BME 6938 Neurodynamics

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BME 6938Neurodynamics

• Instructor Dr Sachin S Talathi

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Neurocomputational Properties

• Integrators Non-existence of sub-threshold
  oscillations (Saddle Node on Invariant Circle and
  Homoclinic Bifurcation)
• Resonators Existence of subthreshold bifurcation
  (Hopf-Bifurcation)

Coexistence of Resting and Spiking State
Yes
No
Saddle-Node Saddle-Node on Invariant Circle
Subcritical-Hopf Bifurcation Supercritical-Hopf Bifurcation
Integrator
Subthreshold oscillations
Resonator
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Neurocomputational Properties
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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
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Frequency Preference
Input
Output
Impedence
Resonator
Impedence Amplitude of Evoked potential/Amplitude
of stimulating oscillating current
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Frequency preference of circuits
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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.

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Mechanism of Frequency Selectivity in Resonators
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What makes resonance interesting
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Threshold for spiking?
Std method to determine threshold
The Dilema!
Threshold Manifolds
Well-define threshold manifolds
Threshold manifolds not well defined
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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

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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

Integrator
Resonator
Resonator-Postinhibitory facilitation
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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
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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
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Flipping from Integrator to Resonator
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Fast-Slow Dynamics
Fast variable includes Membrane voltage
dynamics, fast sodium currents etc.. Slow
variable includes Slow membrane currents such as
h-current
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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

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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.

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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

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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)

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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.