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

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

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.

Identification of biochemical networks by S-tree based genetic programming

MOTIVATION

Most previous approaches to model biochemical networks have focused either on the characterization of a network structure with a number of components or on the estimation of kinetic parameters of a network with a relatively small number of components. For system-level understanding, however, we should examine both the interactions among the components and the dynamic behaviors of the components. A key obstacle to this simultaneous identification of the structure and parameters is the lack of data compared with the relatively large number of parameters to be estimated. Hence, there are many plausible networks for the given data, but most of them are not likely to exist in the real system.

RESULTS

We propose a new representation named S-trees for both the structural and dynamical modeling of a biochemical network within a unified scheme. We further present S-tree based genetic programming to identify the structure of a biochemical network and to estimate the corresponding parameter values at the same time. While other evolutionary algorithms require additional techniques for sparse structure identification, our approach can automatically assemble the sparse primitives of a biochemical network in an efficient way. We evaluate our algorithm on the dynamic profiles of an artificial genetic network. In 20 trials for four settings, we obtain the true structure and their relative squared errors are <5% regardless of releasing constraints about structural sparseness. In addition, we confirm that the proposed algorithm is robust within +/-10% noise ratio. Furthermore, the proposed approach ensures a reasonable estimate of a real yeast fermentation pathway. The comparatively less important connections with non-zero parameters can be detected even though their orders are below 10(-2). To demonstrate the usefulness of the proposed algorithm for real experimental biological data, we provide an additional example on the transcriptional network of SOS response to DNA damage in Escherichia coli. We confirm that the proposed algorithm can successfully identify the true structure except only one relation.