PMC:1570349 / 1954-3260 JSONTXT

{"project":"2_test","denotations":[{"id":"16859561-11955179-1688444","span":{"begin":886,"end":887},"obj":"11955179"},{"id":"16859561-12648679-1688444","span":{"begin":886,"end":887},"obj":"12648679"},{"id":"16859561-14766974-1688444","span":{"begin":886,"end":887},"obj":"14766974"},{"id":"16859561-17337276-1688444","span":{"begin":886,"end":887},"obj":"17337276"},{"id":"16859561-12447975-1688445","span":{"begin":1117,"end":1118},"obj":"12447975"},{"id":"16859561-15446975-1688446","span":{"begin":1119,"end":1120},"obj":"15446975"},{"id":"16859561-16081475-1688447","span":{"begin":1302,"end":1304},"obj":"16081475"}],"text":"In the study of such systems, an important goal is to understand how the observed physiological behavior arises out of gene network topology and parameters p. Some of these questions may be studied via examining the bifurcation manifolds Σ of the ODE system, which partition the parameter space into regions of different qualitative behavior (see e.g., [1] for a general overview to bifurcation theory). From ODE models and measured parameters, the forward problem of computing the bifurcation diagram has contributed significantly towards elucidating the complex mechanisms underlying cellular processes. For instance, mathematical and symbolic bifurcation analysis has led to an understanding of the possible dynamical behaviors that may arise out of simple gene systems (for a monograph, see [2], examples of more recent papers dealing with natural, designed, and model systems are [3-7]). For cell cycle models, bifurcation diagrams have given biologists a systems-level perspective of the roles played by the various constituent modules, as well as providing the ability to predict the behavior of mutant cells [8,9]. The desire to locate regions in parameter space exhibiting interesting dynamics has led to the development of computational tools for the automatic discovery of bifurcation sets [10]."}