Modeling

By our pre research we found out that logarithmic form of intensity and photocurrent which means sensitivity of rhodopsin is similar to sigmoid function. Our new fusion protein’s receptor part is rhodopsin and Ga, Gbr $\alpha,\beta,\gamma$ is from dopamine receptor drd2. We made hypothesis to put variable of intensity instead of ligand concentration.

so $[C_{RP4}]=A\frac{1}{ {1+e ^{-B \times I}}} +C$ can be written (I:intensity, A,B,C: constant) G-protein receptor is very common kind in nature and ther are some popular modeling researches ongoing. By studying some references we were able to make a diagram and derivate equation which could be understood by korean high school chemistry curriculum. G_i/o inhibit Adenyl cyclase which makes camp. inhibiting process was harder to model than promoting effect. We assumed that activated AD level would be inverse proportion to G_i/o. and G_i/o concentration is similar to G* concentration.

$$[C_{RP4}]=A\frac{1}{ {1+e ^{-B \times I}}} +C$$ $$\frac{d[R]}{dt}=\frac{k _{r} [C _{RP4} R]-k _{f} [C _{RP4} ][R]-k _{fr} [R]+k _{fr}} {K _{act} [R ^{*} ]}$$ $$\frac{d[R ^{*} ]}{dt}=k _{r} [C _{RP4} R ^{*} ]- \xi k _{f} [C _{RP4} ][R ^{*} ]+k _{fr} [R]-k _{fr} [C _{RP4} R]$$ $$\frac{d[C _{RP4} R]}{dt}=\frac{k _{f} [C _{RP4} ][R]-k _{r} [C _{RP4} R]+k _{fr}}{( \xi K _{act} )[C _{RP4} R ^{*} ]-k _{fr} [C _{RP4} R]}$$ $$\frac{d[C _{RP4} R ^{*} ]}{dt}=\frac{k _{fr} [C _{RP4} R]-k _{fr}}{( \xi K _{act} )[C _{RP4} R ^{*} ]-k _{ds} [C _{RP4} R ^{*} ]+ \xi k _{f} [C _{RP4} R ^{*} ]-k _{r} [C _{RP4} R ^{*} ]}$$ $$\frac{d[C _{RP4} R _{ds} ]}{dt}=k _{ds} [C _{RP4} R ^{*} ]-k _{r2} [C _{RP4} R _{ds} ]+k _{r2} [C _{RP4} ][R _{ds} ]$$ $$\frac{d[R _{ds} ]}{dt}=k _{r2} [C _{RP4} R _{ds} ]-k _{f2} [C _{RP4} ][R _{ds} ]$$ $$\frac{d[G ^{*} ]}{dt}=k _{a} [G]([C _{RP4} R ^{*} ]+[R ^{*} ])-k _{f} [G ^{*} ]$$ $$\frac{d[G]}{dt}=k _{i} [G ^{*} ]-k _{a} [G]([C _{RP4} R ^{*} ]+[R ^{*} ])$$ $$\frac{d[AD ^{*} ]}{dt}=\frac{d[cAMP]}{dt}=(k _{io} [G ^{*} ]) ^{-1}$$ $R^*$: active form of receptor
$G^*$:active form of G protein
$C_{RP4}R^*$: active form of ligand like/receptor complex
$C_{RP4}$:free ligand like imaginary material
$C_{RP4}R_ds$:desentisized ligand like/receptor complex
$R_{ds}$: desensitized receptor
$\xi$: effect of ligand like binding on receptor activation
$k_{ds}$: desensitization rate
$k_{i}$: inactivation rate
$k_{f}$: ligand like material asscociation rate constant for $R$
$k_{r}$: ligand like material disscociation rate constant for $R$
$k_{f2}$:ligand like material asscociation rate constant for $R_ds$
$k_{r2}$:ligand like material disscociation rate constant for $R_ds$
$K_{d}$:equillibrium dissociation constant($\frac{k_r}{k_f}$)
$k_{\alpha}$: activate rate constant
$k_{io}$: inactivating rate of AD by G_i/o
$R_{tot}$: total receptor number
$G_{tot}$:total number of G-Protein

Team:KOREA/Model

Modeling

References