Neocortical Pyramidal Cells Can Control Signals to Post-Synaptic Cells Without Firing: a model of the axonal plexus Erin Munro Department of Mathematics Boston University 4/14/2011
Gap junctions on pyramidal cell axons Evidence: near somata in 5% of pair recordings in layer 5 of rat neocortex where somata are adjacent (Wang et al. 2010) by immuno-gold labeling in hippocampus (Hamzei-Sichani et al. 2007) by spikelets seen in the hippocampus and neocortex (Draguhn et al. 1998, Steriade et al. 1993) by dye-coupling in the hippocampus and neocortex (Schmitz et al. 2001, Gutnick et al. 1985) Importance: gap junctions are linked with very fast oscillations (VFOs, >80 Hz) epilepsy An axonal plexus is a network of pyramidal cell axons connected by gap junctions.
An axonal plexus can produce externally-driven expanding waves
An axonal plexus can produce re-entrant/spiral waves
Do gap junctions fit in with neocortical processing? Spikes may propagate through the whole network of axons at any time. Somatic voltage seems to control VFOs in experiment. Perhaps somatic voltage controls VFOs by controlling propagation across gap junctions. We show that, in neocortical pyramidal cells: Somatic voltage can control propagation through gap junctions in the initial segment (IS) and main axon (MA). Somatic voltage can t control propagation from gap junctions in collaterals. Number of cells connected by uncontrollable gap junctions is relatively small. Results imply that: Pyramidal cells can control signals to post-synaptic cells by adjusting their somatic voltage. Too many collateral gap junctions may lead to epilepsy.
How could the somatic voltage control spike propagation across gap junctions? 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 spike propagation across gap junctions in the IS across gap junctions in the main axon from gap junctions on collaterals
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: 1. 40 cells from layers 2/3 2. 59 cells from layer 4 3. 57 cells from layer 5. Model neurons: 1. have exact geometry from reconstructions, or 2. have simplified geometry based on reconstructions
Equations used in models taken from Traub et al. 2005 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 only leak current in soma: g L (V s V ) Gap junction at point x in axon A and point y in axon B is modeled by adding the current: g gj (V B,y V A,x ) g gj (V A,x V B,y ) to the equation for A at x, and to the equation for B at y
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 cortical layers 2/3, 4, and 5
Spike propagation across gap junctions in the main axon Stimulate here Gap Junction Test for AP here stimulate one axon twice, test for spikes in other axon vary: gap junction distance from soma somatic voltage (V s ) g Na in main axon find threshold g Na that allows propagation find window of control for g Na where: Spikes propagate when V s = 60 mv Spikes are blocked when V s = 80 mv
V s can control gap junctions in the main axon window of control window of control for 2 spikes
V s can control gap junctions in the IS Soma Stimulate soma here stimulate axon: IS Gap Junction Main axon Or stimulate axon here Test for AP here stimulate soma: windows of control are similar
Model with exact geometry of 3D reconstructions 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 cortical layers find window of control for g Na where: Spikes propagate when V s = 60 mv Spikes are blocked when V s = 80 mv
V s can t control spike 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] L5 030625DS2: [59 59] L5 030625DS2: [52 54] L5 030625DS2: [43 51] L5 030625DS2: [5 15] L5 030625DS2: [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] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 g Na in S/cm 2 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 spikes may propagate from collaterals regardless of somatic voltage
How many cells may be hard-wired together? Hard-wired cells: spikes may propagate between them regardless of somatic voltage. Relative amplitude of VFO (RA) vs. pyramidal cell voltage (V s ) Fig. 5 of Grenier et al. 2001 Data from slow oscillation induced by ketamine-xylazine anesthesia in layer 5 RA is minimal when V s 83 mv How many cells could be firing at VFO frequencies when V s 83 mv? How many cells could be connected together without producing VFOs?
Possible number of cells producing VFOs during cell hyperpolarization number of pyramidal cells in layer 5 within 1 mm 2 : 19,550 (Skoglund et al. 1996, Beaulieu 1993) maximum fraction of cells in a large connected cluster: 2/3 (Traub et al. 1999) minimum RA: 0.01 Number of firing cells: 0.01 2/3 19, 550 130 But there could be groups of cells hard-wired together that are not producing VFOs.
How many cells can be connected together without producing VFOs? Network model of collateral connections arrange groups of axons in hexagonal grid weigh axons according to total axon lengths of 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
Cycles form when there are 70 cells in a cluster 1.8 1.6 1.4 Average number of cycles 1.2 1 0.8 0.6 0.4 0.2 0 0 10 20 30 40 50 60 70 80 90 100 Mean largest cluster size There can be up to 70 cells hard-wired together without producing VFOs. 70<130 maximum number of cells hard-wired together is 130.
What we ve learned so far: V s can control spike propagation across gap junctions in the IS in the main axon V s can t control spike propagation from gap junctions on collaterals Maximum number of cells hard-wired together 130 out of 20,000, or 0.65%
Implications for neocortical processing IS/MA connection collateral connection If black cells depolarize and 1 cell fires, in effect they all fire cells signal post-synaptic cells by depolarizing, not just by firing depolarized cells form cell assemblies large groups of depolarized cells produce VFOs send high-frequency signals to post-synaptic cells alter synapses
Implications for temporal lobe epilepsy Can t control spike propagation from collaterals. Too many connections on collaterals can lead to: many cycles formed by gap junctions on collaterals re-entrant VFOs that cannot be turned off by somatic voltage VFOs kindle post-synaptic cells epilepsy Extra collateral connections may result from lesions in certain directions (Gutnick et al. 1985) axonal sprouting (Salin et al. 1995) Lesions, axonal sprouting, and VFOs are all highly correlated with temporal lobe epilepsy.
Conclusion and Thanks! Pyramidal cells can send signals by depolarizing. Axonal sprouting can lead to epilepsy because axon collaterals form cycles. Acknowledgements: Nancy Kopell Roger Traub Yun Wang Thank you for your attention!