5Pectin is a major component of the primary plant cell wall and is important for cell expan-6 sion. However, the relationship between its chemistry and mechanical properties is not fully 7 understood, especially in vivo. In this study, a protocol for viscoelastic micro-indentation 8 using atomic force microscopy (AFM) was developed and applied to pectin in vitro and in 9 vivo. After determining that linear viscoelasticity was a suitable theoretical framework for in 10 vitro pectin analyses were conducted with both a standard linear solid and fractional Zener 11 model. These indicated a strong coupling between elastic and viscous properties over a range 12 of degrees of methyl-esterification (DM). Both elasticity and viscosity were found to vary 13 non-linearly with DM which had interesting consequences for pectin gels of mixed DM. In 14 Arabidopsis cell walls, the standard linear solid model was found to be appropriate. In this 15 in vivo composite material a weaker elastic-viscous coupling was exhibited, correlated with 16 DM. The viscoelastic testing in vivo of rapidly elongating cell walls, rich in high DM pectin, 17 displayed a longer viscous time-scale. The implications of the testing method and results are 18 discussed in the context of mechanobiology, mechano-chemistry, and cell growth.19 1 Introduction 20 Networks of hydrophilic polymer chains, known as hydrogels, are a critically important class of 21 material in biology [1]. Hydrogels made from pectin, and insights into their mechanical proper-22ties, are useful in applied [2,3] and fundamental contexts [4,5]. In the plant species Arabidopsis 23 thaliana, pectin is the single largest constituent of the primary cell wall [6], the structural layer 24 encasing growing cells which is acknowledged to be a critical arbiter of growth [7]. The umbrella 25 term 'pectin' refers to a variety of pectic polysaccharides which cohabit the cell wall including ho-26 mogalacturonan (HG), rhamnogalacturonan I, rhamnogalacturonan II and xylogalacturonan [8]. 27 In Arabidopsis, HG is the largest component by a significant margin [9]. Key features of HG are its 28 initial state, which is highly methyl-esterified, and its de-esterification when acted upon by pectin 29 methylesterase (PME) enzymes [10]. HG de-esterification can occur in a blockwise contiguous 30 mode or a non-contiguous random mode. The degree of 'blockiness' likely depends on the prop-31 erties of the PMEs themselves [11], of which there are sixty-six (66) in Arabidopsis [12]. Random 32 de-esterification can occur through non-enzymatic means with changes in pH [13]. When a methyl 33 group is removed (i.e. de-esterified) a negative charge is left in its place and two negatively charged 34 sugars can bond using Ca 2+ ions [11]. Indeed, calcium cross-linking is the primary method of gela-35 tion for low degree of methyl-esterification (DM) gels and longer 'blocks' of de-esterified units form 36 stronger bonds -provided there is sufficient free calcium nearby. In contrast, high DM HG relies 37 on hydrogen bond...