Bistability, Oscillations, and Traveling Waves in Frog Egg Extracts
- 603 Downloads
Mathematical modeling is a powerful tool for unraveling the complexities of the molecular regulatory networks underlying all aspects of cell physiology. To support this claim, we review our experiences modeling the cyclin-dependent kinase (CDK) network that controls events of the eukaryotic cell cycle. The model was derived from classic experiments on the biochemistry and molecular genetics of CDKs and their partner proteins. Because the dynamical properties of CDK activity depend in large part on positive and negative feedback loops in the regulatory network, it is difficult to predict its behavior by intuitive reasoning alone. Mathematical modeling is the correct tool for reliably determining the properties of the network in comparison with observed properties of dividing cells and for predicting the behavior of the control system under novel conditions. In this review, we describe six unexpected predictions of our 1993 model of the CDK control system in frog egg extracts and the remarkable experiments, performed much later, that verified all six predictions. The dynamical properties of the CDK network are consequences of feedback signals and ultrasensitive responses of regulatory proteins to CDK activity, and we describe the experimental evidence for the predicted ultrasensitivity. This case study illustrates the novel insights that mathematical modeling, analysis, and simulation can provide cell physiologists, and it points the way to a new “dynamical perspective” on molecular cell biology.
KeywordsMathematical model Cell cycle control M-phase-promoting factor Bifurcation theory
- Novak B, Tyson JJ (1993b) Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J Cell Sci 106:1153–1168Google Scholar
- Obeyesekere MN, Herbert JR, Zimmerman SO (1995) A model of the G1 phase of the cell cycle incorporating cyclin E/cdk2 complex and retinoblastoma protein. Oncogene 11(6):1199–1205Google Scholar
- Tang Z, Coleman TR, Dunphy WG (1993) Two distinct mechanisms for negative regulation of the Wee1 protein kinase. Embo J 12(9):3427–3436Google Scholar