Team:USP-UNESP-Brazil/Associative Memory/Modeling

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\begin{align} &\frac{d}{dt}[S] = k_{-1}[S_{a}] - [S](k_{1}[M] + k_{d}) \nonumber \\ &\frac{d}{dt}[S_{a}] = k_{1}[S][M] + k_{-1}[S_{aa}] + k_{-2}[S_{ab}] - [S_{a}]( k_{1}[M] + k_{-1} + k_{2}[M] + k_{d} ) \nonumber \\ \end{align}

\begin{align} \frac{d}{dt} N_{d} &= r(N_{d}+N_{u})(1 - (N_{d}+N_{u})/K) - \alpha A N_{d} + \beta N_{u} \\ \frac{d}}{dt} N_{u} &= \alpha A N_{1d} - \beta N_{u} \\ \frac{d}{dt} A &= \kappa_{u} N_{u} + \kappa_{d} N_{d} - \alpha A N_{d} - \lambda A \end{align}

[1] J. P. Ward, J.R. King, A. J. Koerber, P. Williams, J. M. Croft and R. E. Sockett Mathematical modelling of quorum sensing in bacteria. Math Med Biol (2001) 18(3)

[2] http://partsregistry.org/