ASPECTOS DE LA PRODUCCIÓN MATERIAL

This project aims to apply experimental techniques to further characterise the struc- ture, dynamics and mechanical properties of pectin networks. A general soft-matter physics approach is utilized to further understand the properties of the constituents, the mechanism of self-assembly, their self assembled architecture, and finally the me- chanical properties of the resulting material. Furthermore, we extend knowledge of the dynamical processes in pectin networks into the low dynamical regime which describes the non-equilibrium state of the systems. The relationship between the structure, dy- namics and mechanical properties of pectin based materials are not well understood, and while pectin is an important part of the plant cell wall, it has been left in the shadows of other more well-studied carbohydrates such as alginate. Previous studies on the structure and dynamics of gelled pectin networks have focus on the high fre- quency dynamics [66,102] and the bundle size of junction zones [67] respectively. The

current work reveals previously unseen slow dynamics in pectin gels and focusses on characterising this slow motion and the structure over a broad range of length scales. The thesis can be divided into three main experimental chapters. Firstly we performed dynamical and rheological measurements on an acid-induced pectin gel at a range of temperatures. A slow dynamical process was measured, this slow motion has not been observed before in pectin gels and initiated the focus on slow dynamics. A phenomeno- logical model, called the glassy wormlike chain model, was employed to further interpret the results. This will be elaborated on in chapter 2. We then further structurally and mechanically characterise pectin acid gels and solutions. We started by measuring the evolution of the gelled structure using time resolved small-angle x-ray scattering. A worm-like chain model was fitted to characterise the structure over length-scales from the radius of dimeric structures and the fractal dimension of the network extracted. Rhe- ological studies were then utilized to monitor the mechanical properties as the gelation process evolved and compared to the evolution of the large-scale structural properties of the network. This work formed chapter three. Finally, we sought understanding of the mechanism behind the slow dynamics that were observed in chapter two. To understand this slow motion we designed gels that we predicted to have different structures, which would result in modifying the slow dynamics. We measured the structure using small- angle x-ray scattering and carried out novel light scattering techniques to measure the dynamics over the period of minutes to hours, which formed chapter 4. Further results on the structure of dilute pectin pectin solutions and pectin gels are reported on in the Annexes.

3. Micro-Rheological and Nonlinear

Rheology Studies Reveal the Glassy

Nature of Acid-Induced Pectin

Networks

As published in:

R R Vincent, B W Mansel, A Kramer, K Kroy, and M A K Williams. Micro- rheological behaviour and nonlinear rheology of networks assembled from polysaccharides from the plant cell wall. New Journal of Physics, 15(3):035002, March 2013. ISSN 1367-2630. doi: 10.1088/1367-2630/15/3/035002.

Abstract

The same fundamental questions that have driven enquiry into cytoskeletal mechanics can be asked of the considerably less-studied, yet arguably just as important, biopolymer matrix in the plant cell wall. In this case, it is well-known that polysaccharides, rather than filamentous and tubular protein assemblies, play a major role in satisfying the mechanical requirements of a successful cell wall, but developing a clear structurefunc- tion understanding has been exacerbated by the familiar issue of biological complexity. Herein, in the spirit of the mesoscopic approaches that have proved so illuminating in the study of cytoskeletal networks, the linear microrheological and strain-stiffening responses of biopolymeric networks reconstituted from pectin, a crucial cell wall polysac- charide, are examined. These are found to be well-captured by the glassy worm-like

chain (GWLC) model of self-assembled semi-flexible filaments. Strikingly, the nonlinear mechanical response of these pectin networks is found to be much more sensitive to tem- perature changes than their linear response, a property that is also observed in F-actin networks, and is well reproduced by the GWLC model. Additionally, microrheological measurements suggest that over long timescales (>10 s) internal stresses continue to redistribute facilitating low frequency motions of tracer particles.

3.1

Introduction

3.1.1 Mesoscopic models

Much progress has been made recently in the study of the mechanical properties of solutions and networks of semi-flexible protein filaments, driven largely by the desire to understand the functionality of the cytoskeleton [21, 103–107]. Indeed, the results gleaned from the study of such biologically relevant structures as F-actin have been exploited by soft-matter physicists interested in modelling the behaviour of all manner of semi-flexible filaments [102,108–110]. In particular the worm-like chain (WLC) model of polymer physics [55,74] has found considerable utility in describing the dynamics and the force-extension behaviour both of single biopolymer chains, and of higher-order semi- flexible assemblies such as multimeric filaments, ribbons, tubes and worm-like micelles. Generally speaking the malleable mechanics and slow dynamics characteristic of soft and biological matter arises from the thermo-reversible assembly of low-dimensional manifolds into (transient) meso-structures.

In order to understand the time and length-scale dependent rheological properties of such systems, the central task is to understand how the interactions interfere with the dynamics of the individual constituents. Inspired by the underlying similarity of constraint release in these systems and the thermally-activated jumping between local traps in soft glasses [73, 111], the glassy worm-like chain (GWLC) model [112–114] addresses this problem by exponentially stretching the relaxation spectrum for single- chain motions involving wavelengths beyond a characteristic backbone length,Λ. While the exponential form of the stretching is not microscopically derived, the model builds on the known mesostructure of the polymer network, and introduces a single sticki- ness parameter that intuitively corresponds to the characteristic depth of the potential

Chapter 3. Micro-Rheological and Nonlinear Rheology Studies Reveal the Glassy Nature of Acid-Induced Pectin Networks 32 well that a cross-linked chain section must escape in order to dissociate. Despite its simplicity, the model has been successfully used to parameterize the frequency- depen- dent linear rheology of such systems, their nonlinear strain-stiffening behaviour, and additionally, by considering the stress dependence of the number of cross-links, their eventual softening [115].

The GWLC theory has not however been previously applied to the analysis of polysac- charide systems, despite the fact that they too play a significant role in controlling the mechanical properties of tissues, ranging from mammalian connective tissues to the ubiquitous plant cell wall. Herein, pectin gels have been studied to test the utility of ex- isting models in describing the rheological properties of networks of this important class of carbohydrate biopolymers. Specifically the acid-gel system was selected where the stickiness of the interaction between network strands originates from hydrogen bonding between extended patches on different chains. Microrheological studies were undertaken using (i) diffusing wave spectroscopy (DWS), which maximizes the accessible frequency range and (ii) multiple-particle tracking (MPT), which allows the homogeneity of the system to be probed. In addition measurements of the stressstrain behaviour following the application of varying pre-stresses were carried out. Results are discussed within the framework of models of semi-flexible networks and slow, glassy network relaxation.