AACIMP 2010 Summer School lecture by Anton Chizhov. "Physics, Chemistry and Living Systems" stream. "Neuron-Computer Interface in Dynamic-Clamp Experiments. Models of Neuronal Populations and Visual Cortex" course. Part 1. More info at http://summerschool.ssa.org.ua

1. Neuron-computer interface
in Dynamic-Clamp experiments
Anton V. Chizhov
A.F.Ioffe Physico-Technical Institute of
Russian Academy Sciences,
St.-Petersburg, Russia

2. 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

3. Leaky Integrate-and-Fire neuron
dV
C   g L (V ( t )  V L )  i S V is the membrane potential; I is the input (synaptic) current,
dt C is the membrane capacity; gL is the membrane
conductance; Vrest is the rest potential; VT is the threshold
If V  VT then V  Vreset potential; Vreset is the reset potential.
C
m 
gL

4. Firing rate dependence on current (F-I-curve)
gL

 V  i / g V 
C ln L S L T
 V  i / g V 

 L S L reset 

5. V(x)
r Внутри V(x+Δx)
jm
C
im
 g S (V  VL )  iS
φ≈0
Снаружи
h
VNa V
gNa
gK
Vrest
VK
[Покровский, 1978]

6. Set of experimental data for Hodgkin-Huxley approximations

7. Model of a pyramidal neuron
dV
C   I Na  I DR  I A  I M  I H  I L  I AHP  iS
dt
p q
E X P Е R I М Е N Т
I ...  g... x (t ) y (t ) (V (t )  V... )
dx x (U )  x
 ,
dt  x (U )
dy y (U )  y

dt  y (U )
Approximations for I Na , I DR , I A , I M , I H
are taken from [L.Graham, 1999]; IAHP is
from [N.Kopell et al., 2000]
Model with noise
Color noise model for
synaptic current IS is the
Ornstein-Uhlenbeck process:
diS 0
  iS (t )  iS  2  (t )
dt

8. E X P E R I M E N T
Control parameters of
a neuron
dV ( t )
C   g Na m 3 (V , t )h (V , t )(V (t )  VNa ) 
dt
4  2V
 g K n (V , t )(V (t )  VK )  g L (V ( t )  VL )  iS  k 2
x
Voltage-gated channels kinetics:
dm m (V )  m
 
MODEL
dt  m (V )
dh h (V )  h [Hodgkin, Huxley, 1952]
 
dt  h (V )
dn n (V )  n
 
dt  n (V )
Property: Neuron is controlled by two parameters
[Покровский, 1978]
iS  GE (V  VE )  GI (V  VI )  I electrode   s (V  V0 )  u
u  GE (VE  V0 )  GI (VI  V0 )  I electrode
s  GE  GI

9. The case of many voltage-independent synapses
dV
C   I ionic channels (V , t )   g S (t ) (V (t )  VS )  I el (t )
dt S
s(t )   g S (t )
S
u (t )   g S (t ) (VS  V0 )  I el (t )
S
,
dV
C   I ionic channels (V , t )  s(t ) (V (t )  V0 )  u(t ),
dt

10. Warning!
The input in current clamp corresponds to negative synaptic conductance!
Cur
rent
-c lam
p is
her
e !

11. Whole-cell patch-clamp:
Current- and Voltage-Clamp modes
“Current clamp”, “Voltage clamp”,
V(t) is registered I(t) is registered
const

12. Whole-cell patch-clamp:
Dynamic-Clamp mode
Conductance clamp (Dynamic clamp):
V(t) is registered,
I(V,t) = gDC (V,t) (V(t)-VDC) is injected
• 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

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

14. Dynamic clamp for synaptic current
[Sharp AA, O'Neil MB, Abbott LF, Marder E. Dynamic clamp: computer-generated
conductances in real neurons. // J.Neurophysiol. 1993, 69(3):992-5]
I  g GABA (t ) (V  VGABA )
 
gGABA (t )  gGABA e  t /  1  e  t /  2 ,  1  5 s,  2  15 s, gGABA  8 nS
max max

15. Control
Dynamic clamp
for spontaneous
potassium
channels
I  g (t )(V  VK )
d 2g dg
 1 2 2  ( 1   2 )  g 
artificial K-channels dt dt
 g max  2 1   (t  ti )
i
 1  5ms,  2  200ms
VK  70mV
g max  1nS

16. Dynamic clamp Model [Graham, 1999] for
to study firing properties of CA1 pyramidal neuron
neuron
Hz
0.6 80
Experiment: pyramidal cell 60
of visual cortex 0.5 40
Hz
0.06 Hz 20
0.4
s, mS/cm2
(2.7; 0.06)
110
0.05 100
0
90
0.04 80 0.3
s, mS/cm2
70
60
0.03 50
40 0.2
(1.7; 0.024) 30
0.02 20
0.01
10
0 0.1
0 1 2 3 0 2 4 6 8 10
2 2
u, A/cm u,mkA/cm

17. Experiment
Bottom point Top point
u=1.7 mkA/cm2 u=2.7 mkA/cm2
20 S=0.024 mS/cm2 20 S=0.06 mS/cm2
0 0
-20 -2 0
V, mV
V, mV
-40 -4 0
-6 0
-60
-8 0
-80
0 500 1000 0 500 1000
t, m s t, m s
Model
u=4 mkA/cm2 u=7.7 mkA/cm2
S=0.15 mS/cm2 S=0.4 mS/cm2

18. Divisive effect of shunting inhibition is due to spike threshold
sensitivity to slow inactivation of sodium channels
dV T V0T  V T
  V T   (t  t i
spike
)
dt  i

19.  2 Rate
Gex Ginh
Total Response (all spikes during 500ms-step)
Only 1st spikes Only 1st interspike intervals

20. Dynamic clamp for voltage-gated current:
compensation of INaP
Hippocampal Pyramidal Neuron In Vitro
[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]

21. Medium
electric Dynamic clamp
conductance for electric
couplings
between real and
modeled neurons
I  g (V exp  V mod )
g  const
High
electric
conductance

22. Dynamic clamp for synaptic conductance
estimations in-vivo
Preferred direction Null direction
V
Эксперимент [Lyle Graham et al.]: Внутриклеточные измерения patch-clamp
в зрительной коре кошки in vivo. Стимул – движущаяся полоска.
V  20 mV
GABAA : GI 10 nS
AMPA : GE 5 nS
1s

23. Threshold voltage, VT Peak voltage, V P
«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
1 ms
and spike amplitude.
τ(V)

25. Conclusions
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