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. 2022 Aug 1;12:13044. doi: 10.1038/s41598-022-16880-2

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© The Author(s) 2022

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Theoretical evaluation of apparent stiffness of the cell wall and estimation of Young’s modulus and turgor pressure based on AFM measurements. (A) Schematic illustrations of shell structure and the indentation process. (B) Apparent stiffness k_as as functions of E and P before (left) and after (right) LP. (C) Apparent stiffness k_as as functions of t and κ_M before (left) and after (right) LP.