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Team:Grenoble/Modeling/Amplification/Stochastic
From 2012.igem.org
Goal
Statistic modeling is a technique of presenting data or predicting outcomes that takes into account a certain degree of randomness or unpredictability. The stochastic process is often used to represent the evolution of some random value, or system, over time.
Why
We have used a stochastic process because in one bacteria we don't have enough molecules to consider that one miological element has a continuous value. The behavior of those biological elements is regulated by probability laws. In biology systems, introducing stochastic noise has been found to help improve the signal strength of the internal feedback loops for balance and other vestibular communication.How
Rather than using fixed variables such as in other mathematical modeling, a stochastic model incorporates random variations to predict future conditions and to see what they might be like. To introduce that randomness we use a new function : propensities.
Gillespie _ Stochastic Simulation Algorithm
The Gillespie algorithm generates a statistically correct trajectory of a stochastic equation. Traditional continuous and deterministic biochemical rate equations do not accurately predict cellular reactions since they rely on bulk reactions that require the interactions of millions of molecules. In contrast, the Gillespie algorithm allows a discrete and stochastic simulation of a system with few reactants because every molecule is explicitly simulated. When simulated, a Gillespie realization represents a random walk of the entire system. We assert :
