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. 2018 Nov 19;8:17035. doi: 10.1038/s41598-018-34766-0

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Pre-steady-state behavior in the oocyte maturation MAPK cascade model. (A) Schematic view of the MAPK cascade. The cascade consists of a MAPK kinase kinase (MAPKKK), a MAPK kinase (MAPKK), and a MAPK. In this model, the dual phosphorylations of MAPK and MAPKK occur by a two-step, distributive mechanism. (B–D) Simulation of the Huang & Ferrell model. MAPK-PP vs. time for three different inputs (B), normalized MAPK-PP versus E_1,tot for the indicated times (C), and n_H versus time (D). The inset in panel D shows early times.