A model invalidation-based approach for elucidating biological signalling pathways, applied to the chemotaxis pathway...

Developing methods for understanding the connectivity of signalling pathways is a major challenge in biological research. For this purpose, mathematical models are routinely developed based on experimental observations, which also allow the prediction of the system behaviour under different experimental conditions. Often, however, the same experimental data can be represented by several competing network models.

In this paper, we developed a novel mathematical model/experiment design cycle to help determine the probable network connectivity by iteratively invalidating models corresponding to competing signalling pathways. To do this, we systematically design experiments in silico that discriminate best between models of the competing signalling pathways. The method determines the inputs and parameter perturbations that will differentiate best between model outputs, corresponding to what can be measured/observed experimentally. We applied our method to the unknown connectivities in the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. We first developed several models of R. sphaeroides chemotaxis corresponding to different signalling networks, all of which are biologically plausible. Parameters in these models were fitted so that they all represented wild type data equally well. The models were then compared to current mutant data and some were invalidated. To discriminate between the remaining models we used ideas from control systems theory to determine efficiently in silico an input profile that would result in the biggest difference in model outputs. However, when we applied this input to the models, we found it to be insufficient for discrimination in silico. Thus, to achieve better discrimination, we determined the best change in initial conditions (total protein concentrations) as well as the best change in the input profile. The designed experiments were then performed on live cells and the resulting data used to invalidate all but one of the remaining candidate models.

We successfully applied our method to chemotaxis in R. sphaeroides and the results from the experiments designed using this methodology allowed us to invalidate all but one of the proposed network models. The methodology we present is general and can be applied to a range of other biological networks.