Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article The Impact of Time Delays on the Robustness of Biological Oscillators and the Effect of Bifurcations on the Inverse Problem | Hindawi Publishing Corporation EURASIP Journal on Bioinformatics and Systems Biology Volume 2009 Article ID 327503 14 pages doi 2009 327503 Research Article The Impact of Time Delays on the Robustness of Biological Oscillators and the Effect of Bifurcations on the Inverse Problem Nicole Radde Institute for Medical Informatics Statistics and Epidemiology University of Leipzig Hiirtelstrafe 16-18 04107 Leipzig Germany Correspondence should be addressed to Nicole Radde Received 30 May 2008 Accepted 14 August 2008 Recommended by Matthias Steinfath Differential equation models for biological oscillators are often not robust with respect to parameter variations. They are based on chemical reaction kinetics and solutions typically converge to a fixed point. This behavior is in contrast to real biological oscillators which work reliably under varying conditions. Moreover it complicates network inference from time series data. This paper investigates differential equation models for biological oscillators from two perspectives. First we investigate the effect of time delays on the robustness of these oscillator models. In particular we provide sufficient conditions for a time delay to cause oscillations by destabilizing a fixed point in two-dimensional systems. Moreover we show that the inclusion of a time delay also stabilizes oscillating behavior in this way in larger networks. The second part focuses on the inverse problem of estimating model parameters from time series data. Bifurcations are related to nonsmoothness and multiple local minima of the objective function. Copyright 2009 Nicole Radde. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The investigation of regulation mechanisms underlying various properties of cellular networks has gained much .
