Difference between revisions of "Team:Freiburg/Modeling"

Modeling

Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.

Here are a few examples from previous teams:

• ETH Zurich 2014
• Waterloo 2014

Detailed System

Transcription

ODE System

\[ tc0(1): \;\;\; \frac{dc^{RNAP}_{free}[t]}{dt}\: =\: c^{RNAP}_{bound}[t] \cdot k^{RNAP}_{gain} - c^{RNAP}_{free}[t] \cdot k^{RNAP}_{loss} \] \[ \hphantom{tc0(1): \;\;\; \frac{dc^{RNAP}_{free}[t]}{dt}\: =\: } + c^{RNAP}_{sigma}[t] \cdot k^{sigma}_{off} - c^{RNAP}_{free}[t] \cdot c^{sigma}[t] \cdot k^{sigma}_{on} \] \[ \hphantom{tc0(1): \;\;\; \frac{dc^{RNAP}_{free}[t]}{dt}\: =\: } + c^{RNAP}_{elongter}[-1][t] \cdot k^{RNAP}_{diss} \]
\[ tc0(2): \;\;\; \frac{dc^{sigma}[t]}{dt}\: =\: c^{sigma}_{bound}[t] \cdot k^{sigma}_{gain} - c^{sigma}[t] \cdot k^{sigma}_{loss} + c^{RNAPsigma}_{bound}[t] \cdot k^{sigma}_{off} \] \[ \hphantom{tc0(2): \;\;\; \frac{dc^{sigma}[t]}{dt}\: =\: } + c^{RNAP}_{sigma}[t] \cdot k^{sigma}_{off} - c^{RNAP}_{free}[t] \cdot c^{sigma}[t] \cdot k^{sigma}_{on} \] \[ \hphantom{tc0(2): \;\;\; \frac{dc^{sigma}[t]}{dt}\: =\: } + c^{RNAP}_{ini}[-1][t] \cdot k^{tc}_{prel} \]
\[ tc0(3.1): \;\;\; \frac{dc^{RNAP}_{sigmaint}[t]}{dt}\: =\: c^{RNAP}_{free}[t] \cdot c^{sigma}[t] \cdot k^{sigma}_{on} - c^{RNAP}_{sigmaint}[t] \cdot k^{sigma}_{off} \] \[ \hphantom{tc0(3.1): \;\;\; \frac{dc^{RNAP}_{sigmaint}[t]}{dt}\: =\: } + c^{RNAP}_{sigma}[t] \cdot k^{RNAPsigma}_{isore} - c^{RNAP}_{sigmaint}[t] \cdot k^{RNAPsigma}_{iso} \] \[ tc0(3.2): \;\;\; \frac{dc^{RNAP}_{sigma}[t]}{dt}\: =\: c^{RNAPsigma}_{bound}[t] \cdot k^{RNAP}_{gain} \cdot c^{RNAP}_{sigma}[t] \cdot k^{RNAP}_{loss} \] \[ \hphantom{tc0(3.2): \;\;\; \frac{dc^{RNAP}_{sigma}[t]}{dt}\: =\: } + \sum \limits_{i=0}^n c^{RNAP}_{on}[i][t] \cdot k^{RNAP}_{off} - c^{RNAP}_{sigma}[t] \cdot p^{DNA} \cdot l^{DNA} \cdot k^{RNAP}_{on} \] \[ \hphantom {tc0(3.2): \;\;\; \frac{dc^{RNAP}_{sigma}[t]}{dt}\: =\: } + c^{RNAP}_{sigmaint}[t] \cdot k^{sigma}_{iso} - c^{RNAP}_{sigma}[t] \cdot k^{RNAPsigma}_{isore} \]
\[ tc0(4): \;\;\; \frac{dc^{RNAP}_{on}[i][t]}{dt}\: =\: c^{RNAP}_{sigma}[t] \cdot p^{DNA} \cdot k^{RNAP}_{on} \] \[ \hphantom{tc0(4): \;\;\; \frac{dc^{RNAP}_{on}[i][t]}{dt}\: =\: } + c^{RNAP}_{on}[i\:-\:v^{RNAP}_{move} \cdot dt][t] \cdot (1 - k^{RNAP}_{off}) - c^{RNAP}_{on}[i][t] \]
\[ tc0(5): \;\;\; \frac{dc^{RNAP}_{prom}[t]}{dt}\: =\: \sum \limits_{i\:=\:n - v^{RNAP}_{move} \cdot dt}^n c^{RNAP}_{on}[i][t] \cdot (1 - k^{RNAP}_{off}) \] \[ \hphantom{tc0(5): \;\;\; \frac{dc^{RNAP}_{prom}[t]}{dt}\: =\: } + c^{RNAP}_{open}[t] \cdot k^{tc}_{closed} - c^{RNAP}_{prom}[t] \cdot k^{tc}_{open} \]
\[ tc0(6): \;\;\; \frac{dc^{RNAP}_{open}[t]}{dt}\: =\: c^{RNAP}_{prom}[t] \cdot k^{tc}_{open} - c^{RNAP}_{open}[t] \cdot k^{tc}_{closed} \] \[ \hphantom{tc0(6): \;\;\; \frac{dc^{RNAP}_{open}[t]}{dt}\: =\: } + c^{RNAP}_{ini}[-1][t] \cdot k^{tc}_{iniab} - c^{RNAP}_{open}[t] \cdot c^{ATP}[t] \cdot c^{X_1 TP}[t] \cdot k^{tc}_{ini1} \]
\[ tc0(7): \;\;\; \frac{dc^{RNAP}_{ini1}[t]}{dt}\: =\: c^{RNAP}_{open}[t] \cdot c^{ATP}[t] \cdot c^{X_1 TP}[t] \cdot k^{tc}_{ini1} - c^{RNAP}_{ini1}[t] \cdot c^{X_2 TP}[t] \cdot k^{tc}_{inix} \]
\[ tc0(8.1): \;\;\; \frac{dc^{RNAP}_{ini}[i][t]}{dt}\: =\: c^{RNAP}_{ini}[i-1][t] \cdot c^{X_i TP}[t] \cdot k^{tc}_{inix} - c^{RNAP}_{ini}[i][t] \cdot c^{X_i+1 TP}[t] \cdot k^{tc}_{inix}, \] \[ \hphantom{tc0(8.1): \;\;\; \frac{dc^{RNAP}_{ini}[i][t]}{dt}\: =\: } (i = 2, ..., l^{ini-1}) \] \[ tc0(8.2): \;\;\; \frac{dc^{RNAP}_{ini}[1][t]}{dt}\: =\: \frac{dc^{RNAP}_{ini1}[t]}{dt} \] \[ tc0(8.3): \;\;\; \frac{dc^{RNAP}_{ini}[-1][t]}{dt}\: =\: c^{RNAP}_{ini}[-2][t] \cdot c^{X_-1 TP}[t] \cdot k^{tc}_{inix} - c^{RNAP}_{ini}[-1][t] \cdot (k^{tc}_{iniab} + k^{tc}_{prel}) \]
\[ tc0(9): \;\;\; \frac{dc^{RNAP}_{prel}[t]}{dt}\: =\: c^{RNAP}_{ini}[-1][t] \cdot k^{tc}_{prel} - c^{RNAP}_{prel}[t] \cdot c^{X_1 TP}[t] \cdot k^{tc}_{elong} \]
\[ tc0(10.1): \;\;\; \frac{dc^{RNAP}_{elong}[i][t]}{dt}\: =\: c^{RNAP}_{elong}[i-1][t] \cdot (1 - prob^{tc}_{mm}) \cdot c^{X_i TP}[t] \cdot k^{tc}_{elong} \] \[ \hphantom{tc0(10.1): \;\;\; \frac{dc^{RNAP}_{elong}[i][t]}{dt}\: =\: } - c^{RNAP}_{elong}[i][t] \cdot ((1 - prob^{tc}_{mm}) \cdot c^{X_1 TP}[t] \cdot k^{tc}_{elong} + prob^{tc}_{mm} \cdot (c^{NTPs}[t] - c^{X_1 TP}[t]) \cdot k^{tc}_{elong}) \] \[ \hphantom{tc0(10.1): \;\;\; \frac{dc^{RNAP}_{elong}[i][t]}{dt}\: =\: } + c^{RNAP}_{elongGreAB}[j + l^{mRNA}_{cl}][t] \cdot k^{GreAB}_{cat}, \] \[ \hphantom{tc0(10.1): \;\;\; \frac{dc^{RNAP}_{elong}[i][t]}{dt}\: =\: } (i = 2, ..., l^{elong-1}),\: (j = i\: and\: j = 2, ..., l^{elong} - l^{mRNA}_{cl}) \] \[ tc0(10.2): \;\;\; \frac{dc^{RNAP}_{elong}[1][t]}{dt}\: =\: c^{RNAP}_{prel}[t] \cdot (1 - prob^{tc}_{mm}) \cdot c^{X_1 TP}[t] \cdot k^{tc}_{elong} \] \[ \hphantom{tc0(10.2): \;\;\; \frac{dc^{RNAP}_{elong}[1][t]}{dt}\: =\: } - c^{RNAP}_{elong}[1][t] \cdot ((1 - prob^{tc}_{mm}) \cdot c^{X_1 TP}[t] \cdot k^{tc}_{elong} + prob^{tc}_{mm} \cdot (c^{NTPs}[t] - c^{X_1 TP}[t]) \cdot k^{tc}_{elong}) \] \[ \hphantom{tc0(10.2): \;\;\; \frac{dc^{RNAP}_{elong}[1][t]}{dt}\: =\: } + c^{RNAP}_{elongGreAB}[l^{mRNA}_{cl}][t] \cdot k^{GreAB}_{cat} \] \[ tc0(10.3): \;\;\; \frac{dc^{RNAP}_{elong}[-1][t]}{dt}\: =\: c^{RNAP}_{elong}[-2][t] \cdot (1 - prob^{tc}_{mm}) \cdot c^{X_{-1} TP}[t] \cdot k^{tc}_{elong} \] \[ \hphantom{tc0(10.3): \;\;\; \frac{dc^{RNAP}_{elong}[-1][t]}{dt}\: =\: } - c^{RNAP}_{elong}[-1][t] \cdot l^{mRNA} \cdot c^{pprot} * k^{pprot}_{on} \]
\[ tc0(11.1): \;\;\; \frac{dc^{RNAP}_{elongter}[i][t]}{dt}\: =\: (c^{RNAP}_{elongter}[i-1][t] - c^{RNAP}_{elongter}[i][t]) \cdot c^{ATP}[t] \cdot k^{pprot}_{cat} \] \[ \hphantom{tc0(11.1): \;\;\; \frac{dc^{RNAP}_{elongter}[i][t]}{dt}\: =\: } + c^{RNAP}_{elong}[i] \cdot c^{pprot} \cdot k^{pprot}_{on}, \] \[ \hphantom{tc0(11.1): \;\;\; \frac{dc^{RNAP}_{elongter}[i][t]}{dt}\: =\: } (i = 2, ..., l^{mRNA}-1) \] \[ tc0(11.2): \;\;\; \frac{dc^{RNAP}_{elongter}[-1][t]}{dt}\: =\: c^{RNAP}_{elongter}[-2][t] \cdot c^{ATP}[t] \cdot k^{pprot}_{cat} - c^{RNAP}_{elongter}[-1][t] * k^{RNAP}_{diss} \] \[ \hphantom{tc0(11.2): \;\;\; \frac{dc^{RNAP}_{elongter}[-1][t]}{dt}\: =\: } + c^{RNAP}_{elong}[-1][t] \cdot c^{pprot}[t] \cdot k^{pprot}_{on} \]
\[ tc0(12): \;\;\; \frac{dc^{mRNA}[t]}{dt}\: =\: c^{RNAP}_{elongter}[-1][t] \cdot k^{RNAP}_{diss} - c^{RNAse}_{onmRNA}[t] \cdot k^{RNAse}_{cat} \]
\[ tc0(13): \;\;\; \frac{dc^{RNAP}_{elongmm}[i][t]}{dt}\: =\: c^{RNAP}_{elong}[i-1][t] \cdot prob^{tc}_{mm} \cdot (c^{NTPs}[t] - c^{X_1 TP}[t]) \cdot k^{tc}_{elong} \] \[ \hphantom{tc0(13): \;\;\; \frac{dc^{RNAP}_{elongmm}[i][t]}{dt}\: =\: } - c^{RNAP}_{elongmm}[i][t] \cdot c^{GreAB}[t] \cdot k^{GreAB}_{on} \]
\[ tc0(14): \;\;\; \frac{dc^{RNAP}_{elongGreAB}[i][t]}{dt}\: =\: c^{RNAP}_{elongmm}[i][t] \cdot c^{GreAB}[t] \cdot k^{GreAB}_{on} - c^{RNAP}_{elongGreAB}[i][t] \cdot k^{GreAB}_{cat} \]
\[ tc0(15): \;\;\; \frac{dc^{RNAse}[t]}{dt}\: =\: c^{RNAse}_{bound}[t] \cdot k^{RNAse}_{gain} - c^{RNAse}[t] \cdot k^{RNAse}_{loss} \] \[ \hphantom{tc0(15): \;\;\; \frac{dc^{RNAse}[t]}{dt}\: =\: } + (c^{RNAse}_{onmRNAcl}[t] + c^{RNAse}_{onmRNAab}[t] + c^{RNAse}_{onmRNA}[t]) \cdot k^{RNAse}_{cat} \] \[ \hphantom{tc0(15): \;\;\; \frac{dc^{RNAse}[t]}{dt}\: =\: } - (c^{mRNAcl}[t] + c^{mRNAab}[t] + c^{mRNA}[t]) \cdot c^{RNAse}[t] \cdot k^{RNAse}_{on} \]
\[ tc0(16): \;\;\; \left( \frac{dc^{RNAse}_{onmRNA}[t]}{dt} ,\: \frac{dc^{RNAse}_{onmRNAab}[t]}{dt} ,\: \frac{dc^{RNAse}_{onmRNAcl}[t]}{dt} \right) \] \[ \hphantom{tc0(16): \;\;\; } = c^{RNAse}[t] \cdot (c^{mRNA}[t],\: c^{mRNAab}[t],\: c^{mRNAcl}[t]) \cdot k^{RNAse}_{on} - \left( c^{RNAse}_{onmRNA}[t],\: c^{RNAse}_{onmRNAab}[t],\: c^{RNAse}_{onmRNAcl}[t] \right) \cdot k^{RNAse}_{cat} \]
\[ tc0(17): \;\;\; \frac{dc^{mRNAab}[t]}{dt}\: =\: c^{RNAP}_{ini}[-1][t] \cdot k^{tc}_{iniab} - c^{RNAse}_{onmRNAab}[t] \cdot k^{RNAse}_{cat} \]
\[ tc0(18): \;\;\; \frac{dc^{mRNAcl}[t]}{dt}\: =\: \sum \limits_{i=1}^n c^{RNAP}_{elongGreAB}[i][t] \cdot k^{GreAB}_{cat} + 2 \cdot c^{RNAse}_{onmRNA}[t] \cdot k^{RNAse}_{cat} - c^{RNAse}_{onmRNAcl}[t] \cdot k^{RNAse}_{cat} \]
\[ tc0(19.1): \;\;\; \frac{dc^{entity}_{bound}[t]}{dt}\: =\: c^{entity}[t] \cdot k^{entity}_{loss} - c^{entity}_{bound}[t] \cdot k^{entity}_{gain}, \] \[ \hphantom{tc0(19.1): \;\;\; \frac{dc^{entity}_{bound}[t]}{dt}\: =\: } (entity \notin \{RNAP, RNAPsigma\}) \]
\[ tc0(19.2): \;\;\; \left( \frac{dc^{RNAP}_{bound}[t]}{dt},\: \frac{dc^{RNAPsigma}_{bound}[t]}{dt} \right) \] \[ \hphantom{tc0(19.2): \;\;\; } = c^{RNAP}[t] \cdot k^{RNAP}_{loss} - c^{RNAP}_{bound}[t] \cdot k^{RNAP}_{gain} + \left( c^{RNAPsigma}_{bound}[t],\: - c^{RNAPsigma}_{bound}[t] \right) \cdot k^{sigma}_{off} \]
\[ tc0(20): \;\;\; \frac{dc^{pprot}[t]}{dt}\: =\: c^{pprot}_{bound}[t] \cdot k^{pprot}_{gain} - c^{pprot}[t] \cdot k^{pprot}_{loss} \] \[ \hphantom{tc0(20): \;\;\; \frac{dc^{pprot}[t]}{dt}\: =\: } + c^{RNAP}_{elongter}[-1][t] \cdot k^{RNAP}_{diss} - c^{RNAP}_{elong}[-1][t] \cdot l^{mRNA} \cdot c^{pprot}[t] \cdot k^{pprot}_{on} \]
\[ tc0(21): \;\;\; \frac{dc^{GreAB}[t]}{dt}\: =\: c^{GreAB}_{bound}[t] \cdot k^{GreAB}_{gain} - c^{GreAB}[t] \cdot k^{GreAB}_{loss} \] \[ \hphantom{tc0(21): \;\;\; \frac{dc^{GreAB}[t]}{dt}\: =\: } + \sum \limits_{i=1}^n c^{RNAP}_{elongGreAB}[i][t] \cdot k^{GreAB}_{cat} - \sum \limits_{i=1}^n c^{RNAP}_{elongmm}[i][t] \cdot c^{GreAB}[t] \cdot k^{GreAB}_{on} \]
\[ tc0(22): \;\;\; \frac{dc^{NTP}[t]}{dt}\: =\: - \sum \limits_{i=2, X_i=N}^n c^{RNAP}_{ini}[i-1][t] \cdot c^{X_i TP}[t] \cdot k^{tc}_{inix} \] \[ \hphantom{tc0(22): \;\;\; \frac{dc^{NTP}[t]}{dt}\: =\: } - c^{RNAP}_{prel}[t] \cdot (1 - prob^{tc}_{mm}) \cdot c^{X_1 TP}[t] \cdot k^{tc}_{elong} \] \[ \hphantom{tc0(22): \;\;\; \frac{dc^{NTP}[t]}{dt}\: =\: } - \sum \limits_{i=2, X_i=N}^{n-1} c^{RNAP}_{elong}[i-1][t] \cdot (1 - prob^{tc}_{mm}) \cdot c^{X_i TP}[t] \cdot k^{tc}_{elong} \] \[ \hphantom{tc0(22): \;\;\; \frac{dc^{NTP}[t]}{dt}\: =\: } \left[ - c^{RNAP}_{open}[t] \cdot c^{ATP}[t] \cdot c^{X_1 TP}[t] \cdot k^{tc}_{ini1}\right]_{for X_1 = N} \] \[ \hphantom{tc0(22): \;\;\; \frac{dc^{NTP}[t]}{dt}\: =\: } \left[ - c^{RNAP}_{open}[t] \cdot c^{ATP}[t] \cdot c^{NTP}[t] \cdot k^{tc}_{ini1} - \sum \limits_{i=1}^{n-1} c^{RNAP}_{elongter}[i][t] \cdot c^{ATP}[t] \cdot k^{pprot}_{cat}\right]_{for N = A} \]
\[ tc0(23): \;\;\; \frac{dc^{NTPs}[t]}{dt}\: =\: \frac{dc^{ATP}[t]}{dt} + \frac{dc^{TTP}[t]}{dt} + \frac{dc^{GTP}[t]}{dt} + \frac{dc^{CTP}[t]}{dt} \]

Translation

ODE System

Amino Acid Activation

\[ tl0(1): \;\;\; \frac{dc^{AaxtRNASyn}[t]}{dt}\: =\: c^{AaxtRNASyn}_{AaatRNA}[t] \cdot k^{AaxtRNASyn}_{cat2} \] \[ \hphantom{tl0(1): \;\;\; \frac{dc^{AaxtRNASyn}[t]}{dt}\: =\: } + c^{AaxtRNASyn}_{Aax}[t] \cdot k^{Aax}_{off} - c^{AaxtRNASyn}_{Aax}[t] \cdot c^{Aax}[t] \cdot k^{Aax}_{on} \]
\[ tl0(2): \;\;\; \frac{dc^{AaxtRNASyn}_{Aax}[t]}{dt}\: =\: c^{AaxtRNASyn}[t] \cdot c^{Aax}[t] \cdot k^{Aax}_{on} - c^{AaxtRNASyn}_{Aax}[t] \cdot k^{Aax}_{off} \] \[ \hphantom{tl0(2): \;\;\; \frac{dc^{AaxtRNASyn}_{Aax}[t]}{dt}\: =\: } - c^{AaxtRNASyn}_{Aax}[t] \cdot c^{ATP}[t] \cdot k^{AaxtRNASyn}_{cat1} \]
\[ tl0(3): \;\;\; \frac{dc^{AaxtRNASyn}_{Aaa}[t]}{dt}\: =\: c^{AaxtRNASyn}_{Aax}[t] \cdot c^{ATP}[t] \cdot k^{AaxtRNASyn}_{cat1} \] \[ \hphantom{tl0(3): \;\;\; \frac{dc^{AaxtRNASyn}_{Aaa}[t]}{dt}\: =\: } + c^{AaxtRNASyn}_{AaatRNA}[t] \cdot k^{tRNA}_{off} - c^{AaxtRNASyn}_{AaatRNA}[t] \cdot k^{AaxtRNASyn}_{cat2} \]
\[ tl0(4): \;\;\; \frac{dc^{AaxtRNASyn}_{AaatRNA}[t]}{dt}\: =\: + c^{AaxtRNASyn}_{Aaa}[t] \cdot c^{tRNA}[t] \cdot k^{tRNA}_{on} - c^{AaxtRNASyn}_{AaatRNA}[t] \cdot k^{tRNA}_{off} \] \[ \hphantom{tl0(4): \;\;\; \frac{dc^{AaxtRNASyn}_{AaatRNA}[t]}{dt}\: =\: } - c^{AaxtRNASyn}_{AaatRNA}[t] \cdot k^{AaxtRNASyn}_{cat2} \]
\[ tl0(5): \;\;\; \frac{dc^{AaxtRNA}[t]}{dt}\: =\: c^{AaxtRNASyn}_{AaatRNA}[t] \cdot k^{AaxtRNASyn}_{cat2} \] \[ \hphantom{tl0(5): \;\;\; \frac{dc^{AaxtRNA}[t]}{dt}\: =\: } + c^{AaxtRNA}_{EFTu}[t] \cdot k^{EFTu}_{off} - c^{AaxtRNA}[t] \cdot c^{EFTu}[t] \cdot k^{EFTu}_{on} \] \[ \hphantom{tl0(5): \;\;\; \frac{dc^{AaxtRNA}[t]}{dt}\: =\: } + c^{tl}_{el1mm}[t] \cdot k^{AaxtRNA}_{reject} \]
\[ tl0(6): \;\;\; \frac{dc^{ftrans}[t]}{dt}\: =\: c^{ftrans}_{MettRNAfMet}[t] \cdot k^{MettRNAfMet}_{off} - c^{ftrans}[t] \cdot c^{MettRNAfMet}[t] \cdot k^{MettRNAfMet}_{on} \] \[ \hphantom{tl0(6): \;\;\; \frac{dc^{ftrans}[t]}{dt}\: =\: } + c^{ftrans}_{MettRNAfMet}[t] \cdot c^{f}[t] \cdot k^{ftrans}_{cat} - c^{ftrans}[t] \cdot c^{fMettRNAfMet}[t] \cdot c^{t}[t] \cdot k^{ftrans}_{deg} \]
\[ tl0(7): \;\;\; \frac{dc^{ftrans}_{MettRNAfMet}[t]}{dt}\: =\: c^{ftrans}[t] \cdot c^{MettRNAfMet}[t] \cdot k^{MettRNAfMet}_{on} - c^{ftrans}_{MettRNAfMet}[t] \cdot k^{MettRNAfMet}_{off} \] \[ \hphantom{tl0(7): \;\;\; \frac{dc^{ftrans}_{MettRNAfMet}[t]}{dt}\: =\: } + c^{ftrans}[t] \cdot c^{fMettRNAfMet}[t] \dot c^{t}[t] \cdot k^{ftrans}_{deg} - c^{ftrans}_{MettRNAfMet}[t] \cdot c^{f}[t] \cdot k^{ftrans}_{cat} \]
\[ tl0(8): \;\;\; \frac{dc^{fMettRNAfMet}[t]}{dt}\: =\: c^{ftrans}_{MettRNAfMet}[t] \cdot c^{f}[t] \cdot k^{ftrans}_{cat} - c^{ftrans}[t] \cdot c^{fMettRNAfMet}[t] \cdot c^{t}[t] \cdot k^{ftrans}_{deg} \] \[ \hphantom{tl0(8): \;\;\; \frac{dc^{fMettRNAfMet}[t]}{dt}\: =\: } + c^{tl}_{ini2}[t] \cdot k^{fMettRNAfMet}_{off} - c^{tl}_{ini1}[t] \cdot c^{fMettRNAfMet}[t] \cdot k^{fMettRNAfMet}_{on} \]

Initialization

\[ tl0(9): \;\;\; \frac{dc^{70s}[t]}{dt}\: =\: c^{30s}[t] \cdot c^{50s}[t] \cdot k^{50s}_{bind} - c^{70s}[t] \cdot c^{IF3}[t] \cdot k^{IF3}_{on} \]
\[ tl0(10): \;\;\; \frac{dc^{70sIF3}[t]}{dt}\: =\: c^{70s}[t] \cdot c^{IF3}[t] \cdot k^{IF3}_{on} - c^{70sIF3}[t] \cdot k^{IF3}_{off} \] \[ \hphantom{tl0(10): \;\;\; \frac{dc^{70sIF3}[t]}{dt}\: =\: } - c^{70sIF3}[t] \cdot k^{50s}_{diss} \]
\[ tl0(11): \;\;\; \frac{dc^{30sIF3}[t]}{dt}\: =\: c^{70sIF3}[t] \cdot k^{50s}_{diss} - c^{30sIF3}[t] \cdot k^{IF3}_{off} \[ \hphantom{tl0(11): \;\;\; \frac{dc^{30sIF3}[t]}{dt}\: =\: } + c^{30sIF3IF1}[t] \cdot k^{IF1}_{off} - c^{30sIF3}[t] \cdot c^{IF1}[t] \cdot k^{IF1}_{on} \]
\[ tl0(12): \;\;\; \frac{dc^{30sIF3IF1}[t]}{dt}\: =\: c^{30sIF3}[t] \cdot c^{IF1}[t] \cdot k^{IF1}_{on} - c^{30sIF3IF1}[t] \cdot k^{IF1}_{off} \] \[ \hphantom{tl0(12): \;\;\; \frac{dc^{30sIF3IF1}[t]}{dt}\: =\: } + c^{tl}_{ini0}[t] \cdot k^{mRNA}_{off} - c^{30sIF3IF1}[t] \cdot c^{mRNA}[t] \cdot k^{mRNA}_{on} \]
\[ tl0(13): \;\;\; \frac{dc^{tl}_{ini0}[t]}{dt}\: =\: c^{30sIF3IF1}[t] \cdot c^{mRNA}[t] \cdot k^{mRNA}_{on} - c^{tl}_{ini0}[t] \cdot k^{mRNA}_{off} \] \[ \hphantom{tl0(13): \;\;\; \frac{dc^{tl}_{ini0}[t]}{dt}\: =\: } + c^{tl}_{ini1}[t] \cdot k^{IF2}_{off} - c^{tl}_{ini0}[t] \cdot c^{IF2}[t] \cdot k^{IF2}_{on} \]
\[ tl0(14): \;\;\; dc^tl_ini1[t]/dt = c^tl_ini0[t] * c^IF2[t] * k^IF2_on - c^tl_ini1[t] * k^IF2_off + c^tl_ini2[t] * k^fMettRNAfMet_off - c^tl_ini1[t] * c^fMettRNAfMet[t] * k^fMettRNAfMet_on tl0(15): dc^tl_ini2[t]/dt = c^tl_ini1[t] * c^fMettRNAfMet[t] * k^fMettRNAfMet_on - c^tl_ini2[t] * k^fMettRNAfMet_off c^tl_inidissIF3[t] * c^IF3[t] * k^IF3_bind - c^tl_ini2[t] * k^IF3_diss tl0(16): dc^tl_inidissIF3[t]/dt = c^tl_ini2[t] * k^IF3_diss - c^tl_inidissIF3[t] * c^IF3[t] * k^IF3_bind + c^tl_inion50s[t] * k^50s_off - c^tl_inidissIF3[t] * c^50s[t] * k^50s_on tl0(17): dc^tl_inion50s[t]/dt = c^tl_inidissIF3[t] * c^50s[t] * k^50s_on - c^tl_inion50s[t] * k^50s_off + c^tl_inidissIF1[t] * c^IF1[t] * k^IF1_bind - c^tl_inion50s[t] * k^IF1_diss tl0(18): dc^tl_inidissIF1[t]/dt = c^tl_inion50s[t] * k^IF1_diss - c^tl_inidissIF1[t] * c^IF1[t] * k^IF1_bind - c^tl_inidissIF1[t] * k^IF2_cat tl0(19): dc^tl_inicat[t]/dt = c^tl_inidissIF1[t] * k^IF2_cat - c^tl_inicat[t] * k^IF2_diss tl0(20): dc^IF1[t]/dt = c^30sIF3IF1[t] * k^IF1_off - c^30sIF3[t] * c^IF1[t] * k^IF1_on + c^tl_inion50s[t] * k^IF1_diss - c^tl_inidissIF1[t] * c^IF1[t] * k^IF1_bind tl0(21): dc^IF3[t]/dt = (c^70sIF3[t] + c^30sIF3[t]) * k^IF3_off - (c^70s + c^30s) * k^IF3_on + c^tl_ini2[t] * k^IF3_diss - c^tl_inidissIF3[t] * c^IF3[t] * k^IF3_bind tl0(22): dc^IF2[t]/dt = c^tl_ini1[t] * k^IF2_off - c^tl_ini0[t] * c^IF2[t] * k^IF2_on + c^IF2_GDP[t] * c^GTP[t] * k^IF2_reg - c^IF2[t] * c^GDP[t] * k^IF2_deg tl0(23): dc^IF2_GDP[t]/dt = c^tl_inicat[t] * k^IF2_diss + c^IF2[t] * c^GDP[t] * k^IF2_deg - c^IF2_GDP[t] * c^GTP[t] * k^IF2_reg

Elongation.

tl0(24.1): dc^tl_el0[i][t]/dt = c^tl_el0AaxtRNA[i][t] * k^AaxtRNAEFTu_off - c^tl_el0[i] * c^AaxtRNA_EFTu[t] * k^AaxtRNAEFTu_on + c^tl_el1mm[i][t] * k^tRNA_reject + c^tl_el3[i-1] * k^tRNA_dissel, (i = 2, ..., l^mRNAcodons) tl0(24.2): dc^tl_el0[1][t]/dt = c^tl_inicat[t] * k^IF2_diss + c^tl_el0AaxtRNA[0][t] * k^AaxtRNAEFTu_off - c^tl_el0[0] * c^AaxtRNA_EFTu[t] * k^AaxtRNAEFTu_on + c^tl_el1mm[0][t] * k^tRNA_reject tl0(25): dc^tl_el0AaxtRNA[i][t]/dt = c^tl_el0[i] * c^AaxtRNA_EFTu[t] * k^AaxtRNAEFTu_on - c^tl_el0AaxtRNA[i][t] * k^AaxtRNAEFTu_off - c^tl_el0AaxtRNA[i][t] * k^EFTu_cat, (i = 1, ..., l^mRNAcodons) tl0(26): dc^tl_el0cat[i][t]/dt = c^tl_el0AaxtRNA[i][t] * k^EFTu_cat - c^tl_el0cat[i][t] * k^EFTu_diss, (i = 1, ..., l^mRNAcodons) tl0(27): dc^tl_el1raw[i][t]/dt = c^tl_el0cat[i][t] * k^EFTu_diss - c^tl_el1raw[i][t] * k^tl_proof, (i = 1, ..., l^mRNAcodons) tl0(28): dc^tl_el1proof[i][t]/dt = c^tl_el1raw[i][t] * k^tl_proof - c^tl_el1proof[i][t] * (prob^tl_mm + (1 - prob^tl_mm)), (i = 1, ..., l^mRNAcodons) tl0(29): dc^tl_el1correct[i][t]/dt = c^tl_el1proof[i][t] * (1 - prob^tl_mm) - c^tl_el1correct[i][t] * k^tl_elong, (i = 1, ..., l^mRNAcodons) tl0(30): dc^tl_el2[i][t]/dt = c^tl_el1correct[i][t] * k^tl_elong + c^tl_el2EFG[i][t] * k^EFG_off - c^tl_el2[i][t] * c^EFG[t] * k^EFG_on, (i = 1, ..., l^mRNAcodons) tl0(31.1): dc^tl_el2EFG[i][t]/dt = c^tl_el2[i][t] * c^EFG[t] * k^EFG_on - c^tl_el2EFG[i][t] * k^EFG_off - c^tl_el2EFG[i][t] * k^EFG_cat, (i = 1, ..., l^mRNAcodons) tl0(31.2): dc^tl_el2EFGcat[i][t]/dt = c^tl_el2EFG[i][t] * k^EFG_cat - c^tl_el2EFGcat[i][t] * k^tl_trans, (i = 1, ..., l^mRNAcodons) tl0(31.3): dc^tl_el2EFGtrans[i][t]/dt = c^tl_el2EFGcat[i][t] * k^tl_trans - c^tl_el2EFGtrans[i][t] * k^EFG_diss (i = 1, ..., l^mRNAcodons) tl0(32): dc^tl_el3[i][t]/dt = c^tl_el2EFGtrans[i][t] * k^EFG_diss - c^tl_el3[i][t] * k^tRNA_dissel (i = 1, ..., l^mRNAcodons) tl0(33): dc^AaxtRNA_EFTu[t]/dt = c^AaxtRNA[t] * c^EFTu[t] * k^EFTu_on - c^AaxtRNA_EFTu[t] * k^EFTu_off + \sum \limits_{i=1}^n c^tl_el0AaxtRNA[i][t] * k^AaxtRNAEFTu_off - \sum \limits_{i=1}^n c^tl_el0[i][t] * c^AaxtRNA_EFTu[t] * k^AaxtRNAEFTu_on tl0(34): dc^tl_el1mm[i][t]/dt = c^tl_el1raw[i][t] * prob^tl_mm - c^tl_el1mm[i][t] * k^AaxtRNA_reject (i = 1, ..., l^mRNAcodons) tl0(35): dc^EFTu_GDP[t]/dt = \sum \limits_{i=1}^n c^tl_el0cat[i][t] * k^EFTu_diss + c^EFTu_GDPEFTS[t] * k^EFTS_off - c^EFTu_GDP[t] * c^EFTS[t] * k^EFTS_on tl0(36): dc^EFTu_GDPEFTS[t]/dt = c^EFTu_GDP[t] * c^EFTS[t] * k^EFTS_on - c^EFTu_GDPEFTS[t] * k^EFTS_off + c^EFTu_EFTS[t] * c^GDP[t] * k^GDP_bindTu - c^EFTu_GDPEFTS[t] * k^GDP_dissTu tl0(37): dc^EFTu_EFTS[t]/dt = c^EFTu_GDPEFTS[t] * k^GDP_dissTu - c^EFTu_EFTS[t] * c^GDP[t] * k^GDP_bindTu + c^EFTu_GTPEFTS[t] * k^GTP_offTu - c^EFTu_EFTS[t] * c^GTP[t] * k^GTP_onTu tl0(38): dc^EFTu_GTPEFTS[t]/dt = c^EFTu_EFTS[t] * c^GTP[t] * k^GTP_onTu - c^EFTu_GTPEFTS[t] * k^GTP_offTu + c^EFTu[t] * c^EFTS[t] * k^EFTS_bind - c^EFTu_GTPEFTS[t] * k^EFTS_diss tl0(39): dc^EFTu[t]/dt = c^AaxtRNA_EFTu[t] * k^EFTu_off - c^EFTu[t] * c^AaxtRNA[t] * k^EFTu_on + c^EFTu_GTPEFTS[t] * k^EFTS_diss - c^EFTu[t] * c^EFTS[t] * k^EFTS_bind tl0(40): dc^EFTS[t]/dt = c^EFTu_GDPEFTS[t] * k^EFTS_off - c^EFTu_GDP[t] * c^EFTS[t] * k^EFTS_on + c^EFTu_GTPEFTS[t] * k^EFTS_diss - c^EFTu[t] * c^EFTS[t] * k^EFTS_bind tl0(41): dc^EFG_GDP[t]/dt = \sum \limits_{i=1}^n c^tl_el2EFGtrans[i][t] * k^EFG_diss + c^EFG_raw[t] * c^GDP[t] * k^GDP_bindG - c^EFG_GDP[t] * k^GDP_dissG tl0(42): dc^EFG_raw[t]/dt = c^EFG_GDP[t] * k^GDP_dissG - c^EFG_raw[t] * c^GDP[t] * k^GDP_bindG + c^EFG[t] * k^GTP_offG - c^EFG_raw[t] * c^GTP[t] * k^GTP_onG tl0(43): dc^EFG[t]/dt = c^EFG_raw[t] * c^GTP[t] * k^GTP_onG - c^EFG[t] * k^GTP_offG + \sum \limits_{i=1}^n c^tl_el2_EFG[i][t] * k^EFG_off - \sum \limits_{i=1}^n c^tl_el2[i][t] * c^EFG[t] * k^EFG_on

Termination.

tl0(44): dc^tl_term0[t]/dt = c^tl_el3[-1][t] * k^tRNA_diss + c^tl_term1[t] * k^RF1_off - c^tl_term0[t] * c^RF1[t] * k^RF1_on tl0(45): dc^tl_term1[t]/dt = c^tl_term0[t] * c^RF1[t] * k^RF1_on - c^tl_term1[t] * k^RF1_off + c^tl_term2[t] * k^RF3_off - c^tl_term1[t] * c^RF3[t] * k^RF3_on tl0(46): dc^tl_term2[t]/dt = c^tl_term1[t] * c^RF3[t] * k^RF3_on - c^tl_term2[t] * k^RF3_off - c^tl_term2[t] * k^protein_diss tl0(47): dc^tl_protrel[t]/dt = c^tl_term2[t] * k^protein_diss - c^tl_protrel[t] * k^30s_diss tl0(48): dc^RF1[t]/dt = c^tl_term1[t] * k^RF1_off - c^tl_term0[t] * c^RF1[t] * k^RF1_on + c^tl_protrel * k^30s_diss tl0(49): dc^RF3[t]/dt = c^tl_term2[t] * k^RF3_off - c^tl_term1[t] * c^RF3[t] * k^RF3_on + c^tl_protrel * k^30s_diss tl0(50): dc^protein[t]/dt = c^tl_term2[t] * k^protein_diss

General.

tl0(51): dc^TLATP[t]/dt = - c^AaxtRNASyn_Aaa[t] * c^ATP[t] * k^AaxtRNASyn_cat1 tl0(52): dc^TLGTP[t]/dt = c^IF2[t] * c^GDP[t] * k^IF2_deg - c^IF2_GDP[t] * c^GTP[t] * k^IF2_reg + c^EFTu_GTPEFTS[t] * k^GTP_offTu - c^EFTu_EFTS[t] * c^GTP[t] * k^GTP_onTu + c^EFG[t] * k^GTP_offG - c^EFG_raw[t] * c^GTP[t] * k^GTP_onG tl0(53): dc^TLGDP[t]/dt = c^IF2_GDP[t] * c^GTP[t] * k^IF2_reg - c^IF2[t] * c^GDP[t] * k^IF2_deg + c^EFTu_GDPEFTS[t] * k^GDP_dissTu - c^EFTu_EFTS[t] * c^GDP[t] * k^GDP_bindTu + c^EFG_GDP[t] * k^GDP_dissG - c^EFG_raw[t] * c^GDP[t] * k^GDP_bindG tl0(54): dc^Aax[t]/dt = c^AaxtRNASyn_Aax[t] * k^Aax_off - c^AaxtRNASyn[t] * c^Aax[t] * k^Aax_on tl0(55): dc^tRNA[t]/dt = c^AaxtRNASyn_AaatRNA[t] * k^tRNA_off - c^AaxtRNASyn_Aaa[t] * c^tRNA[t] * k^tRNA_on + \sum \limits_{i=1}^n c^tl_el3[i][t] * k^tRNA_dissel tl0(56): dc^TLmRNA[t]/dt = c^tl_ini0[t] * k^mRNA_off - c^30sIF3IF1[t] * c^mRNA[t] * k^mRNA_on + c^tl_protrel * k^30s_diss tl0(57): dc^50s[t]/dt = c^70sIF3[t] * k^50s_diss - c^30s[t] * c^50s[t] * k^50s_bind + c^tl_inion50s[t] * k^50s_off - c^tl_inidissIF3[t] * c^50s[t] * k^50s_on + c^tl_protrel * k^30s_diss tl0(58): dc^30s[t]/dt = c^30sIF3[t] * k^IF3_off - c^30s[t] * c^IF3[t] * k^IF3_on - c^30s[t] * c^50s[t] * k^50s_bind + c^tl_protrel * k^30s_diss