1

Oscillator 1

input

output

1

trigger

Introduction to NeurobiologyLecture 13: models of oscillations 1

Oscillator 1

input

output

1

2 3 4 1 3 4 1 2 4 1 2 3

S1

Coupling

trigger

S2

S3

S4

2

Oscillator 2

trigger

Oscillator 3

3

trigger

Oscillator 4

4

trigger

Electronic model of olivary network 2

Oscillator 1

input

output

1

2 3 4 1 3 4 1 2 4 1 2 3

S1

Coupling

trigger

S2

S3

S4

2

Oscillator 2

trigger

Oscillator 3

3

trigger

Oscillator 4

4

trigger

Output control switch

Input control switch

Electronic model of olivary network 2

1

2

4

3

Output control switch

input

output

1

Coupling

trigger

2 3 4

Input control switch

Osci. 1 Osci. 2 Osci. 3 Osci. 4

The electrical activity in the model 3

input

output

1

Coupling

trigger

2 3 4

Input control switch

Osci. 1 Osci. 2 Osci. 3 Osci. 4

input

output

1

Coupling

trigger

2 3 4

Input control switch

Osci. 1 Osci. 2 Osci. 3 Osci. 4

1

2

4

31 +

3

input

output

1

Coupling

trigger

2 3 4

Input control switch

Osci. 1 Osci. 2 Osci. 3 Osci. 4

input

output

1

Coupling

2 3 4

Input control switch

Osci. 1 Osci. 2 Osci. 3 Osci. 4

input

output

1

Coupling

2 3 4

Input control switch

Osci. 1 Osci. 2 Osci. 3 Osci. 4

1

2

4

3

Oscillator 1

input

output

1

2 3 4 1 3 4 1 2 4 1 2 3

S1

Coupling

S2

S3

S4

2

Oscillator 2

Oscillator 3

3

Oscillator 4

4

Output control switch

Input control switch

N

N N N N

The hybrid system4

The responses in the hybrid system

N

1

3

N

1

3

5

The responses in the hybrid system

1

3

N

I

1

3

N

I

6

The heterogeneity model

gL

VL

gCa

VCa

C Vm

C = gL(Vm -VL)+gCa(Vm-VCa)

dVdt

gCa = gCa m3h

gCa (mS/cm2)

gL(m

S/c

m2)

dhdt

hinf(Vm)-h

= th

7

8Oscillations with dynamic clamp

Reconstructing the phase diagramReconstruction of the phase diagram 9

10

Oscillations in a pair of coupled neurons

The line connecting the two cells crosses the oscillating zone.

The combination of the average channel densities falls inside the oscillating or stable zone.

gCa (mS/cm2)

gL(m

S/c

m2)

11

The rule of thumb

12

Oscillations in a network of coupled neurons

13

The architecture of the network

14

The effect of single neuron manipulation