The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

1.
E. H.
Davidson
,
J. P.
Rast
,
P.
Oliveri
 et al,
Science
295
,
1669
(
2002
).
2.
C. Y.
Huang
and
J. E.
Ferrell
, Jr.
,
Proc. Natl. Acad. Sci. U.S.A.
93
,
10078
(
1996
).
3.
B. N.
Kholodenko
,
Eur. J. Biochem.
267
,
1583
(
2000
).
4.
T.
Ideker
,
V.
Thorsson
,
J. A.
Ranish
,
R.
Christmas
,
J.
Buhler
,
J. K.
Eng
,
R.
Bumgarner
,
D. R.
Goodlett
,
R.
Aebersold
, and
L.
Hood
,
Science
292
,
929
(
2001
).
5.
L.
You
,
R. S.
Cox
 III
,
R.
Weiss
, and
F. H.
Arnold
,
Nature (London)
428
,
868
(
2004
).
6.
H. H.
McAdams
and
A.
Arkin
,
Proc. Natl. Acad. Sci. U.S.A.
94
,
814
(
1997
).
7.
M. B.
Elowitz
and
S.
Leibler
,
Nature (London)
403
,
335
(
2000
).
8.
P. S.
Swain
,
M. B.
Elowitz
, and
E. D.
Siggia
,
Proc. Natl. Acad. Sci. U.S.A.
99
,
12795
(
2000
).
9.
M.
Thattai
and
A.
van Oudenaarden
,
Proc. Natl. Acad. Sci. U.S.A.
98
,
8614
(
2001
).
10.
J. M. G.
Vilar
,
C. C.
Guet
, and
S.
Leibler
,
J. Cell Biol.
161
,
471
(
2003
).
11.
J.
Paulsson
,
Nature (London)
427
,
415
(
2004
).
12.
J.
Yu
,
J.
Xiao
,
X.
Ren
,
K.
Lao
, and
X. S.
Xie
,
Science
311
,
1600
(
2006
).
13.
L.
Cai
,
N.
Friedman
, and
X. S.
Xie
,
Nature (London)
440
,
358
(
2006
).
14.
J.
Hasty
,
J.
Pradines
,
M.
Dolnik
, and
J. J.
Collins
,
Proc. Natl. Acad. Sci. U.S.A.
97
,
2075
(
2000
).
15.
J.
Hasty
,
F.
Isaacs
,
M.
Dolnik
,
D.
McMillen
, and
J. J.
Collins
,
Chaos
11
,
207
(
2001
).
16.
C. W.
Gardiner
,
Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences
(
Springer-Verlag
,
Berlin
,
1985
).
17.
N. G.
van Kampen
,
Stochastic Processes in Chemistry and Physics
(
North-Holland
,
Amsterdam
,
1992
).
18.
D. T.
Gillespie
,
J. Phys. Chem.
81
,
2340
(
1977
).
19.
A.
Arkin
,
J.
Ross
and
H. H.
McAdams
,
Genetics
149
,
1633
(
1998
).
20.
T. B.
Kepler
and
T. C.
Elston
,
Biophys. J.
81
,
3116
(
2001
).
21.
M.
Sasai
and
P. G.
Wolynes
,
Proc. Natl. Acad. Sci. U.S.A.
100
,
2374
(
2003
).
22.
A. M.
Walczak
,
M.
Sasai
, and
P. G.
Wolynes
,
Biophys. J.
88
,
828
(
2005
).
23.
J. E. M.
Hornos
,
D.
Schultz
,
G. C. P.
Innocentini
,
J.
Wang
,
A. M.
Walczak
,
J. N.
Onuchic
, and
P. G.
Wolynes
,
Phys. Rev. E
72
,
051907
(
2005
).
24.
T.
Ushikubo
,
W.
Inoue
, and
M.
Sasai
,
Genome Informatics
14
,
314
(
2003
).
25.
D. C.
Mattis
and
M. L.
Glasser
,
Rev. Mod. Phys.
70
,
979
(
1998
).
26.
G. L.
Eyink
,
Phys. Rev. E
54
,
3419
(
1996
).
27.
J.
Wang
and
P. G.
Wolynes
,
Phys. Rev. Lett.
74
,
4317
(
1995
).
28.
E.
Aurell
and
K.
Sneppen
,
Phys. Rev. Lett.
88
,
048101
(
2002
).
29.
X. M.
Zhu
,
L.
Yin
,
L.
Hood
, and
P.
Ao
,
Journal of Bioinformatics and Computational Biology
2
,
785
(
2004
).
You do not currently have access to this content.