From Specification to Parameters: A Linearization Approach
With the improvement of protocols for the assembly of transcriptional parts, synthetic biological devices can now be reliably assembled based on a design. The standardization of the parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified constraints are robustly satisfied. In this chapter 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.
KeywordsLinearization Parameters Temporal logic Linear temporal logic (LTL) Specification functionals Stoichiometric matrix State space Equilibrium point Bifurcation point Inverse bifurcation analysis Inverse bifurcation synthesis
H.K. acknowledges the support from the Swiss National Science Foundation (SNSF) grant number PP00P2_128503.
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