Neuron-computer interfacein Dynamic-Clamp experiments

Anton V. Chizhov

A.F.Ioffe Physico-Technical Institute of Russian Academy Sciences,St.-Petersburg, Russia

Leaky integrate-and-fire model

Hodgkin-Huxley neuron model

Control parameters of neuron

Dynamic-clamp• Artificial synaptic current

• Artificial voltage-dependent current

• Synaptic conductance estimation

SLL iVtVgdtdVC ))((

resetVV TVV If then

Leaky Integrate-and-Fire neuron

V is the membrane potential; I is the input (synaptic) current, C is the membrane capacity; gL is the membrane conductance; Vrest is the rest potential; VT is the threshold potential; Vreset is the reset potential.

Lm g

C

resetLSLTLSL

L

VgiVVgiVC

g

//ln

Firing rate dependence on current (F-I-curve)

h

[Покровский, 1978]

φ≈0

rV(x) V(x+Δx)

im

jm

C

Внутри

Снаружи

V

gK

gNa

VNa

VrestVK

SLS iVVg )(

Set of experimental data for Hodgkin-Huxley approximations

Approximations forare taken from [L.Graham, 1999]; IAHP is from [N.Kopell et al., 2000]

Model of a pyramidal neuron

SAHPLHMADRNa iIIIIIIIdtdVC

HMADRNa IIIII ,,,,

)()(

,)(

)(

UyUy

dtdy

UxUx

dtdx

y

x

))(()()( ......... VtVtytxgI qp

Color noise model for synaptic current IS is the Ornstein-Uhlenbeck process:

)(2)(0 titidtdi

SSS

Model with noise

E X P Е R I М Е N Т

Control parameters of a neuron

electrodeIIEE IVVGVVGu )()( 00

IE GGs

Property: Neuron is controlled by two parameters[Покровский, 1978]

)()(V

hVhdtdh

h

)()(VmVm

dtdm

m

)()(V

nVndtdn

n

2

2

xVk

[Hodgkin, Huxley, 1952]

Voltage-gated channels kinetics:

SLLKK

NaNa

iVtVgVtVtVng

VtVtVhtVmgdttdVC

))(())()(,(

))()(,(),()(

4

3

E X P E R I M E N T

M O D E L

uVVsIVVGVVGi electrodeIIEES )()()( 0

)())(()(),( tIVtVtgtVIdtdVC el

SSSchannelsionic

),())(()(),( 0 tuVtVtstVIdtdVC channelsionic

S

S tgts )()(

,

)()()()( 0 tIVVtgtu elS

SS

The case of many voltage-independent synapses

Warning!The input in current clamp corresponds to negative synaptic conductance!

Current-clamp is here!

“Current clamp”,V(t) is registered

“Voltage clamp”,I(t) is registered

Whole-cell patch-clamp:Current- and Voltage-Clamp modes

const

• For artificial passive leaky channel gDC=const

• For artificial synaptic channel gDC(t) reflects the synaptic kinetics

• For voltage-gated channel gDC(V(t),t) is described by ODEs

Conductance clamp (Dynamic clamp):V(t) is registered,I(V,t) = gDC (V,t) (V(t)-VDC) is injected

Whole-cell patch-clamp:Dynamic-Clamp mode

“Current clamp”Conductance clamp (Dynamic clamp):I(V(t))=gDC (V(t)-VDC) is injected

Dynamic clamp for synaptic current

[Sharp AA, O'Neil MB, Abbott LF, Marder E. Dynamic clamp: computer-generatedconductances in real neurons. // J.Neurophysiol. 1993, 69(3):992-5]

)()( GABAGABA VVtgI nSgsseegtg GABA

ttGABAGABA 8,15,5,)( max

21//max 21

Dynamic clampfor spontaneous

potassium channels

Control

artificial K-channels

iittg

gdtdg

dtgd

)(

)(

12max

212

2

21

msms 200,5 21

mVVK 70

))(( KVVtgI

nSg 1max

u,A/cm2

s,m

S/cm

2

0 1 2 3

0.01

0.02

0.03

0.04

0.05

0.061101009080706050403020100

HzHz

(2.7;0.06)

(1.7;0.024)

Experiment: pyramidal cell of visual cortex

Model [Graham, 1999] for CA1 pyramidal neuron

u,mkA/cm2

s,m

S/c

m2

0 2 4 6 8 10

0.1

0.2

0.3

0.4

0.5

0.6 80

60

40

20

0

Hz

Dynamic clamp to study firing properties of

neuron

0 500 1000-80-60-40-20

020

V, m

V

t, m s0 500 1000

-80

-60

-40

-20

0

20

V, m

V

t, m s

Experiment

Model u=7.7 mkA/cm2

S=0.4 mS/cm2

u=1.7 mkA/cm2

S=0.024 mS/cm2u=2.7 mkA/cm2

S=0.06 mS/cm2

u=4 mkA/cm2

S=0.15 mS/cm2

Bottom point Top point

Divisive effect of shunting inhibition is due to spike thresholdsensitivity to slow inactivation of sodium channels

i

spikei

TTTT

ttVVVdtdV )(0

inhex GGRate

2

Total Response (all spikes during 500ms-step)

Only 1st spikes Only 1st interspike intervals

Hippocampal Pyramidal Neuron In Vitro

Dynamic clamp for voltage-gated current: compensation of INaP

[Vervaeke K, Hu H., Graham L.J., Storm J.F. Contrasting effects of the persistent Na+ current on neuronal excitability and spike timing, Neuron, v49, 2006]

Dynamic clampfor electric couplings

between real and modeled neurons

Medium electric conductance

High electric conductance

constgVVgI

)( modexp

Dynamic clamp for synaptic conductance estimations in-vivo

1s

20 mV

10 nS

5 nS

V

V

IA GGABA :

EGAMPA :

Эксперимент [Lyle Graham et al.]: Внутриклеточные измерения patch-clamp в зрительной коре кошки in vivo. Стимул – движущаяся полоска.

Preferred direction Null direction

«Firing-Clamp»- method of synaptic

conductance estimation

Idea: a patched neuron is forced to spike with a constant rate; gE, gI, are estimated from values of subthreshold voltage and spike amplitude.

Threshold voltage, VT Peak voltage, V P

1 ms

τ(V)

Dynamic Clamp

• is needed for measuring firing characteristics of neuron

• is needed for estimation input synaptic conductances in-vivo

• helps to create artificial ionic intrinsic or synaptic channels

Conclusions