Biology Reference
In-Depth Information
TABLE 15.1
Criteria for the Local Performance of the Pathway in
Figure 15.3
Operating in the Forward Direction
Criterion
number
Definition
Calculation
1
Maximum gain of pathway flux V in response to changes in substrate concentration S
Max L
ð
V
;
S
Þ
2
Minimum gain of pathway flux V in response to changes in product concentration P
Min
j
L
ð
V
;
P
Þj
3
Minimum absolute value of intermediate X
Min X
4
Maximum robustness of flux V to variations in the rate constants of the reaction with S
Min
j
S
ð
V
;
k
S
Þj
5
Maximum robustness of flux V to variations in the rate constants of the reaction with P
Min
j
S
ð
V
;
k
P
Þj
6
Minimum response time
Max l ( Min
2
)
s
1
=
we shall assume the nominal values are log
ð
K
eq
GÞ¼þ
2and
TABLE 15.2
Comparison of Local Performance in the
Three Relevant Phenotypic Regions of
Figure 15.4
according to the Criteria In
Table 15.1
log
1. Although the global tolerances for each
of the parameters and independent variables will require
a calculation in general, the geometry of the system design
space in
Figure 15.4
is so simple that one can determine
the global tolerances from the boundaries by inspection. In
this case, the results are shown on the first line of entries in
Tabl e 15. 3
; similar results are shown on subsequent lines for
the other regions and assumed operating points. These
results make evident a number of symmetries in this system.
Since the assumed operating points were all well removed
from the boundaries, it is not surprising that the global
tolerances are all large fold changes, which is in contrast to
the values for local robustness that are often manifested as
percentage changes.
ð
k
S
=
k
p
Þ¼þ
Preference
y
Criterion
Phenotypic Region
*
1 (Right)
2
4 (Right)
1
\
1
1
1
2
Z
0
0
0
SK
eq
K
eq
3
Z
Sk
S
=
k
p
P
=
4
Z
0
1
1
5
Z
1
0
0
x
k
6
\
k
S
k
P
y
To improve performance, one must have either a high (
\
) or a low (
Z
)
value for the associated criterion.
*Right refers to the right-most region of Cases 1 and 4 in
Figure 15.4
.
x
DESIGN PRINCIPLES
To address the third goal of the Introduction, in this section
I will show how the generic definition of phenotype applies
in a more complex system, generates a more interesting
system design space, and suggests non-intuitive biological
design principles. The system selected for this purpose is
the well-characterized model for the cI gene circuit
involved in controlling lysogeny of bacteriophage lambda.
P
implies
a decrease in the absolute concentration of the intermediate X (Criterion 3).
Decreasing the response time (Criterion 6) by increasing k
and driving it further would move the system into Region 2
with no additional improvement in performance. On the
other hand, if it were driven in the reverse direction, then its
operation wouldmove into the left side of Region 4, which is
not the overall best phenotypic region when functioning in
the reverse direction. Taken together, these results suggest
that operation in the forward direction has some advantages.
This suggestion would be consistent with the data showing
preferential utilization of
a
-
D
-glucose by hexokinase in the
case of human erythrocyte exposed to
D
-glucose at low
concentrations; however, it would be inconsistent with the
data showing preferential utilization of
b
-
D
-glucose at high
concentrations
[51]
.
Alternative Growth Modes of Phage Lambda
Bacteriophage lambda can reproduce in two alternative
modes of growth. In the lytic mode, the phage infects
a bacterial cell, reproduces many copies of itself, lyses the
host cell, and circulates through the environment to infect
another host cell. In the lysogenic mode, the phage infects
a bacterial cell, incorporates its DNA into the chromosome
of the host cell, and remains quiescent, with its DNA being
replicated along with that of the host. Lysogeny is typically
a stable state unless the host cell is compromised in some
fashion (e.g., DNA damaged by UV radiation), and then the
phage undergoes an induction process by which it excises
Global Tolerance
For purposes of illustration, let us assume operating points in
each of the four regions depicted in
Figure 15.4
.InRegion1
