Limits...
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.

Show MeSH

Related in: MedlinePlus

Covering a certain specification range S (black rectangle) by overlapping balls (A) which in turn yields overlapping ellipsoids in the parameter space (B). The precision of the mapping is illustrated by the reverse-forward map in (C). The centers of the balls are illustrated by crosses.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3750501&req=5

Figure 5: Covering a certain specification range S (black rectangle) by overlapping balls (A) which in turn yields overlapping ellipsoids in the parameter space (B). The precision of the mapping is illustrated by the reverse-forward map in (C). The centers of the balls are illustrated by crosses.

Mentions: Hence, for an intermediate size of δ a good trade-off between approximation accuracy and sampling coverage is achievable. A systematic sampling of a predetermined specification area S would proceed by successively sampling overlapping balls with radii adapted to maintain ε under a certain value as illustrated in Figure 5. In this example, the coverage of the region S is above 98% using 50 balls of different radii. The lower left corner of the specification space (Figure 5A) maps to a strongly nonlinear region of the parameter space (upper right corner in Figure 5B) and therefore forces the use of smaller balls to keep the error in acceptable range. On the contrary, the upper right region of the specification space is more linear and larger balls can be used with limited relative error (Figure 5C).


Mapping behavioral specifications to model parameters in synthetic biology.

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

Covering a certain specification range S (black rectangle) by overlapping balls (A) which in turn yields overlapping ellipsoids in the parameter space (B). The precision of the mapping is illustrated by the reverse-forward map in (C). The centers of the balls are illustrated by crosses.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Covering a certain specification range S (black rectangle) by overlapping balls (A) which in turn yields overlapping ellipsoids in the parameter space (B). The precision of the mapping is illustrated by the reverse-forward map in (C). The centers of the balls are illustrated by crosses.
Mentions: Hence, for an intermediate size of δ a good trade-off between approximation accuracy and sampling coverage is achievable. A systematic sampling of a predetermined specification area S would proceed by successively sampling overlapping balls with radii adapted to maintain ε under a certain value as illustrated in Figure 5. In this example, the coverage of the region S is above 98% using 50 balls of different radii. The lower left corner of the specification space (Figure 5A) maps to a strongly nonlinear region of the parameter space (upper right corner in Figure 5B) and therefore forces the use of smaller balls to keep the error in acceptable range. On the contrary, the upper right region of the specification space is more linear and larger balls can be used with limited relative error (Figure 5C).

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