The Axonal Plexus. A description of the behavior of a network of neurons connected by gap junctions. Erin Munro, 4/4/2007

Transcription

1 The Axonal Plexus A description of the behavior of a network of neurons connected by gap junctions Erin Munro, 4/4/2007

2 Why are we interested in studying the axonal plexus? Gap junctions are indicated in: Very Fast Oscillations (VFOs, > 80 Hz) during slow wave-sleep (.5-1 Hz), gamma oscillations (20-80 Hz), and epileptic activity Gamma oscillations without VFOs In 1999, Traub et al showed that an axonal plexus can produce VFOs. (The somata were intrinsically bursting.)

3 VFOs and Slow-Wave sleep Oscillations with Epileptic Activity From Figure 2 of Grenier et al, 2003

4 VFOs on Upswing of Gamma Oscillations From Figure 1 of Traub et al 2003a

5 Gamma Oscillations Without VFOs From Figure 1 of Traub et al 2003b

6 Simulation Setup cell grid Connections made randomly between cells within 10 units on the grid Average 1.6 connections per cell Each cell has at most 4 connections Cells stimulated randomly via a Poisson process with l = 2/s/cell.

7 Cellular Automaton Model Cells have 3 states: on, refractory, excitable Life cycle: excæ ÆexcÆonÆrefrÆrefrÆrefrÆexc Cells become on 1) spontaneously through Poisson process with mean l or 2) when connected neighbor is on for the previous time step. After cells are on for one step, they are refractory for 3 steps.

8

9

10 Closed Wave Broken Wave

11 5-Compartment Model: Axon and Initial Segment from Traub 1999 C k dv k /dt = l g l,k (V l -V k ) + I ionic I ionic = g L,k V k + g Na,k m k3 h k (V na -V k ) + g K(DR),k n k4 (V K -V k ) + I gap_junctions,k + I injected,k Øfixed somatic voltage initial segment Initial segment attached to a soma with fixed voltage. Default voltage is 0 mv. Gap Junctions in penultimate compartment with default conductance 3.66 ns. Stimulated in last compartment gap junctions stimulation

12 Setting the Somatic Voltage: 0 mv

13 Setting the Somatic Voltage: 1 mv

14 Setting the Somatic Voltage: 2 mv

15 Setting the Gap Junction Conductance: 3.5 ns

16 Setting the Gap Junction Conductance: 4 ns

17 Setting the Gap Junction Conductance: 4.5 ns

18 Setting the Gap Junction Conductance: 5 ns

19 Parameter regimes for noise-driven activity vs. re-entrant activity default voltage noise-driven oscillations partial propagation re-entrant oscillations default conductance

20 Neurons must propagate signals some of the time to get re-enrant activity.

21 Transition from partial propagation to re-entrant oscillations V S = 0 mv, g gj = 3.5 ns V S = 0 mv, g gj = 4 ns

22 Transition occurs when neurons with 4 neighbors can fire when 1 neighbor fires Stim 1Æ Stim 2Æ Delay is 0.5 ms Delay is 0.6 ms 3.5 ns 4 ns

23 Changing rule in CA creates partial propagation

24 Transition from re-entrant to noise-driven oscillations V S = 0 mv, g gj = 4.5 ns V S = 0 mv, g gj = 5 ns

25 Transition occurs when all neurons have same refractory period Stimulation Æ g gj = 4.5 ns g gj = 5 ns

26 Changing rule in CA creates re-entrant oscillations

27 69-Compartment Model: Full model from Traub 1999 C k dv k /dt = l g l,k (V l -V k ) - I ionic For Soma and Dendrites: I ionic = g L,k V k + g Na,k m k2 h k (V Na -V k )+ g Ca,k s k2 (V Ca -V k ) + g K(DR),k n k2 (V K -V k ) + g K(A),k a k b k (V K -V k ) + g K(AHP),k q k (V K -V k ) + g K(C),k c k min(1,c k /250)(V K -V k ) 69 compartments: 64 for soma and dendrites, 5 for the initial segment and axon Gap junctions in penultimate axonal compartment with a default conductance of 3.66 ns. Stimulation applied to last axonal compartment

28 69-Compartment Model

29 Intrinsic Bursting

30 Interaction Between Axon and Soma

31 Parameter regimes for noise-driven activity vs. re-entrant activity default conductance

32 Behavior of axonal plexus with intrinsically bursting neurons

33 Behavior of axonal plexus before the burst

34 Behavior of axonal plexus during the burst

35 Parameter regimes for noise-driven activity vs. re-entrant activity Traub 2000b Traub 2000a Traub 1999 Traub 2000a

36 Conclusions We have three parameter regimes for somatic voltage and gap junction conductance where we see: partial propagation, re-entrant oscillations, and noise-driven oscillations. Re-entrant oscillations occur over a broad range of parameters.(lewis, 2001) We see partial propagation outside of the burst, and noisy oscillations during the burst for the results of the 69-compartment model because of varying somatic potential and a higher stimulation frequency. The axonal plexus with varying somatic potential can be a mechanism for VFOs on the upswing of gamma and slow-wave oscillations. (Traub 2003a, Grenier 2001) We can get gamma oscillations withoutvfos in the axonal plexus because of partial propagation. (Traub 2003b)

37 References Grenier, F., Timofeev, I., Steriade, M., (2001) J. Neurophysiol. 86, Lewis, T.J., & Rinzel, J., (2000). Comp. Neural Syst., 11, Lewis, T.J., & Rinzel, J., (2001). Neurocomputing, 38-40, Traub, R.D., Schmitz, D., Jefferys, J.G.R., & Draguhn, A., (1999). Neuroscience, 92, Traub, R.D., Bibbig, A., (2000a) J. Neurosci., 20(6), Traub, R.D., Bibbig, A., Fisahn, A., LeBeau, F.E.N., Whittington, M.A., Buhl, E.H., (2000b) Eur. J. Neurosci. 12, Traub, R.D., Cunningham, M.O., Gloveli, T., LeBeau, F.E.N., Bibbig, A., Buhl, E.H., Whittington, M.A., (2003a) PNAS 100, Traub, R.D., Pais, I., Bibbig, A. LeBeau, F.E.N., Buhl, E.H., Hormudzie, S.G., Monyer, H., Whittington, M.A. (2003b) PNAS 100,

38 Parameter regimes for noise-driven activity vs. re-entrant activity Traub 2000b Traub 2000a Traub 1999 Traub 2000a

39 Behavior of axonal plexus before the burst

40 Behavior of axonal plexus during the burst