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Both authors contributed to writing the paper.

Baltazar D. Aguda is with the Mathematical Biosciences Institute, Ohio State University, Columbus, Ohio, United States of America. Andrew B. Goryachev is with the Centre for Integrative Systems Biology, School of Biological Sciences, University of Edinburgh, United Kingdom.

The authors have declared that no competing interests exist.

The excitement in today's biology is driven by the huge amounts of information generated by high-throughput data-acquisition technologies, and by the expectation that these datasets will soon provide detailed understanding of life's processes. Ultimately, these datasets have to be integrated into a framework that facilitates the study of the dynamics arising from networks of physico–chemical interactions orchestrating the physiology of a biological cell. The bioinformatics community is actively responding to this call for integration in terms of frameworks of pathways databases [

Mathematical models range from qualitative and probabilistic models to quantitative and deterministic kinetic models [

In this article, we illustrate how one extracts a reduced network model from a large preliminary network obtained from databases. The model extraction procedure is explained in the context of a specific biological

We limit our definition of a

An example of a network graph representation commonly encountered in the molecular biology literature is shown in

Growth factors (GFs) trigger certain signaling cascades that lead to the activation of cyclin D/CDK4 complexes. Active CDK4 phosphorylates (thereby deactivating) the retinoblastoma protein (pRb) which inhibits entry into S phase due mainly to inhibitory binding with E2F transcription factors; these factors induce many of the genes required for S phase (such as members of the pre-replication complex, cyclin E, cyclin A, Cdc25A, etc.). Synthesis of cyclins E and A leads to activation of CDK2 which further phosphorylates (thereby deactivates) pRb. Another transcription factor, namely Myc, also contributes to the G1-S transition, but this protein's regulation is not shown. Arrows mean “activate,” and hammerheads mean “inhibit.” The dashed arrows signify the totality of gene expression steps (transcription and translation). Interactions numbered 1 to 10 form a minimal model that can account for the R point behavior.

If further details are known about the interactions, one can transform the _{1}/(_{2}+^{n}_{1} and _{2} are constants, and

Also shown are the known detailed mechanistic steps corresponding to the qNET shown in the upper panel (shaded grey). “a” refers to active, and “i” to inactive. Note that the network in the lower figure uses the chemist's convention of representing reaction steps; also, dashed arrows mean that the protein where the arrow originates from induces or catalyzes the reaction step that the arrow points to.

In this and the next section, we illustrate how one can extract a network model of the _{1} phase [

The lower panel shows the position of the R point (R) which subdivides the G1 phase into G1-pm (post-mitosis) and G1-ps (pre-S-phase). Quiescent or non-dividing cells have to be exposed to continuous growth-factor stimulation up until the R point in order to commit to entry into S-phase. After R and a finite induction period, cyclin E/CDK2 activity increases (shown by the dashed curve labelled E) as reported by Ekholm et al. [

The first step in building a network model is to identify the nodes of the network. It would be easy to use literature reviews written by specialists on the topic, but, as we mentioned earlier, we start afresh by using information taken from online databases. Since R point regulation is embedded in the G1-S regulatory network, one may start by visiting the

A Few Major Pathway and Modeling Resources on the Internet

A comprehensive Internet portal on pathway resources is provided by

The following steps are sufficient to extract a network model of the R point. (i) Start with an

Step (i) requires knowledge of a set of biological markers and processes associated with the phenomenon to be modeled. For the R point, the _{j} → X_{i}} to mean ∂[_{i}_{j}_{j} “activates” X_{i} because _{i}_{j}_{j} –| X_{i}} means ∂[_{i}_{j}_{j} “inhibits” X_{i} because _{i}_{j}_{ij}_{i}_{j}_{i} in the characteristic polynomial above can be expressed as follows:
_{k}_{1}(_{ii}_{2}(_{pq}m_{qp}_{3}(_{vw}m_{ws}m_{sv}_{k}

Carrying out step (ii) above on the network shown in

Simulation of the network model of the R point required the formulation of a system of coupled kinetic equations that can then be solved to determine the dynamics of the biological system [

The main goal of this article is to illustrate the idea that network models can be extracted from pathways databases in a systematic way. Using a specific biological phenomenon, namely the R point in the cell cycle, the modeling task is to explain the origin of the switching behavior of a protein marker when a quiescent cell is exposed to sufficient growth-factor stimulation. A large network of molecular interactions and signaling pathways is integrated from various pathways databases. Despite the lack of quantitative kinetic parameters associated with almost all of the interactions, we demonstrated that the form of qualitative network analysis described here can identify key feedback cycles in the network with potential for instability (the ultimate cause of the switching behavior). The set of these cycles is the basis for the reduced qualitative network model. Computer simulations using the final kinetic model [

The support of Professor Avner Friedman and the US National Science Foundation during BDA's visit at the Mathematical Biosciences Institute is gratefully acknowledged. ABG is supported by an Research Councils United Kingdom Fellowship at the University of Edinburgh.

restriction point