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An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential equation to be mapped to the one that can be represented as a reaction network. The framework is used for construction of… (More)

Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with a focus on multistability, limit cycles and limit cycle bifurcations. The results are then used for construction of two reaction systems, which are at the deterministic level described by twodimensional… (More)

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement of strand-displacement DNA computing, a large class of abstract biochemical networks may be physically realized using DNA molecules. Methods for systematic design of the… (More)

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