Noise in a system is a repeating issues from engineering to science. In a biogical system
noise can intrinsic, for eg from randomness of chemical reactions in side of the cell or
extrinsic, for ex, different operating temperature or cell shape size variety. To model such
behavior we have adopted stochastic simulation algorithm by Gillespie.
Fig.1 Stochastic modeling flowchart
The algorithm model the set of chemical reactions and the instant they occur as
random. The model takes account of intrinsic noise more accurately. After each reaction,
the algorithm determines which reaction will occur next, and how much time will elapse
before it occurs. The flow chart of the Algorithm is presented as Fig.1 which describes
the Monte Carlo simulation based simulation.
Fig.2 GFP expression simulated via Gillispie algorithm
Fig.3 mRNA expression simulated via Gillispie algorithm
Fig.4 Protein expression simulated via Gillispie algorithm
The simulation results presented in the figures show a square wave pattern in the mRNA
and protein level. On simulating the system in stochastic enviornment, few more interesting results comes into picture. One of such is noise propagation in the biological
system. The simulated results show a noisier mRNA expression than the protein level,
which makes the mRNA less stable compared to the protein. On investigating further
we observed the translation procedure is acting as a low pass filter. If we model the
translation process (which is linear in nature) in frequency domain, the transfer function
becomes,
The frequency response of translational dynamics is shown in Fig.5 validate the analysis. The mRNA dynamics which is noisy, and as noises are always are of high frequency in nature, the low pass action provided by the process can attenuate such characteristics.
As the γ increases the bandwidth increases and make the system succeptible to noise, that
is why a ssrA tag protein expression is much faster (owe to the larger bandwidth) but
becomes more noisy (as the system low pass action range is increased with the increase
in bandwidth.)
Fig.5 Frequency response for various degradation rate
