Abstract
In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need a priori determination of the parameters, which can be theoretically or practically impossible. This chapter gives a brief introduction to general results based on the network structure. In particular, we describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates and include many post-translational modification networks. We also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and we point out some of the mathematical questions that arise from this application.
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Acknowledgements
I am very grateful to the Committee for Women in Mathematics of the International Mathematical Union for the organization of this meeting and for the many activities they take in charge to ensure development and recognition of female mathematicians around the world. I am particulary grateful to Carolina Araujo for all her work to make (WM)2 a great success. I also thank Magalí Giaroli, Mercedes Pérez Millán and Enrique Tobis for their help with the figures.
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Dickenstein, A. (2019). Algebra and Geometry in the Study of Enzymatic Cascades. In: Araujo, C., Benkart, G., Praeger, C., Tanbay, B. (eds) World Women in Mathematics 2018. Association for Women in Mathematics Series, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-030-21170-7_2
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