Transcript ppt - Neurodynamics Lab

BME 6938
Neurodynamics
Instructor: Dr Sachin S Talathi
Neurocomputational Properties
Integrators: Non-existence of sub-threshold oscillations
(Saddle Node on Invariant Circle and Homoclinic
Bifurcation)

Resonators: Existence of subthreshold bifurcation (HopfBifurcation)
Coexistence of Resting and Spiking State
Yes
Resonator Integrator
Subthreshold oscillations

No
Saddle-Node
Saddle-Node on Invariant
Circle
Subcritical-Hopf Bifurcation
Supercritical-Hopf Bifurcation
Neurocomputational Properties
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 subthreshold 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
Frequency Preference
Input
Output
Impedence
Resonator
Impedence= Amplitude of Evoked potential/Amplitude of stimulating oscillating current
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.
Mechanism of Frequency Selectivity in
Resonators
What makes resonance interesting
Threshold for spiking?
Std method to determine threshold
The Dilema!
Threshold Manifolds
Well-define threshold manifolds
Threshold manifolds not well defined
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
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
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
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
Flipping from Integrator to Resonator
Fast-Slow Dynamics
Fast variable includes: Membrane voltage dynamics, fast sodium currents etc..
Slow variable includes: Slow membrane currents such as h-current
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
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.
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
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)
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.