Difference between revisions of "Template:SYSU-Software/statics/html/Modeling/SimulationCircuit.html"

       While cooperating, it is important to know more about the designed genetic circuit, and many users want to
       predict the expression rate with our software. To meet this need, we construct an ODE systems model to
       simulate the dynamic behaviors of the genetic system mathematically. We adopt the Hill functions as the
       blueprints of our formula, and construct a general model. After completing their circuit in designer, our
       software can create an ODE system automatically.

       we use mathematical formula to present general interaction between chemical materials and circuits, like
       promotion and inhibition.
       If a circuit express $\alpha$ without other inhibition and promotion from other material, we set the basic
       Concentration-Time ODEs form of a certain protein $\alpha$ as below:
       $$\frac{d[\alpha]}{d_t}=k_\alpha[\alpha_{\textrm{gene}}]-d[\alpha]$$
       $K_{\alpha}$ represents the production or translation rate of $\alpha _{\textrm{gene}}$ .
       $d$ represents the degradation rate of $\alpha _{\textrm{protein}}$.
       $[\alpha _{\textrm{gene}}]$, $[\alpha]$ mean the concentration of $\alpha _{\textrm{gene}}$ and $\alpha _{\textrm{protein}}$.

       If a circuit express $\alpha$ with promotion from $\beta$ , we set the Concentration-Time ODEs form as below:
       $$\frac{d[\alpha]}{d_t}=k_\alpha[\alpha_{\textrm{gene}}][\beta]-d[\alpha]$$
       $k_\alpha$ represents the production or translation rate of $\alpha _{\textrm{gene}}$. $d$ represents the degradation
       rate of $\alpha _{\textrm{protein}}$. $[\alpha _{\textrm{gene}}]$, $[\alpha]$, $[\beta]$ mean the concentration of $\alpha
       _{\textrm{gene}}$ ,$\alpha _{\textrm{protein}}$ and $\beta_{\textrm{protein}}$

       If a circuit express $\alpha$ with inhibition from $\gamma$, we set the concentration-Time ODEs form as blow:

       $$\frac{d[\alpha]}{d_t}=k_\alpha[\alpha_{\textrm{gene}}][\frac{1}{1+[\gamma]^{n\gamma}}]-d[\alpha]$$

       $K_{\alpha}$ represents the production or translation rate of $\alpha _{\textrm{gene}}$ .
       $N_{\gamma}$ represents the $\gamma$ repression coefficient.
       $d$ represents the degradation rate of $\alpha _{\textrm{protein}}$.
       $[\alpha _{\textrm{gene}}]$, $[\alpha]$ ,$[\gamma]$ mean the concentration of $\alpha _{\textrm{gene}}$ ,$\alpha _{\textrm{protein}}$ and
       $\gamma _{\textrm{protein}}$.

       If a chemical is influenced by more than one substance, the multi-one relationship is demonstrated as the
       product of terms of each factor. For example, if a circuit expression $\alpha$ with inhibition from $\beta$ and
       $\gamma$, we set the Concentration-Time ODEs form as blow:

       $$\frac{d[\alpha]}{d_t}=k_\alpha[\alpha_{\textrm{gene}}][\frac{1}{1+[\gamma]^{n\gamma}}][\frac{1}{1+[\beta]^{n\beta}}]-d[\alpha]$$

       $K_{\alpha}$ represents the production or translation rate of $\alpha _{\textrm{gene}}$ .
       $N_{\gamma}$ represents the $\gamma$ repression coefficient.
       $N_{\beta}$ represents the $\beta$ repression coefficient.
       $d$ represents the degradation rate of $\alpha _{\textrm{protein}}$.
       $[\alpha _{\textrm{gene}}]$,$[\alpha]$ ,$[\beta]$ ,$[\gamma]$mean the concentration of $\alpha _{\textrm{gene}}$ ,$\alpha
       _{\textrm{protein}}$ ,$\beta _{\textrm{protein}}$,$\gamma _{\textrm{protein}}$