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From 2011.igem.org

This model is very similar to the one used in <a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis#references">[2]</a>. We consider that the particle diffusing in the cell is a random walker.

We want to see how long it takes for a particle of a given size to diffuse to any point of a cell. We use the following parameters:

• V volume of the cell (10^-18 m³)
• <img src='https://static.igem.org/mediawiki/2011/d/d2/Lambda.png' style='width:20px;'/> characteristic size of the particle (m)
• D diffusion coefficient of the particle (m².s^-1)

We divide the cytoplasm volume V into <img src='https://static.igem.org/mediawiki/2011/7/72/Occupation_sites_general.png' style='width:80px;'/> occupation sites for the walker. The characteristic time <img src='https://static.igem.org/mediawiki/2011/8/84/Tau.png' style='width:20px;'/> associated with the transition from one site to another is:<img src='https://static.igem.org/mediawiki/2011/8/81/Characteristic_time_general.png' style='width:90px;'/> <a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis#references">[3]</a>

If we have R walkers of this type, the probability that a molecule arrives at a given occupation site during the time interval <img src='https://static.igem.org/mediawiki/2011/8/84/Tau.png' style='width:20px;'/> is: <img src='https://static.igem.org/mediawiki/2011/b/bb/Probability_general.png' style='width:80px;'/>.