Biology Reference
In-Depth Information
TABLE 15.6
Global Tolerances Relevant for the Case 11 Phenotype, Including Maintenance of the Phenotype, Proper
Positioning of a Wide Hysteretic Buffer, and Survival of the Temperate Lifestyle
are Best Ensured by
having a Large Net Global Tolerance for all the Parameters. See
Figure 15.8
and the text for discussion
½
T
D
;
T
I
ðD
H
;
P
j
Þ
D
Right
H
K
Upper
D
D
Left
H
K
Lower
D
Parameters
Case 9
Case 17
D
H
Net
K
D
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[83.2,
N
]
[
N
,1.60]
[83.2, 1.60]
K
I
[
N
, 2.40]
[10.9,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[10.9, 2.40]
K
R
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[4.30,
N
]
[
N
, 8.00]
[
N
,
N
]
[
N
,
N
]
[4.30, 8.00]
g
MMax
[2.40,
N
]
[
N
,
N
]
[7.1,
N
]
[
N
,
N
]
[
N
, 8.00]
[
N
,
N
]
[
N
,
N
]
[2.40, 8.00]
g
M
[
N
,
N
]
[
N
, 4.20]
[
N
, 7.1]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[2.02,
N
]
[2.02, 4.20]
g
C
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
, 8.00]
[
N
,
N
]
[1.60,
N
]
[1.60, 8.00]
g
D
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
, 65.0]
[
N
,
N
]
[20.0,
N
]
[20.0, 65.0]
b
D
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[65.0,
N
]
[
N
,
N
]
[
N
, 20.0]
[65.0, 20.0]
d
M
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[8.00,
N
]
[
N
,
N
]
[
N
, 1.60]
[8.00, 1.60]
d
CMax
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
, 4.20]
[8.00,
N
]
[
N
,
N
]
[
N
,
N
]
[8.00, 4.20]
d
C
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
, 4.60]
[
N
, 4.60]
d
D
[
N
,
N
]
[10.9,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
, 1.60]
[10.9, 1.60]
a
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[1.39,
N
]
[
N
, 50.0]
[
N
,
N
]
[
N
,
N
]
[1.39, 50.0]
p
[
N
,1.07]
[1.34,
N
]
[6.0,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[1.34, 1.07]
n
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
[
N
,
N
]
constellation of parameters that constitute the design of the
system arrived at by natural selection. For this reason we
choose to represent an important environmental variable of
interest on the horizontal axis and an important structural
parameter that is most revealing on the vertical axis. In the
case of phage lambda, the environmental variable is the
insult traditionally involving UV radiation (with RecA*
activity as a proxy), and the structural parameter that proves
revealing is the constant representing half-maximal acti-
vation of cI transcription.
The system passes through a progression of qualita-
tively distinct phenotypes - corresponding to Cases 11, 47,
45, 37 and 38 - as the level of RecA* (R) is steadily
increased from its basal level in Region 11. In Case 11, the
level of RecA* is subthreshold and the system, which has
an intermediate level of CI mRNA (M) that sustains a high
level of CI dimer (D), is unresponsive to fluctuations in
RecA* (D is independent of R). In Case 47, the system
responds to the elevated levels of RecA* by derepressing cI
transcription thereby elevating M (M
f
R
2an
=ð
2n
þ
1
Þ
z
R
3
=
4
),
which provides a negative feedback that tends to minimize
the drop in D (D
the
level
of CI
dimer
drops more
precipitously
p
), but the lysogenic
state is still maintained. In these two phenotypes, the system
is still resistant to the damage and is capable of fully
recovering the basal lysogenic state if the environmental
insult is removed. In Case 37, the system becomes
committed to induction, the level of cI transcription drops to
its basal level (M
=
R
2a
R
2
, as opposed to 1
(D
f
1
=
1
=
z
¼
g
M
=
d
M
), and the level of CI dimer
R
2
). This is the only
transition in this progression of phenotypes that corresponds
to a traditional bifurcation. Recovery from this commitment
is only possible with a large decrease in RecA* activity
(sufficient to retreat back across the hysteretic buffer zone).
In Case 38, the level of cI transcription remains at its basal
level (M
R
2a
continues to decrease (D
f
1
=
1
=
z
d
M
), the level of CI dimer no longer
decreases as the level of RecA* activity becomes saturating
(D is independent of R), and recovery is only possible with
a large decrease in RecA* activity (sufficient to retreat back
across the hysteretic buffer zone).
¼
g
M
=
=
p
, as opposed to 1
Avoiding Inappropriate Switching
One of the most important system design principles is made
evident by these qualitatively distinct phenotypes in design
space. Namely, the hysteretic buffer allows the system to
R
2a
=ð
2n
þ
1
Þ
z
R)
and preserve the lysogenic state. In Case 45, the de-repres-
sion of cI transcription is maximal (M
f
1
=
1
=
d
M
),
thereby eliminating the negative feedback component,
¼
g
MMax
=
