Modeling of lac operon regulation

1. Modeling of lac operon regulation Maxim Tikhonov

2. Goals • Create model of lac operon regulation • Investigate the origin of bistability.

3. Mechanistic diagram Iex R2 Y R I Y I I R2 MR MY I R2 LacI Lac Lac

4. ODEs: MR – Repressor RNA R – repressor R2 – repressor dimer O - operon I – internal IPTG I2R2 – inactive repressor MY – permease RNA Y – permease YI – permease/IPTG complex dMR/dt=k_sMR-l_MR*MR dR/dt=k_sR*MR-2*dimeris-l_R*R dR2/dt=dimeris-repres-inactiv-l_R2*R2 dO/dt=-repres+derepres dI/dt=-2e-3*inactiv-2e-3*derepres+1e-3*k_ft*YI +2e-3*l_I2R2*I2R2+1e-3*l_YI*YI+dif dI2R2/dt=inactiv+derepres-l_I2R2*I2R2 dMY/dt=k_s0MY*(Otot-O)+k_s1MY*O-l_MY*MY dY/dt=k_sY*MY-binding-l_Y*Y dYI/dt=binding-l_YI*YI __________ dimeris=k_2R*R^2-k_r2R*R2 repres=k_r*R2*O-k_rr*(Otot-O) binding=-(k_ft+k_rp)*YI+k_p*Y*Iex*1000 inactiv=k_dr1*R2*I^2-k_rdr1*I2R2 derepres=k_dr2*(Otot-O)*I^2-k_rdr2*O*I2R2 dif=k_t*(Iex-I)

5. [Iex] was used as the main bifurcation parameter Within the range [Iex] = 24.2-32.4 uM, two branches of stable steady states exist, separated by branch of unstable steady states.

6. Conclusion • Model of lac operon regulation was implemented. • The system exhibits bistabilitywithin the range [Iex] = 24.2-32.4 uM