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BME 6938 Neurodynamics

BME 6938 Neurodynamics. Instructor: Dr Sachin S Talathi. Recap . Linear stability analysis Bifurcation-Definition and Terminology Normal Form Bifurcation Diagram Saddle Node Bifurcation Transcritical Bifurcation Pitchfork Bifurcation. One Dimensional Neuron models. I fast.

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BME 6938 Neurodynamics

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  1. BME 6938Neurodynamics Instructor: Dr Sachin S Talathi

  2. Recap • Linear stability analysis • Bifurcation-Definition and Terminology • Normal Form • Bifurcation Diagram • Saddle Node Bifurcation • Transcritical Bifurcation • Pitchfork Bifurcation

  3. One Dimensional Neuron models Ifast The dynamics of fast variable is much faster than time scale for membrane dynamics

  4. Types of 1-dimensional neuron models • Ifast: Can be inward or outward • The gating variable can be activating (turned on by depolarization) or deactivating (turned on by hyperpolarization) • We can classify four model types: • Inward activating: Persistent sodium current (INa,p) • Inward de-activating: Fast potassium current (IK) • Outward activating: h-current (I) • Outward de-activating: Potassium inactivation current (IKir)

  5. Summary of 4 models

  6. Amplifying and Resonating Currents Amplifying I’(V)<0: Provide positive Feedback through interation with membrane voltage Eg: INa,p, Ikir Resonating: Damp oscillations by providing negative feedback Eg: IK, Ih Negative feedback Positive feedback

  7. Specific Example: INa,p model Parameters: C=10; Im=0; gL=19; EL=-67; gNa=74; V1/2=1.5; K=16;ENa=60

  8. Dynamical behavior of INa,p model

  9. Bifurcation in INa-P model Lets Verify this bifurcation diagram in XPPAUTO

  10. Makings of action potential Model

  11. Glimpse of Neurocomputational property • Slow transition to spiking: Ghost of saddle node Im=30 Pyramidal cell in rat Visual cortex Read sections 3.2-3.3.7 from Izhikevichs book

  12. Specific Example: INa,p model Parameters: C=10; Im=0; gL=19; EL=-67; gNa=74; V1/2=1.5; K=16;ENa=60

  13. Dynamical behavior of INa,p model

  14. Bifurcation in INa-P model Lets Verify this bifurcation diagram in XPPAUTO

  15. Makings of action potential Model

  16. Glimpse of Neurocomputational property • Slow transition to spiking: Ghost of saddle node Im=30 Pyramidal cell in rat Visual cortex Read sections 3.2-3.3.7 from Izhikevichs book

  17. XPPAUTO-Exercise • Bifurcation analysis using AUTO. • We will use the example provided in Ex2.ode file. • We will soon see that this example is 1d version of the more famous Morris-Lecar Neuron Model.

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