Team-iGEM SJTU BioX 201

Safety-iGEM SJTU BioX 201

Overview of gene circuit

In the following sections, we will explain how we use the model of ODE functions to describe the evolution of transcription and translation of target DNA, which will show the relationship between target protein’s concentration and time. Figure 1 explains the way in which our gene circuit works. Obviously, the system would act differently under different conditions. Our goal is to explicitly describe the system under different conditions. Using ODE functions, the concentrations of the chemical ingredient in the system are considered as variables, which evolves under the law of ODE functions over time. Thus, we can easily use ODE ways to describe how the chemical ingredient concentration changes over time under different situations.

Notations of chemical ingredients and variables

Chemical ingredients and constants

NC9_G %NdCas9 DNA concentration

NC9_G_P_R %Speed at which NdCas9 DNA transfer to mRNA

NC9_R_P_pro %Speed at which NdCas9 mRNA translate to protein

NC9_R_Dis %Speed at which NdCas9 RNA dissipate

NC9_pro_Dis %Speed at which NdCas9 protein dissipate

SG_G %Sg DNA concentration

SG_G_P_R %Speed at which Sg DNA transfer to mRNA

SG_R_Dis %Speed at which SgRNA dissipate

SG_NC_C %the reaction speed factor at which SgRNA react with NdCas9 protein

Possibility %possibility that SgRNA-NdCas9 combine with lure

Sg_NC_Lure_C %the reaction speed factor at which SgRNA-NdCas9 react with lure

L_Con %lure concentration

C_DBD_G %Cluc-DBD DNA concentration

DBD_C %DBD-binding site DNA concentration

ClucDBD_DBDBind_C %the reaction speed factor at which ClucDBD react with DBD_binding site

ClucDBDDBDbindS_SgNdcL_C %the reaction speed factor at which ClucDBD/DBD binding site react with SgRNA_NdCas9_lure

C_DBD_G_P_R %Speed at which CDBD DNA transfer to mRNA

C_DBD_R_Dis %Speed at which CDBD RNA dissipate

SgRNA_NdCas9_lure_reduce %Speed at which SgRNA_NdCas9_lure reverse the reaction

C_DBD_R_P_R %Speed at which CDBD mRNA transfer to protein

C_DBD_PR_Dis %Speed at which CDBD protein dissipate

C_DBD_DBD_bindingsite_Dis %Speed at which CDBD/DBD-bindingsite dissipate

Lure_Dis %Speed at which Lure dissipate

AHL %AHL initial concentration

k1 %times that AHL induce RepL

k2 %pTrig(PAM) RSR speed factor

k3 %the factor that RSR-PAM dissipate

k4 %pTrig decreasing factor

kcat % The turnover number of the firefly luciferase enzyme

km %the concentration of luciferin at which half the active sites are filled

k18 %Speed at which SgRNA-NdCas9-lure decays

k19 %Speed at which CDBD/DBD-bindingsite decays

k20 %Speed at which luc decays

k21 %Speed at which SgRNA-NdCas9 decays

k22 %Speed at which luxl DNA transfer to mRNA

k23 %Speed at which luxl RNA dissipate

dcas9_G %Concentration of dCas9 DNA

k24 %Speed at which dCas9 mRNA translate into protein

k25 %Speed at which dCas9 protein dissipate

k26 %Speed at which luxl DNA transfer into RNA

Luxl_G %luxl DNA concentration

k27 %Speed at which luxl RNA dissipate

k28 %Speed at which luxl RNA translate into protein

k29 %Speed at which luxl protein dissipate

variables

x(1) %represent NdCas9RNA

x(2) %represent NdCas9 protein

x(3) %represent SgRNA

x(4) %represent SgRNA-NdCas9

x(5) %represent SgRNA-NdCas9-lure

x(6) %represent C-DBD RNA

x(7) %represent CDBD protein

x(8) %represent CDBD/DBD-bindingsite

x(9) %represent luc concentration

x(10) %represent dcas9 RNA

x(11) %represent dcas9 protein

x(12) %represent luxl RNA

x(13) %represent luxl protein

Examples of ODE equations

1.How RNA concentration changes

a)$$ \frac{\mathrm{d}}{\mathrm{d} \mathrm{t}} C_{R N A}=k * C_{D N A}-R * C_{R N A} $$

i. R represents the decay of RNA and the k represents the transcription speed from DNA into RNA

ii. Examples:

$$ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{k} 1 \star \mathrm{NdCas} 9_{-} \mathrm{DNA}-\mathrm{k} 3 * \mathrm{x}(1) ; \stackrel{\circ}{\circ} \text { represent } \quad \mathrm{NdCa} \mathrm{S} 9 \mathrm{RNA} $$

$$ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{k} 5 \times \mathrm{Sg}_{-} \mathrm{DNA}-\mathrm{k} 6 * \mathrm{x}(3) ; \% \text { represent } \mathrm{SgRNA} $$

$$ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{C}_{-} \mathrm{DBD}_{-} \mathrm{DNA} * \mathrm{k} 11-\mathrm{k} 12 * \mathrm{x}(6) ; \% \text { represent } \mathrm{C-DBD RNA} $$

2) How protein concentration changes

$$ \text { a) } \frac{\mathrm{d}}{\mathrm{dt}} C_{p r o}=k * C_{R N A}-R * C_{p r o} $$

i. R represents the decay of protein and the k represents the translation speed from RNA into protein

ii. Examples:

$$ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{k} 2^{\star} \mathrm{x}(1)-\mathrm{k} 4* \underline{\mathrm{x}}(2) ; \text{%} \text { represent } \text { NdCas } 9 \text { protein } $$

$$ \begin{array}{l}{\frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{k} 14* \mathrm{x}(6)-\mathrm{k} 15* \mathrm{x}\left(\frac{7}{\mathrm{p}}\right)+\mathrm{k} 16* \mathrm{x}(8) ; \text{%} \mathrm{represent} \text{ }\mathrm{CDBD}} \\ {\text { protein }}\end{array} $$

3) How the speed of chemical reaction changes

a) For first order chemical reaction:

V=k*S % S represents the concentration of reactant and k represents the velocity constant

i. One possible example:

V=E0*kcat % represents the velocity in which luciferin reacts without enzyme

b) For second order chemical reaction:

V=k*S1*S2 % S represents the concentration of reactant and k represents the velocity constant

i. Examples:

$$ \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{x}(3)* \mathrm{x}(2) * \mathrm{k} 7-(\mathrm{k} 14+\mathrm{k} 21)* \mathrm{x}(4)+\mathrm{k} 13* \mathrm{x}(5)-\mathrm{x}(4)*\mathrm{P}*\text{lure}*\mathrm{k}(8);\text{%represent SgRNA-NdCas9} $$

$$ \frac{\mathrm{d} y}{\mathrm{dt}}=\mathrm{x}(\underline{4})* \mathrm{P}* \text { Lure }* \mathrm{k} 8-(\mathrm{k} 13+\mathrm{k} 18)* \mathrm{x}(5)+\mathrm{k} 17* \mathrm{x}(9);\text{%represent SgRNA-NdCas9-lure} $$

4) How the speed of enzyme-chemical reaction changes

a)$$ \mathrm{V}=\mathrm{k}_{2} *[E]_{T} * \frac{[S]}{[S]+K_{m}} $$

i. % S represents the concentration of enzyme, E represents the concentration of reactant and k_2 represents the speed constant of reaction that intermediate product react into final products

ii. One possible example:

V_Lufrin=V_max*y(:,9)./(km+y(:,9))

Here are some of our Results

Team:SJTU-BioX-Shanghai/Project/Gene Circuit

Overview of gene circuit

Notations of chemical ingredients and variables

Examples of ODE equations

1.How RNA concentration changes

Here are some of our Results