Neural Networks 20 (2007) 653–667www.elsevier.com/locate/neunet

Emergence of sequence sensitivity in a hippocampal CA3–CA1 model

Motoharu Yoshidaa,∗, Hatsuo Hayashib

a Department of Computer Science and Electronics, Graduate School of Computer Science and Systems Engineering, Kyushu Institute of Technology,Iizuka 820-8502, Japan

b Department of Brain Science and Engineering, Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology,Kitakyushu 808-0196, Japan

Received 22 June 2006; received in revised form 23 May 2007; accepted 23 May 2007

Abstract

Recent studies have shown that place cells in the hippocampal CA1 region fire in a sequence sensitive manner. In this study we tested ifhippocampal CA3 and CA1 regions can give rise to the sequence sensitivity. We used a two-layer CA3–CA1 hippocampal model that consisted ofHodgkin–Huxley style neuron models. Sequential input signals that mimicked signals projected from the entorhinal cortex gradually modified thesynaptic conductances between CA3 pyramidal cells through spike-timing-dependent plasticity (STDP) and produced propagations of neuronalactivity in the radial direction from stimulated pyramidal cells. This sequence dependent spatio-temporal activity was picked up by specific CA1pyramidal cells through modification of Schaffer collateral synapses with STDP. After learning, these CA1 pyramidal cells responded with thehighest probability to the learned sequence, while responding with a lower probability to different sequences. These results demonstrate thatsequence sensitivity of CA1 place cells would emerge through computation in the CA3 and CA1 regions.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Sequence memory; Hippocampus; Place cell; Propagation; STDP; Spatio-temporal activity; Hodgkin–Huxley model; Self-organization

1. Introduction

Since the discovery of place cells in the rat hippocampus(O’Keefe & Dostrovsky, 1971; O’Keefe & Nadel, 1978),the role of the hippocampus as a cognitive spatial map hasattracted large interest. However, subsequent findings havesuggested that hippocampal place cells are not providingsimple spatial maps. It is reported that when rats visitmultiple places, corresponding place cells fire in sequence ina time-compressed manner (Dragoi & Buzsaki, 2006; Skaggs,McNaughton, Wilson, & Barnes, 1996) through theta phaseprecession (O’Keefe & Recce, 1993). These place cells firein the same sequence during subsequent sleep (Lee & Wilson,2002; Skaggs & McNaughton, 1996) suggesting that sequencesare stored within the hippocampus and recalled during sleep tobe consolidated in the higher cortex as long-term memory.

∗ Corresponding address: Center for Memory and Brain, Boston University,2 Cummington Street, Boston MA, 02215, United States. Tel.: +1 617 3531431.

E-mail addresses: motoharu@bu.edu (M. Yoshida),hayashi@brain.kyutech.ac.jp (H. Hayashi).

0893-6080/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.neunet.2007.05.003

Recent studies have shown more direct involvement ofplace cells with sequences. Wood, Dudchenko, Robitsek, andEichenbaum (2000) have investigated, using a maze that hastwo loops partly connected to each other, the activity of placecells that have place fields in the part of the maze which iscommon to both loops. They have shown that 31 out of 33CA1 place cells fired differently, depending on which of the twoloops the rats came from or were going to. This demonstratesthat a large amount of CA1 place cells are sensitive to sequencesof the past or the future. More recently, Ferbinteanu and Shapiro(2003) have shown that a large portion of rat CA1 place cells isretrospectively sequence-sensitive (sensitive to the sequence ofthe past) using a “+” shaped maze. Frank, Brown, and Wilson(2000) have compared place cells in the superficial layers of theentorhinal cortex (EC) that give input to the hippocampus, withplace cells in the deep layers of the EC that receive output fromthe hippocampus. They have found that place cells in the deeplayer of the EC are more sensitive to sequences than place cellsin the superficial layers, suggesting that sequence sensitivity ofplace cells emerges in the hippocampus.

Varieties of computational models have been proposedto explain sequence learning and recall of place cells.

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Storages and recalls of sequences through asymmetric recurrentconnections between neurons (Tsodyks, Skaggs, Sejnowski, &McNaughton, 1996), particularly in the CA3 area (Jensen &Lisman, 1996a, 1996b; Levy, 1996; Wallenstein & Hasselmo,1997; Yamaguchi, 2003) or in reciprocal dentate-CA3network (Lisman, 1999) have been proposed. Although thesemodels demonstrated that learned sequences were recalledsuccessfully, they did not demonstrate sequence sensitivityof place cells. Recently, Hasselmo and Eichenbaum (2005)proposed a binary model in which place cells respondedsensitively to a sequence. In their model, sequences were storedin the EC layer III and information about previous paths wasstored as a delayed activity in EC layer II neurons. Convergenceof these signals in the CA1 region made sequence-sensitivefiring possible. In this paper, we focus on the retrospectivesequence sensitivity which is the ability of place cells to firedepending not only on the current position of the animal butalso on the places visited in the past. The goal of this study isto test if the hippocampal CA3–CA1 region alone can produceretrospective sequence sensitivity of CA1 place cells, usingmore physiological hippocampal models, learning rules andinput signals.

Hippocampal CA3 and CA1 regions have distinct anatomi-cal and physiological features. The CA3 region has dense exci-tatory recurrent synaptic connections between pyramidal cells(Li, Somogyi, Ylinen, & Buzsaki, 1994; Tamamaki & Nojyo,1991). Anatomical and physiological features of the CA3 re-gion support the idea that this area spontaneously generatesa theta rhythm (Buzsaki, 2002). Synaptic conductances of re-current synapses are modified through spike-timing-dependentsynaptic plasticity (STDP) (Bi & Poo, 1998; Debanne, Gah-wiler, & Thompson, 1998). These experimental observationsimply the possibility of intra-network computation that utilizesspontaneous rhythmic activity and synaptic modification of re-current connections in the CA3 region.

On the other hand, recurrent connections between CA1pyramidal cells are not dense (Tamamaki & Nojyo, 1990;Witter & Amaral, 1991). CA1 pyramidal cells are less activecompared to CA3 pyramidal cells (Fricker, Verheugen, &Miles, 1999). This suggests that spontaneous activity and itspropagation hardly occur in the CA1 region. However, CA1pyramidal cells receive a large number of excitatory synapticinputs from CA3 pyramidal cells through Schaffer collaterals.Each CA1 pyramidal cell has 20–30 thousand Schaffercollateral synapses (Li et al., 1994). Synaptic projection fromeach CA3 pyramidal cell through Schaffer collaterals coverstwo thirds of the longitudinal extent of the CA1 region (Liet al., 1994). Moreover, conductances for the extensive Schaffercollateral synapses are modified through STDP (Bi & Poo,1998; Nishiyama, Hong, Mikoshiba, Poo, & Kato, 2000). Thisimplies that computation may also be executed in feed-forwardsynaptic connections from CA3 to CA1.

We developed a CA3–CA1 hippocampal model endowedwith the anatomical and physiological aspects mentionedabove. Sequential input signals that mimicked signals projectedthrough the perforant path from the EC, were applied to groupsof pyramidal cells in the CA3 and CA1 regions. In the CA3

region, this signal modified the synaptic conductances betweenCA3 pyramidal cells and produced propagations of neuronalactivity in the radial direction from stimulated pyramidal cells.The radial propagations of neuronal activity stored the timingsof input signals by their radii; earlier and later signals causedlarger and smaller ring-shaped neuronal activities, respectively.This firing pattern of the CA3 region was picked up by theconductances of Schaffer collateral synapses through STDP.Accordingly, CA1 pyramidal cells received maximum synapticinput from CA3 and responded with the highest probabilitywhen the sequence of input signals was identical to the learnedsequence. The response rate was lower when the sequence ofinput signals was different from the learned sequence. Theseresults demonstrate that anatomical and physiological featuresof the CA3 and CA1 regions, together with input signals fromplace cells in the EC, allow CA1 place cells to be sequencesensitive. Some of the results of the present paper have beenreported in a conference proceedings (Yoshida & Hayashi,2004b).

2. Methods

2.1. Cell models

The hippocampal CA3–CA1 model consists of pyramidalcells and inhibitory interneurons. Both kinds of neuronsare single-compartment Hodgkin–Huxley type neuron modelsdeveloped by Tateno, Hayashi, and Ishizuka (1998). Theequations of the pyramidal cell model in both the CA3 and CA1regions are as follows:

CdV/dt = gNam2h • (VNa − V ) + gCas2r • (VCa − V )

+ gCa(low)s2lowrlow • (VCa − V ) + gK(DR)n • (VK − V )

+ gK(A)ab • (VK − V ) + gK(AHP)q • (VK − V )

+ gK(C)c • min (1, χ/250) (VK − V ) + gL • (VL − V )

+ gaf •(Vsyn(e) − V

)+ Isyn, (1)

dz/dt = αz • (1 − z) − βzz, (2)dχ/dt = −φ ICa − βχχ. (3)

The constants gy and Vy are the maximum conductanceand the equilibrium potential for ion channels, respectively;the subscript y stands for Na, Ca, Ca(low), K(DR), K(A),K(AHP) and K(C). The constants, gL and gaf, are conductancesfor leakage and afferent excitatory synapses, respectively. VLand Vsyn(e) are equilibrium potentials of leakage and excitatorysynapses, respectively. The variable z is the ion-gating variable;z stands for m, h, s, r , slow, rlow, n, a, b, q and c. ICa is the sumof the second and the third terms on the right-hand side of Eq.(1). Isyn is the sum of the synaptic currents. Parameter valuesand voltage dependence of the rate constants, αz and βz , arelisted in Appendix A.

The larger conductance for the low threshold Ca2+ channel(the third term on the right-hand side of Eq. (1)) enables CA3pyramidal cells to cause spontaneous firing. The low thresholdCa2+ channel provides persistent inward Ca2+ current asobserved in the real CA3 pyramidal cell (Brown & Griffith,

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1983). Because of this inward current, the membrane potentialis depolarized slowly and the cell fires spontaneously withoutany external stimulation (even if the value of gaf is 0 µS). As thefiring increase the intracellular Ca2+ concentration, the Ca2+-activated K+ current and the AHP K+ current (the sixth andseventh terms on the right-hand side of Eq. (1)) are activated,resulting in hyperpolarization. This hyperpolarization interruptsspikes, resulting in bursting activity (See Fig. 4(diii)).

Interneurons in the hippocampus can be classified into fastspiking and non-fast spiking neurons (Kawaguchi & Hama,1987). Since the fast spiking neurons do not cause adaptation,the fast spiking neurons may have greater influence on theactivity of neural networks. We therefore adopted fast spikinginterneurons in this study. The equations of the interneuronmodel are as follows:

CdV/dt = gNam3h • (VNa − V ) + gK(DR)n4• (VK − V )

+ gL • (VL − V ) + Isyn, (4)

dz/dt = αz • (1 − z) − βzz. (5)

The parameters of the interneuron model were adjustedto reproduce the firing pattern of the interneuron observedexperimentally by Kawaguchi and Hama (1987) and Miles(1990a). See Appendix A for the parameter values and voltage-dependence of the rate constants, αz and βz .

2.2. Network structure

The hippocampal CA3–CA1 model consists of two layersof neural networks, CA1 and CA3 (Fig. 1(a)). Each neuralnetwork consists of 256 pyramidal cells placed on 16×16 latticepoints (indicated by triangles) and one inhibitory interneuron(indicated by a filled circle) (Fig. 1(b) and (c)). In the CA1network, each pyramidal cell was connected recurrently tothe nearest and the next nearest neighbors through excitatorysynapses. For example, the CA1 pyramidal cell indicated by thefilled triangle had bidirectional excitatory synaptic connectionswith the eight pyramidal cells in circle E1 (Fig. 1(b)). In theCA3 network, each pyramidal cell was connected recurrentlyto 28 nearby pyramidal cells as shown by circle E3 (Fig. 1(c)).Note that the extent of the recurrent connections betweenpyramidal cells in the CA3 network is larger than that in theCA1 network.

Discharges of inhibitory interneurons are synchronized witheach other and well phase locked to the field theta rhythmin the hippocampus (Buzsaki, Leung, & Vanderwolf, 1983).Electrical coupling between interneurons could be the causeof the synchronization (Uusisaari, Smirnov, Voipio, & Kaila,2002; Yang & Michelson, 2001). In the present model, we usedone interneuron to mimic phase-locked firing without modelingthe electrical couplings. All the pyramidal cells innervatedthe interneuron in an excitatory manner and the interneuroninnervates all the pyramidal cells in an inhibitory manner ineach network.

Each CA1 pyramidal cell receives excitatory synapticinput from all of the CA3 pyramidal cells through Schaffer

Fig. 1. Hippocampal CA3–CA1 neural network model. (a) Overview of themodel. The model consists of the CA3 and CA1 networks. All CA3 pyramidalcells are connected excitatory to each CA1 pyramidal cell through Schaffercollaterals. CA1 and CA3 pyramidal cells receive excitatory synaptic inputsthrough the perforant path fibers and the mossy fibers, respectively. (b)Intra-network connectivity of the CA1 region. The CA1 region consists of256 pyramidal cells (triangles) and one inhibitory interneuron (filled circle).Pyramidal cells are placed at 16 × 16 lattice points. Each CA1 pyramidalcell is connected to surrounding pyramidal cells through excitatory synapses.For example, the pyramidal cell shown by the filled triangle is connected toeight nearby pyramidal cells in the circle E1. The interneuron is located atthe center of the network. The interneuron is innervated excitatory from allCA1 pyramidal cells and innervates all CA1 pyramidal cells inhibitory. (c)Intra-network connectivity of the CA3 region. The CA3 region also consistsof 256 pyramidal cells and one inhibitory interneuron. Each CA3 pyramidalcell is connected to surrounding pyramidal cells through excitatory synapses.For example, the pyramidal cell shown by the filled triangle is connected to 28pyramidal cells in the circle E3. The radius of the circle E3 is larger than that ofthe circle E1. The inhibitory interneuron is innervated excitatory from all CA3pyramidal cells and innervate all CA3 pyramidal cells inhibitory, as in the CA1region.

collaterals. The equations for each type of synaptic current takethe following form:

Isyn = gsyn • (Vsyn − V ), (6)

gsyn = Csyn • (exp(−t/τ1(syn)) − exp(−t/τ2(syn))). (7)

The subscript “syn” denotes the synaptic type: pp CA3,pi CA3 and ip CA3 (pp CA1, pi CA1 and ip CA1) forrecurrent connections between pyramidal cells, excitatoryconnections from pyramidal cells to interneurons, andinhibitory connections from interneurons to pyramidal cellsin the CA3 (CA1) network, respectively. Synaptic terminalsof Schaffer collaterals to CA1, mossy fibers to CA3, andperforant path fibers to CA1 are referred to as sch, mossyand perf, respectively. Parameter values in Eqs. (6) and (7)are listed in Appendix B. While the synaptic conductancesfor recurrent connections in CA1, mossy fibers and perforantpath fibers were fixed to the values listed in Appendix B, thesynaptic conductances for recurrent excitatory connections inCA3 and Schaffer collaterals were modified during simulationas described in the next section. The conductances for theperforant path synapses were set very small so that thisinput alone could not cause firing of CA1 pyramidal cells asexperimentally observed (Colbert & Levy, 1992). The delay ofthe synaptic transmission was set to 1 ms at all synapses based

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on synaptic delays observed in the CA3 region (Miles & Wong,1986; Miles, 1990a, 1990b).

CA3 pyramidal cells on the edges and the corners of thenetwork are connected to less than 28 nearby CA3 pyramidalcells. Less excitation makes CA3 pyramidal cells fire atshorter interburst intervals because of less Ca2+ influx andless hyperpolarization. To reduce this effect, the conductancesgaf of CA3 pyramidal cells on the edges (gaf edge) and thecorners (gaf corner) were set smaller than those of the rest of theCA3 pyramidal cells (gaf center), as listed in Appendix A. Theconductances gaf for all of the CA1 pyramidal cells are zero.

2.3. Synaptic modification

As mentioned above, synaptic conductances for recurrentconnections in CA3 and Schaffer collaterals from CA3 toCA1 are known to be modified through STDP. In ourmodel, conductances for recurrent excitatory synapses inCA3 (Cpp CA3) and Schaffer collateral synapses (Csch) weremodified independently by STDP modification rules duringsimulation. STDP modification functions are as follows:

Fsyn(1t) =

MLTP syn · exp(1t/τsyn) if − T ≤ 1t < 0−MLTD syn · exp(−1t/τsyn) if 0 < 1t ≤ T0 otherwise.

(8)

1t denotes the relative spike timing between pre- andpostsynaptic spikes (the time of the presynaptic spike minus thetime of the postsynaptic spike). The subscript syn denotes thesynaptic type: pp CA3 and sch for CA3 recurrent connectionsand Schaffer collaterals, respectively. The maximal potentiationrate MLTP syn, the maximal depression rate MLTD syn, andthe time constant τsyn are as follows: MLTP pp CA3 =

MLTD pp CA3 = 0.05, τpp CA3 = 20 ms, MLTP sch = 0.04,MLTD sch = 0.06, τsch = 5 ms. Dotted and solid lines inFig. 2 show the STDP modification functions, Fpp CA3 (1t) andFsch (1t), respectively. Fpp CA3(1t) is a simple approximationof the experimental results obtained by Bi and Poo (1998)using dissociated and cultured hippocampal cells. As forFsch(1t), Nishiyama et al. (2000) have reported that the STDPmodification function of Shaffer collateral synapses has avery narrow time window where LTP can be induced. Wetherefore used a smaller value of τpp schfor Fsch(1t). By settingT = 100 ms, we neglected synaptic modification in the 1trange where the absolute amount of the modification function(|F(1t)|) was less than 0.00034.

Each pair of pre- and postsynaptic spikes modified synapticconductance by the following equation:

Csyn → Csyn + Cmax syn · Fsyn(1t). (9)

The synaptic conductance Csyn was limited to the rangeCmin syn ≤ Csyn ≤ Cmax syn, where Cmin pp CA3, Cmax pp CA3,Cmin sch and Cmax sch were 0.0005, 0.002, 0.0003 and 0.001µS, respectively.

Fig. 2. STDP modification functions. Dotted and solid lines show STDPmodification functions for CA3 recurrent synapses and Schaffer collateralsynapses, respectively. Each function is defined by Eq. (8).

2.4. Measurement of spatial asymmetry of recurrent connec-tions between CA3 pyramidal cells

Modification of recurrent synaptic conductances betweenCA3 pyramidal cells produces spatial asymmetry of Cpp CA3.The spatial asymmetry is represented by the orientation and thelength of bars located at every location of pyramidal cells in thenetwork, as shown in Figs. 4(a), 5(a), and 6(a). The bar locatedat the i-th pyramidal cell was obtained as follows. First, vectorsoriented from the presynaptic pyramidal cells (surroundingcells) to the postsynaptic cell (i-th cell) were obtained. Thelength of each vector was proportional to Cpp CA3. Next,these vectors were summed and the length of the summedvector was normalized relative to Cmax pp CA3 · (1 +

√2). The

normalized vector Vi is shown as a bar originating from thelocation of the i-th pyramidal cell. Therefore, the direction andthe length of each bar indicate the local direction in whichexcitatory connection is relatively strong and the degree ofspatial asymmetry, respectively.

2.5. Input signals to the CA3 and CA1 networks

Place cells in the EC have multiple place fields on hexagonalgrids and are called grid cells (Hafting, Fyhn, Molden, Moser,& Moser, 2005). However, CA1 place cells usually have onlyone place field and their place fields can be maintained solelyby direct input from EC to CA1 (Brun et al., 2002). Thissuggests that direct projections from EC to CA1 give sufficientinformation for them to fire in single place, for example,through summation of multiple synaptic inputs. In our model,we assumed that this was also the case for the projections fromEC to CA3 through dentate gyrus and that pyramidal cells ineach subregion in CA3 and CA1 received such informationabout single places (Fig. 3(a)). Specifically, signals about placesA–D were projected to pyramidal cells in subregions A3–D3of CA3, respectively, through mossy fibers, and to A1–D1 ofCA1, respectively, through perforant path fibers (Fig. 3(a)).Each subregion in CA3 (A3–D3) and CA1 (A1–D1) consistedof 9 (3 × 3) and 25 (5 × 5) pyramidal cells, respectively.

Signals from the EC to the hippocampus through perforantpath fibers are modulated by theta oscillations (Kocsis, Bragin,& Buzsaki, 1999), and theta phase precession is observed notonly in the CA1 and CA3 regions but also in the dentate gyrus(Skaggs et al., 1996). Moreover, turning off hippocampal neural

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discharges for 250 ms by commissural pathway stimulationdoes not disrupt theta phase precession (Zugaro, Monconduit,& Buzsaki, 2005). These findings suggest that external inputfrom the EC is crucial for theta phase precession. We thereforeassumed that information about places was coded in a thetacycle in the EC in a time-compressed manner through thetaphase precession (see Skaggs et al. (1996) for the mechanismof time-compressed firing of place cells). Note, therefore, thatwe assume that the cognitive map is obtained in the EC whichis upstream of the hippocampus. In the present study, thetaburst signals that mimicked firing of place cells were appliedsuccessively (A -> B -> C -> D) at intervals of 20 ms to CA3and CA1 through mossy and perforant path fibers as shown inFig. 3(b). Each burst in the signals to CA1 and CA3 consisted oftwo and three pulses, respectively. The interburst interval was100 ms and the interpulse interval was 10 ms. Because perforantpath signals from the EC were projected to CA3 through thedentate gyrus, the signals were applied to CA3 10 ms posteriorto CA1.

3. Results

3.1. Spontaneous spatiotemporal activity of the CA3–CA1network model

We started numerical simulation without the input signalsand the STDP rules to observe the spontaneous spatiotemporalactivity of the model. Fig. 4 shows the synaptic conductanceand spontaneous activity of the hippocampal CA3–CA1network model 4 s after the beginning of the simulation. All ofthe synaptic conductances Cpp CA3 were identical and did notchange with time as shown in Fig. 4(a): Cpp CA3 = 0.001 µS.The radius of each filled circle at locations of CA3 pyramidalcells is proportional to the average of synaptic conductancesCpp CA3 from surrounding pyramidal cells. The bars protrudingfrom the circles indicate local directions in which Cpp CA3 wasrelatively strong (See Section 2.4). As all of the conductancesCpp CA3 were identical across the CA3 network, sizes of thecircles are the same and no bar is seen except at the edges of thenetwork where pyramidal cells received spatially asymmetricsynaptic contacts from less than 28 surrounding pyramidalcells.

CA3 pyramidal cells caused spontaneous bursts of firing(Fig. 4(diii)) and evoked firing of the inhibitory interneuron(Fig. 4(div)). Lower panels in Fig. 4(c) show spontaneousspatio-temporal firing patterns of CA3 pyramidal cells.Intervals between the panels (ci)–(civ) are 20 ms. These firingpatterns were observed in the period between two dotted linesin Fig. 4(d). White squares indicate firing of CA3 pyramidalcells and fade out with time. Pyramidal cells at the lower partof the CA3 network started firing in the first panel (Fig. 4(ci)lower panel), and then pyramidal cells at the upper part of thenetwork started firing in the second panel (Fig. 4(cii) lowerpanel). This firing propagated to the center of the network(Fig. 4(ciii) lower panel), and gave excitatory synaptic inputsto the inhibitory interneuron. Firing of the interneuron, inturn, inhibited the pyramidal cells (Fig. 4(civ) lower panel).

Fig. 3. Input signals to the hippocampal CA3–CA1 model. (a) Projectionsites of input signals. Input signals that represented activities of place cells,A–D, in the EC were projected to the subregions, A1–D1, in CA1 and thesubregions, A3–D3, in CA3 through perforant path fibers and mossy fibers,respectively. The subregions, A1–D1, consist of 5 × 5 CA1 pyramidal cellsand the subregions, A3–D3, consist of 3 × 3 CA3 pyramidal cells. Blackpyramidal cell in subregion D1 indicate pyramidal cell #188. (b) Input signalpatterns. Each signal is a theta-burst signal with 100 ms interburst intervalsand 10 ms interpulse intervals. The number of pulses in each burst is two forthe perforant path signals and three for the mossy fiber signals. Mimickingtemporally compressed firing of place cells, signals were successively fed intothe four subregions in each network at intervals of 20 ms. CA1 pyramidalcells receive inputs directly from the EC through the perforant path, whileCA3 pyramidal cells receive inputs from the EC via the dentate gyrus. Inputsignals through the mossy fibers were, thus, delayed 10 ms compared with thosethrough perforant path fibers.

The spatio-temporal firing pattern varied with time and therewas no consistent spatio-temporal pattern at this stage asthe synaptic conductances Cpp CA3 were identical and keptconstant.

Conductances for all Schaffer collateral synapses (Csch)were also identical as shown in Fig. 4(b). Note that this paneldoes not show the CA1 network but conductances for 256Schaffer collateral synapses connecting CA3 pyramidal cellsto one of the CA1 pyramidal cells (cell #188 in Fig. 3(a))placed at the center of the subregion D1. The CA1 pyramidalcell #188 is indicated by an open circle in the upper panel ofFig. 4(ci). The size of each filled circle in Fig. 4(b) placed at thesame position as the CA3 pyramidal cells is proportional to thestrength of Schaffer collateral connection from correspondingCA3 pyramidal cell to the CA1 pyramidal cell #188. The radiiof the filled circles are the same because all of the synapticconductances Csch were identical.

Receiving the spontaneous activity of the CA3 region,subthreshold membrane potential oscillation at a thetafrequency occurred in the CA1 pyramidal cells as shown inFig. 4(di). Upper panels of Fig. 4(c) show spatio-temporal firingpatterns of the CA1 network. There was no firing becauseSchaffer collateral synaptic conductances Csch were relativelyweak. The CA1 interneuron did not fire either due to the lack offiring of CA1 pyramidal cells (Fig. 4(dii)).

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Fig. 4. Initial state and activity of the CA3–CA1 model. (a) Spatial pattern of CA3 recurrent synaptic conductances. Radius of each small filled circle at the positionof CA3 pyramidal cell is proportional to the sum of the recurrent synaptic conductances of corresponding pyramidal cell. The bars protruding from the circlesrepresent local spatial asymmetry of the recurrent synaptic conductances. Direction of each bar corresponds to the direction in which the local recurrent synapticconductance is strong, and the length of each bar shows the degree of spatial asymmetry (See Methods). (b) Conductances for Schaffer collateral synapses connectingCA3 pyramidal cells to CA1 pyramidal cell #188. The location of CA1 pyramidal cell #188 is indicated by a small circle in Fig. 4(ci) (upper panel). Radius ofeach filled circle at the position of the CA3 pyramidal cell is proportional to the conductance for corresponding Schaffer collateral synapse. The conductanceswere uniform at the initial state. (c) Spatio-temporal firing patterns of the CA1 network (upper panels) and the CA3 network (lower panels). White squares in thelower panels show firing of pyramidal cells in CA3. The intervals between panels (i)–(iv) are 20 ms. Spontaneous firing propagates irregularly in the CA3 regionin the initial state. (d) Firing patterns. (i) CA1 pyramidal cell #188. (ii) CA1 interneuron. (iii) CA3 pyramidal cell #188. (iv) CA3 interneuron. The spatiotemporalactivities of CA3 shown in Fig. 4(c) were observed in the period of time between two dotted lines. In the initial state, CA3 pyramidal cells were spontaneouslyfiring. Excitatory inputs through Schaffer collateral synapses caused subthreshold oscillations but no firing in CA1 pyramidal cell #188.

3.2. Learning in the CA3 network: Recurrent synapses

We next started applying the STDP rules for CA3 recurrentand Schaffer collateral synapses, and sequential input signals.Fig. 5 shows the spatial patterns of synaptic conductances andactivity of the CA3 and CA1 networks 10 s after the onset ofthe signal application. 10 s was chosen because learning at theCA3 recurrent synapses was completed while learning at theSchaffer collateral was not yet to be seen. This is the first stageof sequence learning.

Intervals between bursts of input signals were 100 ms andslightly shorter than the average interval between bursts of thespontaneous activity of CA3 pyramidal cells (about 110 ms).Therefore, CA3 pyramidal cells in the four subregions, A3–D3,often fired prior to the pyramidal cells in the surroundingregion. Synaptic connections from the CA3 pyramidal cells inthe subregions to the CA3 pyramidal cells in the surroundingregion were consequently potentiated by the STDP rule whilesynaptic connections in the opposite directions were depressed.Bars that are oriented in the radial directions from thesubregions show a distinct spatial pattern of Cpp CA3 (Fig. 5(a)).Consequently, neuronal activity of CA3 pyramidal cells tendedto propagate in the radial directions from the stimulus sitesalong the potentiated connections as shown in Fig. 5(c) (lowerpanels). This spatio-temporal firing pattern had been almoststeady in 10 s after the onset of the stimulation. Features ofthe spontaneous rhythmic activity and the radial propagation of

neuronal activity in the CA3 network have been investigatedintensively in our previous study (Yoshida & Hayashi, 2004a).

The propagation in the radial direction occurred successivelyfrom four stimulus sites with the delay of 20 ms due to thetime-compressed sequential input signals. The lower panel ofFig. 5(ci) shows the firing pattern of the CA3 network when thesubregion A3 was stimulated. The pyramidal cells in subregionA3 started firing due to the input signal. The pyramidal cellsin subregion B3 were stimulated 20 ms after the stimulation ofsubregion A3 (Fig. 3(cii) lower panel). It can be seen that firingof pyramidal cells was propagating radially from subregion A3to the surrounding region. The pyramidal cells in subregion C3were then stimulated 20 ms after the stimulation of subregionB3. Firing from A3 was propagating further as shown in thelower panel of Fig. 3(ciii) and firing from subregion B3 wasalso propagating radially. Radial propagation from subregionC3 is seen in the lower panel of Fig. 3(civ). In summary,widening rings of neuronal activity from the four subregionswere organized in CA3, and the radii of the rings depended onthe stimulus time. This means that the temporal sequence ofsignals was transformed into a spatial pattern.

At this stage, no clear spatial pattern of Schaffer collateralsynapses had been organized as shown in Fig. 5(b), while somesynapses were slightly modified. This indicates that the learningof the recurrent synaptic conductances (Cpp CA3) occurred priorto the learning of Schaffer collateral synaptic conductances(Csch). CA1 pyramidal cells in subregion D1 fired occasionally

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Fig. 5. State and activity of the CA3–CA1 model after learning in the CA3 region. (a) Spatial pattern of CA3 recurrent synaptic conductances. Recurrent synapsesfrom the subregions, A3–D3, to their surrounding regions were potentiated, and radial spatial patterns of synaptic conductances were formed. (b) Conductances forSchaffer collateral synapses connecting CA3 pyramidal cells to CA1 pyramidal cell #188. Despite the clear spatial patterns of recurrent synaptic conductances in theCA3 region, the spatial pattern of the Schaffer collateral synaptic conductances was not clear at this stage. (c) Spatio-temporal firing patterns of the CA1 network(upper panels) and the CA3 network (lower panels). White squares in these panels indicate firing pyramidal cells. Intervals between the panels are 20 ms. Firingactivity propagated from the subregions to the surrounding areas along the spatial patterns of the recurrent synaptic conductances in the CA3 region. (d) Firingpatterns. (i) CA1 pyramidal cell #188. (ii) CA1 interneuron. (iii) CA3 pyramidal cell #188. (iv) CA3 interneuron. The spatiotemporal activities of CA3 shown inFig. 5(c) were observed in the period of time between two dotted lines. CA3 pyramidal cells fired in phase with the input signal through mossy fibers. The membranepotential of CA1 pyramidal cell #188 was depolarized by the inputs from CA3 and the perforant path, and the CA1 pyramidal cell fired occasionally. Note, however,that the firing was less frequent compared to the following stage (See Fig. 6(di)).

(Fig. 5(di)), but the firing rate was lower than that at thefollowing stage.

3.3. Learning in the CA1 network: Schaffer collateral synapses

Fig. 6 shows the state of CA3 and CA1 networks 41 safter the beginning of the signal application. The spatial patternof recurrent synaptic conductances (Cpp CA3) had been in asteady state as shown in Fig. 6(a), while distinct spatial patternof Schaffer collateral synaptic conductances (Csch) emergedas shown in Fig. 6(b). This is the second stage of sequencelearning.

CA1 pyramidal cells in subregion D1 fired only when theyreceived excitatory inputs through both perforant path andSchaffer collaterals at the same time (Fig. 6(civ) upper panel).When CA3 pyramidal cells fired just before firing of CA1pyramidal cells, Schaffer collateral synapses between thosepyramidal cells were potentiated through STDP. The lowerpanel of Fig. 6(ciii) shows CA3 pyramidal cells that were firingaround 20 ms prior to the firing of the CA1 pyramidal cells inthe subregion D1. Firing of CA3 pyramidal cells propagatingfrom the subregion A3 were forming a doughnut-shape firingpattern. Firing was also propagating from the subregion B3.Firing of pyramidal cells in the subregion C3 had not yetspread to the surrounding region. Schaffer collateral synapsesfrom these active CA3 pyramidal cells to the CA1 pyramidalcells in the subregion D1 were consequently potentiated by theSTDP rule. The resulting spatial pattern of potentiated Schaffer

collateral synapses in Fig. 6(b) is, therefore, very similar tothe spatial pattern of active CA3 pyramidal cells in the lowerpanel of Fig. 6(ciii). Because of this similarity between the firingpattern in the CA3 network and the spatial pattern of reinforcedSchaffer collateral synapses, CA1 pyramidal cells in subregionD1 received more excitatory synaptic input than that at theformer stage. CA1 pyramidal cell #188 therefore fired moreoften synchronized with the input signal (compare Fig. 5(di)and Fig. 6(di)). Other CA1 pyramidal cells in subregion D1also obtained similar Schaffer collateral synaptic conductancepattern.

Fig. 7 compares spike timings of selected CA3 pyramidalcells and CA1 pyramidal cell #188. Fig. 7(bi) shows firingpattern of CA1 pyramidal cell #188, and Fig. 7(bii)–(bvi) showfiring patterns of CA3 pyramidal cells indicated by whitearrows in Fig. 7(a). Black arrows in Fig. 7(b) indicate the timeup to 30 ms prior to the spike of CA1 pyramidal cell #188.The CA3 pyramidal cell in Fig. 7(bii), which was placed atthe center of the subregion A3, fired more than 30 ms beforespikes of CA1 pyramidal cell #188 every theta cycle. Becausethis difference in spike timing was more negative than the LTPrange of the STDP function Fsch(1t), the Schaffer collateralsynapse from this pyramidal cell to CA1 pyramidal cell #188was not potentiated. Other pyramidal cells in Fig. 7(biii)–(bvi)fired less than 30 ms before spikes of CA1 pyramidal cell #188.The Schaffer collateral synapses from these pyramidal cells toCA1 pyramidal cell #188 were potentiated because spike timingis in the LTP range of the STDP function.

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Fig. 6. State and activity of the CA3–CA1 model after learning in the CA1 region: Schaffer collateral synapses. (a) Spatial pattern of CA3 recurrent synapticconductances. (b) Conductances for Schaffer collateral synapses connecting CA3 pyramidal cells to CA1 pyramidal cell #188. Only the Schaffer collateral synapsesconnecting CA3 pyramidal cells located in the active regions propagating from the subregions, A3–D3, were potentiated. (c) Spatio-temporal firing patterns of theCA1 network (upper panels) and the CA3 network (lower panels). Intervals between the panels are 20 ms. Note the similarity between the firing pattern of theCA3 network in Fig. 6(ciii) (lower panel) and the spatial pattern of Schaffer collateral synapses in Fig. 6(b). (d) Firing patterns. (i) CA1 pyramidal cell #188. (ii)CA1 interneuron. (iii) CA3 pyramidal cell #188. (iv) CA3 interneuron. The spatiotemporal activities of CA3 shown in Fig. 6(c) were observed in the period oftime between two dotted lines. CA3 pyramidal cells fired in phase with the input signal through mossy fibers. CA1 pyramidal cell #188 fired frequently when themembrane potential depolarized by the inputs from CA3 and the perforant path crossed the firing threshold. The firing at this stage was more frequent than that atthe previous stage (See Fig. 5(di)).

3.4. Sequence sensitivity

We next tested the sequence sensitivity of CA1 pyramidalcell #188. After the learning of the sequence of signals A -> B-> C -> D, the spatial pattern of Schaffer collateral synapticconductances were fixed, and those synaptic conductanceswere not allowed to change after that. Input signals were thenchanged from the sequence A -> B -> C -> D to the sequenceC -> B -> A -> D. Note that the fourth place is D inboth sequences and only the sequences prior to place D weredifferent between the two sequences. This is to examine thesequence-sensitive firing property of a place cell in subregionD1, which purely depends on the sequence of the past. Whenthis new sequence of signals were applied, the firing of CA3pyramidal cells propagated farthest from the subregion C3 andfiring had not yet spread from the subregion A3, 20 ms beforethe input to the subregion D1 (Fig. 8(aiii) lower panel). Thisspatial firing pattern of the CA3 network is different fromthat induced by the sequence of signals A -> B -> C -> D.Therefore, this firing pattern does not correspond to the spatialdistribution of conductances for Schaffer collateral synapses(Fig. 6(b)). This mismatch between the spatial firing pattern ofCA3 pyramidal cells and the distribution of potentiated Schaffercollateral synapses reduced the excitatory synaptic input fromthe CA3 network to CA1 pyramidal cell #188. Fig. 8(b) showsfiring patterns of CA1 pyramidal cell #188 when the inputsequences were A -> B -> C -> D (upper trace) and C -> B -> A -> D (lower trace). Clearly, CA1 pyramidal cell#188 responded less frequently to the sequence of signals C-> B -> A -> D than to the learned sequence of signals

A -> B -> C -> D because of less excitatory synaptic inputfrom the CA3 network.

Fig. 8(c) shows the response rate of CA1 pyramidal cell#188 to various input sequences. The number of spikes evokedby each sequence of signals was counted in eight consecutiveperiods of 5 s (total of 40 s). The number of spikes in each 5 swas divided by the number of burst stimuli, and eight responserates were averaged. Error bars show standard deviations. CA1pyramidal cell #188 responded best to the learned sequence ofsignals A -> B -> C -> D showing sequence sensitivity wasindeed obtained.

3.5. Robustness of the present model

In this section, robustness of the model was tested bymodifying the parameters of the model. The key of our modelto obtain the sequence sensitivity is the formation of the spatialpattern of the Schaffer collateral synaptic conductances whichhas multiple ring-shaped regions where synaptic conductancesare strengthened (Fig. 6(b)). Formation of this spatial patternmeans that CA1 pyramidal cell becomes sequence sensitive.We, therefore, compared the spatial patterns of Schaffercollateral synaptic conductances of the cell #188 formed inthe original model (Fig. 6(b)) and the model with modifiedparameters to test the robustness. Comparison was done 41 safter the beginning of the signal application (same time as inFig. 6(b)).

First, we modified the number of stimulation pulses fed tothe CA1 pyramidal cells. The number of intra-burst pulses wasincreased from two (Fig. 9(a)) to three (Fig. 9(b)) so that both

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Fig. 7. Spike timings of selected CA3 pyramidal cells and CA1 pyramidalcell #188. (a) Positions of selected CA3 pyramidal cells. Positions of selectedcells are indicated on the conductance pattern for Schaffer collateral synapses(identical to Fig. 6(b)). (b) Firing patterns. (i) CA1 pyramidal cell #188. (ii)–(vi)CA3 pyramidal cells. Positions of these pyramidal cells in CA3 are indicatedby white arrows in Fig. 7(a). The black arrows in Fig. 7(b) indicate the time upto 30 ms prior to the firing of the CA1 pyramidal cell #188. The CA3 pyramidalcells whose Schaffer collateral synapses were potentiated ((iii)–(vi)) fired in thetime window of 30 ms.

CA3 and CA1 networks received three pulses in each burst.Fig. 9(a) is identical to the Fig. 6(b). As a result, ring-shapedpatterns around A3 to C3 shown in Fig. 9(b) were slightly largerthan those produced in the original model (Fig. 9(a)). This isdue to the fact that additional pulse in each burst tends to keepCA1 cells firing. This results in more LTP induction because ofmore coincidence with firing of CA3 cells, which fire at laterphases of each theta cycle. However, the overall features of thespatial pattern of Schaffer synaptic conductances (Fig. 9(b)) aresimilar to those of the original pattern (Fig. 9(a)).

Second, we changed the time constant of the STDP function(τsch) for Schaffer collateral synapses. The time constant of theSTDP function for CA3 recurrent synapses was not changedbecause this was investigated in our previous work (Yoshida &Hayashi, 2004a). The time constant τsch was changed from theoriginal value of 5 ms to 15 and 20 ms. The ring-shaped patternswere still present as shown in Fig. 9(c) and (d).

Third, we modified the extent of the CA3 recurrentconnections. When the number of recurrent connections fromeach cell to neighboring cells in CA3 was increased from28 to 44, the resulting spatial pattern of Schaffer synapticconductances was similar to that of the original model asshown in Fig. 9(e). However, reduction of the number of CA3

Fig. 8. Sequence sensitivity of CA1 pyramidal cell #188. (a) Spatio-temporalfiring patterns of the CA1 network (upper panel) and the CA3 network (lowerpanel). The sequence of input signals was C -> B -> A -> D. Intervals betweenthe panels (i)–(iv) are 20 ms. Note the difference between the firing pattern inFig. 8(aiii) (lower panel) and the firing pattern in Fig. 6(ciii) (lower panel). (b)Firing patterns of CA1 pyramidal cell #188. The sequences of input signalswere A -> B -> C ->D (upper trace) and C -> B -> A -> D (lower trace). (c)Response rate of CA1 pyramidal cell #188 to various input sequences. See textfor the definition of the response rate. CA1 pyramidal cell #188 has been tunedto the learned sequence, A -> B -> C ->D.

recurrent connections to 20 produced a completely differentSchaffer synaptic conductance pattern (Fig. 9(f)). In thiscase, spontaneous firing often initiated in some place in CA3regardless of the external input signal because the frequencyof the spontaneous activity increased (9.4 Hz). Ring-shapedpropagation of activity that held the timing of input signalwas disrupted by the spontaneous firing (data not shown).The sequence of input signals was therefore not learned wellby the Schaffer synapses. In our model, the frequency ofthe spontaneous activity also depends on the conductance forthe recurrent connections in CA3. By increasing the maximaland minimal recurrent connection conductances (Cmin pp CA3and Cmax pp CA3) to 0.0028 µS and 0.0008 µS, respectively,the frequency of the spontaneous activity was decreased to8.7 Hz. With this increase in conductance for the recurrentconnections, Schaffer synapses learned the ring-shaped spatio-temporal activity even in the case of the 20 CA3 recurrentconnections (Fig. 8(g)). These results suggest that our model isnot sensitive to the extent of the CA3 recurrent connections aslong as the spontaneous frequency of the CA3 region is properlyadjusted.

In our previous work, we used a CA3 network with 25interneurons (Yoshida & Hayashi, 2004a). We explored if the

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Fig. 9. Robustness of the present model. Spatial pattern of Schaffer collateral synaptic conductances of the CA1 pyramidal cell #188 when (a) all parameters areoriginal (identical to Fig. 6(b)), (b) input signal to CA1 has three pulses per theta cycle, (c) the time constant for the STDP function for Schaffer synapses is15 ms,(d) the time constant for the STDP function for Schaffer synapses is 20 ms, (e) the number of the CA3 recurrent connections for each cell is 44, (f) the numberof the CA3 recurrent connections for each cell is 20, and (g) the number of the CA3 recurrent connections for each cell is 20 and conductances for CA3 recurrentconnections are modified. (h) Intra-network connectivity of the CA1 and CA3 regions that include 25 interneurons each. Pyramidal cells are shown as trianglesand interneurons are shown as small circles. For example, 112 pyramidal cells (triangles) in the shadowed circle are connected through excitatory synapses tothe interneuron (filled circle) at the center of the shadowed circle and the interneuron is connected through inhibitory synapses to the same pyramidal cells. (i)Spatial pattern of Schaffer collateral synaptic conductances of the CA1 pyramidal cell #188. The CA1 and CA3 networks include 25 interneurons each. Synapticconductances between interneurons and pyramidal cells were modified. The maximal conductance of Schaffer collateral synapses (Cmax sch) was also modified.

CA1 and CA3 networks, both of which had 25 interneurons,worked well for the sequence learning. Interneurons weredistributed evenly in the networks as shown in Fig. 9(h)(small circles). In the original model used in the currentstudy, all pyramidal cells were synaptically connected toone interneuron and the interneuron was connected to allpyramidal cells. Such connections will remove the effect ofhaving multiple interneurons located at multiple positionsin the network. We, therefore, reduced the extent of theconnections between interneuron and pyramidal cells to therange shown by the shadowed circle in Fig. 9(h) in bothCA1 and CA3 networks. Pyramidal cells in the shadowedcircle (112 pyramidal cells) were connected through excitatorysynapses to the interneuron at the center of the shadowedcircle, and the interneurons were connected through inhibitorysynapses to the pyramidal cells in the shadowed circle. Eachpyramidal cell therefore received synaptic input from at most 14interneurons. Due to the change in the number of connections,we modified the synaptic conductances between interneuronsand pyramidal cells (Cpi CA1 = 0.009 µS, Cip CA1 =

0.0037 µS, Cpi CA3 = 0.0015 µS and Cip CA3 = 0.0037 µS).The maximal conductance for Schaffer synapses was alsomodified (Cmax sch = 0.0008 µS). The resulting spatial patternof Schaffer synaptic conductances showed three ring-shapedregions similar to the original pattern as shown in Fig. 9(i).Therefore, this model is robust to changes in the number ofinterneurons as long as synaptic conductances are set properly.

4. Discussion

We developed a CA3–CA1 network model endowed with

anatomical and physiological properties of the hippocampus.By applying sequential input signals that mimicked a firingpattern of place cells in the EC to subregions of the CA3 andCA1 networks, CA1 pyramidal cells became sequence sensitivethrough the two learning stages. At the first stage, the inputsignals strengthened the recurrent connections from stimulussites to the surrounding regions in the CA3 network. Becauseof this spatial pattern of the recurrent connections, each burstof stimulation caused propagation of neuronal activity in theradial direction from the stimulated site in the CA3 networkmodel. The radial propagations of neural activity stored thesequence of input signals by their radii. At the second stage,conductances for the Schaffer collateral synapses betweenCA3 pyramidal cells that fired in the ring-shaped propagatingwaves and CA1 pyramidal cells that received input signalsthrough the perforant path were potentiated. The radii of thering-shaped spatial patterns of Schaffer collateral synapticconductances specified the sequence of the input signals thatcaused maximum excitatory synaptic input from CA3 to CA1.CA1 pyramidal cells, therefore, responded with the highestprobability when a sequence of input signals was identicalto the learned sequence. These results imply that sequencesensitivity arises in CA1 place cells through intra-hippocampalneural computations during the animal’s spatial activity.

Although previously proposed models of sequence learningand recall do not focus on sequence sensitivity of placecells, some of them imply that place cells in their modelwould be sequence sensitive (Jensen & Lisman, 1996a, 1996b;Yamaguchi, 2003). Here, we call place cells in their model, withneighboring place fields, place cells A to D for explanatorypurpose. In these models, place cells receive gradual synapticinput from prior place cells through recurrent synapses. For

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example, place cell D receives input signal from place cells A,B and C, where synaptic conductance is the weakest from placecell A and strongest from place cell C. Under an assumptionthat excitatory post-synaptic potential decays exponentially,this connection pattern indicates that firing of place cells inthe sequence A -> B -> C provides larger synaptic input toplace cell D than the sequence C -> B -> A provides, becauseplace cell C, which provides the major excitatory input to placecell D, fires just before firing of place cell D in the formercase. However, if the place cells, A, B and C, fire with shorterintervals or in synchrony, this will cause larger excitatory inputto place cell D than the learned sequential input that has originalintervals. In this sense, these models are not truly optimized tothe learned sequence. In contrast, in our model, shorter intervalor synchronized firing of place cells in subregions, A3, B3and C3, does not provide larger input signal to place cells inregion D1 than the learned sequence does, because in such casesring-shaped propagation waves in CA3 does not coincide withlearned spatial pattern of Schaffer synapses (Fig. 6(b)). Placecells in our model are truly optimized to the learned sequencebecause a sequence of input signals that can cause the largestinput to cells in region D1 is the input signals with exactly thesame sequence and timings as learned input signals.

Hasselmo and Eichenbaum (2005) proposed a model ofdifferential firing in the same part of the maze with twoloops (Wood et al., 2000) based on the activity of the EC.In their model, EC layer III stored all possible sequencesand delayed firing of EC layer II neurons held informationabout the loop taken in the previous lap. Signals from the ECwere merged in CA1 area where place cells fired dependingon the previous path taken, meaning that they were sensitiveto sequence from the past. Their model and our modeldiffer in many ways. First, their model relies on the networkand activity of EC, while our model showed emergence ofsequence sensitivity in hippocampal CA3–CA1 network alone.Second, their model consists of simple binary model and usesreinforcement learning, while we used Hodgkin–Huxley stylemore physiological neuron models and STDP rules. Third, theyused delayed firing of EC layer II neurons to produce sequencesensitivity while our model did not rely on it. Their place cellsare not sequence sensitive without this dynamic activity, whileplace cells were sequence sensitive as the result of synapticconductance modification in our model.

We have shown how place cells may become sensitive toa single sequence. In the maze with two loops, rats have tolearn at least two sequences that terminate at the same location(e.g. A -> B- > C-> D and E -> F -> G ->D) where somecells respond to the sequence A -> B -> C -> D while othersrespond to the sequence E -> F -> G -> D at the common partof the two loops (place D). In the present study, we assumedthat signal about place D is uniformly projected to the CA1pyramidal cells in subregion D1 and that they receive uniformSchaffer collateral synaptic input from CA3 cells in the initialcondition. In reality, however, these synaptic projections wouldnot be perfectly uniform with various synaptic conductanceand uneven numbers of synapses. When the rat runs in oneof the loops of the maze and places A, B and C are visited,

Fig. 10. Illustration of sequence recall mechanism. CA3 pyramidal cells inthe white circle, gray ring-shaped region and black ring-shaped region, havelarge Schaffer collateral synaptic conductance with CA1 pyramidal cells insubregions B1, C1 and D1, respectively. Firing of CA3 cells initiated insubregion A3 will produce radial propagation of action potentials (sharp wave)and activate CA1 place cells sequentially.

a spatio-temporal activity is produced in CA3. If the sum ofthe synaptic input produced by this activity and direct inputfrom EC is sufficient to cause firing of a CA1 cell, this cellwill become sensitive to the sequence A -> B -> C -> D asdescribed above. However, this might not be the case for all ofthe CA1 cells in D1 subregion when synaptic projections arenot uniform. When the rat next goes into the other loop visitingplaces E, F and G, this will produce different spatio-temporalfiring pattern in CA3. It is possible that this activity produceslarger excitatory synaptic input and cause firing in some of thecells (in subregion D1) that do not fire in the first loop. Thesecells will become sensitive to the sequence E -> F -> G -> D.In this way, some cells can be sensitive to one and others to theother sequence in the subregion D1. There would also be cellsthat fire in both cases and they will not be sequence sensitivein the maze. Interestingly, some of CA1 place cells are actuallynot sensitive to sequences (Wood et al., 2000).

As mentioned above, place cells in the hippocampal CA1region fire in the same sequence as they fire while awake, oftensynchronized with sharp waves from the CA3 region duringslow wave sleep (Lee & Wilson, 2002; Skaggs & McNaughton,1996). Although this recall of sequences was not tested inthis study, our model has potential to achieve recalls. Fig. 10shows hypothetical spatial pattern of the Schaffer collateralsynapses from CA3 cells that are located near the subregionA3. As shown in the Fig. 6(b), CA3 cells that are located ina ring-shaped region around subregion A3, which correspondsto the black ring in Fig. 10, project strong synaptic inputto CA1 cells in D1 region. Because CA3 cells in the graycolored ring-shaped region will fire earlier in each theta cyclejust before the CA1 pyramidal cells in subregion C1 fire, theyproject strongly to subregion C1. The white colored centralpart of the subregion A3 will project to subregion B1 in the

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same way. Once a sharp wave is initiated at subregion A3,the activity will propagate following the radially potentiatedsynapses to the surrounding area, firing CA3 cells in these ring-shaped regions one by one. This will activate CA1 place cellsin subregions B1 to D1 sequentially. During slow wave sleep,conductance of Schaffer collaterals and CA3 recurrent synapsesare stronger than while awake because of lower acetylcholinelevel (reviewed in Hasselmo, 1999). Synaptic input to theCA1 from the ring-shaped CA3 area alone could, therefore, beenough to fire CA1 place cells sequentially achieving recalls.Similar multi-ring-shaped patterns will be created around othersubregions in CA3, each of them having shifted projectionsto CA1 subregions. Recalled sequences will depend on whichCA3 subregion a sharp wave initiates from (sequences B1-> C1->D1, C1-> D1->E1, D1-> E1->F1 and E1-> F1->G1for CA3 subregions A3, B3, C3 and D3, respectively, assumingthat there are places E to G after place D). Interestingly, arecalled sequence in CA1 is often a part of learned sequence,starting in the middle of an entire sequence, rather than the fullsequence (Lee & Wilson, 2002).

The STDP function for CA3 recurrent synapses was basedon the STDP function that was observed by Bi and Poo (1998)using dissociated and cultured hippocampal cells. The timeconstants (τsyn) of their STDP function for LTP and LTDsides were 16.8 ms and 33.7 ms, respectively. We set the timeconstant (τpp CA3) at 20 ms for both LTP and LTD sides ofthe STDP function because this time constant for the STDPfunction was well tested in other studies (Kitano, Cateau, &Fukai, 2002; Levy, Horn, Meilijson, & Ruppin, 2001; Song,Miller, & Abbott, 2000).

On the other hand, we set the time constant (τsch) at 5 msfor STDP function of Shaffer collateral synapses. As mentionedabove, Nishiyama et al. (2000) have reported that, in Schaffercollateral synapses, the STDP function has a positive peak ataround 1t = −5 ms and negative peak at around 1t = −20ms. This means that LTP at Schaffer collateral synapses occursonly when the CA1 pyramidal cell fires within 10 ms after firingof CA3 pyramidal cells. Although we did not implement thenegative peak at around 1t = −20 ms to keep our modelsimple, the narrow range of 1t for LTP was introduced by a fasttime constant. This allowed CA1 pyramidal cells to pick onlyCA3 pyramidal cells that elicited spikes in a very short periodof time prior to the spikes of the CA1 pyramidal cells in ourmodel. In this way, spatiotemporal activity of the CA3 regionwas transformed to a spatial pattern of the conductances for theSchaffer synapses as if taking a photo. In the real hippocampus,the negative peak of the STDP function at 1t = −20 msmight increase this ability producing a sharper conductancepattern, because spikes of CA3 pyramidal cells elicited in thepropagating wave more than 10 ms prior to the spikes of CA1pyramidal cells causes LTD back-to-back with the LTP due tothe coincidence of spikes within 10 ms.

In Fig. 8(c), CA1 pyramidal cell #188 responded fairlywell to the sequence of signals B -> A -> C ->D thoughresponse rates to other input sequences were significantly lower.With this particular sequence of signals, subregions A3 andB3 were activated in the similar orders (2nd and 1st) to the

learned sequence (1st and 2nd) in the sequence. As the result,when the stimulation was delivered to the D1 subregion, thespatial firing pattern of CA3 pyramidal cells around A3 and B3subregions was very similar to the spatial conductance patternof Schaffer collateral synapses. These two regions (around A3and B3 subregion) were the major sources of excitatory synapticinput to CA1 pyramidal cells in the subregion D1 includingcell #188 (see Fig. 6(b)), and both of these two regions sentconsiderable amount of excitatory input to CA1 pyramidalcells in the subregion D1 only in this case. The response ratewas, therefore, highest among unlearned sequences when thesequence was B -> A -> C -> D. Using a CA3 networkmodel with larger size and faster propagation of activity woulddifferentiate the two doughnut-like spatial patterns of Schaffercollateral synaptic conductances around subregions A3 and B3(Fig. 6(b)). The sequence of signals B -> A -> C -> D wouldthen produce smaller excitatory input to CA1 pyramidal cellsand CA1 pyramidal cells would show lower response rate. Onceseparations between sequences are easily done, it would be alsopossible to increase the number of signals in one sequence. Inthis study, we used four signals in one theta cycle with 20 msof interval between signals and 100 ms theta period. Either bydecreasing the interval between signals or by increasing thetaperiod, more than four firing of place cells would be fit into onetheta cycle. When such a sequential signal is fed into the CA3with larger network size and faster propagation speed, the CA1place cells would become sensitive to sequences that consist ofmore than four places.

As studied in our previous study (Yoshida & Hayashi,2004a), the interburst interval of input signal to CA3 had to beshorter than that of spontaneous activity of CA3 pyramidal cellsto synchronize the spontaneous activity to the input signal. Weused a 10 Hz theta burst signal for stimulation and the frequencyof the spontaneous activity was about 9 Hz. Theta burst signalwhose frequency is lower than that of spontaneous activitywould not be able to make a radial synaptic conductance patternin CA3 and thus would fail to obtain sequence sensitivity.

It has been reported that neurons in the superficial layersof the EC (layer II and layer III) fire in bursts and the burstsare phase locked to the theta rhythm (Alonso & Garcia-Austt,1987). Their intraburst frequency is in a gamma range (Chrobak& Buzsaki, 1998). We, therefore, used a theta burst patternwhere a gamma rhythm (50 Hz) was nested in the theta rhythm(10 Hz) as the input signal from the EC. Alonso and Garcia-Austt (1987) reported that cells in the superficial layers thatwere phase locked to theta rhythm could be categorized intotwo classes. One of them fired at 2.7 Hz and the other fired at16.7 Hz on average during theta activity. These numbers give0.54 and 3.34 spikes per theta cycle, the frequency of the thetarhythm being assumed 5 Hz in their experiment. The number ofpulses used in this study (two for the signal to CA1 and threefor the signal to CA3) were in this range.

Each CA3 pyramidal cell was connected to surroundingpyramidal cells symmetrically in the present CA3 networkmodel. Action potentials evoked by an input signal thereforetended to propagate symmetrically in a radial direction.Although propagation of neural activity in CA3 has been

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reported in whole hippocampus preparations from mice (Wu,Shen, Luk, & Zhang, 2002) and disinhibited hippocampalslices from guinea-pigs (Traub, Jefferys, & Miles, 1993), thereis no direct measurement showing propagation of neuronalactivity in radial directions in the hippocampal CA3 region.The propagation of activity in radial directions was thereforean assumption in our model. In the real hippocampus, synapticconnections to each CA3 pyramidal cell could be asymmetric.This might cause asymmetric propagation of neuronal activity.However, the essence of the present model is that propagatingwaves are induced in CA3 by a sequence of input signalsand firing of CA3 pyramidal cells on the wave frontsaugment specific Schaffer collateral synapses. The shapes ofthe propagating waves have to be the same in each theta cyclebut can be in any shape. Sequence learning would thus be doneeven with asymmetrically propagating waves.

Based on the present model, we predict that the percentageof the place cells that are sequence sensitive is higher in theCA1 region compared to the CA3 region. As far as we know,there is no study that specifically compared sequence sensitivityof place cells in these two regions. It would be possible toclarify this issue by comparing the place cells in CA3 and CA1that have place fields at the common part of the maze as inWood et al. (2000). We expect that more place cells that have aplace field at the common part of the maze and fire dependingon the path (sequence) visited in the past exist in the CA1region than in the CA3 region. Furthermore, our model predictsthat formation of propagation wave in the CA3 region throughmodification of synaptic conductances is crucial. It would bevery interesting to see how the percentage of the sequencesensitive cells drops when synaptic modification in the CA3region is blocked, for example using CA3 NMDA receptorknockout animals.

Acknowledgments

We thank Farhan Khawaja for the critical reading ofthe manuscript. We also thank Prof. Michael Hasselmo andProf. Takeo Watanabe for kindly allowing us to use thelaboratory facilities. This work was supported by (1) 21stCentury Center of Excellence Program (center #J19) grantedto Kyushu Institute of Technology by Japan Ministry ofEducation, Culture, Sports, Science and Technology and(2) Japan Ministry of Education, Culture, Sports, Scienceand Technology (Grant-in-Aid for Scientific Research, No.14580425 and No. 16015289).

Appendix A

Rate constants of ion-gates and parameter values of the CA3pyramidal cell model.

αm =−0.32(51.9 + V )

exp(−(51.9 + V )/4) − 1,

βm =0.28(V + 24.9)

exp((V + 24.9)/5) − 1,

αh = 0.128 exp(

−48 − V18

),

βh =4

1 + exp(−(25 + V )/5),

αs =0.2

1 + exp(−0.072V ), βs =

0.0025(V + 13.9)

exp((V + 13.9)/5) − 1,

αr =

{exp(−(V + 65)/20)

1600(V > −65)

0.000625 (V ≤ −65)

βr =

{0.005 − 8αr

8(V > −65)

0 (V ≤ −65)

αs(low) =1.6

1 + exp(−0.072(V + 40)),

βs(low) =0.02(V + 53.9)

exp((V + 53.9)/5) − 1,

αr(low) =

{exp(−(V + 105)/20)

200(V > −105)

0.005 (V ≤ −105)

βr(low) =

{0.005 − αr(low) (V > −105)

0 (V ≤ −105)

αn =−0.016(29.9 + V )

exp(−(29.9 + V )/5) − 1,

βn = 0.25 exp(

−45 − V40

),

αa =−0.02(51.9 + V )

exp(−(51.9 + V )/10) − 1,

βa =0.0175(V + 24.9)

exp((V + 24.9)/10) − 1,

αb = 0.0016 exp(

−V + 78

18

),

βb =0.05

1 + exp(−(54.9 + V )/5),

αq =

0 ((χ − 140) < 0)

0.00002(χ − 140) (0 ≤ (χ − 140) < 500)

0.01 (500 ≤ (χ − 140))

βq = 0.001

αc =

exp((V + 55)/11 − (V + 58.5)/27)

18.975(V ≤ −15)

2 exp(

−58.5 − V27

)(V > −15)

βc =

2 exp(

−58.5 − V27

)− αc (V ≤ −15)

0 (V > −15)

C = 0.1 (µF).gNa = 1.0, gCa = 0.13, gCa(low) = 0.03,

gK (DR) = 0.08, gK (A) = 0.17, gK (AHP) = 0.07,

gK (C) = 0.366, gL = 0.0033, gaf center = 0.005,

gaf edge = 0.004, gaf center = 0.003 (µS).

VNa = 50, VCa = 75, VK = −80, VL = −65,

Vsyn(e) = −10 (mV ). φ = 50. βχ = 0.075 (m s−1).

Rate constants of ion-gates and parameter values of the CA1pyramidal cell model. Only parameters that are different fromCA3 are listed.

666 M. Yoshida, H. Hayashi / Neural Networks 20 (2007) 653–667

αq =

0 ((χ − 20) < 0)

0.00002(χ − 20) (0 ≤ (χ − 20) < 500)

0.01 (500 ≤ (χ − 20))

gCa(low) = 0.008, gK (DR) = 0.12, gK (AHP) = 0.027,

gK (C) = 0.33, gaf = 0 (µS).φ = 60, βχ = 0.01 (m s−1).

Rate constants of ion-gates and parameter values of theinhibitory interneuron model.

αm =−0.64(51.9 + V )

exp(−(51.9 + V )/4) − 1,

βm =0.56(V + 24.9)

exp((V + 24.9)/5) − 1,

αh =0.128 exp(−(48 + V )/18)

0.65,

βh =4

0.65(1 + exp(−(25 + V )/5)),

αn =−0.016(48.9 + V )

0.65(exp(−(48.9 + V )/5) − 1),

βn =0.25 exp(−(64 + V )/40)

0.65C = 0.1 (µF).gNa = 1.5, gK (DR) = 0.3, gL = 0.02 (µS).

VNa = 50, VK = −80, VL = −65 (mV ).

Appendix B

Parameters for Eqs. (6) and (7) are as follows.Cpp CA3 = 0.0005 − 0.002 (depend on each synapse),

Cpi CA3 = 0.0007, Cip CA3 = 0.05, Cpp CA1 = 0.001,Cpi CA1 = 0.004, Cip CA1 = 0.05 (µS).

Csch = 0.0003 − 0.001 (depend on each synapse), Cperf =

0.05, Cmossy = 0.1 (µS).Vpp CA3 = Vpp CA1 = Vpi CA3 = Vpi CA1 = Vsch = Vperf =

Vmossy = −10, Vip CA3 = Vip CA1 = −70 (mV).τ1(pp CA3) = τ1(pp CA1) = τ1(sch) = τ1(perf) = τ1(mossy) = 3,

τ1(ip CA1) = τ1(ip CA3) = 15, τ1(pi CA3) = τ1(pi CA1) = 1,τ2(pp CA3) = τ2(pp CA1) = τ2(sch) = τ2(perf) = τ2(mossy) = 2,τ2(ip CA3) = τ2(ip CA1) = 10, τ2(pi CA3) = τ2(pi CA1) = 0.5(ms).

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