Unravelling the functional interaction structure of a cellular network from temporal slope information of experimental data.

Due to the unavoidable nonbiological variations accompanying many experiments, it is imperative to consider a way of unravelling the functional interaction structure of a cellular network (e.g. signalling cascades or gene networks) by using the qualitative information of time-series experimental data instead of computation through the measured absolute values. In this spirit, we propose a very simple but effective method of identifying the functional interaction structure of a cellular network based on temporal ascending or descending slope information from given time-series measurements. From this method, we can gain insight into the acceptable measurement error ranges in order to estimate the correct functional interaction structure and we can also find guidance for a new experimental design to complement the insufficient information of a given experimental dataset. We developed experimental sign equations, making use of the temporal slope sign information from time-series experimental data, without a specific assumption on parameter perturbations for each network node. Based on these equations, we further describe the available specific information from each part of experimental data in detail and show the functional interaction structure obtained by integrating such information. In this procedure, we use only simple algebra on sign changes without complicated computations on the measured absolute values of the experimental data. The result is, however, verified through rigorous mathematical definitions and proofs. The present method provides us with information about the acceptable measurement error ranges for correct estimation of the functional interaction structure and it further leads to a new experimental design to complement the given experimental data by informing us about additional specific sampling points to be chosen for further required information.