Model Overview

List of Model Reactions

^*1 Reactions taking place only in the scenario which includes the activating complex $AR_{2}$

^*2 Reactions taking place only in the scenario which includes the antisense RNA interactions

Reactions

$O_{R} + R_{2} \rightleftharpoons O_{R}-R_{2}$ $O_{R}-R_{2} + R_{2} \rightleftharpoons O_{R}-2R_{2}$ $O_{A} + R_{2} \rightleftharpoons O_{A}-R_{2}$ $O_{A}-R_{2} + R_{2} \rightleftharpoons O_{A}-2R_{2}$ $A + R_{2} \rightleftharpoons AR_{2}$ *1 $2C + R_{2} \rightleftharpoons C_{2}-R_{2}$ $O_{A} + AR_{2} \rightleftharpoons O_{A}-AR_{2}$ *1 $O_{A}-R_{2} + AR_{2} \rightleftharpoons O_{A}-R_{2}-AR_{2}$ *1 $O_{A}-2R_{2} + AR_{2} \rightleftharpoons O_{A}-2R_{2}-AR_{2}$ *1 $O_{A}-AR_{2} + R_{2} \rightleftharpoons O_{A}-R_{2}-AR_{2}$ *1 $O_{A}-R_{2}-AR_{2} + R_{2} \rightleftharpoons O_{A}-2R_{2}-AR_{2}$ *1 $S \xrightarrow{A} C$ $O_{R} \rightarrow O_{R} + r$ $O_{A} \rightarrow O_{A} + a$ $O_{A}-AR_{2} \rightarrow O_{A}-AR_{2} + a$ *1 $a + r \rightleftharpoons r-a$ *2 $r \rightarrow r + R$ $a \rightarrow a + A$ $2R \rightleftharpoons R_{2}$ $C \underset{r \cdot D}{\stackrel{D}{\rightleftharpoons}} C_{e}$ $r\rightarrow \varnothing$ $R\rightarrow \varnothing$ $R_{2}\rightarrow \varnothing$ $a\rightarrow \varnothing$ $A\rightarrow \varnothing$ $C\rightarrow \varnothing$ $C_{2}-R_{2}\rightarrow \varnothing$ $AR_{2}\rightarrow \varnothing$ *1 $r-a\rightarrow \varnothing$ *2 $C_{e}\rightarrow \varnothing$

Parameters for model reactions

Reaction	Parameter	Values in literature	Units	Mode	Spread	Location parameter (μ)	Scale parameter (σ)
Binding of R2 to OR operator	$K_{d1},K_{d7}$	0.005−5.8	$nM$	0.299	6.8	0.15471	1.1661
	$k^{-}_{1}, k^{-}_{7}$	0.09−0.846	$min^{-1}$	0.489	1.98	−0.37642	0.58225
Binding of R2 to OA operator	$K_{d2},K_{d8}$	0.005−5.8	$nM$	0.299	6.8	0.15471	1.1661
	$k^{-}_{2},k^{-}_{8}$	0.09−0.846	$min^{-1}$	0.489	1.98	−0.37642	0.58225
Binding of R2 to A	$K_{d3}$	$10^{4}−10^{6}$	$nM$	$9.9 \cdot 10^{4}$	10.02	13.192	1.2977
	$k^{-}_{3}$	$38.3-4.46 \cdot 10^{6}$	$min^{-1}$	1879.7	23.13	9.9423	1.5503
Binding of R2 to C	$K_{d4}$	$0.0011-10400$	$nM$	1.58	730.63	5.9389	2.3412
	$k^{-}_{4}$	$3 \cdot 10^{-4}-126$	$min^{-1}$	0.816	244	4.2872	2.119
Binding of A-R2 to OA' operator	$K_{d5},K_{d9},K_{d10},K_{d11},K_{d12}$	0.005−5.8	$nM$	0.299	6.8	0.15471	1.1661
	$k^{-}_{5},k^{-}_{9},k^{-}_{10},k^{-}_{11},k^{-}_{12}$	0.09−0.846	$min^{-1}$	0.489	1.98	−0.37642	0.58225
Synthesis of C	$K_{C}$	0.00315−85.5	$min^{-1}$	0.094	60.49	0.87914	1.8017
Transcription of r	$\Omega_{R}$	0.16−8.24	$min^{-1}$	0.8346	3.55	0.63056	0.90076
	$k_{F}$	18.2−33	$min^{-1}$	20.7	1.34	3.1107	0.28276
	$k_{onR}$	0.0518-14.5	$min^{-1}$	0.867	4.09	0.78694	0.96428
Transcription of a	$\Omega_{A_{basal}}$	0.001−0.2	$min^{-1}$	0.0037	10.93	−3.8324	1.3259
	$\Omega_{A}$	0.11−5.65	$min^{-1}$	0.572	3.5	0.2514	0.89956
	$k_{onA}$	0.039-8.82	$min^{-1}$	0.587	3.875	0.35255	0.94054
Antisense interaction between r and a	$K_{ar}$	0.4−89	$nM$	7.8	7.27	3.4665	1.1882
	$k^{-}_{ar}$	0.006−6	$min^{-1}$	0.223	4.8	−0.43359	1.0326
Translation of R	$P_{R}$	0.165−5.86	$min^{-1}$	0.744	3.2	0.42952	0.85176
Translation of A	$P_{A}$	0.11−4	$min^{-1}$	0.5	3.2	0.053356	0.85327
Formation of homo-dimer R2	$K_{d6}$	2.58-42.9	$nM$	3.89	1.9	1.6716	0.55779
	$k^{-}_{6}$	0.144-51.2	$min^{-1}$	1.1997	21.7	2.5303	1.5324
Degradation of r	$d_{mR}$	0.03−0.365	$min^{-1}$	0.14	2.06	−1.5916	0.60824
Degradation of R	$d_{R}$	$5.02 \cdot 10^{-4}- 0.00578$	$min^{-1}$	$0.00144$	1.78	−6.2837	0.50981
Degradation of R2	$d_{R_{2}}$	$5.02 \cdot 10^{-4}- 0.00578$	$min^{-1}$	$0.00144$	1.78	−6.2837	0.50981
Degradation of a	$d_{mA}$	0.03−0.365	$min^{-1}$	0.14	2.06	−1.5916	0.60824
Degradation of A	$d_{A}$	$5.02 \cdot 10^{-4}- 0.00578$	$min^{-1}$	$0.00144$	1.78	−6.2837	0.50981
Degradation of C	$d_{C}$	$7.68 \cdot 10^{-5}- 2 \cdot 10^{-2}$	$min^{-1}$	$0.0032$	5.1	−4.6234	1.0539
Degradation of C2-R2	$d_{CR}$	$5.02 \cdot 10^{-4}- 0.00578$	$min^{-1}$	$0.00144$	1.78	−6.2837	0.50981
Degradation of A-R2	$d_{AR}$	$5.02 \cdot 10^{-4}- 0.00578$	$min^{-1}$	$0.00144$	1.78	−6.2837	0.50981
Degradation of r-a	$d_{mRA}$	0.35−69.3	$min^{-1}$	4.9	14.1	2.5669	0.98835
Diffusion of C and Ce	$D$	0.1−24	$min^{-1}$	2.8	4.27	1.9947	0.98233
Degradation of Ce	$d_{C}$	$7.68 \cdot 10^{-5}- 2 \cdot 10^{-2}$	$min^{-1}$	$0.0032$	5.1	−4.6234	1.0539
Cellular growth	Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): μ	0.0004−0.0107	$min^{-1}$	0.0022	7.5	−5.4517	0.80808

Parameters for cell colony growth

Parameter	Value	Units
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): τ	$63-1732$	$min$
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): λ	$0.8$	$-$
$V_{0}$	$1.2$	$μm^{3}$
$V_{tot}$	$2 \cdot 10^{−4}$	$μl$

Initial concentrations of species

Species	Initial concentration	Units	Compartment
OR	0.9592	$nM$	Cell
OA	0.9592	$nM$	Cell
OR-R2	0	$nM$	Cell
OA-R2	0	$nM$	Cell
OA'-AR2	0	$nM$	Cell
r	0	$nM$	Cell
a	0	$nM$	Cell
r-a	0	$nM$	Cell
R	0	$nM$	Cell
R2	0	$nM$	Cell
A	0	$nM$	Cell
C	0	$nM$	Cell
AR2	0	$nM$	Cell
C2R2	0	$nM$	Cell
Ce	0	$nM$	Environment

Differential equations

$\frac{d[OR]}{dt}= -\frac{k^{-}_{1}}{K_{d1}}\cdot [O_{R}]\cdot [R_{2}] + k^{-}_{1}\cdot [O_{R}-R_{2}]+\mu\cdot[OR-2R_2] +\mu\cdot[OR-R_2]$

$\frac{d[OA]}{dt}=\mu\cdot[OA-2R_2] +\mu\cdot[OA-R_2]+\mu\cdot[OA-AR_2]+\mu\cdot[OA-R_2-AR_2]+\mu\cdot[OA-2R_2-AR_2]-\frac{k^{-}_{2}}{K_{d2}}\cdot [O_{A}]\cdot [R_{2}] + k^{-}_{2}\cdot [O_{A}-R_{2}]$ $-\frac{k^{-}_{5}}{K_{d5}}\cdot [O_{A}]\cdot [AR_{2}] + k^{-}_{5}\cdot [O_{A}-AR_{2}]$

$\frac{d[OR-2R_2]}{dt}= \frac{k^{-}_{7}}{K_{d7}}\cdot [O_{R}-R_{2}]\cdot [R_{2}] - k^{-}_{7}\cdot [O_{R}-2R_{2}]-\mu\cdot[OR-2R_2]$

$\frac{d[OR-R_2]}{dt}=\frac{k^{-}_{1}}{K_{d1}}\cdot [O_{R}]\cdot [R_{2}] - k^{-}_{1}\cdot [O_{R}-R_{2}]-\frac{k^{-}_{7}}{K_{d7}}\cdot [O_{R}-R_{2}]\cdot [R_{2}] + k^{-}_{7}\cdot [O_{R}-2R_{2}]-\mu\cdot[OR-R_2]$

$\frac{d[OA-R_2]}{dt}=\frac{k^{-}_{2}}{K_{d2}}\cdot [O_{A}]\cdot [R_{2}] - k^{-}_{2}\cdot [O_{A}-R_{2}]-\frac{k^{-}_{8}}{K_{d8}}\cdot [O_{A}-R_{2}]\cdot [R_{2}] + k^{-}_{8}\cdot [O_{A}-2R_{2}]-\frac{k^{-}_{9}}{K_{d9}}\cdot [O_{A}-R_{2}]\cdot [AR_{2}] + k^{-}_{9}\cdot [O_{A}-R_{2}-AR_{2}]-\mu\cdot[OA-R_2]$

$\frac{d[OA-AR_2]}{dt}=\frac{k^{-}_{5}}{K_{d5}}\cdot [O_{A}]\cdot [AR_{2}] - k^{-}_{5}\cdot [O_{A}-AR_{2}]-\frac{k^{-}_{11}}{K_{d11}}\cdot [O_{A}-AR_{2}]\cdot [R_{2}] + k^{-}_{11}\cdot [O_{A}-R_{2}-AR_{2}]-\mu\cdot[OA-AR_2]$

$\frac{d[r]}{dt}=T_{R}\cdot [O_{R}]-\frac{ k^{-}_{ar}}{K_{ar}}\cdot [r]\cdot [a]+k^{-}_{ar} \cdot [r-a]-d_{mR}\cdot[r]-\mu\cdot[r]$

$\frac{d[a]}{dt}=T_{A_{basal}}\cdot [O_{A}]+T_{A}\cdot [O_{A}]+T_{A}\cdot [O_{A}-AR_{2}]-\frac{ k^{-}_{ar}}{K_{ar}}\cdot [r]\cdot [a]+k^{-}_{ar} \cdot [r-a]-d_{mA}\cdot[a]-\mu\cdot[a]$