Neural Networks 20 (2007) 653–667 www.elsevier.com/locate/neunet
Emergence of sequence sensitivity in a hippocampal CA3–CA1 model Motoharu Yoshida a,∗ , Hatsuo Hayashi b 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 if hippocampal CA3 and CA1 regions can give rise to the sequence sensitivity. We used a two-layer CA3–CA1 hippocampal model that consisted of Hodgkin–Huxley style neuron models. Sequential input signals that mimicked signals projected from the entorhinal cortex gradually modified the synaptic conductances between CA3 pyramidal cells through spike-timing-dependent plasticity (STDP) and produced propagations of neuronal activity in the radial direction from stimulated pyramidal cells. This sequence dependent spatio-temporal activity was picked up by specific CA1 pyramidal cells through modification of Schaffer collateral synapses with STDP. After learning, these CA1 pyramidal cells responded with the highest probability to the learned sequence, while responding with a lower probability to different sequences. These results demonstrate that sequence 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 has attracted large interest. However, subsequent findings have suggested that hippocampal place cells are not providing simple spatial maps. It is reported that when rats visit multiple places, corresponding place cells fire in sequence in a time-compressed manner (Dragoi & Buzs´aki, 2006; Skaggs, McNaughton, Wilson, & Barnes, 1996) through theta phase precession (O’Keefe & Recce, 1993). These place cells fire in the same sequence during subsequent sleep (Lee & Wilson, 2002; Skaggs & McNaughton, 1996) suggesting that sequences are stored within the hippocampus and recalled during sleep to be 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.: +1 617 353 1431. E-mail addresses:
[email protected] (M. Yoshida),
[email protected] (H. Hayashi).
c 2007 Elsevier Ltd. All rights reserved. 0893-6080/$ - see front matter doi:10.1016/j.neunet.2007.05.003
Recent studies have shown more direct involvement of place cells with sequences. Wood, Dudchenko, Robitsek, and Eichenbaum (2000) have investigated, using a maze that has two loops partly connected to each other, the activity of place cells that have place fields in the part of the maze which is common to both loops. They have shown that 31 out of 33 CA1 place cells fired differently, depending on which of the two loops the rats came from or were going to. This demonstrates that a large amount of CA1 place cells are sensitive to sequences of the past or the future. More recently, Ferbinteanu and Shapiro (2003) have shown that a large portion of rat CA1 place cells is retrospectively sequence-sensitive (sensitive to the sequence of the past) using a “+” shaped maze. Frank, Brown, and Wilson (2000) have compared place cells in the superficial layers of the entorhinal cortex (EC) that give input to the hippocampus, with place cells in the deep layers of the EC that receive output from the hippocampus. They have found that place cells in the deep layer of the EC are more sensitive to sequences than place cells in the superficial layers, suggesting that sequence sensitivity of place cells emerges in the hippocampus. Varieties of computational models have been proposed to explain sequence learning and recall of place cells.
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Storages and recalls of sequences through asymmetric recurrent connections 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-CA3 network (Lisman, 1999) have been proposed. Although these models demonstrated that learned sequences were recalled successfully, they did not demonstrate sequence sensitivity of place cells. Recently, Hasselmo and Eichenbaum (2005) proposed a binary model in which place cells responded sensitively to a sequence. In their model, sequences were stored in the EC layer III and information about previous paths was stored as a delayed activity in EC layer II neurons. Convergence of these signals in the CA1 region made sequence-sensitive firing possible. In this paper, we focus on the retrospective sequence sensitivity which is the ability of place cells to fire depending not only on the current position of the animal but also on the places visited in the past. The goal of this study is to test if the hippocampal CA3–CA1 region alone can produce retrospective sequence sensitivity of CA1 place cells, using more physiological hippocampal models, learning rules and input signals. Hippocampal CA3 and CA1 regions have distinct anatomical and physiological features. The CA3 region has dense excitatory recurrent synaptic connections between pyramidal cells (Li, Somogyi, Ylinen, & Buzs´aki, 1994; Tamamaki & Nojyo, 1991). Anatomical and physiological features of the CA3 region support the idea that this area spontaneously generates a theta rhythm (Buzs´aki, 2002). Synaptic conductances of recurrent synapses are modified through spike-timing-dependent synaptic plasticity (STDP) (Bi & Poo, 1998; Debanne, Gahwiler, & Thompson, 1998). These experimental observations imply the possibility of intra-network computation that utilizes spontaneous rhythmic activity and synaptic modification of recurrent connections in the CA3 region. On the other hand, recurrent connections between CA1 pyramidal cells are not dense (Tamamaki & Nojyo, 1990; Witter & Amaral, 1991). CA1 pyramidal cells are less active compared to CA3 pyramidal cells (Fricker, Verheugen, & Miles, 1999). This suggests that spontaneous activity and its propagation hardly occur in the CA1 region. However, CA1 pyramidal cells receive a large number of excitatory synaptic inputs from CA3 pyramidal cells through Schaffer collaterals. Each CA1 pyramidal cell has 20–30 thousand Schaffer collateral synapses (Li et al., 1994). Synaptic projection from each CA3 pyramidal cell through Schaffer collaterals covers two thirds of the longitudinal extent of the CA1 region (Li et al., 1994). Moreover, conductances for the extensive Schaffer collateral synapses are modified through STDP (Bi & Poo, 1998; Nishiyama, Hong, Mikoshiba, Poo, & Kato, 2000). This implies that computation may also be executed in feed-forward synaptic connections from CA3 to CA1. We developed a CA3–CA1 hippocampal model endowed with the anatomical and physiological aspects mentioned above. Sequential input signals that mimicked signals projected through the perforant path from the EC, were applied to groups of pyramidal cells in the CA3 and CA1 regions. In the CA3
region, this signal modified the synaptic conductances between CA3 pyramidal cells and produced propagations of neuronal activity in the radial direction from stimulated pyramidal cells. The radial propagations of neuronal activity stored the timings of input signals by their radii; earlier and later signals caused larger and smaller ring-shaped neuronal activities, respectively. This firing pattern of the CA3 region was picked up by the conductances of Schaffer collateral synapses through STDP. Accordingly, CA1 pyramidal cells received maximum synaptic input from CA3 and responded with the highest probability when the sequence of input signals was identical to the learned sequence. The response rate was lower when the sequence of input signals was different from the learned sequence. These results demonstrate that anatomical and physiological features of the CA3 and CA1 regions, together with input signals from place cells in the EC, allow CA1 place cells to be sequence sensitive. Some of the results of the present paper have been reported in a conference proceedings (Yoshida & Hayashi, 2004b). 2. Methods 2.1. Cell models The hippocampal CA3–CA1 model consists of pyramidal cells and inhibitory interneurons. Both kinds of neurons are single-compartment Hodgkin–Huxley type neuron models developed by Tateno, Hayashi, and Ishizuka (1998). The equations of the pyramidal cell model in both the CA3 and CA1 regions are as follows: CdV /dt = gNa m 2 h • (VNa − V ) + gCa s 2r • (VCa − V ) 2 + gCa(low) slow rlow • (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) − βz z,
(2)
dχ /dt = −φ ICa − βχ χ .
(3)
The constants g y and Vy are the maximum conductance and 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, g L and gaf , are conductances for leakage and afferent excitatory synapses, respectively. VL and Vsyn(e) are equilibrium potentials of leakage and excitatory synapses, 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 sum of the second and the third terms on the right-hand side of Eq. (1). Isyn is the sum of the synaptic currents. Parameter values and voltage dependence of the rate constants, αz and βz , are listed in Appendix A. The larger conductance for the low threshold Ca2+ channel (the third term on the right-hand side of Eq. (1)) enables CA3 pyramidal cells to cause spontaneous firing. The low threshold Ca2+ channel provides persistent inward Ca2+ current as observed in the real CA3 pyramidal cell (Brown & Griffith,
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1983). Because of this inward current, the membrane potential is depolarized slowly and the cell fires spontaneously without any external stimulation (even if the value of gaf is 0 µS). As the firing increase the intracellular Ca2+ concentration, the Ca2+ activated K+ current and the AHP K+ current (the sixth and seventh terms on the right-hand side of Eq. (1)) are activated, resulting in hyperpolarization. This hyperpolarization interrupts spikes, resulting in bursting activity (See Fig. 4(diii )). Interneurons in the hippocampus can be classified into fast spiking 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 the activity of neural networks. We therefore adopted fast spiking interneurons in this study. The equations of the interneuron model are as follows: CdV /dt = gNa m 3 h • (VNa − V ) + gK(DR) n 4 • (VK − V ) + gL • (VL − V ) + Isyn , (4) dz/dt = αz • (1 − z) − βz z.
(5)
The parameters of the interneuron model were adjusted to reproduce the firing pattern of the interneuron observed experimentally by Kawaguchi and Hama (1987) and Miles (1990a). See Appendix A for the parameter values and voltagedependence of the rate constants, αz and βz . 2.2. Network structure The hippocampal CA3–CA1 model consists of two layers of neural networks, CA1 and CA3 (Fig. 1(a)). Each neural network consists of 256 pyramidal cells placed on 16×16 lattice points (indicated by triangles) and one inhibitory interneuron (indicated by a filled circle) (Fig. 1(b) and (c)). In the CA1 network, each pyramidal cell was connected recurrently to the nearest and the next nearest neighbors through excitatory synapses. For example, the CA1 pyramidal cell indicated by the filled triangle had bidirectional excitatory synaptic connections with the eight pyramidal cells in circle E1 (Fig. 1(b)). In the CA3 network, each pyramidal cell was connected recurrently to 28 nearby pyramidal cells as shown by circle E3 (Fig. 1(c)). Note that the extent of the recurrent connections between pyramidal cells in the CA3 network is larger than that in the CA1 network. Discharges of inhibitory interneurons are synchronized with each other and well phase locked to the field theta rhythm in the hippocampus (Buzs´aki, Leung, & Vanderwolf, 1983). Electrical coupling between interneurons could be the cause of the synchronization (Uusisaari, Smirnov, Voipio, & Kaila, 2002; Yang & Michelson, 2001). In the present model, we used one interneuron to mimic phase-locked firing without modeling the electrical couplings. All the pyramidal cells innervated the interneuron in an excitatory manner and the interneuron innervates all the pyramidal cells in an inhibitory manner in each network. Each CA1 pyramidal cell receives excitatory synaptic input from all of the CA3 pyramidal cells through Schaffer
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Fig. 1. Hippocampal CA3–CA1 neural network model. (a) Overview of the model. The model consists of the CA3 and CA1 networks. All CA3 pyramidal cells are connected excitatory to each CA1 pyramidal cell through Schaffer collaterals. CA1 and CA3 pyramidal cells receive excitatory synaptic inputs through the perforant path fibers and the mossy fibers, respectively. (b) Intra-network connectivity of the CA1 region. The CA1 region consists of 256 pyramidal cells (triangles) and one inhibitory interneuron (filled circle). Pyramidal cells are placed at 16 × 16 lattice points. Each CA1 pyramidal cell is connected to surrounding pyramidal cells through excitatory synapses. For example, the pyramidal cell shown by the filled triangle is connected to eight nearby pyramidal cells in the circle E1. The interneuron is located at the center of the network. The interneuron is innervated excitatory from all CA1 pyramidal cells and innervates all CA1 pyramidal cells inhibitory. (c) Intra-network connectivity of the CA3 region. The CA3 region also consists of 256 pyramidal cells and one inhibitory interneuron. Each CA3 pyramidal cell is connected to surrounding pyramidal cells through excitatory synapses. For example, the pyramidal cell shown by the filled triangle is connected to 28 pyramidal cells in the circle E3. The radius of the circle E3 is larger than that of the circle E1. The inhibitory interneuron is innervated excitatory from all CA3 pyramidal cells and innervate all CA3 pyramidal cells inhibitory, as in the CA1 region.
collaterals. The equations for each type of synaptic current take the 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) for recurrent connections between pyramidal cells, excitatory connections from pyramidal cells to interneurons, and inhibitory connections from interneurons to pyramidal cells in the CA3 (CA1) network, respectively. Synaptic terminals of Schaffer collaterals to CA1, mossy fibers to CA3, and perforant path fibers to CA1 are referred to as sch, mossy and perf, respectively. Parameter values in Eqs. (6) and (7) are listed in Appendix B. While the synaptic conductances for recurrent connections in CA1, mossy fibers and perforant path fibers were fixed to the values listed in Appendix B, the synaptic conductances for recurrent excitatory connections in CA3 and Schaffer collaterals were modified during simulation as described in the next section. The conductances for the perforant path synapses were set very small so that this input alone could not cause firing of CA1 pyramidal cells as experimentally observed (Colbert & Levy, 1992). The delay of the 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 the network are connected to less than 28 nearby CA3 pyramidal cells. Less excitation makes CA3 pyramidal cells fire at shorter interburst intervals because of less Ca2+ influx and less hyperpolarization. To reduce this effect, the conductances gaf of CA3 pyramidal cells on the edges (gaf edge ) and the corners (gaf corner ) were set smaller than those of the rest of the CA3 pyramidal cells (gaf center ), as listed in Appendix A. The conductances gaf for all of the CA1 pyramidal cells are zero. 2.3. Synaptic modification
2.4. Measurement of spatial asymmetry of recurrent connections between CA3 pyramidal cells
As mentioned above, synaptic conductances for recurrent connections in CA3 and Schaffer collaterals from CA3 to CA1 are known to be modified through STDP. In our model, conductances for recurrent excitatory synapses in CA3 (Cpp CA3 ) and Schaffer collateral synapses (Csch ) were modified independently by STDP modification rules during simulation. STDP modification functions are as follows: if − T ≤ 1t < 0 MLTP syn · exp(1t/τsyn ) Fsyn (1t) = −MLTD syn · exp(−1t/τsyn ) if 0 < 1t ≤ T 0 otherwise. (8) 1t denotes the relative spike timing between pre- and postsynaptic spikes (the time of the presynaptic spike minus the time of the postsynaptic spike). The subscript syn denotes the synaptic type: pp CA3 and sch for CA3 recurrent connections and Schaffer collaterals, respectively. The maximal potentiation rate MLTP syn , the maximal depression rate MLTD syn , and the 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 in Fig. 2 show the STDP modification functions, Fpp CA3 (1t) and Fsch (1t), respectively. Fpp CA3 (1t) is a simple approximation of the experimental results obtained by Bi and Poo (1998) using dissociated and cultured hippocampal cells. As for Fsch (1t), Nishiyama et al. (2000) have reported that the STDP modification function of Shaffer collateral synapses has a very narrow time window where LTP can be induced. We therefore used a smaller value of τpp sch for Fsch (1t). By setting T = 100 ms, we neglected synaptic modification in the 1t range where the absolute amount of the modification function (|F(1t)|) was less than 0.00034. Each pair of pre- and postsynaptic spikes modified synaptic conductance by the following equation: Csyn → Csyn + Cmax
syn
· Fsyn (1t).
Fig. 2. STDP modification functions. Dotted and solid lines show STDP modification functions for CA3 recurrent synapses and Schaffer collateral synapses, respectively. Each function is defined by Eq. (8).
(9)
The synaptic conductance Csyn was limited to the range Cmin syn ≤ Csyn ≤ Cmax syn , where Cmin pp CA3 , Cmax pp CA3 , Cmin sch and Cmax sch were 0.0005, 0.002, 0.0003 and 0.001 µS, respectively.
Modification of recurrent synaptic conductances between CA3 pyramidal cells produces spatial asymmetry of Cpp CA3 . The spatial asymmetry is represented by the orientation and the length of bars located at every location of pyramidal cells in the network, as shown in Figs. 4(a), 5(a), and 6(a). The bar located at the i-th pyramidal cell was obtained as follows. First, vectors oriented from the presynaptic pyramidal cells (surrounding cells) to the postsynaptic cell (i-th cell) were obtained. The length of each vector was proportional to Cpp CA3 . Next, these vectors were summed and the length of the √summed vector was normalized relative to Cmax pp CA3 · (1 + 2). The normalized vector Vi is shown as a bar originating from the location of the i-th pyramidal cell. Therefore, the direction and the length of each bar indicate the local direction in which excitatory connection is relatively strong and the degree of spatial asymmetry, respectively. 2.5. Input signals to the CA3 and CA1 networks Place cells in the EC have multiple place fields on hexagonal grids and are called grid cells (Hafting, Fyhn, Molden, Moser, & Moser, 2005). However, CA1 place cells usually have only one place field and their place fields can be maintained solely by direct input from EC to CA1 (Brun et al., 2002). This suggests that direct projections from EC to CA1 give sufficient information 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 from EC to CA3 through dentate gyrus and that pyramidal cells in each subregion in CA3 and CA1 received such information about single places (Fig. 3(a)). Specifically, signals about places A–D were projected to pyramidal cells in subregions A3 –D3 of CA3, respectively, through mossy fibers, and to A1 –D1 of CA1, respectively, through perforant path fibers (Fig. 3(a)). Each subregion in CA3 (A3 –D3 ) and CA1 (A1 –D1 ) consisted of 9 (3 × 3) and 25 (5 × 5) pyramidal cells, respectively. Signals from the EC to the hippocampus through perforant path fibers are modulated by theta oscillations (Kocsis, Bragin, & Buzs´aki, 1999), and theta phase precession is observed not only 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 stimulation does not disrupt theta phase precession (Zugaro, Monconduit, & Buzs´aki, 2005). These findings suggest that external input from the EC is crucial for theta phase precession. We therefore assumed that information about places was coded in a theta cycle in the EC in a time-compressed manner through theta phase precession (see Skaggs et al. (1996) for the mechanism of time-compressed firing of place cells). Note, therefore, that we assume that the cognitive map is obtained in the EC which is upstream of the hippocampus. In the present study, theta burst signals that mimicked firing of place cells were applied successively (A -> B -> C -> D) at intervals of 20 ms to CA3 and CA1 through mossy and perforant path fibers as shown in Fig. 3(b). Each burst in the signals to CA1 and CA3 consisted of two and three pulses, respectively. The interburst interval was 100 ms and the interpulse interval was 10 ms. Because perforant path signals from the EC were projected to CA3 through the dentate gyrus, the signals were applied to CA3 10 ms posterior to CA1. 3. Results 3.1. Spontaneous spatiotemporal activity of the CA3–CA1 network model We started numerical simulation without the input signals and the STDP rules to observe the spontaneous spatiotemporal activity of the model. Fig. 4 shows the synaptic conductance and spontaneous activity of the hippocampal CA3–CA1 network model 4 s after the beginning of the simulation. All of the synaptic conductances Cpp CA3 were identical and did not change with time as shown in Fig. 4(a): Cpp CA3 = 0.001 µS. The radius of each filled circle at locations of CA3 pyramidal cells is proportional to the average of synaptic conductances Cpp CA3 from surrounding pyramidal cells. The bars protruding from the circles indicate local directions in which Cpp CA3 was relatively strong (See Section 2.4). As all of the conductances Cpp CA3 were identical across the CA3 network, sizes of the circles are the same and no bar is seen except at the edges of the network where pyramidal cells received spatially asymmetric synaptic contacts from less than 28 surrounding pyramidal cells. 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 spontaneous spatio-temporal firing patterns of CA3 pyramidal cells. Intervals between the panels (ci )–(civ ) are 20 ms. These firing patterns were observed in the period between two dotted lines in Fig. 4(d). White squares indicate firing of CA3 pyramidal cells and fade out with time. Pyramidal cells at the lower part of the CA3 network started firing in the first panel (Fig. 4(ci ) lower panel), and then pyramidal cells at the upper part of the network started firing in the second panel (Fig. 4(cii ) lower panel). This firing propagated to the center of the network (Fig. 4(ciii ) lower panel), and gave excitatory synaptic inputs to the inhibitory interneuron. Firing of the interneuron, in turn, inhibited the pyramidal cells (Fig. 4(civ ) lower panel).
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Fig. 3. Input signals to the hippocampal CA3–CA1 model. (a) Projection sites 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 the subregions, A3 –D3 , in CA3 through perforant path fibers and mossy fibers, respectively. The subregions, A1 –D1 , consist of 5 × 5 CA1 pyramidal cells and the subregions, A3 –D3 , consist of 3 × 3 CA3 pyramidal cells. Black pyramidal cell in subregion D1 indicate pyramidal cell #188. (b) Input signal patterns. Each signal is a theta-burst signal with 100 ms interburst intervals and 10 ms interpulse intervals. The number of pulses in each burst is two for the perforant path signals and three for the mossy fiber signals. Mimicking temporally compressed firing of place cells, signals were successively fed into the four subregions in each network at intervals of 20 ms. CA1 pyramidal cells receive inputs directly from the EC through the perforant path, while CA3 pyramidal cells receive inputs from the EC via the dentate gyrus. Input signals through the mossy fibers were, thus, delayed 10 ms compared with those through perforant path fibers.
The spatio-temporal firing pattern varied with time and there was no consistent spatio-temporal pattern at this stage as the synaptic conductances Cpp CA3 were identical and kept constant. Conductances for all Schaffer collateral synapses (Csch ) were also identical as shown in Fig. 4(b). Note that this panel does not show the CA1 network but conductances for 256 Schaffer collateral synapses connecting CA3 pyramidal cells to one of the CA1 pyramidal cells (cell #188 in Fig. 3(a)) placed at the center of the subregion D1 . The CA1 pyramidal cell #188 is indicated by an open circle in the upper panel of Fig. 4(ci ). The size of each filled circle in Fig. 4(b) placed at the same position as the CA3 pyramidal cells is proportional to the strength of Schaffer collateral connection from corresponding CA3 pyramidal cell to the CA1 pyramidal cell #188. The radii of the filled circles are the same because all of the synaptic conductances Csch were identical. Receiving the spontaneous activity of the CA3 region, subthreshold membrane potential oscillation at a theta frequency occurred in the CA1 pyramidal cells as shown in Fig. 4(di ). Upper panels of Fig. 4(c) show spatio-temporal firing patterns of the CA1 network. There was no firing because Schaffer collateral synaptic conductances Csch were relatively weak. The CA1 interneuron did not fire either due to the lack of firing 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 position of CA3 pyramidal cell is proportional to the sum of the recurrent synaptic conductances of corresponding pyramidal cell. The bars protruding from the circles represent local spatial asymmetry of the recurrent synaptic conductances. Direction of each bar corresponds to the direction in which the local recurrent synaptic conductance is strong, and the length of each bar shows the degree of spatial asymmetry (See Methods). (b) Conductances for Schaffer collateral synapses connecting CA3 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 of each filled circle at the position of the CA3 pyramidal cell is proportional to the conductance for corresponding Schaffer collateral synapse. The conductances were 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 the lower panels show firing of pyramidal cells in CA3. The intervals between panels (i)–(iv) are 20 ms. Spontaneous firing propagates irregularly in the CA3 region in the initial state. (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. 4(c) were observed in the period of time between two dotted lines. In the initial state, CA3 pyramidal cells were spontaneously firing. 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 recurrent and Schaffer collateral synapses, and sequential input signals. Fig. 5 shows the spatial patterns of synaptic conductances and activity of the CA3 and CA1 networks 10 s after the onset of the signal application. 10 s was chosen because learning at the CA3 recurrent synapses was completed while learning at the Schaffer collateral was not yet to be seen. This is the first stage of sequence learning. Intervals between bursts of input signals were 100 ms and slightly shorter than the average interval between bursts of the spontaneous 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 surrounding region. Synaptic connections from the CA3 pyramidal cells in the subregions to the CA3 pyramidal cells in the surrounding region were consequently potentiated by the STDP rule while synaptic connections in the opposite directions were depressed. Bars that are oriented in the radial directions from the subregions show a distinct spatial pattern of Cpp CA3 (Fig. 5(a)). Consequently, neuronal activity of CA3 pyramidal cells tended to propagate in the radial directions from the stimulus sites along the potentiated connections as shown in Fig. 5(c) (lower panels). This spatio-temporal firing pattern had been almost steady in 10 s after the onset of the stimulation. Features of the spontaneous rhythmic activity and the radial propagation of
neuronal activity in the CA3 network have been investigated intensively in our previous study (Yoshida & Hayashi, 2004a). The propagation in the radial direction occurred successively from four stimulus sites with the delay of 20 ms due to the time-compressed sequential input signals. The lower panel of Fig. 5(ci ) shows the firing pattern of the CA3 network when the subregion A3 was stimulated. The pyramidal cells in subregion A3 started firing due to the input signal. The pyramidal cells in subregion B3 were stimulated 20 ms after the stimulation of subregion A3 (Fig. 3(cii ) lower panel). It can be seen that firing of pyramidal cells was propagating radially from subregion A3 to the surrounding region. The pyramidal cells in subregion C3 were then stimulated 20 ms after the stimulation of subregion B3 . Firing from A3 was propagating further as shown in the lower panel of Fig. 3(ciii ) and firing from subregion B3 was also propagating radially. Radial propagation from subregion C3 is seen in the lower panel of Fig. 3(civ ). In summary, widening rings of neuronal activity from the four subregions were organized in CA3, and the radii of the rings depended on the stimulus time. This means that the temporal sequence of signals was transformed into a spatial pattern. At this stage, no clear spatial pattern of Schaffer collateral synapses had been organized as shown in Fig. 5(b), while some synapses were slightly modified. This indicates that the learning of the recurrent synaptic conductances (Cpp CA3 ) occurred prior to 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 synapses from the subregions, A3 –D3 , to their surrounding regions were potentiated, and radial spatial patterns of synaptic conductances were formed. (b) Conductances for Schaffer collateral synapses connecting CA3 pyramidal cells to CA1 pyramidal cell #188. Despite the clear spatial patterns of recurrent synaptic conductances in the CA3 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. Firing activity propagated from the subregions to the surrounding areas along the spatial patterns of the recurrent synaptic conductances in the CA3 region. (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. 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 membrane potential 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 the following stage. 3.3. Learning in the CA1 network: Schaffer collateral synapses Fig. 6 shows the state of CA3 and CA1 networks 41 s after the beginning of the signal application. The spatial pattern of recurrent synaptic conductances (Cpp CA3 ) had been in a steady state as shown in Fig. 6(a), while distinct spatial pattern of Schaffer collateral synaptic conductances (Csch ) emerged as shown in Fig. 6(b). This is the second stage of sequence learning. CA1 pyramidal cells in subregion D1 fired only when they received excitatory inputs through both perforant path and Schaffer collaterals at the same time (Fig. 6(civ ) upper panel). When CA3 pyramidal cells fired just before firing of CA1 pyramidal cells, Schaffer collateral synapses between those pyramidal cells were potentiated through STDP. The lower panel of Fig. 6(ciii ) shows CA3 pyramidal cells that were firing around 20 ms prior to the firing of the CA1 pyramidal cells in the subregion D1 . Firing of CA3 pyramidal cells propagating from the subregion A3 were forming a doughnut-shape firing pattern. Firing was also propagating from the subregion B3 . Firing of pyramidal cells in the subregion C3 had not yet spread to the surrounding region. Schaffer collateral synapses from these active CA3 pyramidal cells to the CA1 pyramidal cells in the subregion D1 were consequently potentiated by the STDP rule. The resulting spatial pattern of potentiated Schaffer
collateral synapses in Fig. 6(b) is, therefore, very similar to the spatial pattern of active CA3 pyramidal cells in the lower panel of Fig. 6(ciii ). Because of this similarity between the firing pattern in the CA3 network and the spatial pattern of reinforced Schaffer collateral synapses, CA1 pyramidal cells in subregion D1 received more excitatory synaptic input than that at the former stage. CA1 pyramidal cell #188 therefore fired more often synchronized with the input signal (compare Fig. 5(di ) and Fig. 6(di )). Other CA1 pyramidal cells in subregion D1 also obtained similar Schaffer collateral synaptic conductance pattern. Fig. 7 compares spike timings of selected CA3 pyramidal cells and CA1 pyramidal cell #188. Fig. 7(bi ) shows firing pattern of CA1 pyramidal cell #188, and Fig. 7(bii )–(bvi ) show firing patterns of CA3 pyramidal cells indicated by white arrows in Fig. 7(a). Black arrows in Fig. 7(b) indicate the time up to 30 ms prior to the spike of CA1 pyramidal cell #188. The CA3 pyramidal cell in Fig. 7(bii ), which was placed at the center of the subregion A3 , fired more than 30 ms before spikes of CA1 pyramidal cell #188 every theta cycle. Because this difference in spike timing was more negative than the LTP range of the STDP function Fsch (1t), the Schaffer collateral synapse from this pyramidal cell to CA1 pyramidal cell #188 was 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 to CA1 pyramidal cell #188 were potentiated because spike timing is 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 synaptic conductances. (b) Conductances for Schaffer collateral synapses connecting CA3 pyramidal cells to CA1 pyramidal cell #188. Only the Schaffer collateral synapses connecting CA3 pyramidal cells located in the active regions propagating from the subregions, A3 –D3 , were potentiated. (c) Spatio-temporal firing patterns of the CA1 network (upper panels) and the CA3 network (lower panels). Intervals between the panels are 20 ms. Note the similarity between the firing pattern of the CA3 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 of time between two dotted lines. CA3 pyramidal cells fired in phase with the input signal through mossy fibers. CA1 pyramidal cell #188 fired frequently when the membrane 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 at the previous stage (See Fig. 5(di )).
3.4. Sequence sensitivity We next tested the sequence sensitivity of CA1 pyramidal cell #188. After the learning of the sequence of signals A -> B -> C -> D, the spatial pattern of Schaffer collateral synaptic conductances were fixed, and those synaptic conductances were not allowed to change after that. Input signals were then changed from the sequence A -> B -> C -> D to the sequence C -> B -> A -> D. Note that the fourth place is D in both sequences and only the sequences prior to place D were different between the two sequences. This is to examine the sequence-sensitive firing property of a place cell in subregion D1 , which purely depends on the sequence of the past. When this new sequence of signals were applied, the firing of CA3 pyramidal cells propagated farthest from the subregion C3 and firing had not yet spread from the subregion A3 , 20 ms before the input to the subregion D1 (Fig. 8(aiii ) lower panel). This spatial firing pattern of the CA3 network is different from that induced by the sequence of signals A -> B -> C -> D. Therefore, this firing pattern does not correspond to the spatial distribution of conductances for Schaffer collateral synapses (Fig. 6(b)). This mismatch between the spatial firing pattern of CA3 pyramidal cells and the distribution of potentiated Schaffer collateral synapses reduced the excitatory synaptic input from the CA3 network to CA1 pyramidal cell #188. Fig. 8(b) shows firing patterns of CA1 pyramidal cell #188 when the input sequences 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 input from the CA3 network. Fig. 8(c) shows the response rate of CA1 pyramidal cell #188 to various input sequences. The number of spikes evoked by each sequence of signals was counted in eight consecutive periods of 5 s (total of 40 s). The number of spikes in each 5 s was divided by the number of burst stimuli, and eight response rates were averaged. Error bars show standard deviations. CA1 pyramidal cell #188 responded best to the learned sequence of signals A -> B -> C -> D showing sequence sensitivity was indeed obtained. 3.5. Robustness of the present model In this section, robustness of the model was tested by modifying the parameters of the model. The key of our model to obtain the sequence sensitivity is the formation of the spatial pattern of the Schaffer collateral synaptic conductances which has multiple ring-shaped regions where synaptic conductances are strengthened (Fig. 6(b)). Formation of this spatial pattern means that CA1 pyramidal cell becomes sequence sensitive. We, therefore, compared the spatial patterns of Schaffer collateral synaptic conductances of the cell #188 formed in the original model (Fig. 6(b)) and the model with modified parameters to test the robustness. Comparison was done 41 s after the beginning of the signal application (same time as in Fig. 6(b)). First, we modified the number of stimulation pulses fed to the CA1 pyramidal cells. The number of intra-burst pulses was increased 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 pyramidal cell #188. (a) Positions of selected CA3 pyramidal cells. Positions of selected cells 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 indicated by white arrows in Fig. 7(a). The black arrows in Fig. 7(b) indicate the time up to 30 ms prior to the firing of the CA1 pyramidal cell #188. The CA3 pyramidal cells whose Schaffer collateral synapses were potentiated ((iii)–(vi)) fired in the time window of 30 ms.
Fig. 8. Sequence sensitivity of CA1 pyramidal cell #188. (a) Spatio-temporal firing patterns of the CA1 network (upper panel) and the CA3 network (lower panel). The sequence of input signals was C -> B -> A -> D. Intervals between the panels (i)–(iv) are 20 ms. Note the difference between the firing pattern in Fig. 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 signals were 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 text for the definition of the response rate. CA1 pyramidal cell #188 has been tuned to the learned sequence, A -> B -> C ->D.
CA3 and CA1 networks received three pulses in each burst. Fig. 9(a) is identical to the Fig. 6(b). As a result, ring-shaped patterns around A3 to C3 shown in Fig. 9(b) were slightly larger than those produced in the original model (Fig. 9(a)). This is due to the fact that additional pulse in each burst tends to keep CA1 cells firing. This results in more LTP induction because of more coincidence with firing of CA3 cells, which fire at later phases of each theta cycle. However, the overall features of the spatial pattern of Schaffer synaptic conductances (Fig. 9(b)) are similar 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 the STDP function for CA3 recurrent synapses was not changed because this was investigated in our previous work (Yoshida & Hayashi, 2004a). The time constant τsch was changed from the original value of 5 ms to 15 and 20 ms. The ring-shaped patterns were still present as shown in Fig. 9(c) and (d). Third, we modified the extent of the CA3 recurrent connections. When the number of recurrent connections from each cell to neighboring cells in CA3 was increased from 28 to 44, the resulting spatial pattern of Schaffer synaptic conductances was similar to that of the original model as shown in Fig. 9(e). However, reduction of the number of CA3
recurrent connections to 20 produced a completely different Schaffer synaptic conductance pattern (Fig. 9(f)). In this case, spontaneous firing often initiated in some place in CA3 regardless of the external input signal because the frequency of the spontaneous activity increased (9.4 Hz). Ring-shaped propagation of activity that held the timing of input signal was disrupted by the spontaneous firing (data not shown). The sequence of input signals was therefore not learned well by the Schaffer synapses. In our model, the frequency of the spontaneous activity also depends on the conductance for the recurrent connections in CA3. By increasing the maximal and minimal recurrent connection conductances (Cmin pp CA3 and Cmax pp CA3 ) to 0.0028 µS and 0.0008 µS, respectively, the frequency of the spontaneous activity was decreased to 8.7 Hz. With this increase in conductance for the recurrent connections, Schaffer synapses learned the ring-shaped spatiotemporal activity even in the case of the 20 CA3 recurrent connections (Fig. 8(g)). These results suggest that our model is not sensitive to the extent of the CA3 recurrent connections as long as the spontaneous frequency of the CA3 region is properly adjusted. In our previous work, we used a CA3 network with 25 interneurons (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 are original (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 number of 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 recurrent connections are modified. (h) Intra-network connectivity of the CA1 and CA3 regions that include 25 interneurons each. Pyramidal cells are shown as triangles and interneurons are shown as small circles. For example, 112 pyramidal cells (triangles) in the shadowed circle are connected through excitatory synapses to the 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. Synaptic conductances 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 were distributed evenly in the networks as shown in Fig. 9(h) (small circles). In the original model used in the current study, all pyramidal cells were synaptically connected to one interneuron and the interneuron was connected to all pyramidal cells. Such connections will remove the effect of having multiple interneurons located at multiple positions in the network. We, therefore, reduced the extent of the connections between interneuron and pyramidal cells to the range shown by the shadowed circle in Fig. 9(h) in both CA1 and CA3 networks. Pyramidal cells in the shadowed circle (112 pyramidal cells) were connected through excitatory synapses to the interneuron at the center of the shadowed circle, and the interneurons were connected through inhibitory synapses to the pyramidal cells in the shadowed circle. Each pyramidal cell therefore received synaptic input from at most 14 interneurons. Due to the change in the number of connections, we modified the synaptic conductances between interneurons and 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 also modified (Cmax sch = 0.0008 µS). The resulting spatial pattern of Schaffer synaptic conductances showed three ring-shaped regions similar to the original pattern as shown in Fig. 9(i). Therefore, this model is robust to changes in the number of interneurons 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 firing pattern of place cells in the EC to subregions of the CA3 and CA1 networks, CA1 pyramidal cells became sequence sensitive through the two learning stages. At the first stage, the input signals strengthened the recurrent connections from stimulus sites to the surrounding regions in the CA3 network. Because of this spatial pattern of the recurrent connections, each burst of stimulation caused propagation of neuronal activity in the radial direction from the stimulated site in the CA3 network model. The radial propagations of neural activity stored the sequence of input signals by their radii. At the second stage, conductances for the Schaffer collateral synapses between CA3 pyramidal cells that fired in the ring-shaped propagating waves and CA1 pyramidal cells that received input signals through the perforant path were potentiated. The radii of the ring-shaped spatial patterns of Schaffer collateral synaptic conductances specified the sequence of the input signals that caused maximum excitatory synaptic input from CA3 to CA1. CA1 pyramidal cells, therefore, responded with the highest probability when a sequence of input signals was identical to the learned sequence. These results imply that sequence sensitivity arises in CA1 place cells through intra-hippocampal neural computations during the animal’s spatial activity. Although previously proposed models of sequence learning and recall do not focus on sequence sensitivity of place cells, some of them imply that place cells in their model would be sequence sensitive (Jensen & Lisman, 1996a, 1996b; Yamaguchi, 2003). Here, we call place cells in their model, with neighboring place fields, place cells A to D for explanatory purpose. In these models, place cells receive gradual synaptic input 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 place cell A and strongest from place cell C. Under an assumption that excitatory post-synaptic potential decays exponentially, this connection pattern indicates that firing of place cells in the sequence A -> B -> C provides larger synaptic input to place cell D than the sequence C -> B -> A provides, because place cell C, which provides the major excitatory input to place cell D, fires just before firing of place cell D in the former case. However, if the place cells, A, B and C, fire with shorter intervals or in synchrony, this will cause larger excitatory input to place cell D than the learned sequential input that has original intervals. In this sense, these models are not truly optimized to the learned sequence. In contrast, in our model, shorter interval or synchronized firing of place cells in subregions, A3 , B3 and C3 , does not provide larger input signal to place cells in region D1 than the learned sequence does, because in such cases ring-shaped propagation waves in CA3 does not coincide with learned spatial pattern of Schaffer synapses (Fig. 6(b)). Place cells in our model are truly optimized to the learned sequence because a sequence of input signals that can cause the largest input to cells in region D1 is the input signals with exactly the same sequence and timings as learned input signals. Hasselmo and Eichenbaum (2005) proposed a model of differential firing in the same part of the maze with two loops (Wood et al., 2000) based on the activity of the EC. In their model, EC layer III stored all possible sequences and delayed firing of EC layer II neurons held information about the loop taken in the previous lap. Signals from the EC were merged in CA1 area where place cells fired depending on the previous path taken, meaning that they were sensitive to sequence from the past. Their model and our model differ in many ways. First, their model relies on the network and activity of EC, while our model showed emergence of sequence sensitivity in hippocampal CA3–CA1 network alone. Second, their model consists of simple binary model and uses reinforcement learning, while we used Hodgkin–Huxley style more physiological neuron models and STDP rules. Third, they used delayed firing of EC layer II neurons to produce sequence sensitivity while our model did not rely on it. Their place cells are not sequence sensitive without this dynamic activity, while place cells were sequence sensitive as the result of synaptic conductance modification in our model. We have shown how place cells may become sensitive to a single sequence. In the maze with two loops, rats have to learn at least two sequences that terminate at the same location (e.g. A -> B- > C-> D and E -> F -> G ->D) where some cells respond to the sequence A -> B -> C -> D while others respond to the sequence E -> F -> G -> D at the common part of the two loops (place D). In the present study, we assumed that signal about place D is uniformly projected to the CA1 pyramidal cells in subregion D1 and that they receive uniform Schaffer collateral synaptic input from CA3 cells in the initial condition. In reality, however, these synaptic projections would not be perfectly uniform with various synaptic conductance and uneven numbers of synapses. When the rat runs in one of the loops of the maze and places A, B and C are visited,
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Fig. 10. Illustration of sequence recall mechanism. CA3 pyramidal cells in the white circle, gray ring-shaped region and black ring-shaped region, have large Schaffer collateral synaptic conductance with CA1 pyramidal cells in subregions B1 , C1 and D1 , respectively. Firing of CA3 cells initiated in subregion 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 of the synaptic input produced by this activity and direct input from EC is sufficient to cause firing of a CA1 cell, this cell will become sensitive to the sequence A -> B -> C -> D as described above. However, this might not be the case for all of the CA1 cells in D1 subregion when synaptic projections are not uniform. When the rat next goes into the other loop visiting places E, F and G, this will produce different spatio-temporal firing pattern in CA3. It is possible that this activity produces larger excitatory synaptic input and cause firing in some of the cells (in subregion D1 ) that do not fire in the first loop. These cells will become sensitive to the sequence E -> F -> G -> D. In this way, some cells can be sensitive to one and others to the other sequence in the subregion D1 . There would also be cells that fire in both cases and they will not be sequence sensitive in the maze. Interestingly, some of CA1 place cells are actually not sensitive to sequences (Wood et al., 2000). As mentioned above, place cells in the hippocampal CA1 region fire in the same sequence as they fire while awake, often synchronized with sharp waves from the CA3 region during slow wave sleep (Lee & Wilson, 2002; Skaggs & McNaughton, 1996). Although this recall of sequences was not tested in this study, our model has potential to achieve recalls. Fig. 10 shows hypothetical spatial pattern of the Schaffer collateral synapses from CA3 cells that are located near the subregion A3 . As shown in the Fig. 6(b), CA3 cells that are located in a ring-shaped region around subregion A3 , which corresponds to the black ring in Fig. 10, project strong synaptic input to CA1 cells in D1 region. Because CA3 cells in the gray colored ring-shaped region will fire earlier in each theta cycle just before the CA1 pyramidal cells in subregion C1 fire, they project strongly to subregion C1 . The white colored central part 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 potentiated synapses to the surrounding area, firing CA3 cells in these ringshaped regions one by one. This will activate CA1 place cells in subregions B1 to D1 sequentially. During slow wave sleep, conductance of Schaffer collaterals and CA3 recurrent synapses are stronger than while awake because of lower acetylcholine level (reviewed in Hasselmo, 1999). Synaptic input to the CA1 from the ring-shaped CA3 area alone could, therefore, be enough to fire CA1 place cells sequentially achieving recalls. Similar multi-ring-shaped patterns will be created around other subregions in CA3, each of them having shifted projections to CA1 subregions. Recalled sequences will depend on which CA3 subregion a sharp wave initiates from (sequences B1 > C1 ->D1 , C1 -> D1 ->E1 , D1 -> E1 ->F1 and E1 -> F1 ->G1 for CA3 subregions A3 , B3 , C3 and D3 , respectively, assuming that there are places E to G after place D). Interestingly, a recalled sequence in CA1 is often a part of learned sequence, starting in the middle of an entire sequence, rather than the full sequence (Lee & Wilson, 2002). The STDP function for CA3 recurrent synapses was based on the STDP function that was observed by Bi and Poo (1998) using dissociated and cultured hippocampal cells. The time constants (τsyn ) of their STDP function for LTP and LTD sides were 16.8 ms and 33.7 ms, respectively. We set the time constant (τpp CA3 ) at 20 ms for both LTP and LTD sides of the STDP function because this time constant for the STDP function was well tested in other studies (Kitano, Cˆateau, & Fukai, 2002; Levy, Horn, Meilijson, & Ruppin, 2001; Song, Miller, & Abbott, 2000). On the other hand, we set the time constant (τsch ) at 5 ms for STDP function of Shaffer collateral synapses. As mentioned above, Nishiyama et al. (2000) have reported that, in Schaffer collateral synapses, the STDP function has a positive peak at around 1t = −5 ms and negative peak at around 1t = −20 ms. This means that LTP at Schaffer collateral synapses occurs only when the CA1 pyramidal cell fires within 10 ms after firing of CA3 pyramidal cells. Although we did not implement the negative peak at around 1t = −20 ms to keep our model simple, the narrow range of 1t for LTP was introduced by a fast time constant. This allowed CA1 pyramidal cells to pick only CA3 pyramidal cells that elicited spikes in a very short period of time prior to the spikes of the CA1 pyramidal cells in our model. In this way, spatiotemporal activity of the CA3 region was transformed to a spatial pattern of the conductances for the Schaffer synapses as if taking a photo. In the real hippocampus, the negative peak of the STDP function at 1t = −20 ms might increase this ability producing a sharper conductance pattern, because spikes of CA3 pyramidal cells elicited in the propagating wave more than 10 ms prior to the spikes of CA1 pyramidal cells causes LTD back-to-back with the LTP due to the coincidence of spikes within 10 ms. In Fig. 8(c), CA1 pyramidal cell #188 responded fairly well to the sequence of signals B -> A -> C ->D though response rates to other input sequences were significantly lower. With this particular sequence of signals, subregions A3 and B3 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, the spatial firing pattern of CA3 pyramidal cells around A3 and B3 subregions was very similar to the spatial conductance pattern of Schaffer collateral synapses. These two regions (around A3 and B3 subregion) were the major sources of excitatory synaptic input to CA1 pyramidal cells in the subregion D1 including cell #188 (see Fig. 6(b)), and both of these two regions sent considerable amount of excitatory input to CA1 pyramidal cells in the subregion D1 only in this case. The response rate was, therefore, highest among unlearned sequences when the sequence was B -> A -> C -> D. Using a CA3 network model with larger size and faster propagation of activity would differentiate the two doughnut-like spatial patterns of Schaffer collateral synaptic conductances around subregions A3 and B3 (Fig. 6(b)). The sequence of signals B -> A -> C -> D would then produce smaller excitatory input to CA1 pyramidal cells and CA1 pyramidal cells would show lower response rate. Once separations between sequences are easily done, it would be also possible to increase the number of signals in one sequence. In this study, we used four signals in one theta cycle with 20 ms of interval between signals and 100 ms theta period. Either by decreasing the interval between signals or by increasing theta period, more than four firing of place cells would be fit into one theta cycle. When such a sequential signal is fed into the CA3 with larger network size and faster propagation speed, the CA1 place cells would become sensitive to sequences that consist of more than four places. As studied in our previous study (Yoshida & Hayashi, 2004a), the interburst interval of input signal to CA3 had to be shorter than that of spontaneous activity of CA3 pyramidal cells to synchronize the spontaneous activity to the input signal. We used a 10 Hz theta burst signal for stimulation and the frequency of the spontaneous activity was about 9 Hz. Theta burst signal whose frequency is lower than that of spontaneous activity would not be able to make a radial synaptic conductance pattern in CA3 and thus would fail to obtain sequence sensitivity. It has been reported that neurons in the superficial layers of the EC (layer II and layer III) fire in bursts and the bursts are phase locked to the theta rhythm (Alonso & Garcia-Austt, 1987). Their intraburst frequency is in a gamma range (Chrobak & Buzs´aki, 1998). We, therefore, used a theta burst pattern where a gamma rhythm (50 Hz) was nested in the theta rhythm (10 Hz) as the input signal from the EC. Alonso and GarciaAustt (1987) reported that cells in the superficial layers that were phase locked to theta rhythm could be categorized into two classes. One of them fired at 2.7 Hz and the other fired at 16.7 Hz on average during theta activity. These numbers give 0.54 and 3.34 spikes per theta cycle, the frequency of the theta rhythm being assumed 5 Hz in their experiment. The number of pulses used in this study (two for the signal to CA1 and three for the signal to CA3) were in this range. Each CA3 pyramidal cell was connected to surrounding pyramidal cells symmetrically in the present CA3 network model. Action potentials evoked by an input signal therefore tended 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 hippocampal slices from guinea-pigs (Traub, Jefferys, & Miles, 1993), there is no direct measurement showing propagation of neuronal activity in radial directions in the hippocampal CA3 region. The propagation of activity in radial directions was therefore an assumption in our model. In the real hippocampus, synaptic connections 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 propagating waves are induced in CA3 by a sequence of input signals and firing of CA3 pyramidal cells on the wave fronts augment specific Schaffer collateral synapses. The shapes of the propagating waves have to be the same in each theta cycle but can be in any shape. Sequence learning would thus be done even with asymmetrically propagating waves. Based on the present model, we predict that the percentage of the place cells that are sequence sensitive is higher in the CA1 region compared to the CA3 region. As far as we know, there is no study that specifically compared sequence sensitivity of place cells in these two regions. It would be possible to clarify this issue by comparing the place cells in CA3 and CA1 that have place fields at the common part of the maze as in Wood et al. (2000). We expect that more place cells that have a place field at the common part of the maze and fire depending on the path (sequence) visited in the past exist in the CA1 region than in the CA3 region. Furthermore, our model predicts that formation of propagation wave in the CA3 region through modification of synaptic conductances is crucial. It would be very interesting to see how the percentage of the sequence sensitive cells drops when synaptic modification in the CA3 region is blocked, for example using CA3 NMDA receptor knockout animals. Acknowledgments We thank Farhan Khawaja for the critical reading of the manuscript. We also thank Prof. Michael Hasselmo and Prof. Takeo Watanabe for kindly allowing us to use the laboratory facilities. This work was supported by (1) 21st Century Center of Excellence Program (center #J19) granted to Kyushu Institute of Technology by Japan Ministry of Education, Culture, Sports, Science and Technology and (2) Japan Ministry of Education, Culture, Sports, Science and Technology (Grant-in-Aid for Scientific Research, No. 14580425 and No. 16015289). Appendix A Rate constants of ion-gates and parameter values of the CA3 pyramidal cell model. −0.32(51.9 + V ) αm = , exp(−(51.9 + V )/4) − 1 0.28(V + 24.9) βm = , exp((V + 24.9)/5) − 1 −48 − V , αh = 0.128 exp 18
4 , 1 + exp(−(25 + V )/5) 0.2 0.0025(V + 13.9) αs = , βs = , 1 + exp(−0.072V ) exp((V + 13.9)/5) − 1 ( exp(−(V + 65)/20) (V > −65) αr = 1600 0.000625 (V ≤ −65) ( 0.005 − 8α r (V > −65) βr = 8 0 (V ≤ −65) 1.6 , αs(low) = 1 + exp(−0.072(V + 40)) 0.02(V + 53.9) βs(low) = , exp((V + 53.9)/5) − 1 ( exp(−(V + 105)/20) (V > −105) αr (low) = 200 0.005 (V ≤ −105) 0.005 − αr (low) (V > −105) βr (low) = 0 (V ≤ −105) −0.016(29.9 + V ) , αn = exp(−(29.9 + V )/5) − 1 −45 − V βn = 0.25 exp , 40 −0.02(51.9 + V ) , αa = exp(−(51.9 + V )/10) − 1 0.0175(V + 24.9) , βa = exp((V + 24.9)/10) − 1 V + 78 αb = 0.0016 exp − , 18 0.05 , βb = 1 + exp(−(54.9 + V )/5) ((χ − 140) < 0) 0 αq = 0.00002(χ − 140) (0 ≤ (χ − 140) < 500) 0.01 (500 ≤ (χ − 140)) βq = 0.001 exp((V + 55)/11 − (V + 58.5)/27) (V ≤ −15) 18.975 αc = −58.5 − V 2 exp (V > −15) 27 −58.5 − V 2 exp − αc (V ≤ −15) βc = 27 0 (V > −15) C = 0.1 (µF).gNa = 1.0, gCa = 0.13, gCa(low) = 0.03, βh =
g K (DR) = 0.08,
g K (A) = 0.17,
g K (AHP) = 0.07,
g K (C) = 0.366,
gL = 0.0033,
gaf center = 0.005,
gaf edge = 0.004, VNa = 50,
gaf center = 0.003 (µS).
VCa = 75,
Vsyn(e) = −10 (mV ).
VK = −80, φ = 50.
VL = −65,
βχ = 0.075 (m s−1 ).
Rate constants of ion-gates and parameter values of the CA1 pyramidal cell model. Only parameters that are different from CA3 are listed.
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((χ − 20) < 0) 0 αq = 0.00002(χ − 20) (0 ≤ (χ − 20) < 500) 0.01 (500 ≤ (χ − 20)) gCa(low) = 0.008, g K (DR) = 0.12, g K (AHP) = 0.027, g K (C) = 0.33,
gaf = 0 (µS).φ = 60,
βχ = 0.01 (m s−1 ).
Rate constants of ion-gates and parameter values of the inhibitory interneuron model. −0.64(51.9 + V ) , exp(−(51.9 + V )/4) − 1 0.56(V + 24.9) , βm = exp((V + 24.9)/5) − 1 0.128 exp(−(48 + V )/18) αh = , 0.65 4 βh = , 0.65(1 + exp(−(25 + V )/5)) −0.016(48.9 + V ) , αn = 0.65(exp(−(48.9 + V )/5) − 1) 0.25 exp(−(64 + V )/40) βn = 0.65 C = 0.1 (µF).gNa = 1.5, g K (DR) = 0.3, VNa = 50, VK = −80, VL = −65 (mV ). αm =
gL = 0.02 (µS).
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