From Pathways Databases to Network Models of Switching Behavior

Abstract

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 [1,2]. This paper addresses the use of these databases as sources of dynamical models for biological phenomena. We focus here on models that are based on molecular interactions and how these interactions are coupled to explain observed cellular behavior. The model-building process that we describe below takes the point of view of a non-biologist who has access to online pathways databases but has not been directly involved in relevant experimental studies. Of course, one could argue that a better approach is for the modeler to collaborate with a biologist who is already familiar with the system and has developed intuition about how it works; in other words, the biologist may already have a “model” in mind—usually called a “hypothesis”—and what remains to be done is to encode this model in the language of mathematics. Note that this “hypothesis-driven” modeling approach already assumes a reduced network in the beginning of the modeling process. In contrast, we would like to show in this paper how a reduced network model is extracted from a much larger network, given a specific biological question and a set of relevant experimental observations. Mathematical models range from qualitative and probabilistic models to quantitative and deterministic kinetic models [3–5]. The chosen set of molecular interactions and processes form what we call a “network model.” Although the networks can have various degrees of detail, they all have the common property of being composed of nodes and edges representing interactions between nodes. Definitions of networks and pathways, as well as an example of a network model are given in the next section. Ultimately, we are interested in mechanistic models with well-defined molecular interactions or reaction mechanisms and corresponding rate equations that are subsequently solved numerically to simulate the phenomenon. Although mechanistic details are becoming available in increasing numbers of online pathways databases and knowledgebases, quantitative values of most kinetic parameters are still lacking—and this problem is compounded by the fact that many details of these pathways can be cell-specific (with regard to cell type, organism, etc.) and can have variability even among the same cell type in an organism. We provide below an overview of pathway resources on the Internet. Note that we are not concerned here with computational methods of determining or inferring network topology, or connectivity from omics data—on this topic the reader is referred to an article of Qi and Ge [3] that appeared in this journal recently. 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 question about a cell cycle checkpoint called the “restriction point” (R point)—that is, what is the smallest subset of interactions in the given network that can account for the switching behavior associated with this checkpoint? A method of qualitative network analysis is proposed to zoom into a core subnetwork which accounts for the essential qualitative behavior being modeled. Once the core network model is established, a kinetic model is constructed and a suite of mathematical analysis and computer programs can be used for further investigation.