Biomedical Engineering Reference
In-Depth Information
12.9
Appendix
Here we describe the leaky integrate-and-fire model [24, 67, 82, 84] driven by con-
ductance changes that was used to generate
Figure 12.1
.
In this model, the membrane
potential
V
evolves according to
t
m
dV
dt
=
−
V
−
g
E
(
t
)(
V
−
V
E
)
−
g
I
(
t
)(
V
−
V
I
)
,
(12.12)
where the resting potential has been set to 0 mV. The spike-generating currents are
substituted by a simple rule: whenever
V
exceeds a threshold (20 mV), a spike is
emitted and
V
is clamped to a reset value (10 mV) for a refractory period (1.8 ms).
After that,
V
continues evolving according to the above equation.
The excitatory
and inhibitory conductances,
g
E
(
, were generated by combining Gaus-
sian random numbers [69], so that the resulting traces would have the desired mean,
standard deviation and correlation time. These parameters were related to input rates
and model synaptic conductances through Equations 12.4. For Figures 12.1a and
1d,
N
E
r
E
=27.5 spikes/ms,
G
E
=0.02, t
E
=2 ms,
N
I
r
I
=12.15 spikes/ms,
G
I
=0.06, and
t
I
=2 ms, with
G
E
and
G
I
in units of the leak conductance (i.e., where the leak con-
ductance equals 1). For Figures 12.1b and 12.1e, t
E
=20 ms. For Figures 12.1c and
12.1f, t
I
=t
E
=20 ms. Correlations between the conductances of different neurons
were generated by drawing correlated Gaussian samples during generation of the
g
E
t
)
and
g
I
(
t
)
(
)
(
)
traces for different neurons. The correlation coefficient for a pair
of conductances, Equation 12.1, is equal to the correlation coefficient between the
corresponding Gaussian samples.
t
and
g
I
t
Other parameters were:
t
m
=20 ms,
V
E
=74 mV,
V
I
=
−
10 mV, D
t
=0
.
1ms.
Acknowledgments
Research was supported by the Howard Hughes Medical Insti-
tute and by startup funds from Wake Forest University School of Medicine. Parts of
this chapter were adapted from [68].
References
[1]
Abbott L.F., and Dayan P. (1999) The effect of correlated activity on the accu-
racy of a population code.
Neural Comput. 11:
91-101.
[2]
Abeles M. (1982) Role of the cortical neuron: Integrator or coincidence detec-
tor?
Israel J Med Sci
18:
83-92.
[3]
Aertsen A., and Arndt M. (1993) Response synchronization in the visual cor-
tex.
Curr. Opin. Neurobiol.
3:
586-594.
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