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. 2019 Feb 28;9:3176. doi: 10.1038/s41598-019-39512-8

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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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Matched Peak Count (MPC) measures goodness of fit between observed and theoretical distributions. Gray and colored peaks represent experiment and theoretical ones respectively, and the filled figure means that experiment and theoretical peaks are similar (the difference is less than ε) in their intensities, increasing MPC value by 1. The tolerance ε is defined for each peak as 10% of theoretical peak’s intensity. (a) Observed deuterated distribution with average deuterium number 8 is shown. (b) Theoretical distribution is first normalized so that its highest peak’s intensity is set to be the same as the observed one at the corresponding position. (c) Weight of theoretical distribution is adjusted to find maximum MPC under given average deuterium number. (d) Finally, the best fit is found, and then its average deuterium number is determined.