Convex Optimisation for Automatic Reconstruction and Design of Biochemical Reaction Networks

View all posters

Wei Pan, Tom Ellis, Guy-Bart Stan

Imperial College London, United Kingdom

We present a unified optimisation framework for (a) the reconstruction and (b) the automatic design of biochemical reaction networks (BRNs) and gene regulatory networks (GRNs). Reconstruction, i.e., automatic inference of the dynamic equations of a BRN/GRN directly from its observed data constitutes one the major problems in systems biology. On the other hand, automatic design of a BRN/GRN capable of generating a desired dynamic behaviour specified in terms of a priori given time-series data constitutes one of the core problems in synthetic biology. Our optimisation formulation allows considering both problems in a unified mathematical framework. When dealing with BRNs/GRNs specific aspects need careful consideration. First, nonlinear time-delayed Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model BRNs/GRNs. Second, the resulting optimisation problem is generally nonconvex, meaning that several suboptimal solutions co-exist and that finding the optimal solution is algorithmically very expensive (NP-hard). Third, prior knowledge typically needs to be incorporated under the form of equality or inequality constraints such as positivity of the species numbers/concentrations and of certain parameters. Finally, typically, the dynamical behaviour of only a few species of the BRN/GRN can be measured/predefined whereas the remaining species defining the BRN are “hidden”. To deal with all the aspects mentioned above, we show how the original optimisation problem can be relaxed into a family of convex optimisation problems. Unlike sampling-based algorithms, our proposed framework has several advantages. It allows for efficient computation of the solution of large-scale BRNs/GRNs reconstruction/design problems (in polynomial time), provides near optimal solutions to the original optimisation problem, and is much less sensitive to optimisation initial guesses. The framework is illustrated on the reconstruction of a simple synthetic GRN (the repressilator), and on the automatic design of GRNs exhibiting desired time-series behaviours (perfect adaptation).