Difference between revisions of "Team:Edinburgh UG/Model"

Differential Equations

\begin{equation} \frac{d[M_R]}{dt} = k_{sMR} - \lambda_{MR}[M_R] \end{equation} \begin{equation} \frac{d[R]}{dt} = k_{sR}[M_R] - 2k_{2R}[R]^2 + 2k_{-2R}[R_2] - \lambda_R[R] \end{equation} \begin{equation} \begin{split} \frac{d[R_2]}{dt} = k_{2R}[R]^2 - k_{-2R}[R_2] - k_{rT7}[R_2][O_{T7}] + k_{-rT7}([O_{T7}]_T-[O_{T7}]) \\ - k_{rY}[R_2][O_Y] + k_{-rY}([O_Y]_T-[O_Y]) - k_{rCre}[R_2][O_{Cre}] \\ + k_{-rCre}([O_{Cre}]_T-[O_{Cre}]) - k_{dr1}[I]^2[R_2] + k_{-dr1}[I_2R_2] - \lambda_{R_2}[R_2]] \end{split} \end{equation} \begin{equation} \begin{split} \frac{d[O_Y]}{dt} = - k_{rY}[R_2][O_Y] + k_{-rY}([O_Y]_T-[O_Y]) \\ + k_{dr4}[I]^2([O_Y]_T-[O_Y]) - k_{-dr4}[I_2R_2][O_Y] \end{split} \end{equation} \begin{equation} \begin{split} \frac{d[O_{T7}]}{dt} = - k_{rT7}[R_2][O_{T7}] + k_{-rT7}([O_{T7}]_T-[O_{T7}]) \\ + k_{dr2}[I]^2([O_{T7}]_T-[O_{T7}]) - k_{-dr2}[I_2R_2][O_{T7}] \end{split} \end{equation} \begin{equation} \begin{split} \frac{d[O_{Cre}]}{dt} = - k_{rCre}[R_2][O_{Cre}] + k_{-rCre}([O_{Cre}]_T-[O_{Cre}]) \\ + k_{dr3}[I]^2([O_{Cre}]_T-[O_{Cre}]) - k_{-dr3}[I_2R_2][O_{Cre}] \end{split} \end{equation} \begin{equation} \begin{split} \frac{d[I]}{dt} = -2k_{dr1}[I]^2[R_2] + 2k_{-dr1}[I_2R_2] - 2k_{dr2}[I]^2([O_{T7}]_T-[O_{T7}]) \\ + 2k_{-dr2}[I_2R_2][O_{T7}] - 2k_{dr3}[I]^2([O_{Cre}]_T-[O_{Cre}]) \\ + 2k_{-dr3}[I_2R_2][O_{Cre}] - 2k_{dr4}[I]^2([O_Y]_T-[O_Y]) + 2k_{-dr4}[I_2R_2][O_Y] \\ + k_{ft}[YI_{ex}] + k_t([I_{ex}]-[I]) + 2\lambda_{I_2R_2}[I_2R_2] + \lambda_{YI_{ex}}[YI_{ex}] \end{split} \end{equation} \begin{equation} \begin{split} \frac{d[I_2R_2]}{dt} = k_{dr1}[I]^2[R_2] - k_{-dr1}[I_2R_2] + k_{dr2}[I]^2([O_{T7}]_T-[O_{T7}]) \\ - k_{-dr2}[I_2R_2][O_{T7}] + k_{dr3}[I]^2([O_{Cre}]_T-[O_{Cre}]) - k_{-dr3}[I_2R_2][O_{Cre}] \\ + k_{dr4}[I]^2([O_Y]_T-[O_Y]) - k_{-dr4}[I_2R_2][O_Y] - \lambda_{I_2R_2}[I_2R_2] \end{split} \end{equation} \begin{equation} \frac{d[M_Y]}{dt} = k_{s0MY}([O_Y]_T-[O_Y]) + k_{s1MY}[O_Y] - \lambda_{MY}[M_Y] \end{equation} \begin{equation} \frac{d[LacY]}{dt} = k_{sY}[M_Y] + (k_{ft} + k_{-p})[YI_{ex}] - k_p[LacY][I_{ex}] - \lambda_Y[LacY] \end{equation} \begin{equation} \frac{d[M_{T7}]}{dt} = k_{s0MT7}([O_{T7}]_T-[O_{T7}]) + k_{s1MT7}[O_{T7}] - \lambda_{M_{T7}}[M_{T7}] \end{equation} \begin{equation} \frac{d[T7]}{dt} = k_{sT7}[M_{T7}] - \lambda_{T7}[T_7] \end{equation} \begin{equation} \frac{d[M_{Cre}]}{dt} = k_{s0Mcre}([O_{Cre}]_T-[O_{Cre}])[T_7] + k_{s1Mcre}[O_{Cre}][T_7] - \lambda_{Mcre}[M_{Cre}] \end{equation} \begin{equation} \begin{split} \frac{d[Cre]}{dt} = k_{sCre}[M_{Cre}] - \lambda_{Cre}[Cre] - k_1[S][Cre] + k_{-1}[SCre] \\ - k_1[SCre][Cre] + k_{-1}[SCre^{(a)}_2] - k_2[SCre][Cre] + k_{-2}[SCre^{(b)}_2] \\ - k_2[SCre^{(a)}_2][Cre] + k_{-2}[SCre_3] - k_1[SCre^{(b)}_2][Cre] + k_{-1}[SCre_3] \\ - k_2[SCre_3][Cre] + k_{-2}[SCre_4] + k_{-2}([QCre_2]+[PCre_2]) \\ - k_2([QCre]+[PCre])[Cre] + k_{-1}([QCre]+[PCre]) - k_1([Q]+[P])[Cre] \end{split} \end{equation} \begin{equation} \frac{d[YI_{ex}]}{dt} = - (k_{ft} + k_{-p})[YI_{ex}] + k_p[LacY][I_{ex}] - \lambda_{YI_{ex}}[YI_{ex}] \end{equation} \begin{equation} \frac{d[S]}{dt} = -k_1[S][Cre] + k_{-1}[SCre] \end{equation} \begin{equation} \begin{split} \frac{d[SCre]}{dt} = k_1[S][Cre] - k_{-1}[SCre] - (k_1 + k_2)[SCre][Cre] \\ + k_{-1}[SCre^{(a)}_2] + k_{-2}[SCre^{(b)}_2] \end{split} \end{equation} \begin{equation} \frac{d[SCre^{(a)}_2]}{dt} = k_1[SCre][Cre] - k_{-1}[SCre^{(a)}_2] - k_2[SCre^{(a)}_2][Cre] + k_{-2}[SCre_3] \end{equation} \begin{equation} \frac{d[SCre^{(b)}_2]}{dt} = k_2[SCre][Cre] - k_{-2}[SCre^{(b)}_2] - k_1[SCre^{(b)}_2][Cre] + k_{-1}[SCre_3] \end{equation} \begin{equation} \begin{split} \frac{d[SCre_3]}{dt} = k_2[SCre^{(a)}_2][Cre] - (k_{-2} + k_{-1})[SCre_3] \\ + k_1[SCre^{(b)}_2][Cre] - k_2[SCre_3][Cre] + k_{-2}[SCre_4] \end{split} \end{equation} \begin{equation} \frac{d[SCre_4]}{dt} = k_2[SCre_3][Cre] - (k_{-2} + k_3)[SCre_4] + k_{-3}[SC] \end{equation} \begin{equation} \frac{d[SC]}{dt} = k_3[SCre_4] - (k_{-3} + k_{-4})[SC] + k_4[QCre_2][PCre_2] \end{equation} \begin{equation} \frac{d[QCre_2]}{dt} = k_{-4}[SC] - k_4[QCre_2][PCre_2] - k_{-2}[QCre_2] + k_2[QCre][Cre] \end{equation} \begin{equation} \frac{d[PCre_2]}{dt} = k_{-4}[SC] - k_4[QCre_2][PCre_2] - k_{-2}[PCre_2] + k_2[PCre][Cre] \end{equation} \begin{equation} \frac{d[QCre]}{dt} = k_{-2}[QCre_2] - k_2[QCre][Cre] - k_{-1}[QCre] + k_1[Q][Cre] \end{equation} \begin{equation} \frac{d[PCre]}{dt} = k_{-2}[PCre_2] - k_2[PCre][Cre] - k_{-1}[PCre] + k_1[P][Cre] \end{equation} \begin{equation} \frac{d[Q]}{dt} = k_{-1}[QCre] - k_1[Q][Cre] \end{equation} \begin{equation} \frac{d[P]}{dt} = k_{-1}[PCre] - k_1[P][Cre] \end{equation} \begin{equation} \frac{d[M_{RFP}]}{dt} = k_{mRFP}([P] + [PCre] + [PCre_2]) - \lambda_{mRFP}[M_{RFP}] \end{equation} \begin{equation} \frac{d[RFP]}{dt} = k_{RFP}[M_{RFP}] - \lambda_{RFP}[RFP] \end{equation}