Biomedical Engineering Reference
In-Depth Information
and the differential equations for each gate are of the form shown in Eq. (3.5). One additional
x
-gate is
defined by
dx
dt
−
c
·
I
Ca
d
−
β
x
·
x.
A
·
The constants for the Traub model appear in Table 3.2.
Table 3.2:
β
x
=
0
.
1
A
=
3320
c
=
5
.
2
d
=
0
.
0005
E
Ca
=
140
mV
E
Na
=
115
mV
E
k
=−
15
mV
g
Na
=
3
.
32
μS
g
kCa
=
0
.
1
μS
g
Ca
=
6
.
64
μS
g
K
=
3
.
98
μS
The additional phenomena the Traub model enables is a repeating cycle of depolarization and
repolarization called
bursting
. Bursting is often modulated by the strength of a sustained input current
and is shown in Fig. 3.11.
2
1
0
0
10
20
30
40
100
50
0
0
10
20
30
40
Time (msec)
Figure 3.11:
Bursting in the Traub membrane model.
3.4.3 Complex Gating
Hodgkin and Huxley assumed that ion gates could be either open or closed. But, the
h
gate was a clue
to the more complex nature of channels. In reality, some channels may be open in more than one way,
closed in more than one way, and even inactivated in more than one way. The method of modeling the
more complex dynamics of an ion channel is through a
Markov State
model. Figure 3.12 is an example of
