Team:Grenoble/Modeling/Amplification/Stochastic

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<h1> Goal </h1>
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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.
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Stochastic modeling is a technique of predicting outcomes that takes into account a certain degree of randomness or unpredictability. In a stochastic modeling, a small amount of randomness is added at each time step of the simulation.
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<center><img src="https://static.igem.org/mediawiki/2012/e/e7/Stochastic_def.png" alt="" /></center>
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It is the probabilistic counterpart to a deterministic process.
It is the probabilistic counterpart to a deterministic process.

Revision as of 12:54, 17 September 2012

iGEM Grenoble 2012

iGEM Grenoble iGEM
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Goal


Stochastic modeling is a technique of predicting outcomes that takes into account a certain degree of randomness or unpredictability. In a stochastic modeling, a small amount of randomness is added at each time step of the simulation.
It is the probabilistic counterpart to a deterministic process.

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.


For example we take four possible reactions. Each reaction has a probability to happen in the next amount of time.


We randomly chose the next reaction regarding the propensities.

When we run the script once, we get a graph. This graph represent the rando evolution of an element. Because of this randomness, if we run the script an other time we will get a different graph. That is why to be able to interpret the results we have to run the cripts hundreds or thousands of times.

Instead of describing a process which can only evolve in one way, in a stochastic or random process there is some indeterminacy : even if the initial condition is known, there are several directions in which the process may evolve.

To model that randomness we use a Gillepsie algorithm or Stoachastic Simulation Algorithm (SSA).

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 :

Each reaction Rj is characterized mathematically by two quantities :


Once we have put the theory of the stochastic approach, we can determine the algorithm.

One iteration of Gillespie algorithm




The algorithm comprises 5 steps.

You can find our script for the stochastic modeling here.

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