Difference between revisions of "Team:IIT Delhi/Stochastic Model"

Stochastic Model

Noise in a system is a repeating issues from engineering to science. In a biogical system noise can intrinsic, for e.g.- from randomness of chemical reactions in side of the cell or extrinsic, for e.g.-, 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                                    Fig.4 Proteins

The simulation results presented in the above 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