Difference between revisions of "Model Overview"

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default [[Welcome to the In-Silico Model of γ-butyrolactone regulation in Streptomyces coelicolor|Go back to overview]]
 
default [[Welcome to the In-Silico Model of γ-butyrolactone regulation in Streptomyces coelicolor|Go back to overview]]
 
</imagemap>
 
</imagemap>
 +
 +
== Model scripts ==
 +
 +
The model scripts for the different scenarios can be found in pdf form here: [[File:GBL_Models.pdf]]
 +
 +
== List of Model Reactions ==
 +
 +
<sup>*1</sup> Reactions taking place only in the scenarios which includes the activating complex <math>AR_{2}</math>
 +
 +
<sup>*2</sup> Reactions taking place only in the scenarios which includes the antisense RNA interactions
 +
 +
<sup>*3</sup> Reactions taking place only in the scenarios which include the activation of ''scbA'' by <math>R_{2}</math>
 +
 +
{|class="wikitable"
 +
<table border='1' style="text-align:center">
 +
! Reactions
 +
|-
 +
|<math>O_{R} + R_{2} \rightleftharpoons O_{R} \bullet R_{2}</math>
 +
 +
<math>O_{R}\bullet R_{2} + R_{2} \rightleftharpoons O_{R}\bullet 2R_{2}</math>
 +
 +
<math>O_{A} + R_{2} \rightleftharpoons O_{A}\bullet R_{2}</math>
 +
 +
<math>O_{A}\bullet R_{2} + R_{2} \rightleftharpoons O_{A}\bullet 2R_{2}</math>
 +
 +
<math>A + R_{2} \rightleftharpoons AR_{2}</math> <sup>*1</sup>
 +
 +
<math>2C + R_{2} \rightleftharpoons C_{2}\bullet R_{2}</math>
 +
 +
<math>O_{A} + AR_{2} \rightleftharpoons O_{A}\bullet AR_{2}</math> <sup>*1</sup>
 +
 +
<math>O_{A}\bullet R_{2} + AR_{2} \rightleftharpoons O_{A}\bullet R_{2}\bullet AR_{2}</math> <sup>*1</sup>
 +
 +
<math>O_{A}\bullet 2R_{2} + AR_{2} \rightleftharpoons O_{A}\bullet 2R_{2}\bullet AR_{2}</math> <sup>*1</sup>
 +
 +
<math>O_{A}\bullet AR_{2} + R_{2} \rightleftharpoons O_{A}\bullet R_{2}\bullet AR_{2}</math> <sup>*1</sup>
 +
 +
<math>O_{A}\bullet R_{2}\bullet AR_{2} + R_{2} \rightleftharpoons O_{A}\bullet 2R_{2}\bullet AR_{2}</math> <sup>*1</sup>
 +
 +
<math>S \xrightarrow{A} C</math>
 +
 +
<math>O_{R} \rightarrow O_{R} + r</math>
 +
 +
<math>O_{A} \rightarrow O_{A} + a</math>
 +
 +
<math>O_{A}\bullet AR_{2} \rightarrow O_{A}\bullet AR_{2} + a</math> <sup>*1</sup>
 +
 +
<math>O_{A}\bullet R_{2} \rightarrow O_{A}\bullet R_{2} + a</math> <sup>*3</sup>
 +
 +
<math>O_{A}\bullet 2R_{2} \rightarrow O_{A}\bullet 2R_{2} + a</math> <sup>*3</sup>
 +
 +
<math>O_{A}\bullet R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet R_{2}\bullet AR_{2} + a</math> <sup>*3</sup>
 +
 +
<math>O_{A}\bullet 2R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet 2R_{2}\bullet AR_{2} + a</math> <sup>*3</sup>
 +
 +
<math>a + r \rightleftharpoons r\bullet a</math> <sup>*2</sup>
 +
 +
<math>r \rightarrow r + R</math>
 +
 +
<math>a \rightarrow a + A</math>
 +
 +
<math>2R \rightleftharpoons R_{2}</math>
 +
 +
<math>C \underset{r \cdot D}{\stackrel{D}{\rightleftharpoons}} C_{e}</math>
 +
 +
<math>r\rightarrow \varnothing</math>
 +
 +
<math>R\rightarrow \varnothing</math>
 +
 +
<math>R_{2}\rightarrow \varnothing</math>
 +
 +
<math>a\rightarrow \varnothing</math>
 +
 +
<math>A\rightarrow \varnothing</math>
 +
 +
<math>C\rightarrow \varnothing</math>
 +
 +
<math>C_{2}\bullet R_{2}\rightarrow \varnothing</math>
 +
 +
<math>AR_{2}\rightarrow \varnothing</math> <sup>*1</sup>
 +
 +
<math>r\bullet a\rightarrow \varnothing</math> <sup>*2</sup>
 +
 +
<math>C_{e}\rightarrow \varnothing</math>
 +
 +
<math>O_{R}\bullet R_{2} \rightarrow O_{R}\bullet R_{2} + O_{R}</math>
 +
 +
<math>O_{R}\bullet 2R_{2} \rightarrow O_{R}\bullet 2R_{2} + O_{R}</math>
 +
 +
<math>O_{A}\bullet R_{2} \rightarrow O_{A}\bullet R_{2} + O_{A}</math>
 +
 +
<math>O_{A}\bullet 2R_{2} \rightarrow O_{A}\bullet 2R_{2} + O_{A}</math>
 +
 +
<math>O_{A}\bullet AR_{2} \rightarrow O_{A}\bullet AR_{2} + O_{A}</math>
 +
 +
<math>O_{A}\bullet R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet R_{2}\bullet AR_{2} + O_{A}</math>
 +
 +
<math>O_{A}\bullet 2R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet 2R_{2}\bullet AR_{2} + O_{A}</math>
 +
 +
|}
  
 
== Parameters for model reactions ==
 
== Parameters for model reactions ==
Line 10: Line 110:
 
! Reaction
 
! Reaction
 
! Parameter
 
! Parameter
! Value
+
! Values in literature
 
! Units
 
! Units
! Distribution
+
! Mode
Mode
+
! Spread
! Confidence
 
Interval Factor
 
 
! Location  
 
! Location  
 
parameter (μ)
 
parameter (μ)
Line 22: Line 120:
 
|-
 
|-
 
|rowspan="2" |[[Binding of R2 to OR operator |Binding of R<sub>2</sub> to OR operator]]
 
|rowspan="2" |[[Binding of R2 to OR operator |Binding of R<sub>2</sub> to OR operator]]
|<math>K_{d1}</math>  
+
|<math>K_{d1},K_{d7}</math>  
 
|0.005−5.8
 
|0.005−5.8
 
|<math> nM </math>
 
|<math> nM </math>
|0.15
+
|0.299
|20
+
|6.8
|−0.72886
+
|0.15471
|1.08086
+
|1.1661
 
|-
 
|-
|<math>k^{-}_{1}</math>  
+
|<math>k^{-}_{1}, k^{-}_{7}</math>  
|0.09−1.2
+
|0.09−0.846
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.3
+
|0.489
|3.5
+
|1.98
|−0.89899
+
|−0.37642
|0.55225
+
|0.58225
 
|-
 
|-
 
|rowspan="2" |[[Binding of R2 to OA operator |Binding of R<sub>2</sub> to OA operator]]
 
|rowspan="2" |[[Binding of R2 to OA operator |Binding of R<sub>2</sub> to OA operator]]
|<math>K_{d2}</math>  
+
|<math>K_{d2},K_{d8}</math>  
 
|0.005−5.8
 
|0.005−5.8
 
|<math> nM </math>
 
|<math> nM </math>
|0.15
+
|0.299
|20
+
|6.8
|−0.72886
+
|0.15471
|1.08086
+
|1.1661
 
|-
 
|-
|<math>k^{-}_{2}</math>  
+
|<math>k^{-}_{2},k^{-}_{8}</math>  
|0.09−1.2
+
|0.09−0.846
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.3
+
|0.489
|3.5
+
|1.98
|−0.89899
+
|−0.37642
|0.55225
+
|0.58225
 
|-
 
|-
 
|rowspan="2" |[[Binding of R2 to A |Binding of R<sub>2</sub> to A]]
 
|rowspan="2" |[[Binding of R2 to A |Binding of R<sub>2</sub> to A]]
 
|<math>K_{d3}</math>  
 
|<math>K_{d3}</math>  
|<math>10^{3}−10^{6}</math>
+
|<math>10^{4}−10^{6}</math>
 
|<math> nM </math>
 
|<math> nM </math>
|<math>7 \cdot 10^{4}</math>
+
|<math>9.9 \cdot 10^{4}</math>
|13
+
|10.02
|12.088
+
|13.192
|0.96535
+
|1.2977
 
|-
 
|-
 
|<math>k^{-}_{3}</math>  
 
|<math>k^{-}_{3}</math>  
|<math>60-2.9 \cdot 10^{4}</math>
+
|<math>38.3-4.46 \cdot 10^{6}</math>
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|<math>1329.8</math>
+
|1879.7
|21.215
+
|23.13
|8.3942
+
|9.9423
|1.0961
+
|1.5503
 
|-
 
|-
 
|rowspan="2" |[[Binding of R2 to C |Binding of R<sub>2</sub> to C]]
 
|rowspan="2" |[[Binding of R2 to C |Binding of R<sub>2</sub> to C]]
 
|<math>K_{d4}</math>  
 
|<math>K_{d4}</math>  
|<math>10^{-2}-10^{-4}</math>
+
|<math>0.0011-10400</math>
 
|<math> nM </math>
 
|<math> nM </math>
|5
+
|1.58
|1000
+
|730.63
|4.5957
+
|5.9389
|1.65856
+
|2.3412
 
|-
 
|-
 
|<math>k^{-}_{4}</math>  
 
|<math>k^{-}_{4}</math>  
 
|<math>3 \cdot 10^{-4}-126</math>
 
|<math>3 \cdot 10^{-4}-126</math>
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|1.3
+
|0.816
|100
+
|244
|2.3977
+
|4.2872
|1.46129
+
|2.119
 
|-
 
|-
 
|rowspan="2" |[[Binding of A-R2 to OA' operator |Binding of A-R<sub>2</sub> to OA' operator]]
 
|rowspan="2" |[[Binding of A-R2 to OA' operator |Binding of A-R<sub>2</sub> to OA' operator]]
|<math>K_{d5}</math>  
+
|<math>K_{d5},K_{d9},K_{d10},K_{d11},K_{d12}</math>  
 
|0.005−5.8
 
|0.005−5.8
 
|<math> nM </math>
 
|<math> nM </math>
|0.15
+
|0.299
|30
+
|6.8
|−0.4965
+
|0.15471
|1.1835
+
|1.1661
 
|-
 
|-
|<math>k^{-}_{5}</math>  
+
|<math>k^{-}_{5},k^{-}_{9},k^{-}_{10},k^{-}_{11},k^{-}_{12}</math>  
|0.09−1.2
+
|0.09−0.846
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.3
+
|0.489
|4
+
|1.98
|−0.8437
+
|−0.37642
|0.6002
+
|0.58225
 
|-
 
|-
 
|[[Synthesis of C]]
 
|[[Synthesis of C]]
 
|<math>K_{C}</math>  
 
|<math>K_{C}</math>  
|0.003−0.01
+
|0.00315−85.5
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.005
+
|0.094
|10
+
|60.49
|−4.5042
+
|0.87914
|0.8911
+
|1.8017
 
|-
 
|-
|[[Transcription of r]]
+
|rowspan="3" |[[Transcription of r]]
|<math>T_{R}</math>  
+
|<math>\Omega_{R}</math>  
 
|0.16−8.24
 
|0.16−8.24
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.88
+
|0.8346
|10
+
|3.55
|0.66625
+
|0.63056
|0.8911
+
|0.90076
 +
|-
 +
|<math>k_{F}</math>
 +
|18.2−33
 +
|<math> min^{-1} </math>
 +
|20.7
 +
|1.34
 +
|3.1107
 +
|0.28276
 +
|-
 +
|<math>k_{onR}</math>
 +
|0.0518-14.5
 +
|<math> min^{-1} </math>
 +
|0.867
 +
|4.09
 +
|0.78694
 +
|0.96428
 
|-
 
|-
|[[Transcription of a]]
+
|rowspan="3" |[[Transcription of a]]
|<math>T_{A}</math>  
+
|<math>\Omega_{A_{basal}}</math>
 +
|0.001−0.2
 +
|<math> min^{-1} </math>
 +
|0.0037
 +
|10.93
 +
|−3.8324
 +
|1.3259
 +
|-
 +
|<math>\Omega_{A}</math>  
 
|0.11−5.65
 
|0.11−5.65
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.60
+
|0.572
|10
+
|3.5
|0.28326
+
|0.2514
|0.8911
+
|0.89956
 +
|-
 +
|<math>k_{onA}</math>
 +
|0.039-8.82
 +
|<math> min^{-1} </math>
 +
|0.587
 +
|3.875
 +
|0.35255
 +
|0.94054
 
|-
 
|-
 
|rowspan="2" |[[Antisense interaction between r and a]]
 
|rowspan="2" |[[Antisense interaction between r and a]]
 
|<math>K_{ar}</math>  
 
|<math>K_{ar}</math>  
|0.30−60
+
|0.4−89
|<math> min^{-1} </math>
+
|<math> nM </math>
|5
+
|7.8
|10
+
|7.27
|2.4035
+
|3.4665
|0.8911
+
|1.1882
 
|-
 
|-
 
|<math>k^{-}_{ar}</math>  
 
|<math>k^{-}_{ar}</math>  
 
|0.006−6
 
|0.006−6
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.6
+
|0.223
|10
+
|4.8
|0.2833
+
|−0.43359
|0.8911
+
|1.0326
 
|-
 
|-
 
|[[Translation of R]]
 
|[[Translation of R]]
Line 154: Line 284:
 
|0.165−5.86
 
|0.165−5.86
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.89
+
|0.744
|10
+
|3.2
|0.6776
+
|0.42952
|0.8911
+
|0.85176
 
|-
 
|-
 
|[[Translation of A]]
 
|[[Translation of A]]
Line 163: Line 293:
 
|0.11−4
 
|0.11−4
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|0.61
+
|0.5
|10
+
|3.2
|0.2998
+
|0.053356
|0.8911
+
|0.85327
 
|-
 
|-
 
|rowspan="2" |[[Formation of homo-dimer R2 |Formation of homo-dimer R<sub>2</sub>]]
 
|rowspan="2" |[[Formation of homo-dimer R2 |Formation of homo-dimer R<sub>2</sub>]]
 
|<math>K_{d6}</math>  
 
|<math>K_{d6}</math>  
|35.3−114
+
|2.58-42.9
 
|<math> nM </math>
 
|<math> nM </math>
|30
+
|3.89
|30
+
|1.9
|4.8018
+
|1.6716
|1.1835
+
|0.55779
 
|-
 
|-
 
|<math>k^{-}_{6}</math>  
 
|<math>k^{-}_{6}</math>  
|2.12−6.84
+
|0.144-51.2
 
|<math> min^{-1} </math>
 
|<math> min^{-1} </math>
|2
+
|1.1997
|30
+
|21.7
|2.094
+
|2.5303
|1.1835
+
|1.5324
 
|-
 
|-
 
|[[Degradation of r]]
 
|[[Degradation of r]]
 
|<math>d_{mR}</math>  
 
|<math>d_{mR}</math>  
|0.03−0.4
+
|0.03−0.365
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|0.15
+
|0.14
|3
+
|2.06
|−1.6523
+
|−1.5916
|0.4947
+
|0.60824
 
|-
 
|-
 
|[[Degradation of R]]
 
|[[Degradation of R]]
 
|<math>d_{R}</math>  
 
|<math>d_{R}</math>  
|<math>8.3 \cdot 10^{-4}- 0.0037</math>
+
|<math>5.02 \cdot 10^{-4}- 0.00578</math>
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|<math>1.62 \cdot 10^{-3}</math>  
+
|<math>0.00144</math>  
|100
+
|1.78
|−4.28997
+
|−6.2837
|1.4613
+
|0.50981
 
|-
 
|-
 
|[[Degradation of R2 |Degradation of R<sub>2</sub>]]
 
|[[Degradation of R2 |Degradation of R<sub>2</sub>]]
 
|<math>d_{R_{2}}</math>  
 
|<math>d_{R_{2}}</math>  
|<math>8.3 \cdot 10^{-4}- 0.0037</math>
+
|<math>5.02 \cdot 10^{-4}- 0.00578</math>
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|<math>1.62 \cdot 10^{-3}</math>
+
|<math>0.00144</math>  
|100
+
|1.78
|−4.28997
+
|−6.2837
|1.4613
+
|0.50981
 
|-
 
|-
 
|[[Degradation of a]]
 
|[[Degradation of a]]
 
|<math>d_{mA}</math>  
 
|<math>d_{mA}</math>  
|0.03−0.4
+
|0.03−0.365
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|0.15
+
|0.14
|3
+
|2.06
|−1.6523
+
|−1.5916
|0.4947
+
|0.60824
 
|-
 
|-
 
|[[Degradation of A]]
 
|[[Degradation of A]]
 
|<math>d_{A}</math>  
 
|<math>d_{A}</math>  
|<math>8.3 \cdot 10^{-4}- 0.0037</math>
+
|<math>5.02 \cdot 10^{-4}- 0.00578</math>
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|<math>1.62 \cdot 10^{-3}</math>  
+
|<math>0.00144</math>  
|100
+
|1.78
|−4.28997
+
|−6.2837
|1.4613
+
|0.50981
 
|-
 
|-
 
|[[Degradation of C]]
 
|[[Degradation of C]]
 
|<math>d_{C}</math>  
 
|<math>d_{C}</math>  
|<math>2.86 \cdot 10^{-4}- 2 \cdot 10^{-2}</math>
+
|<math>7.68 \cdot 10^{-5}- 2 \cdot 10^{-2}</math>
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|<math>2 \cdot 10^{-4}</math>  
+
|<math>0.0032</math>  
|10
+
|5.1
|−7.7231
+
|−4.6234
|0.8911
+
|1.0539
 
|-
 
|-
 
|[[Degradation of C2-R2 |Degradation of C<sub>2</sub>-R<sub>2</sub>]]
 
|[[Degradation of C2-R2 |Degradation of C<sub>2</sub>-R<sub>2</sub>]]
 
|<math>d_{CR}</math>  
 
|<math>d_{CR}</math>  
|<math>8.3 \cdot 10^{-4}- 0.0037</math>
+
|<math>5.02 \cdot 10^{-4}- 0.00578</math>
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|<math>1.62 \cdot 10^{-3}</math>  
+
|<math>0.00144</math>  
|100
+
|1.78
|−4.28997
+
|−6.2837
|1.4613
+
|0.50981
 
|-
 
|-
 
|[[Degradation of A-R2 |Degradation of A-R<sub>2</sub>]]
 
|[[Degradation of A-R2 |Degradation of A-R<sub>2</sub>]]
 
|<math>d_{AR}</math>  
 
|<math>d_{AR}</math>  
|<math>8.3 \cdot 10^{-4}- 0.0037</math>
+
|<math>5.02 \cdot 10^{-4}- 0.00578</math>
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|<math>1.62 \cdot 10^{-3}</math>  
+
|<math>0.00144</math>  
|100
+
|1.78
|−4.28997
+
|−6.2837
|1.4613
+
|0.50981
 
|-
 
|-
 
|[[Degradation of r-a]]
 
|[[Degradation of r-a]]
 
|<math>d_{mRA}</math>  
 
|<math>d_{mRA}</math>  
|0.35−34.7
+
|0.35−69.3
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|5
+
|4.9
|6
+
|14.1
|2.1513
+
|2.5669
|0.7361
+
|0.98835
 
|-
 
|-
 
|[[Diffusion of C and Ce |Diffusion of C and C<sub>e</sub>]]
 
|[[Diffusion of C and Ce |Diffusion of C and C<sub>e</sub>]]
Line 270: Line 400:
 
|0.1−24
 
|0.1−24
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|8  
+
|2.8  
|2
+
|4.27
|2.188
+
|1.9947
|0.3295
+
|0.98233
 
|-
 
|-
 
|[[Degradation of Ce]]
 
|[[Degradation of Ce]]
|<math>d_{C}</math>  
+
|<math>d_{C}</math>
|<math>2.86 \cdot 10^{-4}- 2 \cdot 10^{-2}</math>
+
|<math>7.68 \cdot 10^{-5}- 2 \cdot 10^{-2}</math>
 
|<math>min^{-1}</math>
 
|<math>min^{-1}</math>
|<math>2 \cdot 10^{-4}</math> 
+
|<math>0.0032</math>  
|10
+
|5.1
|−7.7231
+
|−4.6234
|0.8911
+
|1.0539
|-
 
|[[Cellular growth]]
 
|<math>μ</math>  
 
|0.0004−0.011
 
|<math>min^{-1}</math>
 
|0.001
 
|10
 
|−6.1137
 
|0.8911
 
 
|}
 
|}
  
== Parameters for cell colony growth ==
+
== Parameters for cell growth ==
  
 
{|class="wikitable"
 
{|class="wikitable"
 
<table border='1' style="text-align:center">
 
<table border='1' style="text-align:center">
 
! Parameter
 
! Parameter
! Value
+
! Range of values
 
! Units
 
! Units
 
|-
 
|-
| <math>τ</math>
+
|<math>K</math>
|<math> 63-1732 </math>
+
|<math>7.14 \cdot 10^{12} - 9\cdot 10^{12}</math>
|<math> min </math>
+
|cells
 
|-
 
|-
| <math>λ</math>
+
|<math>N_0</math>
|<math> 0.8 </math>
+
|<math>5 \cdot 10^{10} - 2\cdot 10^{11}</math>
|<math> - </math>
+
|cells
 
|-
 
|-
| <math>V_{0}</math>
+
|<math>\mu_{max}</math>
|<math> 1.2 </math>
+
|<math>0.003368 - 0.007499</math>
|<math> μm^{3}</math>
+
|<math>min^{-1}</math>
 
|-
 
|-
|<math>V_{tot}</math>
+
|<math>v</math>
|<math> 2 \cdot 10^{−4} </math>
+
|<math>0.001482 - 0.5814</math>
|<math> μl</math>  
+
|<math>min^{-1}</math>
 +
|-
 +
|<math>m</math>
 +
|<math>0.47 - 2.46</math>
 +
|n.a.
 +
|-
 +
|<math>\lambda</math>
 +
|<math>330.52 - 883</math>
 +
|<math>min</math>
 
|}
 
|}
  
Line 329: Line 458:
 
|-
 
|-
 
|O<sub>R</sub>  
 
|O<sub>R</sub>  
|
+
|0.9592
 
|<math> nM </math>
 
|<math> nM </math>
 
|Cell
 
|Cell
 
|-
 
|-
 
| O<sub>A</sub>
 
| O<sub>A</sub>
|
+
|0.9592
 
|<math> nM </math>
 
|<math> nM </math>
 
|Cell
 
|Cell
|-
 
| O<sub>A</sub>'
 
|
 
|<math> nM </math>
 
| Cell
 
 
|-
 
|-
 
| O<sub>R</sub>-R<sub>2</sub>
 
| O<sub>R</sub>-R<sub>2</sub>
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| O<sub>A</sub>-R<sub>2</sub>
 
| O<sub>A</sub>-R<sub>2</sub>
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| O<sub>A</sub>'-AR<sub>2</sub>
 
| O<sub>A</sub>'-AR<sub>2</sub>
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| r
 
| r
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| a
 
| a
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| r-a
 
| r-a
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| R
 
| R
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| R<sub>2</sub>
 
| R<sub>2</sub>
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| A
 
| A
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| C
 
| C
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| AR<sub>2</sub>
 
| AR<sub>2</sub>
|
+
|0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| C<sub>2</sub>R<sub>2</sub>
 
| C<sub>2</sub>R<sub>2</sub>
|  
+
| 0
 
|<math> nM </math>
 
|<math> nM </math>
 
| Cell
 
| Cell
 
|-
 
|-
 
| C<sub>e</sub>
 
| C<sub>e</sub>
|  
+
| 0
 
|<math> nM </math>  
 
|<math> nM </math>  
 
| Environment  
 
| Environment  
 
|}
 
|}
 
  
 
== Differential equations ==
 
== Differential equations ==
  
To be completed.
+
[[Image:Diffeq.png|850px]]

Latest revision as of 17:10, 16 October 2019

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About this image

Model scripts

The model scripts for the different scenarios can be found in pdf form here: File:GBL Models.pdf

List of Model Reactions

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

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

*3 Reactions taking place only in the scenarios which include the activation of scbA by R_{2}

Reactions
O_{R} + R_{2} \rightleftharpoons O_{R} \bullet R_{2}

O_{R}\bullet R_{2} + R_{2} \rightleftharpoons O_{R}\bullet 2R_{2}

O_{A} + R_{2} \rightleftharpoons O_{A}\bullet R_{2}

O_{A}\bullet R_{2} + R_{2} \rightleftharpoons O_{A}\bullet 2R_{2}

A + R_{2} \rightleftharpoons AR_{2} *1

2C + R_{2} \rightleftharpoons C_{2}\bullet R_{2}

O_{A} + AR_{2} \rightleftharpoons O_{A}\bullet AR_{2} *1

O_{A}\bullet R_{2} + AR_{2} \rightleftharpoons O_{A}\bullet R_{2}\bullet AR_{2} *1

O_{A}\bullet 2R_{2} + AR_{2} \rightleftharpoons O_{A}\bullet 2R_{2}\bullet AR_{2} *1

O_{A}\bullet AR_{2} + R_{2} \rightleftharpoons O_{A}\bullet R_{2}\bullet AR_{2} *1

O_{A}\bullet R_{2}\bullet AR_{2} + R_{2} \rightleftharpoons O_{A}\bullet 2R_{2}\bullet AR_{2} *1

S \xrightarrow{A} C

O_{R} \rightarrow O_{R} + r

O_{A} \rightarrow O_{A} + a

O_{A}\bullet AR_{2} \rightarrow O_{A}\bullet AR_{2} + a *1

O_{A}\bullet R_{2} \rightarrow O_{A}\bullet R_{2} + a *3

O_{A}\bullet 2R_{2} \rightarrow O_{A}\bullet 2R_{2} + a *3

O_{A}\bullet R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet R_{2}\bullet AR_{2} + a *3

O_{A}\bullet 2R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet 2R_{2}\bullet AR_{2} + a *3

a + r \rightleftharpoons r\bullet 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}\bullet R_{2}\rightarrow \varnothing

AR_{2}\rightarrow \varnothing *1

r\bullet a\rightarrow \varnothing *2

C_{e}\rightarrow \varnothing

O_{R}\bullet R_{2} \rightarrow O_{R}\bullet R_{2} + O_{R}

O_{R}\bullet 2R_{2} \rightarrow O_{R}\bullet 2R_{2} + O_{R}

O_{A}\bullet R_{2} \rightarrow O_{A}\bullet R_{2} + O_{A}

O_{A}\bullet 2R_{2} \rightarrow O_{A}\bullet 2R_{2} + O_{A}

O_{A}\bullet AR_{2} \rightarrow O_{A}\bullet AR_{2} + O_{A}

O_{A}\bullet R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet R_{2}\bullet AR_{2} + O_{A}

O_{A}\bullet 2R_{2}\bullet AR_{2} \rightarrow O_{A}\bullet 2R_{2}\bullet AR_{2} + O_{A}

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

Parameters for cell growth

Parameter Range of values Units
K 7.14 \cdot 10^{12} - 9\cdot 10^{12} cells
N_0 5 \cdot 10^{10} - 2\cdot 10^{11} cells
\mu_{max} 0.003368 - 0.007499 min^{-1}
v 0.001482 - 0.5814 min^{-1}
m 0.47 - 2.46 n.a.
\lambda 330.52 - 883 min

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

Diffeq.png