Tutorial 2

8/30 9:15 - 11:45, Hewlett 102

Inverse Dynamical Problems for Synthetic Biology

James Lu, Christoph Flamm, Stefan Mueller and Rainer Machne

RICAM, Austrian Academy of Sciences. Theoretical Biochemistry Group, University of Vienna.

Given a mathematical model for a biological system, there now exists fast and robust tools for the simulation of the dynamic behavior by carrying out time-course simulations or bifurcation analysis. However, the design problems that arise in the field of Synthetic Biology are essentially problems of the inverse type: namely, from the specified dynamical characteristics, one would like to compute possible ways of wiring together well-characterized cellular components that would attain the desired design goals.

Such inverse problems share the common characteristics of being ill-posed, namely: there could be no solutions that meet the specified goals, alternatively the solution could be non-unique and unstable with respect to the specified dynamical characteristics. In order to counteract the ill-posedness, variational regularization strategies can be employed. While stabilizing ill-posed problems, a given regularization strategy also brings about a certain bias. In problems of Synthetic Biology, one typically wishes to identify a smallest set of molecular components and/or connections that achieve a certain design goal. This motivates the use of sparsity-promoting regularization, for which a mathematical theory is being developed.

We start the tutorial by giving a brief overview of symbolic and graph theoretical methods (e.g. the deficiency-zero theorem) which connect the topological structure of a reaction network to a particular qualitative dynamical behaviour, regardless of the values of the rate constants. By ruling out network topologies which are incompatible with the desired dynamical behaviour, these methods can be of great value during the design of synthetic biology circuits. Following that, we demonstrate numeric-based, inverse dynamical analysis algorithms with sparsity regularization that provides a methodology to computationally design synthetic networks and infer core mechanisms (or 'knobs') that could tune specific aspects of their dynamical behaviors. The symbolic and numeric methods together provide computational guidance to the design problems of Synthetic Biology.

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