Embed Size (px)
Citation preview
Scharfman (Ed.)
Progress in Brain Research, Vol. 163
ISSN 0079-6123
Copyright r 2007 Elsevier B.V. All rights reserved
CHAPTER 35
Modeling the dentate gyrus
Robert J. Morgan1,�, Vijayalakshmi Santhakumar2 and Ivan Soltesz1
1Department of Anatomy and Neurobiology, 193 Irvine Hall, University of California, Irvine, CA 92697, USA2Department of Neurology, David Geffen School of Medicine, University of California, Los Angeles, CA, USA
Abstract: Computational modeling has become an increasingly useful tool for studying complex neuronalcircuits such as the dentate gyrus. In order to effectively apply computational techniques and theories toanswer pressing biological questions, however, it is necessary to develop detailed, data-driven models.Development of such models is a complicated process, akin to putting together a jigsaw puzzle with thepieces being such things as cell types, cell numbers, and specific connectivity. This chapter provides awalkthrough for the development of a very large-scale, biophysically realistic model of the dentate gyrus.Subsequently, it demonstrates the utility of a modeling approach in asking and answering questions aboutboth healthy and pathological states involving the modeled brain region. Finally, this chapter discussessome predictions that come directly from the model that can be tested in future experimental approaches.
Keywords: computational model; epilepsy; granule cell; interneuron; mossy cell; sclerosis
The dentate gyrus in the mammalian brain is acomplex neuronal circuit that is thought to serveas a gate for activity propagation throughout thelimbic system (Heinemann et al., 1992; Lothman etal., 1992). Scientific understanding of such com-plex systems has traditionally been obtainedthrough use of animal models, culture systems,and numerous other experimental approaches. Inthe past several decades, however, computationalmodeling has become an increasingly useful toolfor studying and understanding neuronal networkstructure and function. In fact, the dentate gyrushas been the subject of a number of recent com-putational models looking at such issues as mossyfiber sprouting (Lytton et al., 1998; Santhakumaret al., 2005; Dyhrfjeld-Johnsen et al., 2006) andhilar cell loss (Santhakumar et al., 2005; Dyhrf-jeld-Johnsen et al., 2006), interneurons and
shunting inhibition (Bartos et al., 2001; Vida etal., 2006), homeostatic plasticity (Howard et al.,2006), and topological alterations during epilepto-genesis (Dyhrfjeld-Johnsen et al., 2006). Thesestudies demonstrate the importance and utility ofcomputational modeling in contributing to ourunderstanding of the dentate gyrus both in healthyanimals and in pathological states such as epilepsy.
In this chapter, we will use the analogy of ajigsaw puzzle to walk through the process ofmodeling the dentate gyrus neural network. In thefirst and second parts, ‘‘Finding the right pieces’’and ‘‘Putting the pieces together,’’ we will discusswhat types of considerations are necessary whenbuilding a large-scale, data-driven model of a nor-mal, healthy rat dentate gyrus (all data presentedin this chapter comes from the rat dentate). Then,in ‘‘The big picture’’ we will examine how such amodel is useful for studying the effects of struc-tural and functional network alterations that occurduring epileptogenesis. Finally, we will conclude
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
3B2v8:06a=w ðDec 5 2003Þ:51cXML:ver:5:0:1 PBR� V163 : 63035 Prod:Type:
pp:6392659ðcol:fig::NILÞED:
PAGN: SCAN:
�Corresponding author. Tel.: +(949) 824-3967; E-mail: rjmor-
DOI: 10.1016/S0079-6123(07)63035-0 639
with ‘‘Tackling future puzzles and problems’’ bydiscussing future directions for dentate modelingand some predictions that can be tested experi-mentally.
Finding the right pieces
Assembling a computational model is much likeputting together a puzzle. The pieces include celltypes, cell numbers, synapses, and other cellularinteractions such as gap junctions, and distribu-tions of axons and dendrites. These are assembledin a specific fashion upon a backdrop that includesthe software necessary for implementing the modeland the hardware, the physical computer andmemory used for the model calculations. Just asthe number and size of pieces in a puzzle varies,the number of components and the details of thosecomponents vary dramatically in computationalmodels. The precise amount of detail necessary ina model depends directly on the question themodel is designed to answer. Examining the effectsof the loss of specific subgroups of cell types, forexample, requires the model to capture the relativechanges in cell densities, necessitating the devel-opment of large-scale models. The first two sec-tions of this chapter will provide an overview ofthe general approach for developing such a large-scale model to study both the healthy rat dentategyrus and the effects of epileptogenesis with em-phasis on mossy fiber sprouting and hilar cell loss.
With over a million cells and a billion synapsesamongst at least eight distinct cell types in thedentate gyrus, the first step in developing a modelis to determine the anatomy of the dentate net-work. This can be accomplished by creating aconnection matrix of the dentate gyrus (Pattonand Mcnaughton, 1995), which can be thought ofas the border or backbone of our puzzle. The ma-trix itself contains a number of distinct pieces thatare outlined here and described in detail below.The first piece is the cell type. Eight types of dent-ate cells can be identified as anatomically well-de-scribed: granule cells (GCs), mossy cells (MCs),basket cells, axo-axonic cells, molecular layer cellswith axonal projections to the perforant path(MOPP cells), hilar cells with axonal projections to
the perforant path (HIPP cells), hilar cells withaxonal projections to the commissural-associatio-nal pathway (HICAP cells), and interneuron-spe-cific (IS) cells (Fig. 1) (Santhakumar and Soltesz,2004). The second piece is the number of cells ofeach type, data that can be estimated from pub-lished data (Table 1). The third piece is the specificconnectivity between cell types. This quantifiesprecisely how many postsynaptic cells among eachof the eight cell types a single presynaptic neuronof a given type innervates (e.g., from the third row,second column in Table 1; a single basket cell in-nervates approximately 1250 GCs; mean andranges are indicated, with references). The finalpiece required for constructing the connection ma-trix of the dentate is the spatial constraint in cell-to-cell connectivity. For each cell type, the extentof the axons of single cells along the septo-tempo-ral axis of the dentate gyrus can be determinedfrom in vivo single cell fills published in the liter-ature (Fig. 2).
The first piece: cell types
Determination of cell type is based on several fac-tors including: (1) the nature of the neurotrans-mitter released; (2) location in the laminarstructure of the dentate gyrus; (3) morphologicalfeatures such as shape of the soma, dendritic ar-bor, and axonal distribution pattern; and (4) pres-ence of specific markers such as calcium-bindingproteins and neuropeptides (for detailed descrip-tion of cell type discrimination see Freund andBuzsaki, 1996). According to these criteria, twoexcitatory cell types (GCs and MCs) and at leastsix distinct inhibitory interneurons can be identi-fied in the dentate gyrus (Fig. 1).
The second piece: cell numbers
A practical approach for determining cell numbersfor various cell types involves first identifying thecell layers and the total number of neurons in eachlayer. Then, it is possible to estimate subtypenumbers by estimating the percentage of neuronsthat express specific markers (Buckmaster et al.,1996, 2002a; Nomura et al., 1997a, b). The dentate
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
640
gyrus is composed of three cell layers: the molec-ular layer, granule cell layer, and the hilus (Fig. 1).The GCs are the primary projection cells of thedentate gyrus. These are small, densely packedcells, typically located in the granule cell layer ofthe dentate gyrus. The number of GCs in the ratdentate gyrus is approximately 1,000,000 (Gaarsk-jaer, 1978; Boss et al., 1985; West, 1990; Pattonand Mcnaughton, 1995; Freund and Buzsaki,1996). The other major excitatory cell type, theMC, are located in the hilus and do not express theGABA synthetic enzyme glutamic acid dec-arboxylase (GAD). Buckmaster and Jongen-Relo
(1999) estimated the number of GAD-mRNA neg-ative neurons in the dentate hilus (presumed MC)as approximately 30,000. The GABAergic inter-neurons are located in all three layers of the dent-ate gyrus. These include the basket cells,parvalbumin-positive (PV) axo-axonic cells (whoseaxon terminals project exclusively to the axon in-itial segment of excitatory cells), somatostatin-positive HIPP cells (Freund and Buzsaki, 1996;Katona et al., 1999), nitric oxide synthase-positiveHICAP cells (Freund and Buzsaki, 1996), andaspiny and calretinin-positive hilar IS cells (Gulyaset al., 1996). The number of GABAergic cell types
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
Fig. 1. Schematic of the basic circuitry of the dentate gyrus. Relational representation of the healthy dentate gyrus illustrating the
network connections between the eight major cell types (GC, granule cell; BC, basket cell; MC, mossy cell; AAC, axo-axonic cells;
MOPP, molecular layer interneurons with axons in perforant-path termination zone; HIPP, hilar interneurons with axons in perforant-
path termination zone; HICAP, hilar interneurons with axons in the commissural/associational pathway termination zone; IS, in-
terneuron selective cells). The schematic shows the characteristic location of the various cell types within the three layers of the dentate
gyrus. Note, however, that this diagram does not indicate the topography of axonal connectivity or the somato-dendritic location of
the synapses.
641
along the granule cell-hilar border and in the hiluscan be determined based on published histochem-ical data (Buckmaster et al., 1996, 2002a; Nomuraet al., 1997a, b). Buckmaster and Jongen-Relo(1999) estimated the total number of GABAergicneurons in the molecular layer of the dentate gyrusas approximately 10,000. An even distribution be-tween inner, medial, and outer molecular layers isassumed, yielding 4000 MOPP cells with somatalocated in the inner molecular layer (Han et al.,1993). Note that this estimate excludes the molec-ular layer interneurons that project primarily out-side of the dentate gyrus such as the outer
molecular layer interneurons projecting to thesubiculum (Ceranik et al., 1997).
The third piece: connectivity between cell types
In the past decade, a vast amount of high-qualitydata about the connectivity of the dentate gyrushas been collected, and this data serves as an in-valuable resource in constructing the cell-type spe-cific connectivity matrix for the dentate gyrus. Theconnectivity for each cell type is summarized inTable 1 and described below. Each value was
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
Table 1. Connectivity matrix for the neuronal network of the control dentate gyrus
Granule cells Mossy cells Basket cells Axo-axonic ells MOPP cells HIPP cells HICAP cells IS cells
Granule cells X 9.5 15 3 X 110 40 20
(1,000,000) X 7–12 10–20 1–5 X 100–120 30–50 10–30
Ref. [1–5] Ref. [6] Ref. [7] Ref. [6–9] Ref. [6,7,9] Ref. [6] Ref. [4,10,11] Ref. [4,7,10,11] Ref. [7]
Mossy cells 32,500 350 7.5 7.5 5 600 200 X
(30,000) 30,000–35,000 200–500 5–10 5–10 5 600 200 X
Ref. [11] Ref. [4,11–13] Ref. [12,13] Ref. [13] Ref. [13] Ref. [14] Ref. [12,13] Ref. [12,13] Ref. [15]
Basket cells 1250 75 35 X X 0.5 X X
(10,000) 1000–1500 50–100 20–50 X X 0–1 X X
Ref. [16,17] Ref. [4,16–19] Ref.
[11,16,17,19]
Ref.
[16,17,20,21]
Ref. [18] Ref. [18] Ref. [18] Ref. [18] Ref. [10,20]
Axo-axonic
cells
3000 150 X X X X X X
(2000) 2000–4000 100–200 X X X X X X
Ref. [4,22] Ref. [4,18,22] Ref.
[4,5,11,14,23]
Ref. [5,18] Ref. [5,18] Ref. [5,18] Ref. [5,18] Ref. [5,18] Ref. [5,18,19]
MOPP cells 7500 X 40 1.5 7.5 X 7.5 X
(4000) 5000–10,000 X 30–50 1–2 5–10 X 5–10 X
Ref. [11,14] Ref. [14] Ref. [14,24] Ref. [14,25] Ref. [14,26] Ref. [14,25] Ref. [14,20,25] Ref. [14,25] Ref. [14,15]
HIPP cells 1550 35 450 30 15 X 15 X
(12,000) 1500–1600 20–50 400–500 20–40 10–20 X 10–20 X
Ref. [11] Ref. [4,11,20] Ref.
[4,11,12,27,28]
Ref. [4,11,20] Ref. [20,25] Ref. [25] Ref. [14,20,25] Ref. [25] Ref. [15,20]
HICAP cells 700 35 175 X 15 50 50 X
(3000) 700 30–40 150–200 X 10–20 50 50 X
Ref. [5,29,30] Ref. [4,11,20] Ref. [20] Ref. [4,11,20] Ref. [20] Ref. [14,20] Ref. [20] Ref. [20]
IS cells X X 7.5 X X 7.5 7.5 450
(3000) X X 5–10 X X 5–10 5–10 100–800
Ref. [15,29,30] Ref. [15] Ref. [15] Ref. [15,19] Ref. [15] Ref. [19] Ref. [19] Ref. [15]
Notes: Cell numbers and connectivity values were estimated from published data for granule cells, mossy cells, basket cells, axo-axonic cells, molecular
layer interneurons with axonal projections to the perforant path (MOPP), hilar interneurons with axonal projections to the perforant path (HIPP), hilar
interneurons with axonal projections to the commissural/associational pathway (HICAP) and interneuron specific cells (IS). Connectivity is given as
number of connections to a postsynaptic population (row 1) from a single presynaptic neuron (column 1). The average number of connections used in the
1:1 structural model is given in bold. Note, however, that the small world structure (see Section ‘‘Structural alterations in the dentate during epile-
ptogenesis’’) was preserved even if only the extreme low or the extreme high estimates were used for the calculation of L and C. References given in table
correspond to: 1Gaarskjaer (1978), 2Boss et al. (1985), 3West (1990), 4Patton and McNaughton (1995), 5Freund and Buzsaki (1996), 6Buckmaster and
Dudek (1999), 7Acsady et al. (1998), 8Geiger et al. (1997), 9Blasco-Ibanez et al. (2000), 10Gulyas et al. (1992), 11Buckmaster and Jongen-Relo (1999),12Buckmaster et al. (1996), 13Wenzel et al. (1997), 14Han et al. (1993), 15Gulyas et al. (1996), 16Babb et al. (1988), 17Woodson et al. (1989), 18Halasy and
Somogyi (1993), 19Acsady et al. (2000), 20Sik et al. (1997), 21Bartos et al. (2001), 22Li et al. (1992), 23Ribak et al. (1985), 24Frotscher et al. (1991), 25Katona
et al. (1999), 26Soriano et al. (1990), 27Claiborne et al. (1990), 28Buckmaster et al. (2002a), 29Nomura et al. (1997a), 30Nomura et al. (1997b).
642
determined by a detailed survey of the anatomicalliterature and was based on an assumption of uni-form bouton density along the axon of the presy-naptic cell. This assumption is in agreement withthe in vivo data of Sik et al. (1997), and it greatlysimplifies the estimation of connectivity from an-atomical data on axonal length and synapse den-sity per unit length of axon.
Granule cells
Mossy fibers (GC axons) in a healthy rat dentategyrus are primarily restricted to the hilus (97%),with few collaterals (3%) in the GC layer (Buck-master and Dudek, 1999). In addition to MC (Ac-sady et al., 1998), mossy fibers have also beenshown to contact basket cells (Buckmaster andSchwartzkroin, 1994; Geiger et al., 1997) and PV
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
Fig. 2. Gaussian fits to experimentally determined distributions of axonal branch length used in construction of the models of the
dentate gyrus. (A) Plot shows the averaged axonal distribution of 13 granule cells (Buckmaster and Dudek, 1999) and the corre-
sponding Gaussian fit. (B) Fit to the septo-temporal distribution of axonal lengths of a filled and reconstructed basket cell (Sik et al.,
1997). (C) Fit to the axonal distribution of a CA1 axo-axonic cell (Li et al., 1992). (D) Gaussian fit to the averaged axonal distributions
of three HIPP cells from gerbil (Buckmaster et al., 2002a, b)AU :1 . (E) Fit to averaged axonal distributions of three mossy cells illustrates the
characteristic bimodal pattern of distribution (Buckmaster et al., 1996). (F) Histogram of the axonal lengths of a HICAP cell along the
long axis of the dentate gyrus (Sik et al., 1997) and the Gaussian fit to the distribution. All distributions were based on axonal
reconstruction of cells filled in vivo. In all plots, the septal end of the dentate gyrus is on the left (indicated by negative coordinates) and
the soma is located at zero.
643
interneurons (Blasco-Ibanez et al., 2000). With atotal of 400–500 synaptic contacts made by a sin-gle mossy fiber (Acsady et al., 1998), the 3% ofeach axon located in the GC layer (Buckmasterand Dudek, 1999) is estimated to contact 15 basketcells and 3 axo-axonic cells. In the hilus, a singleGC forms large, complex mossy fiber boutons thatinnervate 7–12 MC (Acsady et al., 1998), while anestimated 100–150 mossy fiber terminals target hi-lar interneurons with approximately one synapseper postsynaptic interneuron (Acsady et al., 1998).Gulyas et al. (1992) estimated that a single spinycalretinin-positive cell (presumed HIPP cell) iscontacted by approximately 9000 GCs. With12,000 HIPP cells and 1,000,000 GCs, each GCcan be estimated to contact approximately 110HIPP cells and 40 HICAP cells. Additionally, inagreement with the presence of mossy fiber termi-nals on aspiny calretinin-positive interneurons(Acsady et al., 1998), 15 mossy fibers are expectedto synapse onto IS cells. Since mossy fibers avoidthe molecular layer (Buckmaster and Dudek,1999) in the healthy dentate gyrus, it is assumedthat they do not contact MOPP cells. However, inanimal models of temporal lobe epilepsy, sproutedmossy fibers have been shown to contact up to 500postsynaptic GCs (Buckmaster et al., 2002b).
Mossy cells
A single filled mossy cell axon has been reported tomake 35,000 synapses in the inner molecular layer(Buckmaster et al., 1996; Wenzel et al., 1997). As-suming a single synapse per postsynaptic cell, asingle mossy cell is estimated to contact30,000–35,000 GCs. Of the 2700 synapses madeby a single mossy cell axon in the hilus, approx-imately 40% target GABA-negative neurons(Wenzel et al., 1997). As each mossy cell is esti-mated to make 1–5 synaptic contacts on a singlepostsynaptic mossy cell (Buckmaster et al., 1996),it is estimated that each mossy cell contacts ap-proximately 350 other MCs (this is likely to be agenerous estimate since it is based on the assump-tion that all GAD negative somata in the hilusrepresent MCs). The remaining 60% of the hilarmossy cell axons target GABA-positive cells
(Buckmaster et al., 1996; Wenzel et al., 1997),with no reports demonstrating mossy cell synapsesonto IS cells. Assuming that there is no preferen-tial target selectivity between HIPP and HICAPcells and that each postsynaptic hilar interneuronreceives two synaptic contacts from a single mossycell axon (Buckmaster et al., 1996), each mossy cellis estimated to contact 600 HIPP and 200 HICAPcells. There is very low mossy cell to interneuronconnectivity in the inner molecular layer (Wenzelet al., 1997); MCs could contact 5–10 basket andaxo-axonic cells and approximately 5 MOPP cellswith somata in the inner molecular layer (Han etal., 1993).
Basket cells
In the CA3 region of the rat hippocampus, eachprincipal cell is contacted by approximately 200basket cells (Halasy and Somogyi, 1993), but a GCin the dentate could be contacted by as few as 30basket cells. Assuming that each of the 1,000,000GCs is contacted by 115 basket cells each making1–20 synaptic connections (Halasy and Somogyi,1993; Acsady et al., 2000), it can be estimated thateach basket cell contacts approximately 1250 GCs.MCs receive 10–15 basket cell synapses (Acsady etal., 2000), resulting in an estimate of 75 basket cellto mossy cell synapses. Approximately 1% of the11,000 synapses made by a single basket cell axonin the GC layer are onto other basket cells (Sik etal., 1997) with 3–7 synapses per postsynaptic cell(Bartos et al., 2001). Consequently, each basketcell in the dentate gyrus contacts approximately 35other basket cells. Since hilar and molecular layerinterneurons are not a major target of basket cells(Halasy and Somogyi, 1993), a single basket cellmay contact 0–1 HIPP cells. Similarly, the basketcell synapses onto axo-axonic cells, HICAP, andMOPP cells are assumed to be negligible. As PVcells preferentially contact other PV-positive cellsin the hilus (Acsady et al., 2000), we assume thatbasket cells do not contact calretinin-positive IScells (Gulyas et al., 1992).
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
644
Axo-axonic cells
Most synapses made by axo-axonic cell axons arethought to target GC axon initial segments(Halasy and Somogyi, 1993). However, a smallfraction of axon collaterals also descend into thesuperficial and deep hilus (Han et al., 1993; Freundand Buzsaki, 1996). In neocortex, an axo-axoniccell makes 4–10 synapses on the axon intial seg-ment of a postsynaptic cell (Li et al., 1992). With22,000,000 estimated axon initial segment synapsesin the GC layer (Halasy and Somogyi, 1993) and 4synapses per postsynaptic cell (based on the datafrom the neocortex from Li et al., 1992), each ofthe 2000 axo-axonic cells are estimated to targetapproximately 3000 GCs. MCs receive axo-axoniccell input (Ribak et al., 1985), and with the com-paratively small fraction of axons from axo-axoniccells in the hilus (Han et al., 1993; Freund andBuzsaki, 1996), it can be estimated that axo-axoniccells target a number of MCs equal to approxi-mately 5% of their GC targets, which results inapproximately 150 MCs. Since axo-axonic cellsprimarily target the axon initial segment of non-GABAergic cells (Halasy and Somogyi, 1993;Freund and Buzsaki, 1996), it may be assumedthat these cells do not project to interneurons.
HIPP cells
HIPP cells have been estimated to contact about1600 GCs and 450 basket cells with 1–5 synapsesper postsynaptic cell (Sik et al., 1997). MCs canhave one dendrite in the molecular layer (Amaral,1978; Ribak et al., 1985; Scharfman, 1991) whichcan be targeted by HIPP cell axons, whereas GCshave two primary dendrites (Claiborne et al., 1990;Lubke et al., 1998). Since the mossy cell to GCratio is approximately 1:30, the mossy cell dend-rites constitute only approximately 1/60 of thetargets for HIPP cells. Increasing this fraction toapproximately 1/45 to account for the presence ofa few HIPP cell contacts on MC in the hilus(Buckmaster et al., 2002a) results in an estimatethat each HIPP cell contacts approximately 35MCs. HIPP cell axonal divergence onto HICAPand MOPP cells in the molecular layer can be
assumed to be similar to that of somatostatin-pos-itive cells in CA1 (Katona et al., 1999) and esti-mated to be 15 connections onto each population.The HIPP cell axonal divergence to axo-axoniccells is estimated to be between the divergence tobasket and HICAP cells; therefore the HIPP cellaxon likely contacts 30 axo-axonic cells.
MOPP cells
MOPP cells target an estimated 7500 GCs in therat dentate gyrus. While MOPP cell axons projectin the horizontal axis to a similar extent as HIPPcells, they show considerably less collateralization(Han et al., 1993), resulting in an estimate of halfas many synapses onto MOPP and HICAP cells asHIPP cells make. As MOPP cell axons are re-stricted to the molecular layer (Han et al., 1993)and do not target the basal dendrites of basketcells, they are assumed to contact less than 1/10 thenumber of basket cells targeted by HIPP cells.Likewise, MOPP cells with axons restricted to theouter and middle molecular layers (Han et al.,1993) would not target the hilar dendrites of axo-axonic cells (Soriano et al., 1990) or the axo-axoniccells with somata and proximal dendrites in thehilus (Han et al., 1993). It is estimated that MOPPcells only contact 1–2 axo-axonic cells. As theMOPP cell axonal arbors in the molecular layer(Han et al., 1993) do not overlap with major partsof the dendritic arborizations of MCs (Frotscher etal., 1991), HIPP cells (Han et al., 1993; Sik et al.,1997; Katona et al., 1999) or IS cells (Gulyas et al.,1996), the connectivity to these cells is negligible.
HICAP cells
Sik et al. (1997) estimated that the septo-temporalextent and bouton density of HICAP cell axons issimilar to the HIPP cell axons, whereas the esti-mated axonal length of HICAP cells is approxi-mately half of the HIPP cell axonal length. Thus, itis estimated that HICAP cells contact about halfthe number of GCs contacted by HIPP cells.However, since HICAP cells have an additional3% of axon collaterals in the hilus (Sik et al.,1997), their number of postsynaptic MCs can be
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
645
assumed to be the same as that of the HIPP cells.HICAP cells are assumed to contact less than halfthe number of basket cells targeted by HIPP cells(�175) and a negligible number of axo-axoniccells. With a total of 26,000 synapses from a singleHICAP cell axon (Sik et al., 1997), approximately700 synapses should be present in the hilus. As-suming 2–5 synapses per postsynaptic cell, eachHICAP cell could contact 100–300 hilar cells.Each HICAP cell is assumed to target 50 HIPPand HICAP cells, which, along with 35 synapseson MCs, is in the estimated range. Although thetotal axonal length of HICAP cells is only abouthalf of that of HIPP cells, the number of MOPPcells targeted is assumed to be the same (�10–20),as the HICAP cell axons primarily project to theinner molecular layer where both cell bodies andproximal dendrites of MOPP cells are located(Han et al., 1993).
IS cells
IS cells contact an estimated 100–800 other IS cellsand 5–10 (presumably CCK positive) basket cells(Gulyas et al., 1996). Acsady et al. (2000) sug-gested that CCK cells would include both basketcell and HICAP morphologies and that IS cellsalso project to somatostatin-positive HIPP cells.These data result in an estimate that IS cellsproject to 5–10 HICAP cells and HIPP cells.
The fourth piece: spatial constraints and axonaldistributions
In addition to the number of connections made byany given cell, the distribution of these connectionsalong the septo-temporal axis of the dentate gyrusis very important. Fortunately, in vivo single cellfills have been performed which provide a verycomplete description of the axonal extent of theeight cell types discussed above. Averages of thesein vivo axonal distributions can be fit with either asingle or double Gaussian for each cell type, whichthen defines the model axonal distribution for eachcell of that type (Fig. 2). These Gaussians thendescribe the probability of any given cell
connecting to another cell based on the distancebetween the two.
Putting the pieces together
Once the border of the puzzle is complete (theconnection matrix in our analogy), it is possible tostart assembling the bulk of the picture. In the caseof modeling, this corresponds to a number of dis-tinct obstacles. Single cell models must be createdwith sufficient detail to function appropriately inthe network; network scaling must be implemented(i.e., what percentage of the actual cell numbers,connections, etc., will be represented in the net-work); receptor types and synaptic data must beincluded; and network topology must be deter-mined (will the network be a strip or a ring, e.g.,and how will connection probabilities be imple-mented to account for the shape and size of thenetwork). Finally, the stimulation paradigm mustbe determined so that the fully connected networkwill actually start to produce data. These obsta-cles, and ways to overcome them, are discussed indetail in this section.
Multicompartmental single cell models
In a network model that proposes to simulate bothsomatic and dendritic inputs and model synapticcontacts on specific dendritic compartments, it isnecessary to develop multicompartmental, bio-physically realistic models of individual cell types.It is not always necessary to develop these modelsfrom scratch, however, as ModelDB (http://sense-lab.med.yale.edu/senselab/modeldb/) is a search-able resource that makes published models ofseveral cell types including dentate GCs availablefor download (Aradi and Holmes, 1999a; San-thakumar et al., 2005). These models can be read-ily adapted to a wide variety of networks.Morphological properties for multicompartmentalmodels of other cell types not available on Mod-elDB, such as some of the other dentate cell types,can be developed based on the data reported in theliterature (Buckmaster et al., 1993, 2002b; Freundand Buzsaki, 1996; Geiger et al., 1997; Bartos etal., 2001).
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
646
The intrinsic properties of cell types can bemodeled based on data from whole cell physio-logical experiments obtained in the presence ofblockers of synaptic activity (Lubke et al., 1998).Detailed descriptions of how to model passive andactive properties of individual cells can be found inThe Neuron Book (Carnevale and Hines, 2006), butwe will discuss a couple of relevant issues herebriefly. First, since GCs (Desmond and Levy,1985) and MCs (Amaral, 1978) are rich in dendri-tic spines, it is necessary to account for the mem-brane area contribution of the spines (Rall et al.,1992). This can be accomplished by decreasingmembrane resistivity (increasing leak conduct-ance) and increasing membrane capacitance(Aradi and Holmes, 1999b). An additional con-sideration is the presence of spontaneous activityin some cell types such as MCs (Ishizuka et al.,1995; Ratzliff et al., 2004), as well as their lowerinput resistance in the presence of backgroundsynaptic activity (Ratzliff et al., 2004), comparedto the input resistance in ionotropic glutamate andGABA receptor antagonists (Lubke et al., 1998).Spontaneous firing rate can be simulated via aconstant direct current injection (Santhakumar etal., 2005), and the synaptic background activitycan be simulated as a fluctuating point conduct-ance with balanced excitation and inhibition, asdescribed in Destexhe et al. (2001).
Both excitatory cell types (GCs and MCs) arewell defined and have a vast amount of electro-physiological data available for the construction ofsingle cell models. However, the wealth of infor-mation available for the interneurons is substan-tially less for many cell types. Additionally, therole of interneurons in the network must be con-sidered with regard to the question being asked.For example, in a model network that is pursuingthe question of the role of mossy fiber sproutingand hilar cell loss in epileptogenesis (Santhakumaret al., 2005; Dyhrfjeld-Johnsen et al., 2006), severalfactors must be considered. Inhibition can operatein two principal modes. One mode is feed-forwardinhibition, where an interneuron is activated bythe same afferent input as the excitatory neuronthat it contacts. The basket cell is the primarysource of feed-forward inhibition in the dentategurus (Freund and Buzsaki, 1996). The second
mode is feedback inhibition, where interneuronsare activated by excitatory cells which they subse-quently inhibit. The basket cells and HIPP cells arethe two key feedback inhibitory cells in the dentate(Freund and Buzsaki, 1996; Buckmaster et al.,2002a). Another important aspect of inhibition isthe location of synaptic contact between interneu-ron and principal cell. Perisomatic inhibition bybasket cells is considered crucial in maintainingweak GC activity in response to afferent input.The HIPP cells, on the other hand, synapse on thedendritic region near the afferent inputs, and theyare likely to modulate integration of dendritic in-puts. The loss of this dendritic inhibition with anessentially intact or increased somatic inhibitionhas been proposed to be particularly relevant toepileptogenesis (Cossart et al., 2001). Further-more, basket cells are resistant to cell deathwhereas HIPP cells are extremely vulnerable inepileptic tissue (Buckmaster et al., 2002a). Thesefeatures make the basket and HIPP cells essentialconstituents of the dentate model.
The remaining four interneurons also possessunique features of inhibition. The MOPP cells op-erate by providing GCs with feed-forward dendri-tic inhibition (Halasy and Somogyi, 1993). TheHICAP cells synapse on the proximal dendrites ofGCs, near where mossy cell axons terminate andprovide feedback inhibition (Freund and Buzsaki,1996). The axo-axonic cells provide GABAergicinput at the axon initial segments of granule andMCs and potentially play powerful roles in mod-ifying spike initiation (Freund and Buzsaki, 1996;Howard et al., 2005). The IS cells connect exclu-sively to other interneurons and form a well con-nected network that could modulate excitabilityand synchrony of the network.
Unfortunately, detailed physiological data forthe development of realistic models of MOPP,HICAP, axo-axonic, and IS cells are not readilyavailable. Therefore, in an approach that avoidserrors of commission one could choose to includeonly basket and HIPP cells in the network. How-ever, this makes it essential to perform controlsimulations to examine whether augmenting inhi-bition (in order to compensate for excluded celltypes) influences the overall outcome of the net-work simulations.
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
647
Network scaling
Once the single cell models are complete and readyto go, it is time to start thinking about how big thenetwork is going to be. With the immense in-creases in computational power over the last cou-ple of decades, very large networks are quitefeasible. However, some questions may not requiresuch large networks, and often computational re-sources will be limited. Also important in deter-mining what scale a network should be is whetherthe network includes functional model cells thatrequire a great deal of computational power toprocess. Purely structural network models (that donot use multicompartmental functional single cellmodels), also called network graphs, can provide agreat deal of useful information about neuronalcircuits. Indeed, Dyhrfjeld-Johnsen et al. (2006)created an extraordinarily large 1:1 scale structuralmodel of the dentate gyrus that yielded a greatdeal of new data and will be discussed briefly inSection ‘‘The big picture’’.
Putting purely structural graphs aside for nowthough, and focusing on the functional model thatwe are building in this chapter, we can determinehow to scale the cell numbers. We know that theGC:MC:BC:HIPP ratio is 1000:30:10:12. In agree-ment with these ratios, the Lytton et al. (1998)model that focused on the network effects ofsprouting included 50 GCs, 2 MCs, and 2 inter-neurons. Using this relatively small network rep-resentation of the dentate they demonstrated thatthe effect of sprouting on enhancing network ex-citability was strongly limited by the intrinsic firingproperties of GCs (e.g., strong spike frequencyadaptation). Although this model made the pre-diction that mossy fiber sprouting could lead tohyperexcitability, the network was highly inter-connected as a consequence of the small size. Thisnetwork architecture, combined with a very strongperforant path synaptic conductance, could haveresulted in artificial synchronous activity in thenetwork. Increasing the size of the Lytton et al.(1998) model by 10-fold entails building a 1:2000scale dentate with 500 GCs, 15 MCs, 6 basket cellsand 6 HIPP cells. This 500+ cell model can bereadily simulated on a laptop and allows for ma-nipulating hilar cell numbers and connectivity
patterns (Santhakumar et al., 2005). However,even in a network of this size, artificially largeconductances as well as other factors (e.g., strongedge effects and unrealistic distance dependentcell-type specific connectivity) could influence theresults. With the current computational power ofstate-of-the-art multiprocessor computers the sizeof a realistic dentate model can be scaled up fur-ther to a 1:20 scale model with 50,000 GCs(Dyhrfjeld-Johnsen et al., 2006). The specific con-nection parameters that can be used for a model ofthis size are shown in Table 2. In Section ‘‘The bigpicture,’’ we will discuss results obtained from thisvery large-scale network with direct implicationsfor epileptogenesis.
Receptor types and synapses
Building a model of a dentate network with hun-dreds or thousands of biophysically realistic mul-ticompartmental model cells is only a meaningfulventure if those cells have a way to talk to oneanother. For this reason, we must consider neuro-transmitter-receptor types that must be included inthe network. Again, the types of receptors,synapses, and other cellular interaction devices(such as gap junctions) to include in the networkwill depend on the particular question the networkis designed to answer. For example the network wehave been building throughout this chapter, thegoal is to determine the effects of mossy fibersprouting and hilar cell loss on excitability. Toexamine these effects, the minimal requirement isto incorporate ionotropic glutamatergic AMPAsynapses and GABAA synapses. Experiments fromboth normal and epileptic animals are constantlyongoing, and as the data become available it willbe possible to add other receptors such as NMDAand metabotropic receptors. It would also be in-teresting to incorporate greater diversity at indi-vidual synapses through incorporation ofmechanisms such as short-term plasticity. Eachaddition to the network must be carefully con-sidered, however, as greater complexity necessarilyincreases the load on the computational resources.Since the basic circuit effects of sprouting and cellloss can be simulated by including AMPA and
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
648
GABAA synapses, these will be the types includedin our example model.
Postsynaptic conductances can be represented asa sum of two exponentials (Bartos et al., 2001).The peak conductance (gmax), rise and decay timeconstants, and the synaptic delays (distinct fromthe axonal conduction delay described later) foreach network connection can be estimated fromexperimental data (Kneisler and Dingledine, 1995;Geiger et al., 1997; Bartos et al., 2001; Santhaku-mar et al., 2005) and details of all of the specificcellular and synaptic properties can be found inSanthakumar et al. (2005). When making such es-timates, care must be taken to ensure that compa-rable conditions were used in the experiments thatprovide the data. For example, since the data forsynaptic conductances is typically obtained bypaired recording experiments from several differ-ent groups, the temperature at which the record-ings were performed must be accounted for. Q10
estimates can be used to convert kinetic data from
room temperature recordings to the appropriatevalues at physiological temperature. Axons can bemodeled implicitly by activating a given synapseafter either a static or distance-dependent delayonce a presynaptic cell crosses a preset membranepotential threshold (Bartos et al., 2001).
Network topology
The shape of the network and the way in whichconnections are made depends strongly on the sizeof the network. For instance, a network of ap-proximately 50 or 500 cells (Lytton et al., 1998;Santhakumar et al., 2005, respectively) may re-quire a ring structure to avoid edge effects (i.e.,cells on the edge of a network have as few as halfas many pre- and postsynaptic targets compared tocells in the middle). A network of 50,000+ cells(Dyhrfjeld-Johnsen et al., 2006), on the other handcan be set up as a linear strip, more similar to the
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
Table 2. Parameters of the 50,000+ neuron functional model network
Functional model network parameters
From To –> GC MC BC HC
Granule cellsa Convergence 68.03 78.05 370.95 2266.64
(50,000) Divergence 68.03 2.34 3.71 27.19
Synapse weight (nS) 1.00 0.20 0.94 0.10
Mossy cells Convergence 243.62 87.23 5.59 375.53
(1500) Divergence 8120.82 87.23 1.86 150.21
Synapse weight (nS) 0.30 0.50 0.30 0.20
Basket cells Convergence 3.11 6.31 8.98 n/a
(500) Divergence 313.22 18.93 8.98 n/a
Synapse weight (nS) 1.60 1.50 7.60 n/a
HIPP cells Convergence 4.82 3.76 140.13 n/a
(600) Divergence 401.86 9.39 116.77 n/a
Synapse weight (nS) 0.50 1.00 0.50 n/a
Perforant pathb Synapse weight (nS) 20 17.5 10 n/a
Notes: The cell numbers (column 1) and synaptic connectivity values and strengths in the functional model network used for the activity simulations in
Fig. 4. Note that this network is smaller (50,000+ cells) than the full-scale dentate gyrus (over 1 million cells) model described in Section ‘‘Structural
alterations in the dentate during epileptogenesis’’. Therefore, the connectivity had to be adjusted from what is shown in Table 1. Convergence is given as
number of connections onto a single postsynaptic neuron (row 1) from a presynaptic neuronal population (column 1). For example, 243 mossy cells
converge on a single granule cell in this network. Divergence is given as the number of connections to a postsynaptic population (row 1) from a single
presynaptic neuron (column 1). For example, a single mossy cell makes synapses on 8120 postsynaptic granule cells in this network. The strengths of the
connections are given in nS. For example, the strength of the excitatory synapse formed by a single mossy cell on a single granule cell is 0.3 nS.aGranule cell to granule cell connections represent values at 100% sprouting.bPerforant path input to 5000 granule cells (2 synapses each), 50 basket cells (2 synapses each) and 10 mossy cells (1 synapse each) in the central 10 bins of
the network model.
649
actual topology of the biological dentate. Simi-larly, small networks may require non-topographicconnectivity. That is, the postsynaptic targets ofeach cell are selected at random from the pool ofpotential target neurons while maintaining the celltype specific divergence and convergence. Largernetworks can incorporate the spatial rules dis-cussed above in part D of Section ‘‘Finding theright pieces;’’ the connectivity between cells can bedistributed according to the experimentally de-rived axonal distributions of the various cell types(Fig. 2).
Network stimulation
A network such as the dentate gyrus, in whichmost cells are not designed to be spontaneouslyactive, requires some afferent input to initiate net-work activity. This input can come in a number offorms, again dependent on the specific question aswell as the particular network being modeled. Forthe dentate gyrus as a whole, it makes sense tosimulate a perforant path input from the ent-orhinal cortex. This input to the network is locatedon both dendrites of all GCs and the apical dend-rites of all basket cells. Since 15% of MCs havealso been shown to receive direct perforant pathinput (Scharfman, 1991; Buckmaster et al., 1992),the number of MCs that should receive input in agiven model can be easily calculated. Mass stim-ulation of the perforant path can be simulated byactivating a maximum peak AMPA conductancein cells postsynaptic to the stimulation (Santhaku-mar et al., 2000). The strength of the perforantpath input in the 50,000+ cell functional modelfrom Dyhrfjeld-Johnsen et al. (2006) is given inTable 2 (note the very large synaptic weight forperforant path input compared to the smallweights for cell to cell synapses). In the biologicalnetwork and in physiological studies it is unlikelythat the entire network is activated simultane-ously. Rather, focal activation can be simulated byactivating the input to GCs and basket cells lo-cated in a model hippocampal ‘‘lamella’’. If focalnetwork activation is undesirable, spontaneousnetwork activity can be simulated instead. Thiscan be accomplished by providing uncorrelated
activation (perforant path inputs with Poisson dis-tributed interspike intervals) to each granule cell,basket cell, and 15% of the MCs. Other methodsfor initiation of network activity can be devised asnecessary.
The big picture
Following essentially the strategy outlined in theprevious two sections, dentate gyrus modelershave assembled a number of different puzzles,producing dentate models of a wide range of sizesaimed at answering a large number of importantquestions. We have walked through the creation ofa very large-scale dentate model capable of han-dling functional network simulations with greaterthan 50,000 cells. However, we have not yet dis-cussed how a model of this type can help us gain abetter understanding of disease processes andhopefully how to treat them. Without the abilityto provide information of this nature, models aresimply incomplete representations of reality and oflittle use. Fortunately, models can provide a greatdeal of information because they give scientistscomplete control over variables that cannot beisolated in typical experimental situations. In thissection, we will briefly describe an example inwhich using large scale dentate gyrus modeling al-lowed Dyhrfjeld-Johnsen et al. (2006) to isolatestructural changes in the dentate during epilepto-genesis and conclude that structural changes alonecan lead to hyperexcitability.
Structural alterations in the dentate during
epileptogenesis
As mentioned throughout this chapter, two pri-mary structural alterations occur in the dentategyrus during epileptogenesis: mossy fiber sprout-ing and hilar cell death (including hilar interneu-rons and MC). These two processes (which we willrefer to simply as ‘‘sclerosis,’’ defined here as thetwo common structural changes in the dentate as-sociated with mesial temporal lobe sclerosis) canbe implemented in a dentate gyrus model accord-ing to the data driven approach given above. De-tailed descriptions of how to implement both of
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
650
these processes can be found in Santhakumar et al.(2005) and Dyhrfjeld-Johnsen et al. (2006). Briefly,a maximal level of sclerosis can be simulated byadding an average of approximately 275 granulecell to granule cell connections (Buckmaster et al.,2002b) and by removing all hilar cells from thenetwork. Using this maximum value as a point ofreference, the severity of sclerosis can be approx-imated by simulating percentages of the maximum(e.g., at 50% sclerosis, simulating epileptogenesisfollowing a moderate head injury (Howard et al.,2006), each granule cell would contact approxi-mately 137 other GCs, and 50% of hilar cellswould be lost).
A 1:1 scale structural model of the dentate gyruscan be constructed where each cell is simply a nodein the computer (nodes have no functional prop-erties and are therefore much less computationallydemanding than the multicompartmental cellmodels described previously) and synapses be-tween cells are represented as non-functioning di-rected links (Dyhrfjeld-Johnsen et al., 2006). Thisstructural network can then be utilized to under-stand the basic structure of the healthy dentategyrus and how that structure changes during epile-ptogenesis.
In order to understand how network structurecan be measured and later how structural changeshave functional implications, it is necessary to ex-plain the parameters that define network topology.Two measures that Watts and Strogatz (1998)originally employed to assess the structure of thenervous system of the worm C. elegans can be usedto analyze the structure of the dentate network: theaverage path length, L, and the average clusteringcoefficient, C. The average path length is definedas the average number of steps required to movefrom any node to any other node in the network,and it is therefore a measure of how well connectedthe network is globally. The average clusteringcoefficient, on the other hand, is a measure of localconnectivity. It is defined as the fraction of allpossible connections between ‘‘postsynaptic’’nodes of a given node that are actually formed.The average clustering coefficient for an entirenetwork is simply the average of the clusteringcoefficients for each node in the network.
The topological measures, C and L, can be bestthought of in terms of a social network, or a net-work of friends. C measures the probability thatany two friends of a given person also know eachother. L measures how many steps in a chain offriends or acquaintances would be necessary toconnect two random people. A common theorythat utilizes this parameter is that anyone on theplanet is separated from anyone else by up to sixdegrees of separation, or six people. While thistheory has never been satisfactorily proven, it hasled to interesting experiments and even a partygame called the Six Degrees of Kevin Bacon, inwhich the participants have to connect any actoror actress to Kevin Bacon through their film rolesin as few steps as possible.
Based on these two topological measures, net-works can be divided into three classes: (1) Reg-ular, with a long path length and large clusteringcoefficient; (2) Random, with a short path lengthand small clustering coefficient; and (3) SmallWorld, with a short path length and large cluster-ing coefficient. Representative graphs of thesetypes of networks are displayed in Fig. 3.
As shown, the regular network (Fig. 3A) ischaracterized by a high local connectivity, but thedistance (via connected nodes) between any tworandom nodes, especially nodes at the ends of thegraph, can be quite large. On the other hand, therandom network (Fig. 3B) contains many longdistance connections, contributing to a very shortaverage path length. There is little local connec-tivity however, as nodes are just as likely to con-nect to far away nodes as they are to theirneighbors. The small world network (Fig. 3C) actsas a sort of compromise between the random andregular graphs. Indeed, there is a high degree oflocal connectivity combined with a number oflong-range connections, yielding a both locallyand globally well-connected network. Small worldnetworks can also be thought of in terms of socialnetworking. Humans often form a cohesive groupof friends who are well connected locally due tovarious constraints such as geography, commonactivities and so on. Additionally, any given per-son in the group may know some people who aretotally unrelated to the local group, but who eachhave cohesive local groups of their own, thus
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
651
creating numerous long distance connections be-tween the locally well-connected networks.
So how do these L and C values play a role inunderstanding the dentate gyrus? Analysis of thestructural model of the dentate gyrus in thehealthy state, without any mossy fiber sproutingor hilar cell loss, indicates that the dentate gyrus isa small world network. It has a very high cluster-ing coefficient and a path length that is only 2.68,approximately the same as the path length of theC. elegans nervous system, a nervous system withonly 282 cells! This finding means that any cell isconnected to any of the other one million cells inthe dentate network by less than three synapses,and cells are highly connected locally, resulting infast local computations and the ability to effi-ciently relay signals to distant parts of the net-work.
While the analysis of the healthy dentate gyrusprovides useful and novel information about itsstructure, perhaps the most interesting and coun-terintuitive structural information comes from theanalysis of networks undergoing sclerosis. These
networks demonstrate that the small world char-acteristics of the dentate gyrus are actually en-
hanced up to approximately 80% sclerosis, despitea massive loss of connections (see Section ‘‘Mossycells’’ for MC connectivity; note the massive di-vergence onto GCs that is lost as sclerosisprogresses and MCs die). In fact, the total numberof links in the network decreases by 74% while thetotal number of nodes lost due to hilar cell death isonly 4.5% at maximal sclerosis, yet the networkbecomes seemingly more locally and globally wellconnected. This finding predicts that during epile-ptogenesis, the dentate gyrus may become morereadily able to transmit information throughoutthe network and likely increase synchronous firingas well, phenomena that could very well contributeto a seizure phenotype. It is only at nearly 100%sclerosis that the dentate gyrus network trans-forms into a more regular network structure, pre-dicting a counterintuitive decrease inhyperexcitability at maximal sclerosis.
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
Fig. 3. Schematics of three basic network topologies. (A) Regular network topology. The nodes in a regular network are connected to
their nearest neighbors, resulting in a high degree of local interconnectedness (high clustering coefficient C), but also requiring a large
number of steps to reach other nodes in the network from a given starting point (high average path length L). (B) Random network
topology. In a random network, there is no spatial restriction on the connectivity of the individual nodes, resulting in a network with a
low average path length L but also a low clustering coefficient C. (C) Small world network topology. Reconnection of even a few of the
local connections in a regular network to distal nodes in a random manner results in the emergence of a small world network with a
high clustering coefficient C but a low average path length L.
652
Functional implications of structural alterations
Now that we have discussed the structural analysisof the healthy and sclerotic dentate gyrus, it re-mains to be seen whether network activity is ac-tually influenced by the structural changes in theways we might expect based on the predictions inthe preceding section. As in the 1:1 scale structuralmodel, sclerosis can be implemented in a func-tional model of the dentate gyrus. This modelcontains approximately 50,000 cells, owing to theincreased need for computational resources toperform the calculations necessary with multicom-partmental biophysically realistic cells (see Section‘‘Multicompartmental single cell models’’). Simu-lations can be performed as sclerosis progresses insteps (e.g., perform simulations at 20 then 40%,and so on), and activity in the network can bequantified by a number of different measures.Four different measures were used in Dyhrfjeld-Johnsen et al. (2006): (1) duration of granule cellfiring (the time of the last granule cell action po-tential in the network minus the time of the firstgranule cell action potential); (2) average numberof action potentials per granule cell; (3) time untilactivity of the most distant GCs from the stimu-lation point (i.e., latency to full network activity);and (4) synchrony of granule cell action potentials.
Results of the functional simulations reveal thatnetwork activity very closely parallels structuralalterations in the dentate gyrus. The healthy non-sclerotic dentate model shows very limited firing inresponse to a single perforant path input (Fig. 4A),in accordance with the biological data (Santhaku-mar et al., 2001). Additionally, as sclerosisprogresses, the functional network becomes in-creasingly hyperexcitable up to approximately80% sclerosis (Figs 4B–E), again agreeing with invitro measures of epileptiform activity (Rafiq etal., 1995) and in accordance with the enhancedsmall world features revealed by the structuralanalysis. A very interesting phenomenon then oc-curs at levels of sclerosis exceeding 80%. Hyper-excitability of the functional model networkactually decreases (Fig. 4F)! The level of sclerosisat which hyperexcitability diminishes correspondsperfectly to the point at which the network trans-forms from a small world structure to a more
regular network. Thus, the functional networkfollows the same pattern that is seen in the struc-tural network, and the functional effects are solelydue to the structural network alterations, as nointrinsic cellular or synaptic properties are alteredin the model as sclerosis progresses. Interestingly,network dynamics are also affected by structuralchanges; a relatively uniform pattern of granulecell activity (from 40 to 60% sclerosis; Fig. 4C, D)transforms into a pattern with distinct waves ofactivity (from 80 to 100% sclerosis; Fig. 4E, F)that can collide and mutually annihilate (Netoff etal., 2004; Roxin et al., 2004).
These findings not only support the importantrole of structural alterations in determining func-tional network activity, but they are in agreementwith experimental observations in both epilepticanimals and humans. Indeed, no studies that havequantified hilar cell loss in animal models of ep-ilepsy ever reported 100% cell loss (Cavazos andSutula, 1990; Cavazos et al., 1994; Leite et al.,1996; Buckmaster and Dudek, 1997; Mathern etal., 1997; Buckmaster and Jongen-Relo, 1999;Gorter et al., 2001; van Vliet et al., 2004; Zap-pone and Sloviter, 2004). Additionally, in surgi-cally removed specimens from pharmacologicallyintractable human temporal lobe epilepsy patients(Gabriel et al., 2004), cell counts showed that onlyapproximately 80% of hilar cells were lost, even inpatients with severe sclerosis (Blumcke et al.,2000) AU :2. This finding coincides perfectly with theperiod of maximal hyperexcitability in the func-tional model networks, when sclerosis reaches80%.
Understanding the limitations of models
It is important to consider that no model can everfully replicate the system that it is modeling. As aresult, it is crucial to be certain that results andconclusions derived from models are robust undera number of potentially confounding situations.The modeling strategy presented in this chapterattempts to ensure that available biological data isrepresented and accounted for. However, a num-ber of specific components of the dentate circuitand connectivity often cannot be modeled due to
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
653
lack of precise data. Additionally, depending onthe particular question the model is designed toanswer, several factors may be purposely omittedin order to best focus on the relevant issues. Forthe model presented in this section, for example,changes to intrinsic cellular and synaptic proper-ties during sclerosis were omitted since the exper-iments were designed to study structuralalterations in isolation. For these reasons, an ex-tensive series of control simulations must be per-formed to test the effects of a wide variety ofconditions that are not well constrained by theavailable experimental data. Controls will varyfrom model to model, but many are needed in anysituation. Those performed for the structuralmodel presented here were the following:
1) Variations in cell numbers.
2) Variations in connectivity estimates.3) Inhomogeneous distribution of neuron den-
sities along the septo-temporal axis.4) Inhomogeneity in connectivity along the
transverse axis.5) Altered axonal distributions at the septal and
temporal poles (the anatomical boundaries ofthe dentate gyrus).
6) Offset degrees of sprouting and hilar neuronloss.
7) Implementation of a bilateral model of thedentate gyrus including commissural projec-tions.
All of the controls employed for the structuralmodel were also used as controls for the functionalmodel. In addition, the functional model had itsown set of controls, including:
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
Fig. 4. Effects of the sclerosis-related topological changes on granule cell activity in functional model networks. A–F. Raster plots of
the first 300ms of action potential discharges of granule cells in the 50,000+ neuron functional model network (granule cells number
1–50,000, plotted on the y-axis; each dot corresponds to an action potential fired by a granule cell) at increasing degrees of sclerosis.
Network activity was initiated by a single stimulation of the perforant path input to granule cells number 22,500–27,499 and to 10
mossy cells and 50 basket cells (distributed in the same area as the stimulated granule cells) at t ¼ 5ms (as in Santhakumar et al., 2005).
Note that the most pronounced hyperactivity was observed at sub-maximal (80%) sclerosis.
654
1) Double inhibitory synaptic strengths.2) Axonal conduction delays.3) Spontaneous instead of stimulation-evoked
activity.
All of the results from these control simulationssupported the basic findings of the original mod-els, thus greatly strengthening the primary conclu-sions.
Tackling future puzzles and problems
Modeling has come a long way in the last severaldecades. Even 10 years ago, large-scale realisticmodeling was nearly impossible due to computa-tional restrictions and the requirement of vast su-percomputers to perform necessary calculations.Today, however, it is possible to perform quite in-depth modeling studies on a home desktop. Mod-els such as the 50,000 cell network in Dyhrfjeld-Johnsen et al. (2006) can be realistically run on adual processor system (albeit with 16–32 GB ofRAM). Smaller networks such as the 500 cellmodel in Santhakumar et al. (2005) can be run in afew minutes on a typical laptop. These are won-derful advancements, as the development of large-scale models that can simulate brain circuits withgreater realism is critical to our understanding ofthe experimentally determined cellular and molec-ular underpinnings of diseases like epilepsy. Ad-ditionally, large-scale realistic networks arenecessary for our understanding of structure–func-tion relationships, especially in a highly plasticsystem like the dentate gyrus.
The exact structural changes that occur in manypathological states such as epilepsy are as yet un-known. For example, recent evidence indicatesthat local connection probability in various brainareas may be modified by intra-class correlations(Yoshimura and Callaway, 2005; Yoshimura et al.,2005) and over-representation of small networkmotifs (Milo et al., 2002; Reigl et al., 2004; Spornsand Kotter, 2004; Song et al., 2005). While no di-rect evidence is present to implicate such factors inthe dentate gyrus, it is likely that unknown struc-tural alterations have a significant impact on net-work activity. Computational modeling studiesprovide an excellent tool for determining what the
probable result of a wide variety of structural al-terations could be. Subsequent animal model ex-periments can then attempt to visualize thestructural alterations predicted by the computa-tion models. In an example of this type of ap-proach, Morgan and Soltesz (2006) have studiedprobable connectivity patterns within the recurrentGC network that results from mossy fiber sprout-ing. Their results indicate that the presence of asmall number (at most 5%) of GCs with increasedconnectivity (on average, 5–6 times the averagenumber of connections) could serve as hubs andstrongly promote hyperexcitability within the scle-rotic dentate gyrus network. Interestingly, thisfinding is supported by the presence, in epilepticrats, of a small percentage of GCs that have basaldendrites (Spigelman et al., 1998) and which re-ceive a vast number of additional mossy fiber con-tacts (Buckmaster and Thind, 2005).Computational modeling studies provide the bestway of isolating structural changes from intrinsiccellular and synaptic changes that occur simulta-neously in virtually all pathological states.
Large-scale simulations will also make it possi-ble to hold structure constant and test the circuiteffects of specific therapeutic interventions,thereby allowing fast, cheap, efficient, and specificanalysis of treatments for a variety of pathologicalprocesses. The fast pace at which scientists aregleaning knowledge about the dentate from animalmodels will allow for inclusion of a complete com-plement of interneuronal subtypes, various recep-tor and modulatory systems, realistic channeldistributions, dendritic integration processes, andsynaptic plasticity into computational models.These additions will greatly broaden the scope ofquestions that a model can address and themodel’s predictive power. In the coming years, re-alistic modeling is only going to become more im-portant in bridging the gaps between animals andhumans, molecules and behavior.
References
Acsady, L., Kamondi, A., Sik, A., Freund, T. and Buzsaki, G.
(1998) GABAergic cells are the major postsynaptic targets of
mossy fibers in the rat hippocampus. J. Neurosci., 18:
3386–3403.
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
655
Acsady, L., Katona, I., Martinez-Guijarro, F.J., Buzsaki, G.
and Freund, T.F. (2000) Unusual target selectivity of peri-
somatic inhibitory cells in the hilar region of the rat hippo-
campus. J. Neurosci., 20: 6907–6919.
Amaral, D.G. (1978) A Golgi study of cell types in the hilar
region of the hippocampus in the rat. J. Comp. Neurol., 182:
851–914.
Aradi, I. and Holmes, W.R. (1999a) Role of multiple calcium
and calcium-dependent conductances in regulation of hippo-
campal dentate granule cell excitability. J. Comput. Neuro-
sci., 6: 215–235.
Aradi, I. and Holmes, W.R. (1999b) Active dendrites regulate
spatio-temporal synaptic integration in hippocampal dentate
granule cells. Neurocomputing, 26–27: 45–51.
Babb, T.L., Pretorius, J.K., Kupfer, W.R. and Brown, W.J.
(1988) Distribution of glutamate-decarboxylase-immunore-
active neurons and synapses in the rat and monkey hippo-
campus: light and electron-microscopy. J. Comp. Neurol.,
278: 121–138.
Bartos, M., Vida, I., Frotscher, M., Geiger, J.R.P. and Jonas, P.
(2001) Rapid signaling at inhibitory synapses in a dentate
gyrus interneuron network. J. Neurosci., 21: 2687–2698.
Blasco-Ibanez, J.M., Martinez-Guijarro, F.J. and Freund, T.F.
(2000) Recurrent mossy fibers preferentially innervate parv-
albumin-immunoreactive interneurons in the granule cell
layer of the rat dentate gyrus. Neuroreport, 11: 3219–3225.
Boss, B.D., Peterson, G.M. and Cowan, W.M. (1985) On the
number of neurons in the dentate gyrus of the rat. Brain Res.,
338: 144–150.
Buckmaster, P.S. and Dudek, F.E. (1997) Network properties
of the dentate gyrus in epileptic rats with hilar neuron loss
and granule cell axon reorganization. J. Neurophysiol., 77:
2685–2696.
Buckmaster, P.S. and Dudek, F.E. (1999) In vivo intracellular
analysis of granule cell axon reorganization in epileptic rats.
J. Neurophysiol., 81: 712–721.
Buckmaster, P.S. and Jongen-Relo, A.L. (1999) Highly specific
neuron loss preserves lateral inhibitory circuits in the dentate
gyrus of kainate-induced epileptic rats. J. Neurosci., 19:
9519–9529.
Buckmaster, P.S., Strowbridge, B.W., Kunkel, D.D., Schmiege,
D.L. and Schwartzkroin, P.A. (1992) Mossy cell axonal pro-
jections to the dentate gyrus molecular layer in the rat hip-
pocampal slice. Hippocampus, 2: 349–362.
Buckmaster, P.S., Strowbridge, B.W. and Schwartzkroin, P.A.
(1993) A comparison of rat hippocampal mossy cells and
CA3c pyramidal cells. J. Neurophysiol., 70: 1281–1299.
Buckmaster, P.S. and Schwartzkroin, P.A. (1994) Hippocampal
mossy cell function: a speculative view. Hippocampus, 4:
393–402.
Buckmaster, P.S. and Thind, K. (2005) American epilepsy so-
ciety meeting abstract. Epilepsia, 46: 91–131.
Buckmaster, P.S., Wenzel, H.J., Kunkel, D.D. and Schwa-
rtzkroin, P.A. (1996) Axon arbors and synaptic connections
of hippocampal mossy cells in the rat in vivo. J. Comp. Ne-
urol., 366: 270–292.
Buckmaster, P.S., Yamawaki, R. and Zhang, G.F. (2002a)
Axon arbors and synaptic connections of a vulnerable pop-
ulation of interneurons in the dentate gyrus in vivo. J. Comp.
Neurol., 445: 360–373.
Buckmaster, P.S., Zhang, G.F. and Yamawaki, R. (2002b)
Axon sprouting in a model of temporal lobe epilepsy creates
a predominantly excitatory feedback circuit. J. Neurosci., 22:
6650–6658.
Carnevale, N.T. and Hines, M.L. (2006) The Neuron Book.
Cambridge University Press, Cambridge, UK.
Cavazos, J.E., Das, I. and Sutula, T.P. (1994) Neuronal loss
induced in limbic pathways by kindling: evidence for induc-
tion of hippocampal sclerosis by repeated brief seizures. J.
Neurosci., 14: 3106–3121.
Cavazos, J.E. and Sutula, T.P. (1990) Progressive neuronal loss
induced by kindling: a possible mechanism for mossy fiber
synaptic reorganization and hippocampal sclerosis. Brain
Res., 527: 1–6.
Ceranik, K., Bender, R., Geiger, J.R.P., Monyer, H., Jonas, P.,
Frotscher, M. and Lubke, J. (1997) A novel type of GAB-
Aergic interneuron connecting the input and the output re-
gions of the hippocampus. J. Neurosci., 17: 5380–5394.
Claiborne, B.J., Amaral, D.G. and Cowan, W.M. (1990) Quan-
titative, three-dimensional analysis of granule cell dendrites
in the rat dentate gyrus. J. Comp. Neurol., 302: 206–219.
Cossart, R., Dinocourt, C., Hirsch, J.C., Merchan-Perez, A.,
De Felipe, J., Ben-Ari, Y., Esclapez, M. and Bernard, C.
(2001) Dendritic but not somatic GABAergic inhibition is
decreased in experimental epilepsy. Nat. Neurosci., 4: 52–62.
Desmond, N.L. and Levy, W.B. (1985) Granule cell dendritic
spine density in the rat hippocampus varies with spine shape
and location. Neurosci. Lett., 54: 219–224.
Destexhe, A., Rudolph, M., Fellous, J.M. and Sejnowski, T.J.
(2001) Fluctuating synaptic conductances recreate in vivo-
like activity in neocortical neurons. Neuroscience, 107:
13–24.
AU :3Dyhrfjeld-Johnsen, J., Santhakumar, V., Morgan, R.J., Huerta,
R., Tsimring, L. and Soltesz, I. (2006) Topological determi-
nants of epileptogenesis in large-scale structural and func-
tional models of the dentate gyrus derived from experimental
data. J. Neurophysiol., epub ahead of print. doi:10.1152/
jn.00950.2006.
Freund, T.F. and Buzsaki, G. (1996) Interneurons of the hip-
pocampus. Hippocampus, 6: 347–470.
Frotscher, M., Seress, L., Schwerdtfeger, W.K. and Buhl, E.
(1991) The mossy cells of the fascia dentata: a comparative
study of their fine structure and synaptic connections in ro-
dents and primates. J. Comp. Neurol., 312: 145–163.
Gaarskjaer, F.B. (1978) Organization of mossy fiber system of
rat studied in extended hippocampi.1. Terminal area related
to number of granule and pyramidal cells. J. Comp. Neurol.,
178: 49–71.
Gabriel, S., Njunting, M., Pomper, J.K., Merschhemke, M.,
Sanabria, E.R.G., Eilers, A., Kivi, A., Zeller, M., Meencke,
H.-J., Cavalheiro, E.A., Heinemann, U. and Lehmann, T.-N.
(2004) Stimulus and potassium-induced epileptiform activity
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
656
in the human dentate gyrus from patients with and without
hippocampal sclerosis. J. Neurosci., 24: 10416–10430.
Gorter, J.A., van Vliet, E.A., Aronica, E. and Lopes da Silva,
F.H. (2001) Progression of spontaneous seizures after status
epilepticus is associated with mossy fibre sprouting and ex-
tensive bilateral loss of hilar parvalbumin and somatostatin-
immunoreactive neurons. Eur. J. Neurosci., 13: 657–669.
Geiger, J.R.P., Lubke, J., Roth, A., Frotscher, M. and Jonas, P.
(1997) Submillisecond AMPA receptor-mediated signaling at
a principal neuron-interneuron synapse. Neuron, 18:
1009–1023.
Gulyas, A.I., Hajos, N. and Freund, T.F. (1996) Interneurons
containing calretinin are specialized to control other inter-
neurons in the rat hippocampus. J. Neurosci., 16: 3397–3411.
Gulyas, A.I., Miettinen, R., Jacobowitz, D.M. and Freund,
T.F. (1992) Calretinin is present in nonpyramidal cells of the
rat hippocampus .1. A new type of neuron specifically asso-
ciated with the mossy fiber system. Neuroscience, 48: 1–27.
Halasy, K. and Somogyi, P. (1993) Subdivisions in the multiple
gabaergic innervation of granule cells in the dentate gyrus of
the rat hippocampus. Eur. J. Neurosci., 5: 411–429.
Han, Z.S., Buhl, E.H., Lorinczi, Z. and Somogyi, P. (1993) A
high-degree of spatial selectivity in the axonal and dendritic
domains of physiologically identified local-circuit neurons in
the dentate gyrus of the rat hippocampus. Eur. J. Neurosci.,
5: 395–410.
Heinemann, U., Beck, H., Dreier, J.P., Ficker, E., Stabel, J. and
Zhang, C.L. (1992) The dentate gyrus as a regulated gate for
the propagation of epileptiform activity. Epilepsy Res. Sup-
pl., 7: 273–280.
Howard, A., Tamas, G. and Soltesz, I. (2005) Lighting the
chandelier: new vistas for axo-axonic cells. Trends Neurosci.,
28: 310–316.
Howard, A.L., Neu, A., Morgan, R.J., Echegoyen, J.C. and
Soltesz, I. (2006) Opposing modifications in intrinsic currents
and synaptic inputs in post-traumatic mossy cells: evidence
for single-cell homeostasis in a hyperexcitable network. J.
Neurophysiol., epub ahead of print. doi:10.1152/
jn.00509.2006.
Ishizuka, N., Cowan, W.M. and Amaral, D.G. (1995) A quan-
titative analysis of the dendritic organization of pyramidal
cells in the rat hippocampus. J. Comp. Neurol., 362: 17–45.
Katona, I., Acsady, L. and Freund, T.F. (1999) Postsynaptic
targets of somatostatin-immunoreactive interneurons in the
rat hippocampus. Neuroscience, 88: 37–55.
Kneisler, T.B. and Dingledine, R. (1995) Synaptic input from
CA3 pyramidal cells to dentate basket cells in rat hippocam-
pus. J. Physiol., 487(Pt 1): 125–146.
Leite, J.P., Babb, T.L., Pretorius, J.K., Kuhlman, P.A., Yeo-
man, K.M. and Mathern, G.W. (1996) Neuron loss, mossy
fiber sprouting, and interictal spikes after intrahippocampal
kainate in developing rats. Epilepsy Res., 26: 219–231.
Li, X.G., Somogyi, P., Tepper, J.M. and Buzsaki, G. (1992)
Axonal and dendritic arborization of an intracellularly labe-
led chandelier cell in the ca1 region of rat hippocampus. Exp.
Brain Res., 90: 519–525.
Lothman, E.W., Stringer, J.L. and Bertram, E.H. (1992) The
dentate gyrus as a control point for seizures in the hippo-
campus and beyond. Epilepsy Res. Suppl., 7: 301–313.
Lubke, J., Frotscher, M. and Spruston, N. (1998) Specialized
electrophysiological properties of anatomically identified
neurons in the hilar region of the rat fascia dentata. J. Ne-
urophysiol., 79: 1518–1534.
Lytton, W.W., Hellman, K.M. and Sutula, T.P. (1998) Com-
puter models of hippocampal circuit changes of the kindling
model of epilepsy. Artif. Intell. Med., 13: 81–97.
Mathern, G.W., Bertram III, E.H., Babb, T.L., Pretorius, J.K.,
Kuhlman, P.A., Spradlin, S. and Mendoza, D. (1997) In
contrast to kindled seizures, the frequency of spontaneous
epilepsy in the limbic status model correlates with greater
aberrant fascia dentata excitatory and inhibitory axon
sprouting, and increased staining for N-methyl-D-aspartate,
AMPA and GABA(A) receptors. Neuroscience, 77:
1003–1019.
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii,
D. and Alon, U. (2002) Network motifs: simple building
blocks of complex networks. Science, 298: 824–827.
Morgan, R.J. and Soltesz, I. (2006) American epilepsy society
meeting abstract. Epilepsia, 47: 18–28.
Netoff, T.I., Clewley, R., Arno, S., Keck, T. and White, J.A.
(2004) Epilepsy in small-world networks. J. Neurosci., 24:
8075–8083.
Nomura, T., Fukuda, T., Aika, Y., Heizmann, C.W., Emson,
P.C., Kobayashi, T. and Kosaka, T. (1997a) Laminar distri-
bution of non-principal neurons in the rat hippocampus, with
special reference to their compositional difference among
layers. Brain Res., 764: 197–204.
Nomura, T., Fukuda, T., Aika, Y., Heizmann, C.W., Emson,
P.C., Kobayashi, T. and Kosaka, T. (1997b) Distribution of
nonprincipal neurons in the rat hippocampus, with special
reference to their dorsoventral difference. Brain Res., 751:
64–80.
Patton, P.E. and Mcnaughton, B. (1995) Connection matrix of
the hippocampal-formation .1. The dentate gyrus. Hippo-
campus, 5: 245–286.
Rafiq, A., Zhang, Y.F., DeLorenzo, R.J. and Coulter, D.A.
(1995) Long-duration self-sustained epileptiform activity in
the hippocampal-parahippocampal slice: a model of status
epilepticus. J. Neurophysiol., 74: 2028–2042.
Rall, W., Burke, R.E., Holmes, W.R., Jack, J.J., Redman, S.J.
and Segev, I. (1992) Matching dendritic neuron models to
experimental data. Physiol. Rev., 72: S159–S186.
Ratzliff, A.H., Howard, A.L., Santhakumar, V., Osapay, I. and
Soltesz, I. (2004) Rapid deletion of mossy cells does not result
in a hyperexcitable dentate gyrus: implications for epilepto-
genesis. J. Neurosci., 24: 2259–2269.
AU :4Reigl, M., Alon, U. and Chklovskii, D.B. (2004) Search for
computational modules in the C. elegans brain. BMC Biol., 2:
25.
Ribak, C.E., Seress, L. and Amaral, D.G. (1985) The develop-
ment, ultrastructure and synaptic connections of the mossy
cells of the dentate gyrus. J. Neurocytol., 14: 835–857.
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
657
Roxin, A., Riecke, H. and Solla, S.A. (2004) Self-sustained ac-
tivity in a small-world network of excitable neurons. Phys.
Rev. Lett., 92: 198101.
Santhakumar, V., Aradi, I. and Soltesz, I. (2005) Role of mossy
fiber sprouting and mossy cell loss in hyperexcitability: a
network model of the dentate gyrus incorporating cell types
and axonal topography. J. Neurophysiol., 93: 437–453.
Santhakumar, V., Bender, R., Frotscher, M., Ross, S.T., Ho-
llrigel, G.S., Toth, Z. and Soltesz, I. (2000) Granule cell
hyperexcitability in the early post-traumatic rat dentate
gyrus: the ‘irritable mossy cell’ hypothesis. J. Physiol.,
524(Pt 1): 117–134.
Santhakumar, V., Ratzliff, A.D., Jeng, J., Toth, Z. and Soltesz,
I. (2001) Long-term hyperexcitability in the hippocampus
after experimental head trauma. Ann. Neurol., 50: 708–717.
Santhakumar, V. and Soltesz, I. (2004) Plasticity of intern-
euronal species diversity and parameter variance in neuro-
logical diseases. Trends Neurosci., 27: 504–510.
Scharfman, H.E. (1991) Dentate hilar cells with dendrites in the
molecular layer have lower thresholds for synaptic activation
by perforant path than granule cells. J. Neurosci., 11:
1660–1673.
Sik, A., Penttonen, M. and Buzsaki, G. (1997) Interneurons in
the hippocampal dentate gyrus: an in vivo intracellular study.
Eur. J. Neurosci., 9: 573–588.
Song, S., Sjostrom, P.J., Reigl, M., Nelson, S. and Chklovskii,
D.B. (2005) Highly nonrandom features of synaptic connec-
tivity in local cortical circuits. PLoS Biol., 3: e68.
Soriano, E., Nitsch, R. and Frotscher, M. (1990) Axo-axonic
chandelier cells in the rat fascia dentata: Golgi-electron mi-
croscopy and immunocytochemical studies. J. Comp. Ne-
urol., 293: 1–25.
Spigelman, I., Yan, X.X., Obenaus, A., Lee, E.Y., Wasterlain,
C.G. and Ribak, C.E. (1998) Dentate granule cells form
novel basal dendrites in a rat model of temporal lobe epi-
lepsy. Neuroscience, 86: 109–120.
Sporns, O. and Kotter, R. (2004) Motifs in brain networks.
PLoS Biol., 2: e369.
Vida, I., Bartos, M. and Jonas, P. (2006) Shunting inhibition
improves robustness of gamma oscillations in hippocampal
interneuron networks by homogenizing firing rates. Neuron,
49: 107–117.
van Vliet, E.A., Aronica, E., Tolner, E.A., Lopes da Silva, F.H.
and Gorter, J.A. (2004) Progression of temporal lobe epilepsy
in the rat is associated with immunocytochemical changes in
inhibitory interneurons in specific regions of the hippocampal
formation. Exp. Neurol., 187: 367–379.
Watts, D.J. and Strogatz, S.H. (1998) Collective dynamics of
‘small-world’ networks. Nature, 393: 440–442.
Wenzel, H.J., Buckmaster, P.S., Anderson, N.L., Wenzel, M.E.
and Schwartzkroin, P.A. (1997) Ultrastructural localization
of neurotransmitter immunoreactivity in mossy cell axons
and their synaptic targets in the rat dentate gyrus. Hippo-
campus, 7: 559–570.
West, M.J. (1990) Stereological studies of the hippocampus: a
comparison of the hippocampal subdivisions of diverse spe-
cies including hedgehogs, laboratory rodents, wild mice and
men. Prog. Brain Res., 83: 13–36.
Woodson, W., Nitecka, L. and Benari, Y. (1989) Organization
of the gabaergic system in the rat hippocampal-formation: a
quantitative immunocytochemical study. J. Comp. Neurol.,
280: 254–271.
Yoshimura, Y. and Callaway, E.M. (2005) Fine-scale specificity
of cortical networks depends on inhibitory cell type and
connectivity. Nat. Neurosci., 8: 1552–1559.
Yoshimura, Y., Dantzker, J.L. and Callaway, E.M. (2005) Ex-
citatory cortical neurons form fine-scale functional networks.
Nature, 433: 868–873.
Zappone, C.A. and Sloviter, R.S. (2004) Translamellar disin-
hibition in the rat hippocampal dentate gyrus after seizure-
induced degeneration of vulnerable hilar neurons. J. Neuro-
sci., 24: 853–864.
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
658
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
PBR� V163 : 63035
AUTHOR QUERY FORM
Book: PBR-V163
Chapter: 63035
Please eail or fax your responses and any corrections to:
Eail:
Fax:
Dear Author,
During the preparation of your manuscript for typesetting, some questions may have arisen. These are listed below. Please check your
typeset proof carefully and mark any corrections in the margin of the proof or compile them as a separate list*.
Disk use
Sometimes we are unable to process the electronic file of your article and/or artwork. If this is the case, we have proceeded by:
& Scanning (parts of) your article & Rekeying (parts of) your article
& Scanning the artwork
Bibliography
If discrepancies were noted between the literature list and the text references, the following may apply:
& The references listed below were noted in the text but appear to be missing from your literature list. Please complete the list or
remove the references from the text.
& Uncited references: This section comprises references that occur in the reference list but not in the body of the text. Please position
each reference in the text or delete it. Any reference not dealt with will be retained inthis section
Queries and/or remarks
Location in
Article
Query / remark Response
AU:1 Since there are two publications
of Buckmaster et al., 2002, as per
style, we cross-refer it as ‘2002a’
and ‘2002b’ for tagging purposes.
Please go through each citation
and check whether the reference
is 2002a or 2002b.
AU:2 The reference Blumcke et al.,
2000 is not included in the
reference list. Please provide
complete details of the reference.
AU:3 Please provide the volume
number and page range for
references Dyhrfjeld-Johnsen et
al., 2006; Howard et al., 2006.
AU:4 Please provide last-page number
for references Reigl et al., 2004;
Roxin et al., 2004; Song et al.,
2005; Sporns and Kotter, 2004.
