Abstract
The role of noise in stochastic system could be constructive or destructive depending on the topology of the biochemical network, interaction mechanism and strength of the noise. The noise in genetic and chemical oscillators is studied using chemical Langevin equation and numerically using stochastic simulation algorithm to study the role of noise. The temporal behaviors of the variables in genetic oscillator are found to maintain their oscillatory nature at small system size limit (V ≤ 13 ± 3), but above this the oscillatory behaviors get start destroying by getting transition from fluctuated limit cycle to no oscillation limit as V → ∞. However, in chemical oscillator case, in the limit V → ∞ the oscillatory behaviors of the variables get transition from fluctuated limit cycle (tending destroy oscillatory behavior) to normal limit cycle (maintain sustain oscillations). The noise parameter calculated as a function of V for genetic oscillator first slowly decrease and increases as V increases. However the noise parameter in chemical oscillator decreases first (V ≤ 50 ± 5) and then remains constant as V increases. The calculated noise parameter via stochastic simulation algorithm is always found to be larger than that is obtained via chemical Langevin equation.
Highlights
The noise in stochastic system is due to random particle/ molecular interaction of the participating particles/molecules in the system [1,2], and exchange of external fluctuations of the surrounding environment with the system such as thermal, environmental fluctuations [3,4]
There are important constructive roles of noise in stochastic systems, for example, detection and amplification of weak noise, the phenomenon known as stochastic resonance [6,7], lifting of cellular expression at different distinct expression state [8], noise in gene expression can drive stochastic switching among such states [9,10], noise induced stochastic phenotypic switching to different new level in living cells [11], noise induce generation of coherent motion [12], noise induced synchronization of stochastic systems [13] that can be found in intercircadian networks via environmental fluctuations [14,15,16] etc
The opposite function of noise, as we found in genetic oscillator, is obtained in chemical oscillator case supported by the transition from fluctuated limit cycle to normal limit cycle as V→∞
Summary
The noise in stochastic system is due to random particle/ molecular interaction of the participating particles/molecules in the system (intrinsic noise) [1,2], and exchange of external fluctuations of the surrounding environment with the system such as thermal, environmental fluctuations (external noise) [3,4] This noise, in general, is known to be a parameter that induces hindrance to the signal associated with dynamical variables of the system [5].
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