Biomedical Engineering Reference
In-Depth Information
by using one of the preceding algorithms and following only processes that oc-
cur on the time scale of interest. The ability to determine the stochastic proper-
ties of gene expression will allow a more quantitative determination of the range
of possible cellular responses to a stimulus or treatment, which will be increas-
ingly important as treatments become more targeted and personalized. This
should be especially useful in gene therapy, where the variability of the gene
product could be controlled. It can also provide insight into the possible causes
of disease, as in tumor formation from variations in phenotype due to haploin-
sufficiency (27). On the other hand, the ability to determine the stochastic prop-
erties of a circuit will permit increasingly complex metabolic engineering,
allowing for higher-order traits like robustness or stability to be included in the
design rather than painstakingly evolved (28).
5.
NOTES
1. In this case, the sums only go up to
n
, instead of . However, the extra
terms that appear when applying the change of variables cancel with each other.
2. This can be summarized in a very practical way (13) in terms of the loga-
rithmic gains to obtain an equation that reflects the resulting components of the
noise.
3. For the case where
q
(
x
) is not constant, the stochastic differential equa-
tion will be understood to follow the Stratonovich interpretation (19,22). This
allows a general Fokker-Planck equation to be written in this form, but will not
be necessary in the cases of interest.
4. From the Wiener-Khinchin theorem; see (23).
(
)
1
d
X
1
(
n
1/2
5.
ยจ
, where
( )
(
,
(
)(
)
=
(
n
=
n
1
n
1
()
(
)
n
2
Q
21
n
(
n
2
QH
XH
2
+
2
()
, and
()
.
(
11
=
(
1/ 2
Q
=
6.
REFERENCES
1.
Ptashne M. 1992.
A genetic switch: phage lambda and higher organisms
. Cell Press, Cam-
bridge.
2.
Arkin A, Ross J, McAdams HH. 1998. Stochastic kinetic analysis of developmental pathway
bifurcation in phage lambda-infected
Escherichia coli
cells.
Genetics
149
:1633-1648.
3.
van de Putte P, Goosen N. 1992. DNA inversions in phages and bacteria.
Trends Genet
8
:457-
462.
4.
von Dassow G, Meir E, Munro EM, Odell GM. 2000. The segment polarity network is a robust
developmental module.
Nature
406
:188-192.
5.
Becskei A, Serrano L. 2000. Engineering stability in gene networks by autoregulation.
Nature
405
:590-593.
