Team:TU Delft/Modeling/HC regulation/Sensitivity

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Sensitivity analysis

In this study we analyze the effect of (1) The maximal protein production rate b (lumped variable for transcriptions speed, translation speed, promoter strength and rbs strength),

(2) The equilibrium constant ll K

Using a sensitivity analysis. Therefore the parameter values were varied in the range of 50% to 200% of their original values.

The variation is performed in small steps, a simulation is performed and the concentration of AlkB as well as the time for reaching 95% of the reference value are displayed.

The time and steady-state concentration for the variation study of β^max_S1, β^max_S2, β^max_B, β^max_AlkS, β^max_{AlkB are shown in Fig. 1 - 5. The influence of binding affinities is shown in Fig. 6-9.}

Figure 1 – Sensitivity analysis of parameter β^max_S1

Figure 2 – Sensitivity analysis of parameter β^max_S2

Figure 3 – Sensitivity analysis of parameter β^max_B

Figure 4 – Sensitivity analysis of parameter β^max_AlkS

Figure 5 – Sensitivity analysis of parameter β^max_AlkB

Figure 6 – Sensitivity analysis of parameter K_HC

Figure 7 – Sensitivity analysis of parameter K_S1

Figure 8 – Sensitivity analysis of parameter K_S2

Figure 9 – Sensitivity analysis of parameter K_B

Conclusion

Most parameters have a linear or slightly exponential effect on the steady state concentration. The time it takes to reach steady state is more complexly correlated to the parameters. The wave functions for β^max_B and β^max_AlkB can be explained (1) by the small variations (see scale) and (2) numerical integration errors resp. interpolation artifacts.

The results of the parameter variation study are summarized in table 1.

Table 1; results for sensitivity analysis for the gene regulation model: '0': insensitive, '+' sensitive, '++' very sensitive.

Parameter	Sensitive for steady state concentration	Sensitive for reaching steady state concentration
β^max_S1	0	+
β^max_S2	+	+
β^max_B	++	0
β^max_AlkS	+	+
β^max_AlkB	++	0
K_HC	+	+
K_S1	0	+
K_S2	+	+
K_B	+	+

β^max_S1 and β^max_S1 have the strongest effect on the steady state concentration of AlkB. These parameters have a direct influence on the production rate of of AlkB and the mRNA translation rate of AlkB in the ODE model. Interestingly they have no significant influence on how fast the system reaches steady state.

The second observation that can be made from the results is that β^max_S1 and K_S1 have no significant influence on the steady state concentration of AlkB. This can be explained by the fact that pAlkS1 is more repressed at high alkane concentrations and under these condition the contribution of AlkS to the production of AlkB is low.

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@@ Line 1: / Line 1: @@
 ==Sensitivity analysis==
-For all beta parameters (lumped variables for transcriptions speed, translations speed, promoter strength and rbs strength) and all K parameters (equilibrium constant for binding of AlkS with alkanes and coefficients for the activity of promoters) a sensitivity analysis has been performed. This was done by varying the parameters from 50% of their original values to 200% of their original values.
+In this study we analyze the effect of
+(1) The maximal protein production rate b (lumped variable for transcriptions speed, translation speed, promoter strength and rbs strength),
-For this range of parameter values it is checked how much the steady state concentration of AlkB is and how long it takes for 95% of the steady state concentration of AlkB to be reached from steady state values for no alkanes to steady state values for 1 µM of alkanes.
+(2) The equilibrium constant ll K
-In the figures below are the results for this sensitivity analysis.
+Using a  sensitivity analysis. Therefore the parameter values were varied in the range of 50% to 200% of their original values.
+The variation is performed in small steps, a simulation is performed and the concentration of AlkB as well as the time for reaching 95% of the reference value are displayed.
+The time and steady-state concentration for the variation study of β<sup>max</sup><sub>S1</sub>, β<sup>max</sup><sub>S2</sub>, β<sup>max</sup><sub>B</sub>, β<sup>max</sup><sub>AlkS</sub>, β<sup>max</sup><sub>AlkB are shown in Fig. 1 - 5. The influence of binding affinities is shown in Fig. 6-9.
@@ Line 22: / Line 27: @@
 == Conclusion ==
-Most parameters have a linear or slightly exponential effect on the steady state concentration. The time it takes to reach steady state is more complexly correlated to the parameters. The wave functions for β<sup>max</sup><sub>B</sub> and β<sup>max</sup><sub>AlkB</sub> can be explained by the numerical integration steps. The number of time steps of the integration is finite, through interpolation the value the concentration reaches 95% of the steady state concentration is approximated. This can result however in numerical artifacts as displayed by these two functions.
+Most parameters have a linear or slightly exponential effect on the steady state concentration. The time it takes to reach steady state is more complexly correlated to the parameters. The wave functions for β<sup>max</sup><sub>B</sub> and β<sup>max</sup><sub>AlkB</sub> can be explained (1) by the small variations (see scale) and (2)  numerical integration errors resp. interpolation artifacts.
-These results are summarized in table 1. A '0' means insensitive, a '+' means somewhat sensitive and a '++' is very sensitive.
+The results of the parameter variation study are summarized in table 1.
-''Table 1; results for sensitivity analysis for the gene regulation model''
+''Table 1; results for sensitivity analysis for the gene regulation model: '0': insensitive, '+' sensitive, '++' very sensitive.''
 {|
@@ Line 71: / Line 76: @@
-β<sup>max</sup><sub>S1</sub> and β<sup>max</sup><sub>S1</sub> have the strongest effect on the steady state concentration of AlkB. This is logical as they directly influence the concentrations of AlkB and the mRNA of AlkB in the ODE. Interestingly they have no significant influence on how fast the system reaches steady state.
+β<sup>max</sup><sub>S1</sub> and β<sup>max</sup><sub>S1</sub> have the strongest effect on the steady state concentration of AlkB. These parameters have a direct influence on the production rate of  of AlkB and the mRNA translation rate of AlkB in the ODE model. Interestingly they have no significant influence on how fast the system reaches steady state.
-The second observation that can be made from the results is that β<sup>max</sup><sub>S1</sub> and K<sub>S1</sub> have no significant influence on the steady state concentration of AlkB. This is logical as AlkB is expressed with higher alkane concentrations. In this situation pAlkS1 is more repressed and does not contribute much at the total AlkS and AlkB concentrations.
+The second observation that can be made from the results is that β<sup>max</sup><sub>S1</sub> and K<sub>S1</sub> have no significant influence on the steady state concentration of AlkB. This can be explained by the fact that pAlkS1 is more repressed at high alkane concentrations and under these condition the contribution of AlkS to the production of AlkB is low.
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