The adaptive responses of a living cell to internal and external signals are controlled by networks of proteins whose interactions are so complex that the functional integration of the network cannot be comprehended by intuitive reasoning alone. Mathematical modeling, based on biochemical rate equations, provides a rigorous and reliable tool for unraveling the complexities of molecular regulatory networks. The budding yeast cell cycle is a challenging test case for this approach, because the control system is known in exquisite detail and its function is constrained by the phenotypic properties of >100 genetically engineered strains. We show that a mathematical model built on a consensus picture of this control system is largely successful in explaining the phenotypes of mutants described so far. A few inconsistencies between the model and experiments indicate aspects of the mechanism that require revision. In addition, the model allows one to frame and critique hypotheses about how the division cycle is regulated in wild-type and mutant cells, to predict the phenotypes of new mutant combinations, and to estimate the effective values of biochemical rate constants that are difficult to measure directly in vivo.

735hardly imagine today's electronics industry, with its powerful, visually oriented design and automation tools, without having first established standard notations for circuit diagrams. Such was not the case in biology 2 . Despite the visual nature of much of the information exchange, the field was permeated with ad hoc graphical notations having little in common between different researchers, publications, textbooks and software tools. No standard visual language existed for describing biochemical interaction networks, inter-and intracellular signaling gene regulation-concepts at the core of much of today's research in molecular, systems and synthetic biology. The closest to a standard is the notation long used in many metabolic and signaling pathway maps, but in reality, even that lacks uniformity between sources and suffers from undesirable ambiguities (Fig. 1). Moreover, the existing tentative representations, however well crafted, were ambiguous, and only suitable for specific needs, such as representing metabolic networks or signaling pathways or gene regulation.The molecular biology era, and more recently the rise of genomics and other high-throughput technologies, have brought a staggering increase in data to be interpreted. It also favored the routine use of software to help formulate hypotheses, design experiments and interpret results. As a group of biochemists, modelers and computer scientists working in systems biology, we believe establishing standard graphical notations is an important step toward more efficient and accurate transmission of biological knowledge among our different communities. Toward this goal, we initiated the SBGN project in 2005, with the aim of developing and standardizing a systematic and unambiguous graphical notation for applications in molecular and systems biology. Historical antecedentsGraphical representation of biochemical and cellular processes has been used in biochemical textbooks as far back as sixty years ago 3 , reaching an apex in the wall charts hand drawn by Nicholson 4 and Michal 5 . Those graphs describe the processes that transform a set of inputs into a set of outputs, in effect being process, or state transition, diagrams. This style was emulated in the first database systems that depicted metabolic networks, including EMP 6 , EcoCyc 7 and KEGG 8 . More notations have been 'defined' by virtue of their implementation in specialized software tools such as pathway and network designers (e.g., NetBuilder 9 , Patika 10 , JDesigner 11 , CellDesigner 12 ). Those "Un bon croquis vaut mieux qu'un long discours" ("A good sketch is better than a long speech"), said Napoleon Bonaparte. This claim is nowhere as true as for technical illustrations. Diagrams naturally engage innate cognitive faculties 1 that humans have possessed since before the time of our cave-drawing ancestors. Little wonder that we find ourselves turning to them in every field of endeavor. Just as with written human languages, communication involving diagrams requires that authors and readers agr...

Cytokines such as TNF and FASL can trigger death or survival depending on cell lines and cellular conditions. The mechanistic details of how a cell chooses among these cell fates are still unclear. The understanding of these processes is important since they are altered in many diseases, including cancer and AIDS. Using a discrete modelling formalism, we present a mathematical model of cell fate decision recapitulating and integrating the most consistent facts extracted from the literature. This model provides a generic high-level view of the interplays between NFκB pro-survival pathway, RIP1-dependent necrosis, and the apoptosis pathway in response to death receptor-mediated signals. Wild type simulations demonstrate robust segregation of cellular responses to receptor engagement. Model simulations recapitulate documented phenotypes of protein knockdowns and enable the prediction of the effects of novel knockdowns. In silico experiments simulate the outcomes following ligand removal at different stages, and suggest experimental approaches to further validate and specialise the model for particular cell types. We also propose a reduced conceptual model implementing the logic of the decision process. This analysis gives specific predictions regarding cross-talks between the three pathways, as well as the transient role of RIP1 protein in necrosis, and confirms the phenotypes of novel perturbations. Our wild type and mutant simulations provide novel insights to restore apoptosis in defective cells. The model analysis expands our understanding of how cell fate decision is made. Moreover, our current model can be used to assess contradictory or controversial data from the literature. Ultimately, it constitutes a valuable reasoning tool to delineate novel experiments.