Difference between revisions of "Team:Freiburg/Modeling"

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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): \(dc^RNAP_prom[t]/dt = sum \limits_{i=n-v^RNAP_move*dt}^n c^RNAP_on[i][t] * (1-k^RNAP_off) + c^RNAP_open[t] * k^tc_closed - c^RNAP_prom[t] * k^tc_open \) tc0(6): \(dc^RNAP_open[t]/dt = c^RNAP_prom[t] * k^tc_open - c^RNAP_open[t] * k^tc_closed + c^RNAP_ini[-1][t] * k^tc_iniab - c^RNAP_open[t] * c^ATP[t] * c^{X_1 TP}[t] * k^tc_ini1 \) tc0(7): \(dc^RNAP_ini1[t]/dt = c^RNAP_open[t] * c^ATP[t] * c^{X_1 TP}[t] * k^tc_ini1 - c^RNAP_ini1[t] * c^{X_2 TP}[t] * k^tc_inix \) tc0(8.1): \(dc^RNAP_ini[i][t]/dt = c^RNAP_ini[i-1][t] * c^{X_i TP}[t] * k^tc_inix - c^RNAP_ini[i][t] * c^{X_i+1 TP}[t] * k^tc_inix, (i = 2, ..., l^ini-1) \) tc0(8.2): \(dc^RNAP_ini[1][t]/dt = dc^RNAP_ini1[t]/dt \) tc0(8.3): \(dc^RNAP_ini[-1][t]/dt = c^RNAP_ini[-2][t] * c^{X_-1 TP}[t] * k^tc_inix - c^RNAP_ini[-1][t] * (k^tc_iniab + k^tc_prel) \) tc0(9): \(dc^RNAP_prel[t]/dt = c^RNAP_ini[-1][t] * k^tc_prel - c^RNAP_prel[t] * c^{X_1 TP}[t] * k^tc_elong \) tc0(10.1): \(dc^RNAP_elong[i][t]/dt = c^RNAP_elong[i-1][t] * (1-prob^tc_mm) * c^{X_i TP}[t] * k^tc_elong - c^RNAP_elong[i][t] * ((1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong + prob^tc_mm * (c^NTPs[t] - c^{X_1 TP}[t]) * k^tc_elong) + c^RNAP_elongGreAB[j+l^mRNA_cl][t] * k^GreAB_cat, (i = 2, ..., l^elong-1 and j = i and j = 2, ..., l^elong - l^mRNA_cl) \) tc0(10.2): \(dc^RNAP_elong[1][t]/dt = c^RNAP_prel[t] * (1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong - c^RNAP_elong[1][t] * ((1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong + prob^tc_mm * (c^NTPs[t] - c^{X_1 TP}[t]) * k^tc_elong) + c^RNAP_elongGreAB[l^mRNA_cl][t] * k^GreAB_cat \) tc0(10.3): \(dc^RNAP_elong[-1][t]/dt = c^RNAP_elong[-2][t] * (1-prob^tc_mm) * c^{X_-1 TP}[t] * k^tc_elong - c^RNAP_elong[-1][t] * l^mRNA * c^pprot * k^pprot_on \) tc0(11.1): \(d^cRNAP_elongter[i][t]/dt = (c^RNAP_elongter[i-1][t] - c^RNAP_elongter[i][t]) * c^ATP[t] * k^pprot_cat + c^RNAP_elong[i] * c^pprot * k^pprot_on, (i = 2, ..., l^mRNA-1) \) tc0(11.2): \(dc^RNAP_elongter[-1][t]/dt = c^RNAP_elongter[-2][t] * c^ATP[t] * k^pprot_cat - c^RNAP_elongter[-1][t] * k^RNAP_diss + c^RNAP_elong[-1][t] * c^pprot[t] * k^pprot_on \) tc0(12): \(dc^mRNA[t]/dt = c^RNAP_elongter[-1][t] * k^RNAP_diss - c^RNAse_onmRNA[t] * k^RNAse_cat \) tc0(13): \(dc^RNAP_elongmm[i][t]/dt = c^RNAP_elong[i-1][t] * prob^tc_mm * (c^NTPs[t] - c^{X_1 TP}[t] * k^tc_elong - c^RNAP_elongmm[i][t] * c^GreAB[t] * k^GreAB_on \) tc0(14): \(dc^RNAP_elongGreAB[i][t]/dt = c^RNAP_elongmm[i][t] * c^GreAB[t] * k^GreAB_on - c^RNAP_elongGreAB[i][t] * k^GreAB_cat \) tc0(15): \(dc^RNAse[t]/dt = c^RNAse_bound[t] * k^RNAse_gain - c^RNAse[t] * k^RNAse_loss + (c^RNAse_onmRNAcl[t] + c^RNAse_onmRNAab[t] + c^RNAse_onmRNA[t]) * k^RNAse_cat - (c^mRNAcl[t] + c^mRNAab[t] + c^mRNA[t]) * c^RNAse[t] * k^RNAse_on \) tc0(16): \((dc^RNAse_onmRNA[t]/dt , dc^RNAse_onmRNAab[t]/dt , dc^RNAse_onmRNAcl[t]/dt) = c^RNAse[t] * (c^mRNA[t], c^mRNAab[t], c^mRNAcl[t]) * k^RNAse_on - (c^RNAse_onmRNA[t], c^RNAse_onmRNAab[t], c^RNAse_onmRNAcl[t]) * k^RNAse_cat \) tc0(17): \(dc^mRNAab[t]/dt = c^RNAP_ini[-1][t] * k^tc_iniab - c^RNAse_onmRNAab[t] * k^RNAse_cat \) tc0(18): \(dc^mRNAcl[t]/dt = sum \limits_{i=1}^n c^RNAP_elongGreAB[i][t] * k^GreAB_cat + 2 * c^RNAse_onmRNA[t] * k^RNAse_cat - c^RNAse_onmRNAcl[t] * k^RNAse_cat \) tc0(19.1): \(dc^entity_bound[t]/dt = c^entity[t] * k^entity_loss - c^entity_bound[t] * k^entity_gain, (entity not in {RNAP, RNAPsigma}) \) tc0(19.2): \((dc^RNAP_bound[t]/dt, dc^RNAPsigma_bound[t]/dt) = c^RNAP[t] * k^RNAP_loss - c^RNAP_bound[t] * k^RNAP_gain + (c^RNAPsigma_bound[t], -c^RNAPsigma_bound[t]) * k^sigma_off \) tc0(20): \(dc^pprot[t]/dt = c^pprot_bound[t] * k^pprot_gain - c^pprot[t] * k^pprot_loss + c^RNAP_elongter[-1][t] * k^RNAP_diss - c^RNAP_elong[-1][t] * l^mRNA * c^pprot[t] * k^pprot_on \) tc0(21): \(dc^GreAB[t]/dt = c^GreAB_bound[t] * k^GreAB_gain - c^GreAB[t] * k^GreAB_loss + sum \limits_{i=1}^n c^RNAP_elongGreAB[i][t] * k^GreAB_cat - sum \limits_{i=1}^n c^RNAP_elongmm[i][t] * c^GreAB[t] * k^GreAB_on \) tc0(22): \(dc^NTP[t]/dt = - sum \limits_{i=2, X_i=N}^n c^RNAP_ini[i-1][t] * c^{X_i TP}[t] * k^tc_inix - c^RNAP_prel[t] * (1-prob^tc_mm) * c^{X_1 TP}[t] * k^tc_elong - sum \limits_{i=2, X_i=N}^n-1 c^RNAP_elong[i-1][t] * (1-prob^tc_mm) * c^{X_i TP}[t] * k^tc_elong [- c^RNAP_open[t] * c^ATP[t] * c^X_1 TP[t] * k^tc_ini1]_{for X_1 = N} [-c^RNAP_open[t] * c^ATP[t] * c^NTP[t] * k^tc_ini1 - sum \limits_{i=1}^n-1 c^RNAP_elongter[i][t] * c^ATP[t] * k^pprot_cat]_{for N = A} \) tc0(23): \(dc^NTPs[t]/dt = dc^ATP[t]/dt + dc^TTP[t]/dt + dc^GTP[t]/dt + dc^CTP[t]/dt \)