Unraveling the functional interaction structure of a biomolecular network through alternate perturbation of initial conditions

Abstract

Various approaches attempting to infer the functional interaction structure of a hidden biomolecular network from experimental time-series measurements have been developed; however, due to both experimental limitations and methodological complexities, a large majority of these approaches have been unsuccessful. In particular, with respect to the elucidation of such networks, there are (i) a dimensionality problem: too many network nodes with too few available sampling points, (ii) a computational complexity problem: exponential complexity if a priori information is unavailable for regulatory nodes, and (iii) an experimental measurement problem: no guidelines for an appropriate experimental design for distinguishing direct and indirect influences among network nodes. Here, we sought to develop a new methodology capable of identifying the correct functional interaction structure with only a few sampling points through relatively simple computations. We also attempted to provide guidelines for an experimental design capable of supporting this methodology by taking proper measurements of the direct influences among the network nodes. In the present study, we considered an experiment where measurements were taken at two sampling time points with alternate perturbation (up-regulation or down-regulation) of initial conditions while keeping the same initial conditions for unperturbed network nodes, and propose a new method of identifying the functional interaction structure from such measurements. The proposed method is able to avoid the dimensionality problem caused by the practically limited number of sampling time points, and does not suffer from the computational complexity problem, as it only uses a simple algebra based on the Mean Value Theorem (see Supplementary mathematical descriptions) without any other complicated computation. In addition, we provide a detailed guideline for an experimental design that can take proper measurements of the direct influences among the network nodes through perturbation of initial conditions. The proposed method is particularly useful for cases investigating the local interaction structure around a specific network node of interest. An example, based on simulated data, is provided to illustrate the proposed method.