Biomedical Engineering Reference
In-Depth Information
a
b
Control
Single knockout
400
400
Clone 1
Clone 2
Clone 3
Clone 4
300
300
200
200
100
100
0
0
0
5
10
15
0
5
10
15
Time (days)
Time (days)
c
d
Double knockout
Triple knockout
400
400
300
300
200
200
100
100
0
0
0
5
10
15
0
5
10
15
Time (days)
Time (days)
Fig. 7
Basic immunodominance model: time evolution of effector cell populations for Scenario 2.
Four T cell clones are present with the same reactivity
p
i
2 and initial concentrations
K
1
(
=
1
/
0
)=
04,
K
2
(
01,
K
3
(
10
−
3
,and
K
4
(
10
−
4
0
L. All other parameters are
taken from Table
1
.(
a
) Control experiment: clones 1-4 all respond. (
b
) SKO: clone 1 is removed.
Only clones 2-4 respond. (
c
) DKO: clones 1 and 2 are removed. Only clones 3 and 4 respond.
(
d
) TKO: clones 1-3 are removed. Only clone 4 responds
.
0
)=
0
.
0
)=
2
.
5
×
0
)=
6
.
25
×
k/
μ
primary response in which the more reactive clone starts at a lower concentration
than the less reactive clone. For our hypothetical secondary response, the initial
concentrations are reversed.
1. Reactivity:
p
1
=
2
Initial concentration:
K
1
(
1
/
0
)=
0
.
004 (primary), 0.04 (secondary) k/
μ
L
2. Reactivity:
p
2
=
4
Initial concentration:
K
2
(
1
/
0
)=
0
.
04 (primary), 0.004 (secondary) k/
μ
L
Figure
8
shows numerical solutions for Scenario 3. In Fig.
8
aweseethat
the clone with the higher initial concentration dominates during the primary
response. Indeed, clone 2 produces a response that is about three times as high as
the response of clone 1. However, by day 10, the population of clone 1 persists
whereas the population of clone 2 has nearly vanished. The more reactive clone,
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