Team:TU Delft/Modeling/HC regulation/Sensitivity

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==Sensitivity analysis==
==Sensitivity analysis==
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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.
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In this study we analyze the effect of
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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.
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# The maximal protein production rates β<sup>max</sup>, the lumped variable for transcriptions speed, translation speed, promoter strength and rbs strength,
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# The binding affinities K.
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In the figures below are the results for this sensitivity analysis.
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Using a  sensitivity analysis. Therefore the parameter values were varied in the range of 50% to 200% of their original values.
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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.
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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</sub> are shown in Fig. 1 - 5. The influence of binding affinities is shown in Fig. 6-9.
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[[Image:Team_TUDelft_K_B.png|thumb|600 px|centre|'''Figure 9''' – Sensitivity analysis of parameter K<sub>B</sub>]]
[[Image:Team_TUDelft_K_B.png|thumb|600 px|centre|'''Figure 9''' – Sensitivity analysis of parameter K<sub>B</sub>]]
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== Conclusion ==
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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.
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The results of the parameter variation study are summarized in table 1.
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''Table 1; results for sensitivity analysis for the gene regulation model: '0': insensitive, '+' sensitive, '++' very sensitive.''
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{|
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|'''Parameter'''
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|'''Sensitive for steady state concentration'''
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|'''Sensitive for reaching steady state concentration'''
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|-
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|β<sup>max</sup><sub>S1</sub>
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|'''0'''
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|'''+'''
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|-
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|β<sup>max</sup><sub>S2</sub>
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|'''+'''
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|'''+'''
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|-
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|β<sup>max</sup><sub>B</sub>
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|'''++'''
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|'''0'''
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|-
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|β<sup>max</sup><sub>AlkS</sub>
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|'''+'''
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|'''+'''
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|-
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|β<sup>max</sup><sub>AlkB</sub>
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|'''++'''
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|'''0'''
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|-
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|K<sub>HC</sub>
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|'''+'''
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|'''+'''
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|-
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|K<sub>S1</sub>
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|'''0'''
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|'''+'''
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|-
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|K<sub>S2</sub>
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|'''+'''
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|'''+'''
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|-
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|K<sub>B</sub>
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|'''+'''
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|'''+'''
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|}
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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.
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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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=== Navigation ===
Go back to the model explanation [[Team:TU_Delft/Modeling/HC_regulation|here]]
Go back to the model explanation [[Team:TU_Delft/Modeling/HC_regulation|here]]
Go back to the main modeling page [[Team:TU_Delft/Modeling|here]]
Go back to the main modeling page [[Team:TU_Delft/Modeling|here]]

Latest revision as of 19:27, 27 October 2010

Sensitivity analysis

In this study we analyze the effect of

  1. The maximal protein production rates βmax, the lumped variable for transcriptions speed, translation speed, promoter strength and rbs strength,
  2. The binding affinities 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 βmaxS1, βmaxS2, βmaxB, βmaxAlkS, βmaxAlkB are shown in Fig. 1 - 5. The influence of binding affinities is shown in Fig. 6-9.


Figure 1 – Sensitivity analysis of parameter βmaxS1
Figure 2 – Sensitivity analysis of parameter βmaxS2
Figure 3 – Sensitivity analysis of parameter βmaxB
Figure 4 – Sensitivity analysis of parameter βmaxAlkS
Figure 5 – Sensitivity analysis of parameter βmaxAlkB
Figure 6 – Sensitivity analysis of parameter KHC
Figure 7 – Sensitivity analysis of parameter KS1
Figure 8 – Sensitivity analysis of parameter KS2
Figure 9 – Sensitivity analysis of parameter KB

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 βmaxB and βmaxAlkB 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
βmaxS1 0 +
βmaxS2 + +
βmaxB ++ 0
βmaxAlkS + +
βmaxAlkB ++ 0
KHC + +
KS1 0 +
KS2 + +
KB + +


βmaxS1 and βmaxS1 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 βmaxS1 and KS1 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.

Navigation

Go back to the model explanation here

Go back to the main modeling page here

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