Team:Grenoble/Modeling/Amplification/Stochastic

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<a href="https://2012.igem.org/wiki/index.php?title=Team:Grenoble/Modeling/Amplification/Sensitivity"><img src="https://static.igem.org/mediawiki/2012/a/a4/Sensitivity_and_parameters.png" alt="" /></a>
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<a href="https://2012.igem.org/wiki/index.php?title=Team:Grenoble/Modeling/Amplification/Stochastic"><img src="https://static.igem.org/mediawiki/2012/a/ad/Stochastic_analysis.png" alt="" /></a>
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<h1> Goal </h1>
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<a href="https://2012.igem.org/wiki/index.php?title=Team:Grenoble/Modeling/Amplification/Stochastic/what"><img src="https://static.igem.org/mediawiki/2012/d/d9/What.png" alt="" /></a>
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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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<a href="https://2012.igem.org/Team:Grenoble/Modeling/Amplification/Stochastic/results"><img src="https://static.igem.org/mediawiki/2012/1/17/Results.png" alt="" /></a>
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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.
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<center><img src="https://static.igem.org/mediawiki/2012/3/38/Diagram_stoch.png" alt="" /></center>
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<h1> Why </h1>
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Gene expression is a stochastic process due to the inherent unpredictability of molecular collisions resulting from Brownian motion : the binding or unbinding of RNA polymerase to a promotor is partially random.
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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.
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<h1> How </h1>
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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.
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To introduce that randomness we use a new function : propensities.
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<center><img src="https://static.igem.org/mediawiki/2012/c/ca/Propensity.png" alt="" /></center>
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For example we take four possible reactions. Each reaction has a probability to happen in the next amount of time.
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<center><img src="https://static.igem.org/mediawiki/2012/8/8c/Reactions.png" alt="" /></center>
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We randomly chose the next reaction regarding the propensities.
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The possibility of one random variation implies that many could occur. For this reason, stochastic models are not run just once, but hundreds or even thousands of times.
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<center><img src="https://static.igem.org/mediawiki/2012/9/9c/Curves.png" alt="" /></center>
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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.
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To model that randomness we use a Gillepsie algorithm or Stoachastic Simulation Algorithm (SSA).
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