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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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(A) The forward problem of defining a parameter set from which trajectories and their behavioral features are computed. (B) The inverse problem of finding a parameter regions for a predetermined behavioral specification region S. Columns from left to right correspond to parameter space, trajectory space and behavioral feature space, respectively. Connected convex sets can map to nonconvex non-connected regions.
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Figure 1: (A) The forward problem of defining a parameter set from which trajectories and their behavioral features are computed. (B) The inverse problem of finding a parameter regions for a predetermined behavioral specification region S. Columns from left to right correspond to parameter space, trajectory space and behavioral feature space, respectively. Connected convex sets can map to nonconvex non-connected regions.

Mentions: Mathematically, the design problem is an inverse problem and hence inherits the general feature of such problems, namely ill-posedness [15,16]. More specifically, for a certain behavioral specification one aims to find the corresponding parameter set that gives rise to such behavior. An simple example for a quantity in feature space could be the concentration of a molecular species at particular time-points. The problem is closely related to parameter optimization and even more so to robust optimization, where an objective function - generally encoding some behavioral constraint (e.g. making model trajectories close to the measurements) - is optimized to yield the optimal parameter set. Ill-posedness refers to the observation that two close-by points in specification or behavioral feature space may map to very distant points in the parameter space, indicating that this mapping is generally not contractive but rather expansive. The inverse and corresponding forward problem is illustated in Figure 1.


Mapping behavioral specifications to model parameters in synthetic biology.

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

(A) The forward problem of defining a parameter set from which trajectories and their behavioral features are computed. (B) The inverse problem of finding a parameter regions for a predetermined behavioral specification region S. Columns from left to right correspond to parameter space, trajectory space and behavioral feature space, respectively. Connected convex sets can map to nonconvex non-connected regions.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: (A) The forward problem of defining a parameter set from which trajectories and their behavioral features are computed. (B) The inverse problem of finding a parameter regions for a predetermined behavioral specification region S. Columns from left to right correspond to parameter space, trajectory space and behavioral feature space, respectively. Connected convex sets can map to nonconvex non-connected regions.
Mentions: Mathematically, the design problem is an inverse problem and hence inherits the general feature of such problems, namely ill-posedness [15,16]. More specifically, for a certain behavioral specification one aims to find the corresponding parameter set that gives rise to such behavior. An simple example for a quantity in feature space could be the concentration of a molecular species at particular time-points. The problem is closely related to parameter optimization and even more so to robust optimization, where an objective function - generally encoding some behavioral constraint (e.g. making model trajectories close to the measurements) - is optimized to yield the optimal parameter set. Ill-posedness refers to the observation that two close-by points in specification or behavioral feature space may map to very distant points in the parameter space, indicating that this mapping is generally not contractive but rather expansive. The inverse and corresponding forward problem is illustated in Figure 1.

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