Cutting the Wires: Modularization of Cellular Networks for Experimental Design

Abstract

Understanding naturally evolved cellular networks requires the consecutive identification and revision of the interactions between relevant molecular species. In this process, initially often simplified and incomplete networks are extended by integrating new reactions or whole subnetworks to increase consistency between model predictions and new measurement data. However, increased consistency with experimental data alone is not sufficient to show the existence of biomolecular interactions, because the interplay of different potential extensions might lead to overall similar dynamics. Here, we present a graph-based modularization approach to facilitate the design of experiments targeted at independently validating the existence of several potential network extensions. Our method is based on selecting the outputs to measure during an experiment, such that each potential network extension becomes virtually insulated from all others during data analysis. Each output defines a module that only depends on one hypothetical network extension, and all other outputs act as virtual inputs to achieve insulation. Given appropriate experimental time-series measurements of the outputs, our modules can be analyzed, simulated, and compared to the experimental data separately. Our approach exemplifies the close relationship between structural systems identification and modularization, an interplay that promises development of related approaches in the future.

Modular Parameter Identification of Biomolecular Networks

“…2A and 5) that describes the directed information flow in a biomolecular network. In [23], we showed that…”

“…, n M modules. Similar to our previous work [23], we require that each module contains exactly one output y m (t). Furthermore, each module's dynamics can depend on n M trajectories u(t) = (u 1 (t), .…”

“…, n R }. To find the minimal sets of speciesÎ X,m and reactionsÎ R,m for each module, we apply our previous results (Lemma 10 in [23]) based on a so called species-reaction graph (see Figs. 2A and 5) that describes the directed information flow in a biomolecular network.…”

“…1) that uses ideas from MRA and multiple-shooting to combine the advantages of both approaches. As previously [23], we define modules such that all species in the modules' interfaces are experimentally measured. In this way good initial estimates of the interface species' dynamics can be derived directly from the ex-perimental data-similar to multiple-shooting [24].…”

Multistability equivalence between gene regulatory networks of different dimensionality with application to a differentiation network

“…The aim of model decomposition, in contrast, is to partition a high-dimensional model into weakly connected modules, which can be analyzed by systems-theoretic methods [14]. Furthermore, the concept of modular subnetworks has been employed by other authors to discriminate between several possible networks (see, for example, [15], and references therein). Overall, this demonstrates that the relationship between realistic high-dimensional models and analyzable low-dimensional models is a highly present topic in systems biology.If this question of multistability equivalence could be answered, methods and results from systems analysis of low-dimensional systems and modeling via high-dimensional systems could be combined and thus greatly enhance the understanding of a particular GRN system at hand.…”