Modeling

  Leaving cell transmit signal through chemical modifications of signal-related molecules like phosphorylation, methylation, acetylation or ubiquitination. And these chemical modifications are basically chemical reactions. Therefore, we can assume signal transduction pathway as sequential chemical reactions. We applied this assumption to signal transduction initiated by modified FGFR-antigen binding. Signal transduction follows these steps.

1. Antigen binds to the single chain antibody of modified FGFR and form FGFR-complex(FGFRC).
2. Two FGFR-complexes bind each other and form FGFR-complex-dimer(FGFRCD).
3. FGFRCD phosphorylate each other and form FGFR-complex-dimer-phosphorylate (FGFRCDnP)
4. FGFRCDnP phosphorylate STAT1 to for STAT1P.
5. Two STAT1Ps bind each other and form STAT1P-dimer.
6. STAT1P-dimer near cell surface diffuse to inside of nucleus of yeast.
7. STAT1P-dimer in nucleus binds to GAS element and activate GFP gene.

  And these steps may be formulated as these reactions.

  And we can expect that the concentration of FGFRCDnP is constant at equilibrium state. The concentration of FGFRCDnP is

  And the concentration of FGFRCD is

  And the concentration of FGFRC is

  Therefore, the concentration of FGFRCDnP as the function of concentration of FGFR [FGFR], that of antigen [antigen] and phosphorylation number n is