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

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Introduction

Project Overview

Plasmid
Plug&Play

Associative Memory Network

Extras

Introduction

Project Overview

Plasmid Plug&Play

Associative Memory
Network

Extras

\begin{align} \frac{d}{dt} N_{d} &= rN_{t}\Big[1 - \frac{N_{t}}{K}\Big] - \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 \\ N_{t} &= N_{d} + N_{u} \end{align}

\begin{align} \frac{d}{dt}N_{Ad} &= rN_{At}\Big[1 - \frac{N_{At}}{K}\Big] - \alpha_A A N_{Ad} + (\beta_A + \phi_B B)N_{Au} \\ \frac{d}{dt}N_{Bd} &= rN_{Bt}\Big[1 - \frac{N_{Bt}}{K}\Big] - \alpha_B A N_{Bd} + (\beta_B + \phi_A A)N_{Bu} \\ \frac{d}{dt}N_{Au} &= \alpha_A A N_{Ad} - \beta_A N_{Au} - \phi_B B N_{Au}\\ \frac{d}{dt}N_{Bu} &= \alpha_B B N_{Bd} - \beta_B N_{Bu} - \phi_A A N_{Bu} \\ \frac{d}{dt}A &= \kappa_{Au} N_{Au} + \kappa_{Ad} N_{Ad} - \alpha_A A N_{Ad} - \lambda_A A - \phi_A A N_{Bu} \\ \frac{d}{dt}B &= \kappa_{Bu} N_{Bu} + \kappa_{Bd} N_{Bd} - \alpha_B B N_{Bd} - \lambda_B B - \phi_B B N_{Au} \\ N_{At} &= N_{Ad}+N_{Au} \\ N_{Bt} &= N_{Bd}+N_{Bu} \end{align}

\begin{align} &-\alpha_A A N_{Ad} + \beta_A N_{Au} + \phi_B B N_{Au} = 0 \\ &\kappa_{Au} N_{Au} + \kappa_{Ad} N_{Ad} - \alpha_A A N_{Ad} - \lambda_A A - \phi_A A N_{Bu} = 0 \\ &-\alpha_B B N_{Bd} + \beta_B N_{Bu} + \phi_A A N_{Bu} = 0 \\ &\kappa_{Bu} N_{Bu} + \kappa_{Bd} N_{Bd} - \alpha_B B N_{Bd} - \lambda_B B - \phi_B B N_{Au} = 0 \\ &N_{Au} + N_{Ad} = K \\ &N_{Bu} + N_{Bd} = K \end{align}

Fig 2.

Fig 2

[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/

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@@ Line 14: / Line 14: @@
 \begin{align}
-\frac{d}{dt} N_{d} &= r(N_{d}+N_{u})\Big[1 - \frac{(N_{d}+N_{u})}{K}\Big] - \alpha A N_{d} + \beta N_{u} \\
+\frac{d}{dt} N_{d} &= rN_{t}\Big[1 - \frac{N_{t}}{K}\Big] - \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
+\frac{d}{dt} A &= \kappa_{u} N_{u} + \kappa_{d} N_{d} - \alpha A N_{d} - \lambda A \\
+N_{t} &= N_{d} + N_{u}
 \end{align}
 \begin{align}
-\frac{d}{dt}N_{Ad} &= r(N_{Ad}+N_{Au})\Big[1 - \frac{(N_{Ad}+N_{Au})}{K}\Big] - \alpha_A A N_{Ad} + (\beta_A + \phi_B B)N_{Au} \\
+\frac{d}{dt}N_{Ad} &= rN_{At}\Big[1 - \frac{N_{At}}{K}\Big] - \alpha_A A N_{Ad} + (\beta_A + \phi_B B)N_{Au} \\
-\frac{d}{dt}N_{Bd} &= r(N_{Bd}+N_{Bu})\Big[1 - \frac{(N_{Bd}+N_{Bu})}{K}\Big] - \alpha_B A N_{Bd} + (\beta_B + \phi_A A)N_{Bu} \\
+\frac{d}{dt}N_{Bd} &= rN_{Bt}\Big[1 - \frac{N_{Bt}}{K}\Big] - \alpha_B A N_{Bd} + (\beta_B + \phi_A A)N_{Bu} \\
 \frac{d}{dt}N_{Au} &= \alpha_A A N_{Ad} - \beta_A N_{Au} - \phi_B B N_{Au}\\
 \frac{d}{dt}N_{Bu} &= \alpha_B B N_{Bd} - \beta_B N_{Bu} - \phi_A A N_{Bu} \\
 \frac{d}{dt}A &= \kappa_{Au} N_{Au} + \kappa_{Ad} N_{Ad} - \alpha_A A N_{Ad} - \lambda_A A - \phi_A A N_{Bu} \\
-\frac{d}{dt}B &= \kappa_{Bu} N_{Bu} + \kappa_{Bd} N_{Bd} - \alpha_B B N_{Bd} - \lambda_B B - \phi_B B N_{Au}
+\frac{d}{dt}B &= \kappa_{Bu} N_{Bu} + \kappa_{Bd} N_{Bd} - \alpha_B B N_{Bd} - \lambda_B B - \phi_B B N_{Au} \\
+N_{At} &= N_{Ad}+N_{Au} \\
+N_{Bt} &= N_{Bd}+N_{Bu}
 \end{align}