jonathan & pooya computational neuroscience summer school june 17-29, 2007

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

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ncy

of th

e D

rive

r

Spike count in 200 ms

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ode:

Tri

al c

ount

out

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100

No Driver Excit Inhib

10

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1000

Log

arit

hmic

incr

ease

in th

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ncy

of th

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Spike count in 200 ms

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No Driver Excit Inhib

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Log

arit

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incr

ease

in th

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ncy

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Spike count in 200 ms

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out

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No Driver Excit Inhib

10

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Log

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incr

ease

in th

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ncy

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Spike count in 200 ms

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out

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No Driver Excit Inhib

10

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Log

arit

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incr

ease

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ncy

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Spike count in 200 ms

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out

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No Driver Excit Inhib

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Log

arit

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incr

ease

in th

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ncy

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Spike count in 200 ms

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out

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100

No Driver Excit Inhib

10

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Log

arit

hmic

incr

ease

in th

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ncy

of th

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Spike count in 200 ms

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ount

out

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100

No Driver Excit Inhib

10

100

1000

Log

arit

hmic

incr

ease

in th

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ncy

of th

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Spike count in 200 ms

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ode:

Tri

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out

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100

No Driver Excit Inhib

10

100

1000

Log

arit

hmic

incr

ease

in th

e fr

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ncy

of th

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rive

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Spike count in 200 ms

Col

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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

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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

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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: