Team:IPN-UNAM-Mexico/Modeling

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Modelling

Month-icon.pngIntroduction: Developing an Activator-Inhibitor network


Month-icon.pngFirst approach: Classical model with estimated diffusion constants


Month-icon.pngSecond approach: Activator-Inhibitor dynamics on a single cell


Month-icon.pngThird approach: Spatial model

Month-icon.pngThird approach: Spatial model

Afterward we described as ordinary differential equations the time change of the concentrations of PAI and AI based on the kinetic law equations, being x PAI and y AI


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Here all the constants are sums or products of kinetic constants.


With this system of differential equations describing the kinetic basis of the reaction and diffusion we proceeded to make a qualitative analysis of its behavior as a 2x2 system of equations using [http://en.wikipedia.org/wiki/Grapher Grapher].


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From this analysis we can see simply by looking at its vectorial field that it behaves as the system:


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We wanted to check if this equations as chemical kinetics into a system of the reaction-diffusion dynamics can produce spatiotemporal patterns; to do this we made a simulation using [http://www.comsol.com/ ComsolMultipysics] as previously described


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Month-icon.pngReferences

Month-icon.pngReferences

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