1. Presented by Suganya Karunakaran Reduction of Spike Afterdepolarization by Increased Leak Conductance Alters Interspike Interval Variability Fernando R. Fernandez and John A.White The Journal of Neuroscience, January 28, 2009 29(4):973–986 973

2. Spike Afterdepolarization  Membrane potential depolarization that follows an action potential  May occur before (early) or after (delayed) full repolarization  Common in cardiac muscles  Sometimes occurs in tissues not normally excitable

3. Leak Conductance  Leak conductance is generated by membrane damage surrounding an electrode and an increase in K + permeability evoked by cytosolic elevations of Sodium and Calcium

4. Interspike Interval Variability  Inter-spike Interval  Variability of neuronal spike train – important indicator of the type of processing a neuron performs on its synaptic inputs  Simplest measure – Coefficient of Variability CV = standard deviation of ISI distribution/mean ISI  Refractory period lowers the CV at high firing rates when it tends to force regularity in the ISI duration

5. High-Conductance state  State of neurons in an active network  Total synaptic conductance received by the neuron (over a period of time) is larger than its resting conductance  Found in thalamocortical system especially cerebral cortex  Neurons can integrate differently in this state  Can be reproduced by dynamic-clamp experiments

6. Computational Consequence  Neuronal responses in high-conductance states are probabilistic because of the high variability of responses due to the presence of fluctuating background activity  Change the response properties of neurons Red- deterministic neuron Green- probabilistic neuron

7. Computational Consequence  May fundamentally chance dendrite integration properties  Reduced membrane time constant – change in Temporal Processing High conductance State Decrease in integration time constant Increase in spike output variability

8. Previous Results  Effects of background synaptic conductance activity on ISI variability depends on neuron type For a conductance based stimulus,  In pyramidal cells lacking spike frequency adaptation, variability increased  In pyramidal cells displaying spike frequency adaptation, variability decreased ( τ differs between two subtypes)  Leak – bifurcation parameter Reduces afterdepolarization (ADP) Decrease the gain of frequency-current relationship

9. Model

10. Model ctnd.

11. Parameters

12. Non adapting Cells  The ability of a high conductance state to increase ISI variability depends on the subtype of pyramidal cell. High conductance state – Leakier membranes Faster decay rates for synaptic inputs Increases ISI variability

13. Model  3 Dimensions V h (I Na inactivation ) n (I KCa activation)  Single pulse-excited spike produces a larger ADP under control conditions than with added leak conductance

14. Single pulse Excitation Matlab Model- Reproduced Result

15. Decrease in CV

16. Phase Plane Analysis - Control Blue – Stable fixed point Black – Unstable fixed point Reproduced Result

17. Phase Plane Analysis – with leak

18. Phase Plane Analysis

19. Bifurcation Analysis

20. Conclusion  The decrease in CV of the model with added leak conductance can be explained as a consequence of a lower gain in the F-I relationship resulting from the changes in the ADP and bifurcation in the fast subsystem of the model