A realistic neocortical axonal plexus model has implications for neocortical processing and temporal lobe epilepsy

Transcription

1 A realistic neocortical axonal plexus model has implications for neocortical processing and temporal lobe epilepsy Neocortical Pyramidal Cells Can Send Signals to Post-Synaptic Cells Without Firing Erin Munro & Nancy Kopell 11/10/2010

2 Gap junctions are demonstrated: 1. near somata in 5% of pair recordings in layer 5 of rat neocortex where somata are adjacent (Wang et al. 2010) 2. by immuno-gold labeling in hippocampus (Hamzei-Sichani et al. 2007) 3. by spikelets seen in the hippocampus and neocortex (Draguhn et al. 1998, Steriade et al. 1993) 4. by dye-coupling in the hippocampus and neocortex (Schmitz et al. 2001, Gutnick et al. 1985)

3 Fast activity is correlated with cell depolarization VFOs in vivo Grenier et al. 2001, Fig. 11 Millisecond synchrony during a depolarized state (Wang et al. 2009) Very Fast Oscillations (VFOs, >80 Hz) during cell depolarization 1. slow-wave sleep (Grenier et al. 2001) 2. in active areas during processing (Edwards et al. 2010)

4 An axonal plexus 1. is a network of pyramidal cells axons connected by gap junctions 2. can produce millisecond synchrony 3. can produce VFOs with cell depolarization (Munro & Börgers 2010) Our questions are: 1. If a cell is connected in an axonal plexus, can it control APs propagating into its axon from other cells by its somatic voltage? 2. How does axonal sprouting effect the axonal plexus?

5 Modeling a neocortical axonal plexus We know that: AP propagation failure determines network behavior (Munro & Börgers 2010) noise, re-entrant VFOs (topological spiral waves), externally driven VFOs (topological target patterns) We hypothesize that: Gap junctions may be on any length of unmyelinated axon initial segment (IS), main axon (MA), axon collaterals So we: Model the effects of somatic voltage on AP propagation across gap junctions in the IS across gap junctions in the main axon from gap junctions on collaterals

6 3D pyramidal cell reconstructions downloaded from neuromorpho.org rat somatosensory cortex (Schubert et al. 2006, Shepherd & Svoboda 2005, Staiger et al 2004, Wang et al. 2002) 156 cells total: cells from layers 2/ cells from layer cells from layer 5. Translated reconstructions into NEURON using cvapp Model neurons: 1. have exact geometry from reconstructions, or 2. have simplified geometry based on reconstructions

7 Simplified axon model for IS/MA gap junctions soma IS { { main axon sharp taper shallow taper main axon (MA) fixed diameter d MA 12 electrotonic units (λ) long initial segment (IS) 40 µm long 2 linear tapers diameter between tapers is d IS sharp taper is lc λ long soma fixed diameter d s = d IS s ratio length is same as diameter d Ma, d IS, l c, s ratio based on reconstructions, different values for layers 2/3, 4, and 5

8 Equations for models taken from Traub et al C dv dt = g L (V L V ) + g Na m 3 h(v Na V ) + g K n 4 (V K V ) m, h, n are determined by dz dt = z (V ) z τ z (V ) g Na = g K =0.45 S/cm 2 by default in the IS g Na = g K =0.2 S/cm 2 by default in the main axon V L = 70 mv, V Na = 50 mv, V K = 95 mv, and g L = S/cm 2 in axon only leak in soma: g L (V s V ), g L = S/cm 2 Also tried conductances from Schmidt-Hieber et al and Yu et al

9 AP propagation across gap junctions in the main axon Stimulate here Gap Junction Test for AP here stimulate one axon twice, test for APs in other axon vary: gap junction distance from soma V s gna in main axon find threshold g Na that allows propagation find window of control for g Na where: AP propagates when V s = 60 AP fails when Vs = 80

10 V s can control gap junctions in the MA window of control window of control for VFOs g gj =4e 3, v s = 80 g =4e 3, v = 70 gj s g gj =4e 3, v s = 60 g =6e 3 gj g gj =8e cutoff for propagation cutoff for propagation within 5 ms g Na in S/cm g Na in S/cm electrotonic distance from IS electrotonic distance from IS

11 V s can control gap junctions in the IS stimulate axon: Stimulate soma here g gj =6e 3, v s = 80 g gj =6e 3, v s = 70 g gj =6e 3, v s = 60 g =8e 3 gj Soma IS g =1e 2 gj g =2e 2 gj Gap Junction g Na in S/cm Main axon distance from soma in µm Or stimulate axon here Test for AP here stimulate soma: window of control encompassed entire range of g Na tried for g gj = , µs

12 Model with 3D reconstruction for collateral gap junctions Stimulate here Test for AP here v same conductances as simplified model first 40 µm below soma counts as IS stimulate collaterals from 11 representative cells from all layers find window of control for g Na where: APs propagate when V s = 60 APs fail when Vs = 80

13 V s can t control AP propagation from collaterals L23 C170797A P1: [6 6] L23 C190898A P2: [1 1] L23 C190898A P2: [7 8] L23 C190898A P2: [11 14] L23 C190898A P2: [32 34] L23 C230797B P4: [1 7] L23 C230797B P4: [23 23] L23 C230797B P4: [34 36] L23 C230797B P4: [26 27] L23 C280199C P1: [1 8] L23 C280199C P1: [13 20] L23 C280199C P1: [23 25] L23 C280199C P1: [27 29] L23 C280199C P1: [33 34] L23 C280199C P1: [43 43] L4 C031097B P3: [3 5] L4 C031097B P3: [9 11] L4 C031097B P3: [13 19] L4 C031097B P3: [35 35] L4 C031097B P3: [28 28] L4 C200897C P3: [36 40] L4 C200897C P3: [33 34] L4 C200897C P3: [27 29] L4 C200897C P3: [26 26] L4 C200897C P3: [22 24] L4 C200897C P3: [20 20] L4 C200897C P3: [17 19] L4 C200897C P3: [16 16] L4 C271097A P2: [1 1] L4 C271097A P2: [3 8] L4 C271097A P2: [36 40] L4 C271097A P2: [18 22] L4 C271097A P2: [35 35] L4 IF4_140201: [82 84] L4 IF4_140201: [53 75] L4 IF4_140201: [36 39] L4 IF4_140201: [36 41] L4 IF4_140201: [22 23] L4 IF4_140201: [15 15] L4 IF4_140201: [14 14] L4 IF4_140201: [13 13] L4 IF4_140201: [12 12] L DS2: [59 59] L DS2: [52 54] L DS2: [43 51] L DS2: [5 15] L DS2: [19 27] L5 C040896A P3: [40 43] L5 C040896A P3: [40 64] L5 C040896A P3: [26 34] L5 C040896A P3: [13 16] L5 C261296A P1: [40 61] L5 C261296A P1: [39 39] L5 C261296A P1: [30 34] L5 C261296A P1: [13 19] L5 C261296A P1: [13 24] L5 C261296A P1: [4 8] v s = 80 v s = 70 v s = 60 v s = 50 windows of control do not overlap: between cells between collaterals in the same cell between stimulation sites on the same collateral there is no g Na where V s can control all collaterals simultaneously g Na required to propagate through axon

14 How many cells may be hard-wired together by collateral gap junctions? Relative amplitude of VFO (RA) vs. pyramidal cell voltage (V s ) Fig. 5 of Grenier et al Data from slow oscillation under ketamine-xylazine anesthesia RA is minimal when V s 83 mv How many cells could be firing at VFO frequencies when V s 83? How many cells must be connected together to see a VFO?

15 Network model of collateral connections arrange groups of axons in hexagonal grid weight axons according to lengths in 3D reconstructions randomly connect axons within 9 units on grid according to p: probability of connecting per µm 2 Need 1 cycle for re-entrant VFOs. As p varies, find: average number of cycles (m cy ) size of largest cluster when m cy = 1

16 Need 75 cells in a cluster to get cycles Average number of cycles Mean largest cluster size There can be up to 75 cells hard-wired together without seeing VFOs.

17 Field potential model estimate number of cells firing at VFO frequencies We want: to interpret relative amplitude (RA) in Fig. 5 of Grenier et al. where V s 83 mv M : number of cells generating field potential v l,j = w l,j + X l,j : membrane potential of cell l at time j w l,j is deterministic is random, µ = 0 and standard deviation σ X l,j v j = 1 M M l=1 v l,j: field potential at time j E( ˆvk 2 ) : amplitude of field potential at frequency 2πk

18 Relative amplitude according to field potential model m max assume M : number of cells generating field potential m : number of cells firing at VFO frequency 2πk : maximum number of cells that ever fire at frequency 2πk ŵ l,k are all the same σ = α ŵ l,k E( ˆvk 2 m ) = 2 ŵ M 2 l,k 2 + M m RA = r r m 2 M 2 ŵ l,k 2 + M m M 2 M 2 σ 2 σ2 = mmax 2 M 2 ŵ l,k 2 + M m max M 2 σ 2 m 2 +α 2 (M m) m 2 max +α 2 (M m max )

19 Maximum number of cells firing at VFO is 130 M: beneath 1 mm 2 of somatosensory cortex: number of cells: 133,000 number of cells in layer 5: 23,000 number of pyramidal cells in layer 5: 19,550 m max : percentage of cells participating in a VFO 30% of cells show spikelets during slow-wave sleep 2/3 of cells in large cluster in previous network model based on neocortical connectivity RA 0.01 when V s = 83 mv, estimate α 0.01 M m max m 23,000 (.3)19, (2/3)19, ,000 (.3)19, (2/3)19,

20 Summary V s can control AP propagation across gap junctions in the IS in the main axon V s can t control AP propagation from gap junctions on collaterals Maximum number of cells hard-wired together 130

21 Implications for neocortical processing IS/MA connection collateral connection If pink cells depolarize and 1 cell fires, in effect they all fire cells send signals to post-synaptic cells by depolarizing, not just by firing depolarized cells form cell assemblies large groups of depolarized cells exhibit VFOs, send tetanic signals to post-synaptic cells

22 Implications for temporal lobe epilepsy Too many connections on collaterals cycles formed by gap junctions on collaterals persistent re-entrant VFOs VFOs kindle post-synaptic cells epilepsy Extra collateral connections may result from lesions in certain directions axonal sprouting Lesions, axonal sprouting, and VFOs are all highly correlated with temporal lobe epilepsy.

23 Scenario for re-entry with a cycle among collaterals 2: AP blocked at main axon close to soma v 1: Soma fires 4: AP propagates into collateral close to soma, perpetuates around cycle v gap junctions 3: AP propagates at main axon far soma