1. BME 6938 Neurodynamics Instructor: Dr Sachin S Talathi

2. Neurocomputational Properties  Integrators: Non-existence of sub-threshold oscillations (Saddle Node on Invariant Circle and Homoclinic Bifurcation)  Resonators: Existence of subthreshold bifurcation (Hopf- Bifurcation) Saddle-NodeSaddle-Node on Invariant Circle Subcritical-Hopf BifurcationSupercritical-Hopf Bifurcation Coexistence of Resting and Spiking State Subthreshold oscillations YesNo Integrator Resonator

3. Neurocomputational Properties

4. Sub-threshold oscillations Distinguishable feature of an oscillator near the threshold for Hopf Bifurcation Fast low threshold potassium currents are primarily involved in the generation of these sub- threshold oscillations Noise makes these oscillations sustainable Slow sub-threshold oscillations however are not related to the particular bifurcation mechanism and result from interplay of slow currents with fast channel kinetics Fast Slow

5. Frequency Preference InputOutputImpedence Impedence= Amplitude of Evoked potential/Amplitude of stimulating oscillating current Resonator

6. Frequency preference of circuits

7. Frequency Preference Integrators prefer high frequency Inputs They act as coincidence detectors Resonators prefer selective frequency inputs, that is dependent on the natural frequency of their sub-threshold oscillations.

8. Mechanism of Frequency Selectivity in Resonators

9. What makes resonance interesting

10. Threshold for spiking? Std method to determine thresholdThe Dilema! Threshold Manifolds Well-define threshold manifolds Threshold manifolds not well defined

11. Post Inhibitory Spike-Prolonged hyperpolarization Prolonged injection of hyperpolarization current and sudden release can produce a rebound spike. This can happen in both integrator and resonator models and is independent of bifurcation. Often these are caused by hyperpolarization activated h currents, which slowly build up

12. Post inhibitory spike-brief hyperpolarization Post inhibitory spike resulting from brief hyperpolarization is dependent on the type of bifurcation Integrators cannot exhibit post inhibitory spike After brief hyperpolarization IntegratorResonatorResonator-Postinhibitory facilitation

13. Inhibition induced spiking Neurons with slow hyperpolarization activated h currents and T-currents can produced inhibition induced spiking Resonators can exhibit this phenomenon independent of particular ion channel properties

14. Spike Latency Potassium A-channels (with fast activation and slow deactivation) are typically responsible for the observation of spike latency in neuron models. They activate immediately on depolarization, preventing the neuron from producing action potential Existence of spike latency is an innate neurocomputational property of integrators

15. Flipping from Integrator to Resonator

16. Fast-Slow Dynamics Fast variable includes: Membrane voltage dynamics, fast sodium currents etc.. Slow variable includes: Slow membrane currents such as h-current

17. Neurocomputational properties resulting from fast-slow interactions  Spike Frequency adaptation: Decrease in instantaneous spiking frequency A feature commonly observed in many cortical neurons. Slow resonant variables play an important role in this dynamics. It builds up with each spiking and slows down the spiking frequency

18. I-V Curve: Fast Slow subsystem Example of a Fast Slow System: Fast subsystem governs the spike generation mechanism through SNIC On long time scale IK(M) dominates making the IV curve monotonic. The model can now indeed exhibit some resonant properties such as post inhibitory rebound.

19. Slow sub-threshold oscillations  One possible mechanism involving slow variables resulting in this observation is  I-V curve has two stable fixed points and the slow resonant variable changes the dynamics between these 2 states

20. Rebound response and voltage sag  Slow resonating h-currents generate voltage sag and corresponding rebound spike (cortical pyramidal cells)  Slow amplifying low threshold calcium currents generate rebound spikes without voltage sag (eg. Thalamocortical neurons)

21. After-hyperpolarization and depolarization (AHP/ADP)  Slow resonating currents such as calcium activated potassium currents result in AHP  Slow amplifying currents such as T-type calcium currents generate ADP.