1. Neural Synchronization via Potassium Signaling

2. Neurons Interactions Neurons can communicate with each other via chemical or electrical synapses. Chemical synapses are most typical for nerve cells, however, electrical synapses may also contribute to neuron signaling. Closely located cells can interact via the temporally varying concentrations of extra cellular ions produced by neighbouring cells. Francisco F.De-Miguel, Mariana Vargas-Caballero, Elizabeth Garcia- Perez, Spread Of Synaptic Potentials Through Electrical Synapses In Retzius Neurons Of The Leech, The Journal of Experemental Biology 204, 3241-3250 (2001)‏ 2 Dentrietes of two neurons Extracellular volume has complex configuration

3. Example A: Ischemia studies Hansen (1978)‏ Hill&Gettes (1980)‏ Wilde et al. (1990)‏ Yan et al. (1996)‏ Quantitative ODE based modeling: Yi et al. (2003)‏ Extra-cellular potassium [K + ] e rise during Ischemia: brain tissue: 5 mM  80 mM cardiac tissue: 4-6 mM  8-14 mM and more Example B: Neural-glial interactions Giant glial cell of the medical leech is activated by the [K + ] e rise above 10mM (normal level is 4 mM). Deitmer et al. (1999)‏ Example C: neuronal firing in vivo At high neuronal activity [K + ] e rises from 3.5mM to 9mM Sykova (1983)‏

4. Schematic representation of the potassium signaling pathways interaction via potassium signaling «Candidates» for ionic signaling: Sodium Calcium Potassim 4 interaction via potassium signaling and gap- junction

5. action potential [K] current The bath cell [K + ] e is constant [K + ] i is constant Hodgkin-Huxley model in its traditional form does not take into account possible changes of environment (i) To develop a simple model that describes the potassium signaling between neighboring cells (ii) To study the main features induced by this type of coupling with focus on noise-induced effects Objectives:

6. action potential [K] current Na-K pump The bath diffusion pumping back cell 1cell 2 [K + ] Limited extracellular space can be responsable for [K + ] modulation

7. The bath cell 1cell 2 Nearby located cells may interact !

8. Neuron model Our model is based on four-dimensional set of Hodgkin-Huxley type equations for the leech P-neuron (R.Guantes, G.G de Polavieja 2005, Variability in noise-driven integrator neurons)‏ где 5

9. Balance of extracellular potassium concentration neuron potassium currents diffusion process, governed by the concentration differnce Main control parameters: W – extracellular volume γ – diffusion constant 6

10. Individual neuron: Bifurcation diagrams 7 With varying of I app system demonstrates exciteble and self- sustainded properties The same regimes can be observed with variation of potassium concentration

11. Coupled identical neurons: Synchronous regimes The changes in extracellular volume and diffusion rate are responsable for competing of in-phase and anti-phase synchronization patterns 8 Identical cells: I1=I2=16.0 μA/cm 2

12. Coupled heterogeneous cells I app1 ≠ I app2 : Synchronous regimes In-phase regime becomes limited with increasing mismatch Anti-phase synchronization can only be observed in a narrow region close to the origin Most part of the diagram is occupied by the asynchronous regime 9 Small mismatch: Iapp 1 =16.0, Iapp 2 =16.1 Strong mismatch: Iapp 1 =16.0, Iapp 2 =18.0

13. Coupled heterogeneous cells: Synchronous regimes on (I app2, γ ) plane The transition between anti-phase and in-phase synchronous pattrens with varying diffusion rate γ At intermediate value of γ, a set of synchronous regimes coexist 10

14. Coupling induced chaotic firing (d) starting from an initial point P, the trajectory fills out the phase volume of the disapeared chaotic attractor and spends considerably time following its structure while approaches the vicinity of stable equilibrium E and converges to it 11 a) Individual system is in excitable regime b) Potassium signaling induces chaotic behavior c) gap-junction coupling destroys chaos d) transient image of chaotic saddle without gap-junction coupling with gap-junction coupling

15. Chaotic transient and system´s response A small variation of the stimulus intensity can lead to a large change of the length of the spike train, generated in response to the stimulus 12 stimulus Different response of the first cell at stimulus intensityThe duration of this response τ vs. stimulus intensityΔI app ΔIapp1= 1.04 ΔIapp1= 1.05 ΔIapp1= 1.06

16. Noise-induced firing patterns At the same noise intensity, coupled and uncoupled neurons fire in a different way firing-induced depolarization

17. Interspike intervals show different time scales Beside the expected time scale of 20ms, new time scales are detected. There is the noise-controlled time lag between the firing events in neurons

18. New time scale: explanation Example time series: formation of approx. 30ms time scale A: 1 st  2 nd B: 2 nd  1 st A  A  A... B  B  B... No 30ms time scale A  B.. B  A...there is !

19. Noise-induced collective discharges in ensembles of 4 and 8 neurons ? synchronous firing events On-Off numeric experiment All noise-induced spikes appear with 4-6ms time lagfrom “leading” neuron

20. Noise-induced collective discharges in ensembles of 4 and 8 neurons collective responce signal: 24 neurons (wild)‏ 24 On-Off (w=4)‏ 24 On-Off (W=20)‏ 24 On-Off (W=40)‏ Ocassional noise-indiced spike produced by one of neurons provokes the collective noise-induced discharge of all other neurons. 24 neuron demo: top row of 4 leading neurons