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

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Thus, the equilibrium points $(x,y)$ are placed in the intersection between the solutions for the relations above. Depending on the set of parameters, one can find two to four equilibria - the first one close to $(0,0)$, representing the repression of both populations, and the second one close to $(1,1)$, representing the activation of both populations, as presented in Fig. 2. In this case we used the parameters presented in Table 1, for 20% serum solution growth medium. The same behavior was found using the parameters for LB growth medium.  
Thus, the equilibrium points $(x,y)$ are placed in the intersection between the solutions for the relations above. Depending on the set of parameters, one can find two to four equilibria - the first one close to $(0,0)$, representing the repression of both populations, and the second one close to $(1,1)$, representing the activation of both populations, as presented in Fig. 2. In this case we used the parameters presented in Table 1, for 20% serum solution growth medium. The same behavior was found using the parameters for LB growth medium.  
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We limitated the range of the variables $x$ and $y$ to [0,1] since it is the range that has a biological meaning. The entire curve can be seen in [https://2012.igem.org/File:Phisiguais_2jpg.jpeg].
We limitated the range of the variables $x$ and $y$ to [0,1] since it is the range that has a biological meaning. The entire curve can be seen in [https://2012.igem.org/File:Phisiguais_2jpg.jpeg].
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{{:Team:USP-UNESP-Brazil/Templates/LImage | image=Phis100.jpg | left | caption=Fig. 3. When $\frac{\phi_A}{\phi_B} \gg 1$, besides the equilibria close to $(0,0)$ and $(1,1)$, there is also a point close to to $(1,0)$. | size=350px}}
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{{:Team:USP-UNESP-Brazil/Templates/RImage | image=Phis100.jpg | caption=Fig. 3. When $\frac{\phi_A}{\phi_B} \gg 1$, besides the equilibria close to $(0,0)$ and $(1,1)$, there is also a point close to to $(1,0)$. | size=350px}}
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A third equilibrium point emerges when $\frac{\phi_A}{\phi_B} \gg 1$ - which means the repression of population A over population B is much greater than its counterpart, Fig. 3. In this case, the system reaches an equilibrium close to $(1,0)$: population A activated, population B repressed. The behavior is analogous if $\frac{\phi_A}{\phi_B} \ll 1$.
A third equilibrium point emerges when $\frac{\phi_A}{\phi_B} \gg 1$ - which means the repression of population A over population B is much greater than its counterpart, Fig. 3. In this case, the system reaches an equilibrium close to $(1,0)$: population A activated, population B repressed. The behavior is analogous if $\frac{\phi_A}{\phi_B} \ll 1$.
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{{:Team:USP-UNESP-Brazil/Templates/RImage | image=Phis100ab.jpg | caption=Fig. 4. When $\frac{\phi_A}{\alpha_A} \gg 1$ and $\frac{\phi_B}{\alpha_B} \gg 1$, there are four equilibria, close to $(0,0)$, $(1,1)$, $(1,0)$ and $(0,1)$.} | size=350px}}
{{:Team:USP-UNESP-Brazil/Templates/RImage | image=Phis100ab.jpg | caption=Fig. 4. When $\frac{\phi_A}{\alpha_A} \gg 1$ and $\frac{\phi_B}{\alpha_B} \gg 1$, there are four equilibria, close to $(0,0)$, $(1,1)$, $(1,0)$ and $(0,1)$.} | size=350px}}
   
   
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Finally, when both $\phi_A$ and $\phi_B$ are big when compared to $\alpha_A$ and $\alpha_B$, both populations A and B are able to  
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repress each other, depending on the initial conditions: there are equilibria both close to $(1,0)$ and to $(0,1)$ - with repression  
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of one population and activation of the other, Fig. 4.
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Finally, when both $\phi_A$ and $\phi_B$ are large when compared to $\alpha_A$ and $\alpha_B$, both populations A and B are able to  
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repress each other. In this case, the system can reach both equilibruim point $(1,0)$ and $(0,1)$ - repression  
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of one population and activation of the other, Fig. 4. This is the desirable

Revision as of 01:04, 27 September 2012