*4.8. Statistical and Mathematical Analysis*

Where error bars are given, experimental data are presented as mean ± standard deviation, calculated using Microsoft Office Excel (Microsoft Corporation, Redmond, WA, USA). Strain at time t relative to time 0 are true strains calculated from Ln(Lt/L0), where Lt is the segment length at time t and L0 is the length at time 0 (time 0 was immediately before the stress applied to the segment was increased unless otherwise stated). Modeling and parameterization of extensiometric data used the Microsoft Office Excel solver to minimize the squares of differences between modeled and experimental data.

**Author Contributions:** All experimental work except that presented in Figures 5 and A1 was carried out by A.I. under the supervision of D.S.T. The data presented in Figures 5 and A1 was obtained by D.S.T. Conceptualization: D.S.T.; methodology, D.S.T. and A.I.; software, D.S.T.; formal analysis, D.S.T. and A.I.; investigation, A.I.; resources, D.S.T.; data curation, D.S.T. and A.I.; writing—original draft preparation, D.S.T.; writing—review and editing, D.S.T.; visualization, D.S.T. and A.I.; supervision, D.S.T.; project administration, D.S.T.; funding acquisition, D.S.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding. A.I. received a Cavendish Research PhD Scholarship from the University of Westminster.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Acknowledgments:** We thank Simon McQueen-Mason of the University of York for his donation of the CsExp1 used in these experiments. The extensiometer was constructed by Philip Smith at Lancaster University.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

**Appendix A**

**Figure A1.** Time course of weight changes in cell walls from sunflower hypocotyls exposed to a water potential of −0.62 MPa generated by an osmoticum able to permeate the wall rapidly (glucose, red circles), an osmoticum partly excluded from the wall but expected to diffuse through it more slowly than water (PEG 1000, blue squares), and an osmoticum substantially excluded from the wall (PEG 6000, green triangles).

**Figure A2.** Image of tubes containing 2% (*w*/*v*) solutions of apple pectin of pH 3.03, 3.46, 3.99, 4.59, 5.05, 5.45, and 6.01 containing 10 mM CaCl2 five minutes after the tubes were inverted.
