The rational design of network behavior is a central goal of synthetic biology. Here we combine in silico evolution with nonlinear dimensionality reduction to redesign the response of a fixed-topology signaling network and to characterize sets of kinetic parameters that underlie various input-output relations. We specifically consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 order of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. For each targets input—output relation, we conduct many independent runs of the evolutionary algorithm and use nonlinear dimensionality reduction to embed the resulting data in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the case of T cell receptor signaling, the network topology exhibits significant flexibility in generating alternative response curves, with distinct patterns of kinetic rates emerging for different targeted responses.
