To clarify the hierarchy of network organization, we have defined steps, paths, pathways and networks of pathways. A step is a combination of several components with a reaction between them; it is as an elementary functional unit of a network A path is a linear combination of several steps, e.g. a sequence of steps. It takes into account the direction of steps and avoids using each step more than one time. Each path begins with one step (entry) and ends with another one step (exit): the input-output relationship within a path is of 1:1 type. A pathway is a combination of several paths that either start at the same entry or end at the same exit, and it may form a multiple branched structure. Accordingly, in this case, the input-output relationship is of either 1:n type or n:1 type. Then, a network of pathways is defined as a collection of several pathways. We say one network of pathways has several entries and several exits. A network of pathways operates with m:n type of the input-output relationship.
To model an architecture, we combined two different approaches based on a relatively simple string description and more refined matrix description of the regulatory networks. A special formalism has been applied: it treats processes of different complexity as multiple conditional events and is based on propositional logic (e.g., an algebra the original purpose of which is to model reasoning). Pathways and their networks are described with logical expressions that are Boolean functions and can serve as causal models. As a result, signal transduction pathways are represented in an algebraic form suitable for storage and computer-assisted analysis. This form is a specifically structured set of prerequisites which should be fulfilled in order to make the corresponding processes possible. By evaluating these expressions, the architectural robustness of each pathway can be calculated and represented as a real number. The robustness is the measure of the logical redundancy of network compositions and reflects the ability of a system to continue functioning in face of substantial changes (mutational damage) of its components.
An important advantage of our modeling approach is its simplicity. Our models focus on the connectivity within a network, they are basically static and do not need to simulate step by step the corresponding processes. The approach enables a quantitative estimation of the architectural role of individual elements in complex pathways and their networks. This can help to find elements and/or groups of elements which play a critical role in sustaining the integrity of the networks. Such elements might be potential targets for drugs. Determining the effect of gene deletion is a fundamental approach used by the molecular geneticists to understand gene function: gene disruption allows the consequence of loss of gene function to be experimentally determined. Our approach enables an alternative way based on in silico modeling the effects of alterations, e.g., pathologically relevant mutations, in distinct components of a regulatory network.
The approach has been applied to insulin receptor signaling pathways as they are provided by the TRANSPATH database on signal transduction. Insulin signaling at the target cell results in a large array of biological outcomes that are essential for normal growth and development and for normal homeostasis of glucose, fat, and protein metabolism. Understanding these signaling pathways is a prerequisite for understanding of the pathophysiology of insulin resistance associated with obesity and type 2 diabetes. Insulin receptor signaling involves two major pathways - the Ras/Raf/MAP kinase pathway, that is the mitogen-activated one, and PI3K pathway, via which the metabolic response to insulin is primarily mediated. Both pathways are rather large and intensively branched. Moreover, although these pathways are often described in a linear fashion, they could, under certain circumstances, activate the other. Therefore, the precise analysis of the pathways is a much more complicated task than it is often considered.
At the moment we are able to model only fragments of the insulin signaling network - by starting at any element (molecule or reaction) and with the radius of search up to 4 steps both downstream and upstream of an element. While increasing the search radius, the number of molecules, reactions and paths, that are included in the analysis, growths exponentially. For instance, the numbers of reactions, molecules and paths positioned downstream of the insulin receptor are respectively: 12, 13 and 12 for the first step, 70, 51 and 59 for the second step, 181, 134 and 291 for the third step, and 535, 306 and 1346 for the fourth step. Particular attention has been paid by us to the pathways, that regulate the activity of transcription factors. Thus, the Raf-1-dependent pathway controls the activity of 12 particular transcription factors (c-Myc, c-Ets-1, CREB, p53, Egr-1, Smad1, Smad2, Smad3, c-Myb, Tal, STATs, and c-Jun) by means of 42 paths. While, the Akt-dependent pathway controls the activity of 6 transcription factors (CREB, NF-kappaB, c-Jun, FKHRL1, FOXO1, and FOXO4) using at least 6 different paths. The pathways are displayed according to their hierarchical organization, e.g., as a combination of many paths, and each path is represented as a sequence of steps, each of which, in its turn, can be decomposed into 'reactions' and 'molecules' of the TRANSPATH database.
The results of such in silico analysis help to find key molecules and processes that might be potential targets for pharmacological agents to treat the insulin resistance and type 2 diabetes.
