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. 2019 Aug 19;9:11980. doi: 10.1038/s41598-019-48468-8

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© The Author(s) 2019

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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Model predictions for the approximate limiting DNA concentration for different promoter strengths, UTR strengths, and lengths of gene. Each data set was constructed by varying each specific constant (k_cap,m, k_cat,p, L_m) and fit to a power function, then combined to form the final Eq. (28). The factor of 250 in Eq. (28) is due to the length of gene not being normalized, 2.19 10² is divided by the limiting DNA concentration at the length of deGFP (800 nt), which is 4.43 nt. That value is multiplied by the limiting DNA concentration for P70a-deGFP, where P = 1, U = 1, and L_m = 800, which is 5 nM. The power function is chosen only because it is a good fit phenomenologically, not for some physiological reasons. The load calculator is just a tool to approximate when the resources will become limiting and the protein synthesis rate will not be in the linear regime. The obtained value tells us how sensitive each parameter is to the limiting DNA concentration, such that they can be combined in one single TXTL load calculator equation.