Cooperation and competition between lateral and medial perforant path synapses in the dentate gyrus

Neural Networks 24 (2011) 233–246

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Cooperation and competition between lateral and medial perforant path synapses in the dentate gyrus Hatsuo Hayashi ∗ , Yukihiro Nonaka 1 Department of Brain Science and Engineering, Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, Hibikino 2-4, Wakamatsu-ku, Kitakyushu 808-0196, Japan

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Article history: Received 19 May 2010 Received in revised form 5 December 2010 Accepted 20 December 2010 Keywords: Dentate granule cell Multi-compartmental model Lateral perforant path Medial perforant path STDP Synaptic cooperation Synaptic competition

abstract It has been suggested that non-spatial and spatial pieces of information are transmitted to the dentate gyrus from entorhinal cortex layer II through the lateral and medial perforant paths (LPP and MPP), which establish synapses on granule cell dendrites in the outer and middle one-thirds of the dentate molecular layer, respectively. In the present paper, we first investigated cooperation and competition between MPP and LPP synapses being subject to STDP rules, using a four-compartmental granule cell model. MPP and LPP were stimulated simultaneously by periodic and random pulse trains, respectively. Both synapses were gradually enhanced by cooperation between those synapses in the early stage, and then either the MPP or the LPP synapse was rapidly enhanced through synaptic competition in the following stage, depending on their initial synaptic conductances. The dominant cause of synaptic competition is that the distance between the MPP synapse and the soma is shorter than that between the LPP synapse and the soma. These results suggest that the LPP and MPP synapses tend to be enhanced in the dentate supraand infrapyramidal blades, respectively, taking account of the thickness of each of the LPP and MPP fiber laminae in the blades. The dentate gyrus may select spatial and non-spatial pieces of information through synaptic cooperation, and may open a gate for each piece of information through synaptic competition. Then we investigated the role of inhibitory local circuits in synaptic competition in the dentate gyrus. The feed-forward GABAB inhibition suppressed unusual high-frequency firing of the granule cell, and consequently prevented excessive synaptic depression due to synaptic competition through STDP. The feed-forward and feedback GABAA inhibitions tend to reduce synaptic conductance fluctuations resulting from large increments and decrements due to very small spike-timings happening occasionally. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction The dentate gyrus is supposed to be a crucial area where spatial and non-spatial pieces of information first converge in the hippocampus. Since pathways run from sensory cortical regions (all modalities) to layer II of the lateral entorhinal cortex via the perirhinal cortex, it has been suggested that non-spatial information is transmitted to the dentate gyrus through the lateral perforant path (LPP) originating from lateral entorhinal cortex layer II. In contrast, pathways from visual and visuospatial cortical regions run to layer II of the medial entorhinal cortex via the postrhinal cortex, so that spatial information is suggested to be transmitted to the dentate gyrus through the medial perforant path (MPP) originating from medial entorhinal cortex layer II (Burwell,

∗

Corresponding author. Tel.: +81 93 695 6089; fax: +81 93 695 6089. E-mail addresses: [email protected] (H. Hayashi), [email protected] (Y. Nonaka). 1 Tel.: +81 93 695 6099; fax: +81 93 695 6099. 0893-6080/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.neunet.2010.12.004

2000; Hargreaves, Rao, Lee, & Knierim, 2005). In other words, spatial and non-spatial pieces of information converge at dendrites of the dentate granule cells. Projections from entorhinal cortex layer II to the dentate gyrus are well organized; LPP and MPP from layers II of the lateral and medial entorhinal cortices are terminated on dendrites of dentate granule cells in the outer one-third and the middle onethird of the dentate molecular layer, respectively (Burwell & Amaral, 1998; Hjorth-Simonsen, 1972; Hjorth-Simonsen & Jeune, 1972; McNaughton & Barnes, 1977; Steward, 1976; Wyss, 1981). Moreover, although the lamination of projection fibers from entorhinal cortex layer II to the dentate gyrus is basically the same in the supra- and infrapyramidal blades of the dentate gyrus, the LPP fiber lamina is thick in the suprapyramidal blade and thin in the infrapyramidal blade, while the MPP fiber lamina is thin in the suprapyramidal blade and thick in the infrapyramidal blade (Tamamaki, 1997). Neurons in layer II of the medial entorhinal cortex cause synchronized subthreshold theta oscillations, and consequently firing of the neurons is phase-locked to the synchronized oscillations when depolarized slightly (Alonso & García-Austt,

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1987; Alonso & Klink, 1993). This implies that theta-related periodic spike trains elicited in MEC by afferent signals are fed to dentate granule cells through MPP fibers. In contrast, neurons in layer II of the lateral entorhinal cortex cause weak subthreshold oscillations, which do not show clear periodicity. Consequently, spikes of those neurons are rather irregular (Tahvildari & Alonso, 2005; Wang & Lambert, 2003). This implies that theta-related but irregular spike trains elicited in LEC by afferent signals are fed to the dentate granule cells through LPP fibers. Taking account of the feature of spike-timing-dependent synaptic plasticity (STDP) in the dentate gyrus (Lin et al., 2006), it seems that impulse patterns of those signals are crucial when plastic change in synaptic weights takes place in the dentate gyrus. However, spike trains to dentate granule cells through LPP and MPP would not correlate with each other. Actually, coherence between activities of LEC and MEC is low, and LEC also generates rhythmic activity in the beta band (35–40 Hz) (Boeijinga & Lopes da Silva, 1988). Despite of the above findings, it is still unclear how spatial and non-spatial pieces of information cooperate and/or compete with each other in dendrites of dentate granule cells and how the cooperation and/or competition produce plastic changes in LPP and MPP synapses through the STDP rule. In the present paper, we first investigated cooperation and competition between LPP and MPP synapses, which are subject to STDP rules, using a four-compartmental model of the dentate granule cell. Uncorrelated signals, whose frequencies were in the theta range, were simultaneously fed to the dentate granule cell through LPP and MPP synapses. Both synapses were gradually enhanced by cooperation between those synapses in the early stage, and then either LPP or MPP synapse was enhanced by competition between those synapses in the following stage, depending on their initial synaptic conductances. The dominant cause of the synaptic competition is that the distance between the MPP synapse and the soma is shorter than that between the LPP synapse and the soma. These results suggest that the LPP and MPP synapses tend to be enhanced in the dentate supra- and infrapyramidal blades, respectively, through synaptic competition, taking account of the thickness of each of the LPP and MPP fiber laminae based on anatomical data (Tamamaki, 1997). The dentate gyrus may select spatial and non-spatial pieces of information fed to the dentate gyrus through the synaptic cooperation, and may open gates to the hippocampus for the spatial and non-spatial pieces of information in the infra- and suprapyramidal blades, respectively, through the synaptic competition. Then we investigated the role of inhibitory local circuits in synaptic competition in the dentate gyrus. The feed-forward GABAB inhibition suppressed unusual high-frequency firing of the granule cell caused by an input whose frequency was above the theta range. This consequently prevented either LPP or MPP synapse being depressed excessively due to synaptic competition through STDP. The feedforward and feedback GABAA inhibitions tend to reduce fluctuations of the synaptic conductance resulting from large increments and decrements due to very small spike-timings happening occasionally, and consequently stabilize the time course of plastic change in synapses. Preliminary data have been reported in conference proceedings (Nonaka & Hayashi, 2009, 2010). 2. Methods 2.1. Dentate granule cell model The present four-compartmental model of the dentate granule cell was developed by reducing the 47-compartmental model proposed by Aradi and Holmes (1999). It consists of one compartment for the soma and three compartments for the

dendrites (Fig. 1(a)). Equations of the present granule cell model are as follows: C m ,j

dzj dt dsj dt

dVj

= gNa,j m3j hj (ENa − Vj ) + gfKDR,j n4f,j (EK − Vj )

dt

+ gsKDR,j n4s,j (EK − Vj ) + gKA,j kj lj (EK − Vj ) + gTCa,j a2j bj (ECa − Vj ) + gNCa,j cj2 dj (ECa − Vj ) + gLCa,j e2j (ECa − Vj ) + gBK,j rj s2j (EK − Vj ) + gSK,j q2j (EK − Vj ) + gL (EL − Vj ) + rj,j+1 (Vj+1 − Vj ) X Y + rj,j−1 (Vj−1 − Vj ) + Isyn (1) (e) + Isyn(i) ,

= αz ,j − (αz ,j + βz ,j )zj (zj : mj , hj , nf ,j , ns,j , kj , lj , aj , bj , cj , dj , ej , rj , qj ), =

s∞ − sj

d[Ca2+ ]j dt

τs

(s∞ = 1/(1 + 4/[Ca2+ ]j )),

= Bj (ITCa,j + INCa,j + ILCa,j ) −

[Ca2+ ]j − [Ca2+ ]∞ . τ

(2) (3)

(4)

Cm,j is the membrane capacitance and Vj is the membrane potential of the compartment j. The subscripts of the maximum conductances, gNa,j etc., on the right-hand side of Eq. (1) denote as follows: Na, the sodium channel; fKDR, the fast delayed potassium channel; sKDR, slow delayed potassium channel; KA, the Atype potassium channel; TCa, the T-type calcium channel; NCa, the N-type calcium channel; LCa, the L-type calcium channel; BK, the B-type calcium-dependent potassium channel; SK, the S-type calcium-dependent potassium channel; L, the leakage. ENa , EK , ECa , and EL are sodium, potassium, calcium, and leakage equilibrium potentials, respectively. rj,j+1 is the conductance connecting compartments, j and j + 1, and calculated by the following equation: 2

r j ,j + 1 = 

lj RAj

(φj /2)2 π

+

lj+1 RAj+1

.

(5)

(φj+1 /2)2 π

See Table A.2 for the parameters, lj , RAj , and φj . The ion-gating variable zj in Eq. (2) stands for mj , hj , nf,j , ns,j , kj , lj , aj , bj , cj , dj , ej , rj , and qj . The ion-gating variable sj is represented in Eq. (3), and depends on the intracellular calcium concentration [Ca2+ ]j . The time constant τs is 10 ms. The ion-gating variable qj of the S-type calcium-dependent potassium channel also depends on the calcium concentration [Ca2+ ]j because the rate functions, αq and βq , depend on the calcium concentration (see Appendix A). ITCa,j , INCa,j , and ILCa,j in Eq. (4) are T-, N-, and L-type calcium currents, i.e. the fifth, sixth, and seventh terms on the right-hand side of Eq. (1), respectively. [Ca2+ ]∞ (0.07 µM) is the steady-state intracellular calcium concentration, and τ (9 ms) is the calcium removal rate. Bj = 5.2 × 10−6 /(Sj · δ)(mol/(C cm3 )) for a compartment of surface area Sj and thickness δ (0.2 µm). The equilibrium potential ECa was calculated at each time step using the intracellular calcium concentration [Ca2+ ]j with the Nernst equation; the extracellular calcium concentration was 2000 µM. The forth order Runge–Kutta algorithm was used to integrate the equations. The step size was 0.01 ms. See Appendix A for the rate functions, αz ,j and βz ,j , and other parameter values. The second last term on the right-hand side of Eq. (1) is the excitatory synaptic current. Equations of the excitatory synaptic X current Isyn (e) are as follows: X X Isyn (e) = gsyn(e) (Esyn(e) − Vj ), X X gsyn (e) = C



    t t exp − − exp − . τ1,X τ2,X

(6) (7)

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235

Fig. 1. Dentate granule cell model. (a) Four-compartmental model consisting of three dendrite compartments (1–3) and one soma compartment (4). The lateral perforant path (LPP) and the medial perforant path (MPP) form excitatory synapses on the distal and middle dendrites, respectively. The LPP was stimulated by a random pulse train whose distribution of interpulse intervals was Gaussian (standard deviation = mean interpulse interval × 0.25). The MPP was stimulated by a periodic pulse train (8 Hz). See Table A.2 for dimensions of each compartment. (b) Responses of the present granule cell model to DC pulses. Pulse currents are −80, −60, −40, −20, −10, 10, 20, 40, 60 pA. Action potentials are truncated. (c) Responses of the present granule cell model to a DC pulse current (80 pA). (d) STDP rule approximated by exponential functions. The LPP and MPP synapses are subject to asymmetric STDP rules in the present model.

As LPP and MPP terminate at the compartments of the distal (j = 1) and middle (j = 2) dendrites, respectively (Fig. 1(a)), the subscript X denotes LPP for the LPP synapse and MPP for the MPP synapse. The equilibrium potential Esyn(e) (−6 mV) is common X to the excitatory synapses. The synaptic conductance gsyn (e) is

represented by Eq. (7), and the coefficient C X is modified through a STDP rule as mentioned below. The time constants, τ 1,X and τ 2,X , are common to the LPP and MPP synapses (see Appendix A for the values). Responses of the present four-compartmental granule cell model to DC pulse currents applied to the soma (Fig. 1(b) and (c)) well reproduced the responses of the dentate granule cell observed in the experiments (Fig. 6 in Spruston & Johnston, 1992; Fig. 3 in Staley, Otis, & Mody, 1992) and responses of the 47-compartmental granule cell model (Fig. 5 in Aradi & Holmes, 1999). 2.2. Input signals to the granule cell model through LPP and MPP synapses As neurons in medial entorhinal cortex layer II (primarily stellate cells), whose axons form MPP to the dentate gyrus, generate synchronized subthreshold membrane potential oscillations in the theta frequency range, firing of the stellate cells are phase-locked to the subthreshold oscillations when the cells are slightly depolarized (Alonso & Klink, 1993). In the present model, a periodic pulse train (interpulse interval = 125 ms) was, therefore, fed to the dentate granule cell through MPP as a signal conveying spatial information. On the other hand, neurons in lateral entorhinal cortex layer II (primarily fan cells), whose axons form LPP to the dentate gyrus, generate weak subthreshold oscillations. Those subthreshold oscillations do not show clear periodicity, and spikes of the fan cells are rather random (Tahvildari & Alonso, 2005). Therefore, a random pulse train (mean interpulse interval = 25, 50, 100,

or 167 ms, standard deviation = mean interpulse interval × 0.25, Gaussian distribution) was fed to the dentate granule cell through LPP as a signal conveying non-spatial information. A random pulse train (mean interpulse interval = 10 or 20 ms, standard deviation = mean interpulse interval × 0.25, Gaussian distribution) was also fed to the dentate granule cell through LPP as a rather unusual input to investigate the role of inhibitory interneurons in Section 3.3. The Gaussian random pulse train would be suitable because activation of many perforant path fibers is required to discharge the granule cell (McNaughton, Barnes, & Andersen, 1981). The sequence of interpulse intervals being subject to a Gaussian distribution was obtained from uniform random numbers generated by a computer, using the Box–Muller algorithm. 2.3. Synaptic plasticity of LPP and MPP synapses The LPP synaptic conductance was modified through an asymmetric STDP rule in Fig. 1(d). Although it has not been elucidated whether the MPP synapse is subject to a STDP rule, it is hypothesized in the present model that the MPP synapse is also modified through the asymmetric STDP rule. The asymmetric STDP rule is defined as follows: ALTP exp(−1t /τLTP ) ALTD exp(1t /τLTD ) 0

 F (1t ) =

if 0 < 1t ≤ 100 if −100 ≤ 1t < 0 otherwise,

(8)

where, ALTP = 0.61, τLTP = 26 ms, and τLTD = 36 ms. The amplitude of the LTD window ALTD (<0) is changed to manipulate the area of the LTD window. In the present four-compartmental model, action potentials are generated in the soma by synaptic inputs, and they propagate backward along the dendrite. The spike-timing 1t is, therefore, defined by the time difference between a presynaptic pulse and a backpropagated action

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in the present model, because mossy cells send output primarily to granule cells at distant septotemporal levels (Patton & McNaughton, 1995). Equations of a single-compartmental model are common to the MOPP cell and the basket cell, and are represented as follows: Cm

dV dt

= gNa m3 h(ENa − V ) + gK n4 (EK − V ) − X + gL (EL − V ) + Isyn ( e) ,

(10)

X

dz dt

Fig. 2. Local circuits of feed-forward and feedback inhibitions mediated by the MOPP cell and the basket cell. The MOPP cell (MC) receives excitatory inputs through lateral and medial perforant paths (LPP and MPP), and its axons form GABAB inhibitory synapses on the distal and middle dendrite compartments of the granule cell (GC). The feed-forward inhibition of the middle dendrite is 20% of that of the distal dendrite. The basket cell (BC) receives excitatory inputs through synapses originating from LPP and MPP fiber collaterals and the synapse originating from the granule cell. The axon of the basket cell forms a GABAA inhibitory synapse on the soma compartment. The soma of the granule cell is, therefore, inhibited by the basket cell in feed-forward and feedback fashion.

potential (BAP); 1t is positive (negative) when the presynaptic pulse precedes (follows) the BAP. Each pair of the presynaptic pulse and BAP modifies the coefficient C X in Eq. (7) by the following equation: C X = C X + Cmax F (1t ).

(9)

If C X > Cmax , C X is set equal to Cmax , and if C X < Cmin , C X is set equal to Cmin . Cmax = 0.03 µS and Cmin = 0.004 µS. In Sections 3.1 and 3.3, the initial value of C X is 0.01 µS. All presynaptic spikes were paired to all postsynaptic spikes within ±100 ms to modify the synaptic conductance. 2.4. Dentate granule cell model with inhibitory local circuits A four-compartmental dentate granule cell model with feedforward and feedback inhibitory local circuits was developed to investigate the role of the inhibitory circuits in synaptic competition in Section 3.3. Although at least five kinds of inhibitory interneurons exist in the dentate gyrus (Freund & Buzsáki, 1996), the MOPP and basket cells are concentrated in the present model as representatives of the feed-forward GABAB inhibition and the feed-forward and feedback GABAA inhibitions, respectively (Fig. 2). Axons of the MOPP cells, which receive excitatory inputs through lateral and medial perforant paths, form GABAB inhibitory synapses on the dendrites of the granule cells in the outer twothirds of the dentate molecular layer (Freund & Buzsáki, 1996; Wang & Wojtowicz, 1997), and the feed-forward inhibition of the dendrites in the middle one-third of the dentate molecular layer is weaker than that of the distal dendrites (Wang & Wojtowicz, 1997). Therefore, in the present model, compartments of the distal (j = 1) and middle (j = 2) dendrites are inhibited by the MOPP cell (Fig. 2), and the inhibition of the middle dendrite is 20% of that of the distal dendrite. Basket cells receive excitatory inputs, which originate from lateral and medial perforant paths and axon collaterals of dentate granule cells, and establish GABAA inhibitory synapses on cell bodies and nearby dendrites of the dentate granule cells (Freund & Buzsáki, 1996; Kraushaar & Jonas, 2000). In the present model, the soma compartment (j = 4) of the granule cell is inhibited by the basket cell in feed-forward and feedback fashion, as shown in Fig. 2. Mossy cells in the hilus are excitatory interneurons, which connect granule cells. Mossy cells are, however, not employed

= αz − (αz + βz )z (z : m, h, n).

(11)

Cm , V , gNa , gK , and gL are the membrane capacitance, the membrane potential, the maximal sodium conductance, the maximal potassium conductance, and the leak conductance, respectively. ENa , EK , and EL are the sodium, potassium, and leakage equilibrium potentials, respectively. The gating variable z stands for m, h, and n. The last term on the right-hand side of Eq. (10) is excitatory synaptic currents. The superscript X denotes as follows: LPP → MC and MPP → MC for the MOPP cell; LPP → BC, MPP → BC, and GC → BC for the basket cell. These excitatory synaptic currents are also given by Eqs. (6) and (7). The equilibrium potential Esyn(e) is 0 mV. The coefficients C X of the excitatory synapses formed on these interneurons are constant. See Appendix B for the rate functions, αz and βz , and parameter values. When the model includes inhibitory local circuits, inhibitory synaptic currents flow the granule cell as indicated by the last term on the right-hand side of Eq. (1). The MOPP cells inhibit dendrites of the dentate granule cells in the outer two-thirds of the dentate molecular layer, as mentioned above. The superscript Y of the last term of Eq. (1), therefore, denotes MC → GC1, MC → GC2, and BC → GC4 for the compartments (j = 1, 2, and 4), respectively. The inhibitory current is given by the following equations: Y Y Isyn (i) = gsyn(i) (Esyn(i) − Vj ), Y Y gsyn (i) = C



 exp −

t

τ1,Y



(12)

 − exp −

t

τ2,Y



.

(13)

The equilibrium potential Esyn(i) (−70 mV) is common to the inhibitory synapses. The coefficients C Y of the inhibitory synapses formed on the granule cell is constant. See Appendix B for parameter values. 3. Results 3.1. Cooperation and competition between LPP and MPP synapses when each synapse is subject to an asymmetric STDP rule A periodic pulse train (8 Hz) and a random pulse train (mean frequency = 6, 10, 20, or 40 Hz) were fed to the MPP and LPP synapses, respectively. Each synapse was subject to an asymmetric STDP rule whose ratio of the area of the LTD window to that of the LTP window (LTD/LTP) was 1.2. The initial synaptic conductances of both synapses were the same: C LPP = C MPP = 0.01 µS. Both synapses were enhanced slightly in the early stage P1 (Fig. 3). The conductance of the MPP synapse increased rapidly and reached the maximum level in the following stage P2, while the conductance of the LPP synapse tend to decrease. This trend was almost the same when the mean frequency of the random pulse train fed to the LPP synapse was below 40 Hz. The dominant cause of the synaptic competition is that the distance between the MPP synapse and the soma is shorter than that between the LPP synapse and the soma, as mentioned below. The spike latency of the granule cell was obtained to investigate the cause of the synaptic competition that started at the beginning

H. Hayashi, Y. Nonaka / Neural Networks 24 (2011) 233–246

237

Fig. 3. Cooperation and competition between synapses on middle and distal dendrites of the granule cell. LPP and MPP were stimulated by a random pulse train and a periodic pulse train (8 Hz), respectively. The mean frequency of the random pulse train was (a) 6 Hz, (b) 10 Hz, (c) 20 Hz, or (d) 40 Hz. Each synapse was subject to the asymmetric STDP rule shown in Fig. 1(d). The ratio of the area of the LTD window to that of the LTP window (LTD/LTP) was 1.2. The upper and lower panels in each graph are LPP and MPP synaptic conductances, respectively, as functions of time. Both synaptic conductances were slightly enhanced in the early stage P1. In the following stage P2, the MPP synaptic conductance increased rapidly and reached the maximum level, while the LPP synaptic conductance tend to decrease. Initial synaptic conductances of the LPP and MPP synapses were the same (C LPP = C MPP = 0.01 µS). The granule cell was not inhibited here by the MOPP and basket cells. Ten traces simulated using random pulse trains with different initial conditions are overlaid in each panel.

Fig. 4. Spike latency of the granule cell. Synaptic conductances of the LPP and MPP synapses were constant (C LPP = C MPP = 0.01 µS). (a) Membrane potential of the soma of the granule cell as a function of time. Vertical green and blue arrows indicate LPP and MPP stimuli, respectively. Time differences between the stimuli, TLPP − TMPP , are −8, −4, 0, 4, and 8 ms from the bottom, where TLPP and TMPP are times when the LPP and MPP synapses are stimulated, respectively. The spike latency TLatency is defined by the time from the second stimulus to the peak of the action potential (horizontal arrows). As the depolarization caused by two stimuli was just above the spike threshold, the spike latency was somewhat longer. (b) Spike latency as a function of the time difference, TLPP − TMPP . The spike latency when the MPP stimulus followed the LPP stimulus was shorter than that when the MPP stimulus preceded the LPP stimulus, given that the time differences |TLPP − TMPP | were the same (e.g. spike latencies indicated by the red lines). This implies that the average spike latency at the MPP synapse is shorter than that at the LPP synapse when the LPP and MPP synapses are stimulated by random and periodic pulse trains, respectively, and consequently enhancement of the MPP synaptic conductance is slightly larger than that of the LPP synaptic conductance in the early stage P1 indicated in Fig. 3.

of the following stage P2. Stimuli were applied successively to the LPP synapse (vertical green arrows) and MPP synapse (vertical blue arrows), as shown in Fig. 4(a). As the depolarization caused by two stimuli was just above the spike threshold, the spike latency was somewhat longer. The spike latency (TLatency ) defined by the time spent from the second stimulus to the peak of the action potential (horizontal arrows) was plotted as a function of the time difference, TLPP − TMPP , (Fig. 4(b)). TLPP and TMPP are the times of stimuli indicated by vertical green and blue arrows, respectively. TLatency depended on the order of the stimuli, and was shorter when

the stimulation of the MPP synapse followed the stimulation of the LPP synapse; for example, compared with TLatency at TLPP − TMPP = 10 ms, TLatency at TLPP − TMPP = −10 ms was shorter (Fig. 4(b)). This indicates that the average spike-timing at the MPP synapse is shorter than that at the LPP synapse if the distribution of the time difference, TLPP − TMPP , is symmetric with respect to the central axis (TLPP − TMPP = 0), when the LPP and MPP synapses are stimulated by random and periodic pulse trains, respectively. As the time spent from the first stimulus to the action potential is longer than that from the second stimulus to the action potential,

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Fig. 5. Backpropagated action potentials. As each synaptic conductance was just above the spike threshold (C LPP = C MPP = 0.017 µS), the spike latency was somewhat longer. (a) Action potential (red) elicited in the soma (4) by the LPP stimulus and backpropagated action potentials (dark brown, blue, and green) in the dendrite compartments (3, 2, and 1), respectively. (b) Action potentials (red) elicited in the soma (4) by the MPP stimulus and backpropagated action potentials (dark brown, blue, and green) in the dendrite compartments (3, 2, and 1), respectively. The action potential propagated from the soma compartment (4) to the distal dendrite compartment (1) in 1.6 ms.

the influence of the first stimulus on the plastic change of the synapses is smaller than that of the second stimulus because of the exponentially decay function of the STDP rule. The action potential propagates backward from the soma to the distal dendrite in about 2 ms in a cortical neuron (Stuart & Sakmann, 1994). Although it has not been reported what is the time that the action potential spends to propagate from the soma to the distal dendrites in the dentate granule cell, the action potential elicited in the soma by a synaptic input propagated to the distal dendrite in 1.6 ms and the time spent from the middle dendrite to the distal dendrite was about 0.6 ms in the present granule cell model (Fig. 5). The backpropagated action potential was, therefore, not significantly responsible for the difference between the spiketimings at the LPP and MPP synapses, but the different distances between the synapses and the soma was, as shown in Fig. 4. Histograms of spike-timings were obtained to comprehend the mechanisms of synaptic cooperation and competition (Fig. 6(b)). Although the pulse trains fed to the LPP and MPP synapses did not correlate with each other, all of the spike-timings at the MPP synapse and most of the spike-timings at LPP synapses were positive in the early stage P1 (Fig. 6(b)(i), inside of red circles). This is because the granule cell was barely fired by either LPP or MPP stimulation in the early stage, but was fired by integrated EPSPs evoked by occasional pairing of LPP and MPP pulses (Fig. 7(i)). When the LPP and MPP synapses cooperated to fire the granule cell, the average spike-timing at the MPP synapse was slightly shorter than that at the LPP synapse, as inferred from the spike latency shown in Fig. 4. As a result, the enhancement of the MPP synapse by repetition of occasional pairing was slightly larger than that of the LPP synapse, and finally the granule cell was fired by the stimulation of the MPP synapse alone at the end of the early stage P1. Since the granule cell was fired by the stimulation of the MPP synapse alone at the end of the early stage P1, the MPP synaptic conductance increased rapidly in the following stage P2, as shown

in Fig. 6(a). This is because almost all the spike-timings were positive (i.e. pre → post) at the MPP synapse in the stage P2 (Fig. 6(b)(ii) and (b)(iii), lower panels). In other words, the granule cell was almost always fired by each EPSP evoked at the MPP synapse (Fig. 7(ii) and (iii)). In contrast, spike-timings at the LPP synapse were distributed over the range from −100 to 100 ms (Fig. 6(b)(ii) and (b)(iii), upper panels), since the random pulse train through the LPP synapse did not correlate with the periodic pulse train through the MPP synapse. In other words, the granule cell was barely fired by the stimulation of the LPP synapse alone, and EPSPs evoked at the LPP synapse did not correlate with spikes of the granule cell fired by the stimulation of the MPP synapse. The LPP synapse was consequently not enhanced in competition with the MPP synapse as shown in Fig. 6(a), but tend to be depressed in the stage P2 because the area of the LTD window of the STDP rule was slightly larger than that of the LTP window. As the shape of the STDP rule often depends on the location of synapses on the dendrite, areas of the LTD windows were varied at MPP and LPP synapses (Fig. 8). Initial synaptic conductances of both synapses were the same (0.01 µS, dotted lines). First, areas of the LTD windows were simultaneously varied at both synapses. The LPP synapse was not enhanced when the ratio of the area of the LTD window to that of the LTP window (LTD/LTP) was more than 1.1, though the LPP synapse was enhanced if the ratio was less than 1.1 (Fig. 8(a), left panel). In contrast, the MPP synapse was always enhanced having nothing to do with the ratio (LTD/LTP) (Fig. 8(a), right panel). The ratio (LTD/LTP) in distal dendrites of the dentate granule cell is about 1.2 in the experiments (Lin et al., 2006), as mentioned above. Second, the ratio (LTD/LTP) was varied only at the MPP synapse while being held at 1.2 at the LPP synapse. The LPP synapse was not enhanced but the MPP synapse was, regardless of the ratio (Fig. 8(b)). These results suggest that the competition between the LPP and MPP synapses is not influenced by the ratio (LTD/LTP) of the MPP synapse if the area of the LTD window is slightly larger than that of the LTP window at the LPP synapse. 3.2. Dependence of the synaptic competition on initial synaptic conductances The lateral and medial perforant path fibers terminate on the dendrites of the dentate granule cell in the outer one-third and the middle one-third of the dentate molecular layer, respectively, as mentioned above. Although the supra- and infrapyramidal blades of the dentate gyrus have the same lamination of the projection fibers, the LPP fiber lamina is thick in the suprapyramidal blade and thin in the infrapyramidal blade (Fig. 9(a), green belts), and the MPP fiber lamina is thin in the suprapyramidal blade and thick in the infrapyramidal blade (Fig. 9(a), blue belts) (Tamamaki, 1997). We, therefore, investigated the dependence of the synaptic competition on initial synaptic conductances, supposing that spatially integrated EPSPs in distal dendrites tend to be larger than that in middle dendrites in the suprapyramidal blade, and vise versa in the infrapyramidal blade. The LPP and MPP synapses are subject to the same STDP rules whose ratio (LTD/LTP) is 1.2. When the initial conductance of the MPP synapse was larger than that of the LPP synapse, the MPP synapse was enhanced and the LPP synapse was not (Fig. 9(b), upper left corner of each panel). However, when the initial conductance of the LPP synapse was larger than that of the MPP synapse, the LPP synapse was enhanced and the MPP synapse was not (Fig. 9(b), lower right corner of each panel). When the initial LPP synaptic conductance was considerably large, the LPP synaptic conductance was the first to cross the level where the granule cell was fired by the LPP input alone, although both synaptic conductances increased gradually in the early stage P1 and the rise in LPP synaptic conductance was slower than the rise in MPP synaptic conductance. Consequently,

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Fig. 6. Distribution of spike-timings. Green and blue histograms of spike-timings were obtained from 5 s data at the LPP and MPP synapses, respectively. The LPP synapse was stimulated by a random pulse train (mean frequency = 10 Hz) and the MPP synapse was stimulated by a periodic pulse train (8 Hz). The LPP and MPP synapses were both subject to asymmetric STDP rules in which the ratio of the area of the LTD window to that of the LTP window was 1.2. (a) Cooperation and competition between LPP and MPP synapses. The LPP synapse was not enhanced but the MPP synapse was, as well as in Fig. 3. (b-(i)) Spike-timing distributions obtained in the early stage P1. Upper and lower panels show histograms of spike-timings obtained at LPP and MPP synapses, respectively. Most of the spike-timings were positive at both LPP and MPP synapses (bars in red circles). (b-(ii)) Spike-timing distributions obtained at the beginning of the following stage P2. The distribution of spike-timings was getting sharp at MPP synapse (blue histogram), and the number of pre-post spike pairs also increased. Consequently, the MPP synaptic conductance increased rapidly. In contrast, the spike-timings distributed over the range from −100 to 100 ms at the LPP synapse (green histogram), and the peak of the distribution within the red circle in (b-(i)) was blurred at the beginning of the stage P2. Consequently, EPSPs evoked at the LPP synapse were not correlated with spikes elicited by stimulation of the MPP synapse. The LPP synaptic conductance tend to decrease in the stage P2. (b-(iii)) Spike-timing distributions obtained at the end of the stage P2. The distribution of spike-timings was very sharp at the MPP synapse, and the spike-timings were smaller because of small spike latencies due to enhanced synaptic conductance (blue histogram). In contrast, the spike-timings distributed more uniformly over the range from −100 to 100 ms at the LPP synapse (green histogram).

as most of the spike-timings were positive (i.e. pre → post) at the LPP synapse in the following stage P2, the LPP synaptic conductance increased rapidly. On the other hand, spike-timings were distributed over the range from −100 to 100 ms at the MPP synapse, and the rise in the MPP synaptic conductance was suppressed. These results suggest that the LPP synapse tends to be enhanced in the suprapyramidal blade where the LPP fiber lamina is thick, while the MPP synapse tends to be enhanced in the infrapyramidal blade where the MPP fiber lamina is thick. If both synapses have the same initial synaptic conductance, the MPP synapse was enhanced, while the LPP synapse was not, as shown in Fig. 9(b). This is because the distance from the soma to the distal dendrite is longer than that from the soma to the middle dendrite. Therefore, the initial conductance of the LPP synapse must be considerably larger than that of the MPP synapse so that the LPP synapse alone is enhanced. In the present model, when the ratio of the initial synaptic conductance of the LPP to that of the MPP was above 1.2, only the LPP synapse was enhanced. This is consistent with the anatomical knowledge, which shows that the ratio of the thickness of the LPP fiber lamina to that of the MPP fiber lamina is about 1.3 in the suprapyramidal blade (Tamamaki, 1997). 3.3. Role of inhibitory interneurons in synaptic competition We investigated the role of inhibitory local circuits in synaptic competition because many inhibitory interneurons exist in the

dentate gyrus, which are roughly classified into feed-forward and feedback GABAA inhibitions and feed-forward GABAB inhibition. In the present model, the firing rate of the granule cell increased up to 35 Hz when the mean frequency of the random pulse train fed to the LPP synapse was increased up to 100 Hz (Fig. 10, open circles). The basket cell, which is responsible for feed-forward and feedback GABAA inhibitions, and the MOPP cell, which is responsible for feed-forward GABAB inhibition, exist in the dentate gyrus, as mentioned above. The firing rate of the granule cell was remarkably reduced by both of the basket and MOPP cells when the LPP synapse was stimulated by a random pulse train whose mean frequency was above 20 Hz (Fig. 10, filled circles). Local inhibitory circuits were helpful in moderating responses of the granule cell to unusual high-frequency stimulation. High-frequency firing of the granule cells would be undesirable for the dentate gyrus and the hippocampus; for example, excessive plastic change in the synaptic weight would take place. In the present model, the LPP synapse was not enhanced but the MPP synapse was enhanced by a high-frequency LPP input as well as in Section 3.1 when the initial conductances of LPP and MPP synapses were the same (Fig. 11(a)). The LPP synapse was, however, excessively suppressed when the mean frequency of the random pulse train was unusually high (around 100 Hz). This is because the area of the LTD window of the STDP rule is slightly larger than that of the LTP window. In other words, since the number of prepost and post-pre spike pairs, whose spike-timings are distributed over the range from −100 to 100 ms, increases considerably due

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Fig. 7. Firing patterns of the granule cell model caused by stimulation pulses fed to the LPP and MPP synapses. Upper, middle, and lower traces in each panel show spikes of the granule cell, random pulses fed to the LPP synapse, and regular pulses fed to the MPP synapse, respectively. (i) Traces in the early stage P1. The granule cell fired a spike when LPP and MPP pulses almost coincided with each other; otherwise, the granule cell did not fire and only EPSPs were evoked. Spike-timings were, therefore, positive at both LPP and MPP synapses, as shown in Fig. 6(b)(i). (ii), (iii) Traces at the beginning and the end of the following stage P2, respectively. The granule cell was almost always fired only by EPSPs evoked at the MPP synapse, and stimulation of the LPP synapse barely fired the granule cell. Almost all the spiketimings were, therefore, positive at the MPP synapse, and spike-timings at the LPP synapse distributed over the range from −100 to 100 ms, as shown in Fig. 6(b)(ii) and (b)(iii).

to a high-frequency stimulation, the LPP synaptic conductance is reduced rapidly. Feed-forward and feedback GABAA inhibitions mediated by the basket cell did not prevent the excessive suppression of the LPP synapse (Fig. 11(b), right panel). This is because the duration of the IPSP evoked by the basket cell is only a few milliseconds in addition to a short spike latency of the basket cell. As the mean interspike interval of the granule cell elicited by a 100 Hz LPP stimulation was about 30 ms, the GABAA IPSPs could not sufficiently suppress EPSPs evoked by the high-frequency perforant path input; consequently, the firing rate of the granule cell was not markedly reduced. The fast IPSPs, however, reduced the number of EPSPs whose intervals were very short, and resulted in reducing the number of very small spike-timings. In other words, the fast IPSPs was able to suppress fluctuations of the synaptic conductance resulting from large increments and decrements due to very small spiketimings happening occasionally, and consequently stabilize the time course of plastic change in synapses (compare Fig. 11(a) and (b), central two panels). In contrast, the feed-forward GABAB inhibition mediated by the MOPP cell was sufficient to prevent the excessive suppression of the LPP synapse (Fig. 11(c), right panel). The duration of the IPSP evoked by the MOPP cell was tens of milliseconds, so that EPSPs evoked by a 100 Hz LPP stimulation were readily suppressed, and consequently the LPP synapse was not excessively depressed because of a low firing rate of the granule cell. The feed-forward GABAB inhibition also stabilized the time course of the synaptic conductance (compare Fig. 11(a) and (c), central two panels), because the feed-forward inhibition also reduced the number of small spike-timings. When the granule cell was stimulated by a random pulse train whose mean frequency was 100 Hz and inhibited by both of the basket and MOPP cells, the LPP and MPP synaptic conductances

Fig. 8. Dependence of the LPP and MPP synaptic conductance enhancement on the ratio of the area of the LTD window to that of the LTP window (LTD/LTP). The LPP synapse was stimulated by a random pulse train whose mean frequency was 5 (), 10 (⃝), 20 (△), or 40 (▽) Hz. The MPP synapse was stimulated by a periodic pulse train (8 Hz). The average synaptic conductances after stimulation for 50 s were obtained from ten trials. Bars indicate standard deviations. The initial conductances of the LPP and MPP synapses were 0.01 µS (dotted lines). The LPP and MPP synapses were subject to asymmetric STDP rules. (a) Left and right, LPP and MPP synaptic conductances, respectively. Ratios (LTD/LTP) of the STDP rules for both synapses were changed simultaneously. The MPP synapse was enhanced and the LPP synapse was not when the ratios were more than 1.1. (b) Left and right, LPP and MPP synaptic conductances, respectively. Only the ratio (LTD/LTP) of the STDP rule for the MPP synapse was changed, and the ratio of the STDP rule for the LPP synapse was constant (LTD/LTP = 1.2). The MPP synapse was enhanced and the LPP synapse was not, regardless of the ratio (LTD/LTP) of the STDP rule for the MPP synapse.

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Fig. 9. Schematic picture of lateral and medial perforant path projections (LPP and MPP) from entorhinal cortex layer II to the dentate gyrus and the dependence of the synaptic competition on LPP and MPP initial synaptic conductances. (a) Schematic picture of the lateral and medial perforant paths. The left panel is the schematic picture of the hippocampus, and the right panel depicts a magnified dentate gyrus. The lateral and medial perforant path fibers terminate in the outer one-third and the middle one-third of the dentate molecular layer (m.l.), respectively. Although this lamination structure is the same in the dentate supra- and infrapyramidal blades, the LPP and MPP fiber laminae are thick in the supra- and infrapyramidal blades, respectively (Tamamaki, 1997). g.l., granule cell layer. (b) LPP and MPP synaptic conductances established after the simultaneous stimulation of LPP and MPP synapses for 50 s. Left, LPP synaptic conductance. Right, MPP synaptic conductance. The ordinate and abscissa are initial conductances of the MPP and LPP synapses, respectively. The LPP synapse was stimulated by a random pulse train whose mean frequency was 10 Hz. The MPP synapse was stimulated by a periodic pulse train (8 Hz). Both synapses were subject to the same asymmetric STDP rules, and the ratio of the area of the LTD window to that of the LTP window was 1.2. When the initial conductance of the MPP synapse was not less than that of the LPP synapse, the MPP synapse was enhanced and the LPP synapse was not (upper left corner of each panel). However, when the initial conductance of the LPP synapse was larger than that of the MPP synapse, the LPP synapse was enhanced and the MPP synapse was not (lower right corner of each panel). Given that the effective synaptic conductance is approximately proportional to the thickness of the perforant path fiber lamina, it is suggested that the LPP and MPP synapses are enhanced in the supra- and infrapyramidal blades, respectively.

Fig. 10. Firing rate of the granule cell model as a function of the mean frequency of the LPP stimulation. The LPP and MPP synapses were stimulated by a random pulse train and a regular pulse train (8 Hz), respectively. Synaptic conductances of the LPP and MPP synapses were constant (0.01 µS). The abscissa is logarithmic. Open circles indicate the firing rate of the granule cell without inhibition. Filled circles indicate the firing rate of the granule cell that is inhibited by both of the MOPP cell (GABAB feed-forward inhibition) and the basket cell (GABAA feed-forward and feedback inhibitions). The firing rate was reduced effectively by these inhibitions in the frequency range of the random pulse train above 20 Hz.

showed no change in the present model (Fig. 11(d), right panel). As a large number of EPSPs were suppressed by the feed-forward and feedback inhibitions and the firing rate of the granule cell was below 1 Hz, spike-timings that contributed to visible plastic change were hardly produced. Given that the high-frequency signals result from unusual activity occurring in areas upstream of the dentate gyrus, they do not convey relevant information, and it would be reasonable that no plastic change takes place as shown in Fig. 11(d) (right panel). It has been actually supposed that the dentate gyrus

is a barrier to propagation of seizure activity in areas upstream of the dentate gyrus to the hippocampus (Dreier & Heinemann, 1991; Heinemann et al., 1992; Heinemann, Clusmann, Dreier, & Stabel, 1990). It should, however, be noted that the inhibitions barely influenced the time course of the synaptic conductance when the frequency was below 20 Hz (Fig. 11, left column). When the ratio (LTD/LTP) was above 1.1 and the mean frequency of the LPP input was below 40 Hz, the MPP synapse was enhanced and the LPP synapse was not in the granule cell inhibited by the MOPP and basket cells (Fig. 12) as well as in the granule cell without inhibition (Fig. 8). It should be noted that the standard deviation of the LPP synaptic conductance is much smaller in the granule cell inhibited by the interneurons than in the granule cell without inhibition. 4. Discussion It has been manifested that excitatory synapses on the distal dendrites of the dentate granule cell are subject to an asymmetric STDP rule and the area of the LTD window is slightly larger than that of the LTP window (Lin et al., 2006). Given that synapses on both distal and middle dendrites were subject to such asymmetric STDP rules, both synapses were slightly enhanced in the early stage in the present model, because the granule cell was fired by integrated EPSPs evoked by occasional pairing of MPP and LPP pulses. Then, the MPP synapse was enhanced and the LPP synapse was not in the following stage when the initial conductances of the LPP and MPP synapses were the same. The dominant cause of the synaptic competition is that the distance between the MPP synapse and the soma is shorter than that between the LPP synapse and the soma. Which synapse was enhanced, however, depended on the

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Fig. 11. Influence of the inhibitory interneurons on the time courses of the LPP and MPP synaptic conductances. The LPP synapse was stimulated by a random pulse train whose mean frequency was 10 (left column), 20 (second column from the left), 50 (second column from the right), or 100 (right column) Hz, and the MPP synapse was stimulated by a periodic pulse train (8 Hz). Both synapses were subject to the same STDP rules. The ratio of the area of the LTD window to that of the LTP window (LTD/LTP) was 1.1. The initial conductance of the LPP synapse was the same as that of the MPP synapse (C LPP = C MPP = 0.01 µS). Ten trials are overlaid in each panel. (a) Without inhibition. Fluctuations in time courses of the LPP synaptic conductance increased when the mean frequency of the random pulse train was around 50 Hz, and the LPP synapse was excessively depressed around 100 Hz. (b) With GABAA feed-forward and feedback inhibitions mediated by the basket cell. Fluctuations in the time course of the LPP synaptic conductance was reduced even when the mean frequency of the random pulse train was around 50 Hz. However, the excessive depression of the LPP synapse caused by a 100 Hz stimulation was not prevented. (c) With GABAB feed-forward inhibition mediated by the MOPP cell. The excessive depression by a 100 Hz stimulation was prevented, and the fluctuations in the time course of the LPP synaptic conductance was also reduced. (d) With the GABAB feed-forward inhibition mediated by the MOPP cell in addition to the GABAA feed-forward and feedback inhibitions mediated by the basket cell. Plastic change in the LPP and MPP synapses hardly took place when the frequency of LPP stimulation was around 100 Hz, because the firing rate of the granule cell was less than 1 Hz.

Fig. 12. Dependence of the LPP and MPP synaptic conductance enhancement on the ratio (LTD/LTP). The MOPP cell was responsible for GABAB feed-forward inhibition of the granule cell, and the basket cell was responsible for GABAA feed-forward and feedback inhibitions of the granule cell. The LPP synapse was stimulated by a random pulse train whose mean frequency was 5 (), 10 (⃝), 20 (△), or 40 (▽) Hz. The MPP synapse was stimulated by a periodic pulse train (8 Hz). The initial conductances of the LPP and MPP synapses were 0.01 µS (dotted lines). The average synaptic conductances after stimulation for 50 s were obtained from ten trials. Bars indicate standard deviations. The LPP and MPP synapses were subject to the same asymmetric STDP rules. Ratios (LTD/LTP) of asymmetric STDP rules for the LPP and MPP synapses were changed simultaneously. (a) LPP synaptic conductance. (b) MPP synaptic conductance. The MPP synapse was enhanced and the LPP synapse was not in the range of the ratio (LTD/LTP) above 1.1, even if the MOPP and basket cells were responsible for inhibitions of the granule cell.

initial synaptic conductances. Although only the MPP synapse was enhanced when the initial conductance of the MPP synapse was not less than that of the LPP synapse, the LPP synapse was enhanced and the MPP synapse was not when the initial conductance of the LPP synapse was considerably larger than that of the MPP synapse. Of interest in connection with the above results is the difference of the projection fiber lamination between the supra- and infrapyramidal blades. As mentioned above, lateral perforant path fibers conveying non-spatial information and medial perforant path fibers conveying spatial information terminate on dendrites

of the dentate granule cells in the outer one-third and the middle one-third of the dentate molecular layer, respectively (Burwell & Amaral, 1998; Hjorth-Simonsen, 1972; Hjorth-Simonsen & Jeune, 1972; McNaughton & Barnes, 1977; Steward, 1976; Wyss, 1981). Although the supra- and infrapyramidal blades of the dentate gyrus have the same lamination of the projection fibers, the LPP and MPP fiber laminae are thick in the supra- and infrapyramidal blades, respectively (Tamamaki, 1997). Therefore, spatially integrated, large EPSPs would be evoked in distal dendrites in the suprapyramidal blade and in middle dendrites

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Fig. 13. Schematic pictures illustrating the process for opening gates for LPP and MPP signals. (a), (b) Initial state. As stimulation of either LPP or MPP synapses does not fire the granule cell, information from the entorhinal cortex (green and blue arrows) is not transmitted to the hippocampus. (c) Simultaneous stimulation of LPP and MPP synapses may fire the granule cell because of integrated EPSPs. When the LPP and MPP synapses are stimulated by random and periodic pulse trains, respectively, EPSPs are evoked occasionally at almost the same time at individual synapses, and may fire the granule cell. Consequently, information from the entorhinal cortex is transmitted to the hippocampus through the dentate gyrus on occasion (green and blue arrows passing through the dentate gyrus). The LPP and MPP synapses are, therefore, enhanced little by little in both of the dentate blades, as a result of repetition of occasional firing. (d), (e) Finally, the granule cell in the suprapyramidal (infrapyramidal) blade is fired by LPP (MPP) synaptic input alone (green arrow in (d) and blue arrow in (e)). Individual gates, therefore, open for the MPP and LPP signals, and relevant spatial and non-spatial pieces of information from the entorhinal cortex are transmitted efficiently to the hippocampus. It is suggested that the dentate gyrus selects spatial and non-spatial pieces of information transmitted simultaneously to the dentate gyrus from the entorhinal cortex through the synaptic cooperation and opens gates for them through the synaptic competition.

in the infrapyramidal blade, given that signals conveying each information are transmitted concurrently through many parallel fibers of each perforant path. In fact, activation of many afferent fibers is required to discharge the granule cell, because mean EPSP amplitude resulting from single afferent fiber activation has been estimated as only 0.1 mV (McNaughton et al., 1981). It could, therefore, be assumed that the effective conductance of the LPP synapse is larger than that of the MPP synapse in the suprapyramidal blade, whereas the effective conductance of the MPP synapse is larger than that of the LPP synapse in the infrapyramidal blade. Taking these anatomical data and the present results together, it is suggested that the LPP and MPP synapses tend to be enhanced in the supra- and infrapyramidal blades, respectively, if spatial and non-spatial pieces of information are transmitted simultaneously through individual perforant path fiber bundles. The gating function of the dentate gyrus suggested by the present study is summarized in Fig. 13. It would be plausible to assume that the granule cell is not fired by an EPSP evoked by either LPP or MPP stimulus (Fig. 13(a) and (b)) while the granule cell is fired by an integrated EPSP evoked by simultaneous LPP and MPP stimuli and information is transmitted to the hippocampus (Fig. 13(c)). When the LPP and MPP synapses are stimulated simultaneously by random and periodic pulse trains,

respectively, the LPP and MPP synapses are enhanced gradually in both supra- and infrapyramidal blades. This is because EPSPs are evoked occasionally at almost the same time at individual synapses and an integrated EPSP fires the granule cell. Repetition of occasional firing enhances the LPP and MPP synapses little by little in both blades. Finally, the granule cell in the suprapyramidal (infrapyramidal) blade is fired by LPP (MPP) synaptic input alone (Fig. 13(d) and (e)). This implies that gates are open for the LPP signal in the suprapyramidal blade and for the MPP signal in the infrapyramidal blade. In other words, spatial information accompanied by non-spatial information may be selected by cooperation between synapses located on distal and middle dendrites of granule cells, and pathways for spatial and nonspatial pieces of information may be provided by competition between those synapses in the infra- and suprapyramidal blades, respectively. After the gates are open, a pair of signals carrying spatial and non-spatial pieces of information would be efficiently transmitted to the hippocampal CA3 through individual pathways, and the two pieces of information would be processed in CA3 and CA1 in order to store a sequence of significant places with valuable non-spatial information such as odor. Present model suggests that the dentate gyrus opens gates for the pair of spatial and non-spatial pieces of information. It has been reported that both of the LPP and MPP synapses are enhanced when LPP and MPP are stimulated simultaneously

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by periodic pulse trains (100–400 Hz) in the experiments using anesthetized rats (McNaughton, Douglas, & Goddard, 1978; Wang & Wojtowicz, 1997). These stimulus frequencies are quite high, considering that the firing rate of neurons in the entorhinal cortex is in the theta or beta range. Moreover, both stimuli fed simultaneously to the LPP and MPP are periodic pulse trains whose frequencies are the same. The present model also showed that both of the LPP and MPP synapses were enhanced when the same periodic pulse trains, whose frequencies were in the theta range, were fed to the LPP and MPP synapses (data not shown). This is because spike-timings are always positive (i.e. pre → post) at both synapses. It has also been reported that LTP is induced at MPP synapses while LTD is induced at LPP synapses when single pulses fed to LPP are interleaved between high-frequency bursts fed to MPP at intervals of 200 ms in the experiments using anesthetized rats (Christie & Abraham, 1992; Christie, Stellwagen, & Abraham, 1995). Given that the probability of granule cell firing caused by bursts is higher than that caused by single pulses and spike-timing is a major cause of synaptic plasticity, almost all of the spike-timings would be positive (i.e. pre → post) and negative (i.e. post → pre) at MPP and LPP synapses, respectively. Consequently, LTP and LTD would be induced at MPP and LPP synapses, respectively. Activity of neurons in the entorhinal cortex, however, suggests that input to the dentate gyrus would be rather trains of spikes than trains of bursts. A spiking neuron model of the granule cell receiving LPP and MPP synaptic inputs has been proposed to reproduce homosynaptic LTP and heterosynaptic LTD induced by high-frequency MPP stimulation (400 Hz) in the experiments done by Abraham, Mason-Parker, Bear, Webb, and Tate (2001) (Benuskova & Abraham, 2007). Those synapses on the granule cell model are subject to a STDP rule combined with the Bienenstock, Cooper, and Munro (BCM) sliding threshold, and are stimulated by trains of high-frequency (400 Hz) bursts. If the synapses were stimulated simply by the trains of high-frequency bursts, the firing rate of the granule cell would increase. This would lead to the increase in the sliding BCM threshold resulting in increase in the area of the LTD window of the STDP rule, and consequently homosynaptic LTP would not be induced but homosynaptic LTD. In order to avoid this difficulty, the trains of bursts are fed to either LPP or MPP at intervals of 30–60 s in the LTP induction period, and uncorrelated low-frequency noises are fed to both perforant paths in the intervals between trains of bursts in order to reduce the firing rate of the granule cell during the LTP induction period. Consequently, the sliding BCM threshold is reduced, the area of the LTP window of the STDP rule is increased, and then the homosynaptic LTP is reproduced successfully. However, as mentioned above, it would be plausible that inputs through LPP and MPP are trains of spikes around the theta frequency range, rather than trains of highfrequency bursts, taking account of activity of EC neurons. Moreover, the effect of the distance between synapses and the soma is not taken into account in the spiking neuron model because it is a simple lump model without dendrites. A multi-compartmental model with dendrites would be necessary to investigate cooperation and competition between LPP and MPP synapses. The dentate gyrus is not the only area where synaptic competition takes place. Synaptic competition may take place if afferents originating from different sites are localized on dendrites of target neurons and distances from the synapses to the soma are different. For example, Schaffer collaterals from CA3 pyramidal cells and perforant path fibers from entorhinal cortex layer III terminate on the proximal and distal dendrites of the CA1 pyramidal cells, respectively. Mossy fibers from the dentate gyrus and perforant path fibers from entorhinal cortex layer II also terminate on proximal and distal dendrites of CA3 pyramidal

cells, respectively. Competitions between those synapses and their functional roles are interesting future issues which still remain to be clarified. The firing rate of the present granule cell model without feed-forward and feedback inhibition increased up to 35 Hz when the mean frequency of stimulation of the LPP synapse was increased up to 100 Hz. Such unusual high-frequency firing of the granule cell excessively depressed the LPP synapse. Moreover, time courses of the LPP synaptic conductance were different in every trial when the frequency of the LPP stimulation was around 50 Hz. Inhibitions by the MOPP and basket cells were effective in reducing the bad influences of the high-frequency stimulation and/or very small spike-timings. Feed-forward GABAB inhibition mediated by the MOPP cell was effective in reducing the firing rate of the granule cell and preventing excessive synaptic depression caused by synaptic competition. Feed-forward and feedback GABAA inhibitions suppressed fluctuations of the LPP synaptic conductance caused by very small spike-timings and stabilized the time course of the synaptic conductance. These inhibitions contribute to the moderate and stable plastic change in synaptic conductances. Acknowledgements The authors are grateful to Dr. Katsumi Tateno, Dr. Motoharu Yoshida, and Dr. Toshikazu Samura for valuable comments on the manuscript. This work was supported by Grant-in-Aid for Scientific research (C) (19500126) granted to Dr. Hatsuo Hayashi by the Japan Society for the Promotion of Science. Appendix A. Four-compartmental granule cell model Rate functions of the four-compartmental granule cell model are as follows:

−0.3(V + 47)

αm =

exp(−(V + 43)/5) − 1 0.23

αh =

exp((V + 65)/20)

αnf = αns = αk = αl = αa =

,

,

−0.07(V + 18) exp(−(V + 18)/6) − 1

−0.028(V + 32) exp(−(V + 32)/6) − 1

βh =

βnf =

,

βns =

,

βk =

−0.05(V + 25) ,

βl =

0.6(19.26 − V ) exp((19.26 − V )/10) − 1

αb = 10−6 exp(−V /16.26), αc =

0.19(19.88 − V )

,

,

0.264 exp((V + 43)/40) 0.1056 exp((V + 55)/40)

, ,

0.09(V + 15)

αe =

1 exp((39 − V )/10) + 1 15.69(81.5 − V )

βa = 0.009 exp(−V /22.03), 1 exp((29.79 − V )/10) + 1

,

βc = 0.046 exp(−V /20.73),

, ,

,

,

αd = 1.6 × 10−4 exp(−V /48.4), βd =

,

,

exp((V + 15)/8) − 1 0.06

exp(−(V + 68)/12) + 1

βb =

exp((19.88 − V )/10) − 1

0.3(V + 14) exp((V + 14)/5) − 1 3.33

exp(−(V + 12.5)/10) + 1

,

exp(−(V + 25)/15) − 1 0.00015 exp((V + 13)/15)

βm =

βe = 0.29 exp(−V /10.86),

exp((81.5 − V )/10) − 1 0.11 αr = 8.0, βr = , exp((V − 35)/14.9)

H. Hayashi, Y. Nonaka / Neural Networks 24 (2011) 233–246 Table A.1 Parameter values of the four-compartmental granule cell model. Parameters

Cm (µF/cm2 ) gNa (mS/cm2 ) gfKDR gsKDR gKA gTCa gNCa gLCa gBK gSK ENa (mV) EK EL C LPP (µS) τ1,LPP (ms)

τ2,LPP C MPP

τ1,MPP τ2,MPP

Table B.1 Parameter values of synapses in excitatory and inhibitory local circuits. Soma (j = 4)

X

C X (µS)

τ1,X (ms)

τ2,X (ms)

1.6

1.0

10

13

120

LPP → MC MPP → MC LPP → BC MPP → BC GC → BC

0.004 0.004 0.013 0.013 0.013

5.5 5.5 5.5 5.5 0.3

1.5 1.5 1.5 1.5 0.6

1 8 0 1.5 1 0 1.9 0 55 −73 −68

1 6 0 1.5 1 0.5 1.9 0 55 −73 −68

4 6 0 1 1 7.5 1.5 0.01 55 −73 −68

16 6 10 0.3 2 7 0.4 0.27 55 −73 −68

Y

C Y (µS)

τ1,Y (ms)

τ2,Y (ms)

MC → GC1 MC → GC2 BC → GC4

0.002 0.0004 0.0016

60 60 5.5

10 10 0.26

Plastic 5.5 1.5 – – –

– – – Plastic 5.5 1.5

– – – – – –

– – – – – –

Dendrite Distal (j = 1)

Middle (j = 2)

Proximal (j = 3)

1.6

1.6

0

References

Table A.2 Compartment parameters. Rm : membrane resistance, RA : resistance along the axial direction of the compartment, l: length, φ : diameter. The leak conductance of each compartment was obtained by the following equation: RL = l · πφ/Rm . Parameters

Rm ( cm2 ) RA ( cm) l (µm) φ (µm)

αq = βq =

Soma (j = 4)

Dendrite Distal (j = 1)

Middle (j = 2)

Proximal (j = 3)

15 000 210 150 3

15 000 210 150 3

15 000 210 150 3

0.00246 exp(−(12log ([Ca2+ ]) + 28.48)/4.5) 0.006 exp((12log ([Ca2+ ]) + 60.4)/35)

25 000 210 16.8 16.8

,

.

Parameter values are shown in Tables A.1 and A.2. Appendix B. Single-compartmental model of the MOPP cell and the basket cell Rate functions and parameter values are common to the MOPP cell and the basket cell. Rate functions are as follows:

αm =

0.52(V + 49) 1 − exp(−(V + 49)/4)

,

βm =

0.48(V + 27) exp((V + 27)/5) − 1

,

αh = 0.054 exp(−(V + 50)/18), βh = αn =

245

3 1 + exp(−(V + 27)/5) 0.052(V + 52) 1 − exp(−(V + 52)/5)

, ,

βn = 0.3 exp(−(V + 57)/40).

Parameter values of the inhibitory cells: Cm = 1 µF/cm2 , gNa = 120 mS/cm2 , gK = 20 mS/cm2 , gLeak = 0.7 mS/cm2 , ENa = 50 mV, EK = −80 mV, ELeak = −67 mV, l = 16.0 µm, φ = 16.0 µm. Parameter values of synapses in excitatory and inhibitory local circuits are shown in Table B.1.

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