jonathan & pooya computational neuroscience summer school june 17-29, 2007
TRANSCRIPT
Jonathan & PooyaComputational Neuroscience summer school
June 17-29, 2007
Intrinsic bursting properties of thalamic relay cells.
• Low threshold calcium conductance:
Whenever the neuron is hyperpolarised, the calcium conductance is de-inactivated and if the membrane potential is depolarised (e.g:by an EPSP), the neuron triggers a calcium spike, on the top of which usually other fast Na-K spikes occurs.
Hodgkin-Huxley like models…
Dynamics of the membrane potential:
… and few parameters to characterise it!!!
Leaky integrate-and-fire-or-burst : A simple model for the low-threshold Ca2+ current.• 2-D discontinuous flow reproducing
the low-threshold Ca2+ current at the origin of the bursting properties of thalamic relay cells.
• Low Threshold (-65mV) : Boundary under which IT is de-inactivated.
• Classical Threshold (-45mV) : Boundary where you trigger a usual NaK fast spike and then come back to reset for a refractory time.
• Dynamic of the model :
LIFB
Spontaneous noise
LIFB
Spontaneous noise Excitatory drive
LIFB
Spontaneous noise Inhibitory drive
Goal: Detecting the existence of the Driver signal. Is there a driver signal there or is the input of the LIFB entirely coming from noise?
Independent variables:1- noise frequency (rate of Poisson process= 10-1000 Hz : 20 log steps)2- Driver frequency (rate of Poisson process= 10-1000 Hz : 20 log steps)3- Driver weight (no Driver Or excit. Or inhib.)Trial #100 for each combination of independent variables: different input times
Dependant variable: output spike count and its distribution across 100 trials
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
10
100
1000
Log
arit
hmic
incr
ease
in th
e fr
eque
ncy
of th
e D
rive
r
Spike count in 200 ms
Col
or c
ode:
Tri
al c
ount
out
of
100
No Driver Excit Inhib
Area under ROC close to 1
a
b
c d
PFA
Phit
ab
c
d
PFA
Phit
Detection: Right Side: spike count larger than criterion= Driver detected.
Excitatory driver and Burst-inducing inhibitory driver
Detection Rule: Left Side spike count less than criterion= Driver detected.
Inhibitory driver
abcd
abcd
Area under ROC close to 0.5
Detection: Right Side: spike count larger than criterion= Driver detected.
Excitatory driver and Burst-inducing inhibitory driver
Detection Rule: Left Side spike count less than criterion= Driver detected.
Inhibitory driver
abcd
abcd
ab
cd
PFA
Phit
ab
cd
PFA
Phit
The area under the ROC curve was calculated for any combination of noise level with the level of excitatory input.
10 100 1000
1000
100
10
Hz Excitatory Drive
Hz
Spo
ntan
eous
noi
se
Results of the original article
The area under the ROC curve for any combination of noise level with the level of inhibitory input.
Hz Inhibitory Drive
Hz
Spo
ntan
eous
noi
se
Results of the original article
For calculating the area under the ROC curve for detection of Inhibitory inputs, we calculated with both right-side (burst) and left-side (inhibituion) detection assumptions. For any single data point (noise X driver) the maximum of the two was taken as the result of ROC calculation. We only guessed this should be the methods that the authors have used because they have referred the reader to an internet website that has expired for the details of their methods. Map of the left-side detection versus right-side: