were used during the recall phase.
The recall performance metric used for measuring the
distance between the recalled output pattern, C, from the
required output pattern, C*, was the correlation (i.e., degree
of overlap) metric, calculated as the normalized dot product:
Fig. 2. Recall performance of pattern vector as a function of input
pattern presentation period (adapted with permission from ). (A)
Many-trials learning; (B) One-trial learning. Black bar: 10% cue
loading; Gray bar: 50% cue loading; White bar: 75% cue loading.
where NC is the number of output units. The correlation
takes a value between 0 (no correlation) and 1 (the vectors
are identical). The higher the correlation, the better the recall
B. Simulation Results and Model Predictions
We tested the recall performance of our network to an
already stored set of patterns. This set of patterns was stored
by generating a weight matrix based on a clipped Hebbian
learning rule, and using the weight matrix to pre-specify the
CA3 to CA1 PC connection weights. Each pattern consisted
of 20 randomly chosen PCs out of the population of 100.
The 100 by 100 dimensional weight matrix was created by
setting matrix entry (i, j), wij = 1 if input PC i and output PC
j were both active in the same pattern pair; otherwise
weights were 0. The weight matrix was then 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.
To test recall of a previously stored pattern, the associated
input pattern was applied as cue in the form of spiking of
active CA3 inputs (the pattern) distributed within a gamma
frequency time window (40 Hz). At the same time, the 20
EC inputs also fired randomly distributed within a 25 ms
gamma window, while preceding the CA3 activity by 9ms.
The recall of the first pattern in a set of five is shown in
Figure 3. Subplots (3a) and (3b) are raster plots of the
spiking of (a) septal (top 10 rows), EC (next 20 rows) and
CA3 (bottom 100 rows) input and (b) CA1 PCs when EC
input is not present, respectively. The CA1 PCs are active
two or three times during a recall cycle, with their spiking
activity a very close match to the stored pattern. Subplot (3c)
shows the PC recall performance when the EC input is
present. The pattern is nearly perfectly recalled on each
gamma cycle during a recall theta half-cycle.
We then tested the influence of the inhibitory pathways on
recall by selectively removing different inhibitory pathways.
In the model bistratified cell inhibition to proximal PC
dendrites mediated thresholding of PC firing during recall.
Removal of BC and AAC inhibition did not spoil recall
quality in accord with this hypothesis (Fig. 3d). Removal of
all inhibitory pathways led to gamma frequency firing of
virtually all PCs during recall cycles and the EC cued pattern
during recall cycles (Fig. 3e).
Recall performance was calculated by measuring the CA1
Fig. 5. Memory capacity of the CA1 microcircuit model (adapted
from  with permission). Recall quality drops as the number of
stored patterns increase.
Fig. 4. Recall performance when recall is cued by the CA3 input, but
EC input due to a different spurious pattern is present on PCs (adapted
from  with permission). (a) Raster plot of PC activity in full network.
(b) Recall quality in (a). (c) PC activity when OLM inhibition is
removed. (d) Recall quality in (c).
Fig. 3. Recall performance when recall is cued by the CA3 input
(adapted from  with permission). Raster plots of (a) network inputs
(b) PCs in full network (c) EC input now connected to PCs, so
provides some recall cueing. (d) BC and AAC inhibition removed, so
that recall is mediated only by BSC inhibition (EC disconnected from
PCs). (e) BSC inhibition also removed. The pattern recalled was the
firing activities of the cells activated by the EC input pattern.
PC spiking activity during a sliding 10 ms time window. For
each window a binary vector of length 100 was formed, with
entries having a value of 1 if the corresponding PC spikes in
the window. The correlation of this vector with the expected
pattern vector was calculated to give a measure of recall
quality between 0 and 1, with 1 corresponding to perfect
In the model OLM inhibition removed interference from
spurious EC input during recall. Recall in this situation, with
and without OLM inhibition to the SLM PC dendrites is
shown in Figure 4. Recall was disrupted by the spurious EC
input, but this disruption was significantly worse if the OLM
inhibition is absent.
As was expected, average recall quality degraded when
too many patterns were stored as PCs received more
excitation from cue patterns they did not belong to, leading
to spurious firing. Figure 5 shows the mean recall quality as
the number of stored patterns is increased.
IV. THETA PHASE PRECESSION IN REGION CA1
A. The Model
We used the model of the CA1 microcircuit (see Fig 6)
described in section III in order to investigate the roles
different classes of the hippocampal and septal inhibitory
interneurons play in the gating of the correct order of spatial
memories in a sequence and the generation and maintenance
of theta phase precession of pyramidal cells (place cells) in
CA1 [7-9]. The present model was changed from the model
in section III in the following ways: This reduced model
consisted of four PCs, one BC, one BSC, one AAC and one
OLM. Two additional types of inhibitory interneurons were
also added to the current network: four IVY cells and four
neurogliaform (NGL) cells. The IVYs inhibited the proximal
dendrites of the PCs, whereas the NGLs inhibited the distal
dendrites of the PCs. Each PC consisted of only four
compartments (an axon, a soma, a proximal dendrite and a
distal dendrite), whereas each IN consisted of a single
In contrast to the model described in section III, PCs
contained a fast Na+ current, a delayed K+ rectifier current, a
low-voltage-activated (LVA) L-type Ca2+ current, an A-type
K+ current, and a calcium activated mAHP K+ current.
Active properties of BC, AAC, BSC and IVY included a fast
Na+, a delayed rectifier K+, a leakage and a type-A K+
currents , . Active properties of the OLM cell included
a fast Na+ current, a delayed rectifier K+ current, a persistent
Na+ current, a leakage current and an h-current , whereas
those of the NGL cell included a fast Na+ current, a delayed
rectifier K+ current and a leakage current.
In contrast to the previous model, each PC in the present
model was inhibited in the axon by the AAC, in the soma by
the BC, in proximal dendrite by the BSC and IVY cells, and
in the distal dendrite by the NGL and OLM cells. Inhibitory
interneurons were inhibited by MS180 and MS360 GABAergic
cells, and which in turn inhibited the MS cells.
AMPA, NMDA, and GABA-A synapses were considered.
AMPA and GABA-A were present in all compartments of
INs and PCs. NMDA synapses were present both in
proximal and distal dendrites of the PCs. Presynaptic
GABA-B inhibition modulated the strength of the CA3
Schaffer collateral input to PC proximal synapses as before.
In contrast to the previous model, the EC and CA3 inputs
arrived at the same time in the PC proximal dendrite. EC and
CA3 inputs excited the AAC and the BC. BSC was excited
only by the CA3 input, whereas NGL was excited only by
the EC input. IVY and OLM cells were excited only by the
PCs in the network. No other INs in the network received
feedback excitation from the PCs.
Each pyramidal cell in the network received a different set
of EC and CA3 inputs (PC1 was excited by EC1 and CA31,
PC2 by EC2 and CA32, PC3 by EC3 and CA33 and PC4 by
EC4 and CA34) (see Fig 6). The proper order by which the
EC and CA3 inputs were presented to each PC (EC1 and
CA31 first, followed by EC2 and CA32, then by EC3 and
CA33 and finally by EC4 and CA4) was ensured (gated) by
dopamine in the distal layer. Dopamine acted as the gate
keeper who opened the gate when a high frequency EC input
impinged on both NGL and PC and closed the gate when a
low frequency EC input impinged on both NGL and PC
. When the place cell was inside its place field, it
received a high frequency (100Hz) input from EC. When the
place cell was outside its place field, the frequency of the EC
input was low (1-3 spikes per theta oscillation). The duration
of each set of EC and CA3 inputs is 2250ms, which
corresponded to nine theta cycles, each theta cycle with
duration of 250ms. The presentation frequencies of the EC
and CA3 inputs were set to 100Hz (interspike interval (ISI)
= 10ms) and 50Hz (ISI = 20ms), respectively .
Fig. 6. Hippocampal CA1 microcircuit model showing major cell
types and their connectivity (adapted from [8-9]). Black arrow lines:
extra-hippocampal excitatory connections. Light gray arrow lines: PC
excitatory connections to OLM cell. Black filled lines: CA1
inhibitory connections. Dark gray filled circles: septal inhibitory
connections. EC: Layer III entorhinal cortical input. CA3: CA3
Schaffer collateral input. PC: pyramidal cell. AAC: axo-axonic cell.
BC: basket cell. BSC: bistratified cell. OLM: oriens lacunosum-
moleculare cell. NGL: neurogliaform cell. IVY: ivy cell. Note there is
no recurrent connectivity between pyramidal cells in the circuit.
In contrast to the phenomenological STDP rule used in
model from section III, a biophysical STDP learning rule
 was applied to both the proximal and distal NMDA
synapses of the PCs in the present model. The mechanism
had a modular structure consisting of three biochemical
detectors: a potentiation (P) detector, a depression (D)
detector and a veto (V) detector. Each detector responded to
the instantaneous calcium level and its time course in the
dendrite. The potentiation (P) detector triggered LTP every
time the calcium levels were above a high-threshold (4μM).
The depression (D) detector detected calcium levels
exceeding a low threshold level (0.6μM). When the calcium
levels remained above this threshold for a minimum time
period, LTD was triggered. The veto (V) detector detected
levels exceeding a mid-level threshold (2μM) and triggered a
veto to the D response. P and D compete to influence the
plasticity variable W, which serves as a measure of the sign
and magnitude of synaptic strength changes from the
baseline. In contrast to the previous models, the STDP
learning rule was left on throughout all theta oscillations (i.e.
weights were no longer fixed during the second half of
B. Simulation Results and Model Predictions
Experimental studies have shown that place cells have
specific properties when rats are inside the cell’s place field:
(1) all place cells start firing at the same initial phase ;
(2) the initial phase is on average the same on each entry of
the rat into the place field of a place cell ; (3) the total
amount of phase precession is always less than 360° ;
(4) the firing rate of the place cell increases as the position
of the rat in the place field increases, reaching a maximal
value at about 200° and beyond this point it decreases again.
The model, although it is not an explicit model of motion
or direction of movement, was able to capture the observed
properties of the place cells (see PC spiking activity with
respect to theta oscillation in Fig. 7). The model predicted
that in order for the place cells to phase precess to a full 360°
as the rat reaches the end of the place field (ninth theta
cycle), then an excitatory phase precessing CA3 input,
should drive not only the PCs, but also the inhibitory
interneurons causing them to also precess. An additional
phase precessing inhibitory input (MS180 and MS360), which
inhibits the CA1 inhibitory interneurons, is also required to
ensure that the phase relationships between the PCs and the
inhibitory INs during theta are maintained, as has been
observed experimentally [12-14].
Furthermore, the model predicted that in order for the
place cells to increase and decrease their firing activity in a
similar way to experimental data, then (1) a CA3 phase
precessed input should drive both CA1 PCs and INs, and the
frequency should linearly increase from the start till the
middle of the place field and subsequently decrease linearly
by the same amount till the end of the field, (2) a constant
frequency phase precessed MS and presynaptic GABAB
inhibition should also drive the CA1 INs and PCs,
respectively, and (3) the PC proximal synapse should be
Three computational models of the region CA1 of the
hippocampus at various levels of biological detail have been
presented. The models were successful at addressing issues
such as retrieval of memories as a function of cue loading
and presentation frequency in “one-trial” and “many-trials”
learning schemes, memory capacity, recall performance and
place cell firing rate and theta phase precession in the
presence of neuromodulators (e.g. dopamine) and various
classes of inhibitory interneurons. The models provided
experimental testable clues of how encoding and retrieval of
memories are achieved in
demonstrated how detailed computational models grounded
on experimental data can provide clues on the types of
computations performed in the hippocampus.
the hippocampus and
We would like to thank the two anonymous reviewers for
their comments. This work was supported by the EPSRC
project grant EP/D04281X/1 and the NSF Science for
Learning Center CELEST grant SMA 0835976.
Fig. 7. (Top) A rat running along a linear track. Gray filled ellipses
represent the place fields of four pyramidal cells (place cells) in the
network. Note their fields are non-overlapping. The time the rat
spends in each place field is equal to nine theta cycles, with each theta
cycle lasting 250ms, a total time of 2250ms. As the rat transverses the
place field, each PC shifts its firing to earlier phases of the theta
rhythm. (Bottom) Spiking activity of CA1 and septal cells with
respect to simulated theta oscillation as measured from the pyramidal
layer of CA1 (adapted from ). Arrows indicate the phase the place
cell fired with respect to theta.
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