We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from stochastic to deterministic regime. In stochastic regime, this noise parameter is found to be increased as system size decreases, whereas in deterministic regime it remains constant to minimum value as system size increases. This let the transition from fluctuating to fixed limit cycle oscillation as the system goes from stochastic to deterministic transition. We also numerically estimated the strength of the noise parameter involved both in chemical Langevin equation and Master equation formalisms and found that strength of this parameter is much smaller in the former than the latter.

References

References
1.
Rao
,
C. V.
,
Wolf
,
D. M.
, and
Arkin
,
A. P.
,
2002
, “
Control, Exploitation and Tolerance of Intracellular Noise
,”
Nature (London)
,
420
, pp.
231
237
.10.1038/nature01258
2.
Swain
,
P. S.
,
Elowitz
,
M. B.
, and
Siggia
,
E. D.
,
2002
, “
Intrinsic and Extrinsic Contributions to Stochasticity in Gene Expression
,”
Proc. Natl. Acad. Sci. U.S.A.
,
99
, pp.
12795
12800
.10.1073/pnas.162041399
3.
Gillespie
,
D. T.
,
1977
, “
Exact Stochastic Simulation of Coupled Chemical Reactions
,”
J. Phys. Chem.
,
81
, pp.
2340
2361
.10.1021/j100540a008
4.
Gillespie
,
D. T.
,
2000
, “
The Chemical Langevin Equation
,”
J. Chem. Phys.
,
113
, pp.
297
306
.10.1063/1.481811
5.
Blake
,
W. J.
,
Kaern
,
M.
,
Cantor
,
C. R.
, and
Collins
,
J. J.
,
2003
, “
Noise in Eukaryotic Gene Expression
,”
Nature (London)
,
422
, pp.
633
637
.10.1038/nature01546
6.
Scott
,
M.
,
Ingalls
,
B.
, and
Kaern
,
M.
,
2006
, “
Estimations of Intrinsic and Extrinsic Noise in Models of Nonlinear Genetic Networks
,”
Chaos
,
16
, p.
026107
.10.1063/1.2211787
7.
Hanggi
,
P.
,
2002
, “
Stochastic Resonance in Biology How Noise can Enhance Detection of Weak Signals and Help Improve Biological Information Processing
,”
Chem. Phys. Chem.
,
3
, pp.
285
290
.10.1002/1439-7641(20020315)3:3<285::AID-CPHC285>3.0.CO;2-A
8.
Anishchenko
,
V. S.
,
Neiman
,
A. B.
,
Moss
,
F.
, and
Schimansky-Geier
,
L.
,
1990
, “
Stochastic Resonance: Noise-Enhanced Order
,”
Phys.-Usp.
,
42
, pp.
7
36
.10.1070/PU1999v042n01ABEH000444
9.
Bassler
,
B. L.
,
1999
, “
How Bacteria Talk to Each Other: Regulation of Gene Expression by Quorum Sensing
,”
Curr. Opin. Microbiol.
,
2
, pp.
582
587
.10.1016/S1369-5274(99)00025-9
10.
Gillespie
,
D. T.
,
2009
, “
Deterministic Limit of Stochastic Chemical Kinetics
,”
J. Phys. Chem. B
,
113
, pp.
1640
1644
.10.1021/jp806431b
11.
Scott
,
M.
,
Hwa
,
T.
, and
Ingalls
,
B.
,
2007
, “
Deterministic Characterization of Stochastic Genetic Circuits
,”
Proc. Nat. Acad. Sci. U.S.A.
,
104
, pp.
7402
7407
.10.1073/pnas.0610468104
12.
McQuarrie
,
D. A.
,
1967
, “
Stochastic Approach to Chemical Kinetics
,”
J. Appl. Probab.
,
4
, pp.
413
478
.10.2307/3212214
13.
Field
,
R. J.
, and
Noyes
,
R. M.
,
1974
, “
Oscillations in Chemical Systems. IV. Limit Cycle Behavior in a Model of a Real Chemical Reaction
,”
J. Chem. Phys.
,
60
, pp.
1877
1884
.10.1063/1.1681288
14.
Tyson
,
J. J.
,
1973
, “
Some Further Studies of Nonlinear Oscillations in Chemical Systems
,”
J. Chem. Phys.
,
58
, pp.
3919
3930
.10.1063/1.1679748
15.
Tyson
,
J. J.
, and
Light
,
J. C.
,
1973
, “
Properties of Two-Component Bimolecular and Trimolecular Chemical Reaction Systems
,”
J. Chem. Phys.
,
59
, pp.
4164
4173
.10.1063/1.1680609
16.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
,
1992
,
Numerical Recipe in Fortran
,
Cambridge University Press
,
New York.
17.
Papoulis
,
A.
, and
Pillai
,
S. U.
,
2002
,
Probability, Random Variables and Stochastic Processes
,
Mc-Graw Hill
,
New York
.
You do not currently have access to this content.