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Mapping behavioral specifications to model parameters in synthetic biology.

Koeppl H, Hafner M, Lu J - BMC Bioinformatics (2013)

Bottom Line: In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model.First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction.The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology.

View Article: PubMed Central - HTML - PubMed

ABSTRACT
With recent improvements of protocols for the assembly of transcriptional parts, synthetic biological devices can now more reliably be assembled according to a given design. The standardization of parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal design specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified design constraints are robustly satisfied. In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model. We solve this inverse problem by linearizing the forward operator that maps parameter sets to specifications, and then inverting it locally. This approach has two advantages over brute-force random sampling. First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction. The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology.

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Related in: MedlinePlus

Contours of  (blue) in feature space (first row) are mapped back to the parameter space via L† (second row) and mapped forward using F (red) for increasing size of δ (from left to right).
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Figure 4: Contours of (blue) in feature space (first row) are mapped back to the parameter space via L† (second row) and mapped forward using F (red) for increasing size of δ (from left to right).

Mentions: For this case study we assume that we have means to design the binding rate of the inhibitor to the dimer k7 and the binding rate of the dimer to the promoter k9. To assess the error incurred by the linearization we consider the reverse-forward mapping as described in (7). Hence for various size of δ we perform the inverse mapping with L† and the forward mapping with F. If the inverse map is exact we should obviously obtain a ball with the same δ. Any deviation ε thereof reflects the approximation of F−1 by L†. In Figure 4 the images of under L† and F ◦ L† are shown for various radii δ.


Mapping behavioral specifications to model parameters in synthetic biology.

Koeppl H, Hafner M, Lu J - BMC Bioinformatics (2013)

Contours of  (blue) in feature space (first row) are mapped back to the parameter space via L† (second row) and mapped forward using F (red) for increasing size of δ (from left to right).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750501&req=5

Figure 4: Contours of (blue) in feature space (first row) are mapped back to the parameter space via L† (second row) and mapped forward using F (red) for increasing size of δ (from left to right).
Mentions: For this case study we assume that we have means to design the binding rate of the inhibitor to the dimer k7 and the binding rate of the dimer to the promoter k9. To assess the error incurred by the linearization we consider the reverse-forward mapping as described in (7). Hence for various size of δ we perform the inverse mapping with L† and the forward mapping with F. If the inverse map is exact we should obviously obtain a ball with the same δ. Any deviation ε thereof reflects the approximation of F−1 by L†. In Figure 4 the images of under L† and F ◦ L† are shown for various radii δ.

Bottom Line: In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model.First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction.The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology.

View Article: PubMed Central - HTML - PubMed

ABSTRACT
With recent improvements of protocols for the assembly of transcriptional parts, synthetic biological devices can now more reliably be assembled according to a given design. The standardization of parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal design specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified design constraints are robustly satisfied. In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model. We solve this inverse problem by linearizing the forward operator that maps parameter sets to specifications, and then inverting it locally. This approach has two advantages over brute-force random sampling. First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction. The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology.

Show MeSH
Related in: MedlinePlus