Microrheological studies reveal semiflexible networks in gels of a ubiquitous cell wall polysaccharide

Microrheological measurements have been carried out on ionotropic gels made from an important cell wall polysaccharide, using diffusing wave spectroscopy and multiple particle tracking. These gels were formed by the interaction of calcium ions with negatively charged groups on the polymer backbone, which is a copolymer of charged and uncharged sugars, galacturonic acid, and its methylesterified analog, respectively. The results suggest that semiflexible networks are formed in these systems, with a low frequency, frequency independent storage modulus $(G^{\prime }>G^{″})$, and a high frequency scaling of both $G^{\prime }$ and $G^{″}$ with ${\omega }^{3∕4}$. The differences observed between gels obtained using polysaccharide samples with different amounts and patterns of the charged ion-binding groups could comfortably be accommodated within this theoretical framework, assuming that the elementary semiflexible elements of the network are filaments consisting of two polymer chains bridged with calcium. In particular, a sample that was engineered to possess a blockwise intramolecular distribution of calcium chelating moieties clearly exhibited the high frequency scaling of both moduli with ${\omega }^{3∕4}$ across some three orders of magnitude, and the concentration dependences of the elastic modulus, at both high and low frequency, were found to follow power laws with predicted exponents. Furthermore, quantitative agreement of the moduli with theory was found for realistic estimates of the molecular parameters, suggesting that the physics of semiflexible networks is not only exploited by protein components of the cytoskeleton but also by polysaccharides in plant cell walls.

Figure 1

(Color online) A schematic diagram of the proposed assembly process in ionotropic pectin gels. (a) Charged galacturonic acid residues and uncharged methylesterified analogs are represented by open and filled circles, respectively. (b) (i) Galacturonic acid residues on neighboring chains zip-up with calcium ions, represented by diamonds, and (ii) forming stiff fibrils. (c) Interfibrillar crosslinks may also be formed with calcium depending on the amount of calcium available.

Figure 2

(a) The MSDs obtained from experiments using DWS (filled circles), and multiple particle tracking (open circles), on an ionotropic gel of the polysaccharide pectin formed as described in the Experimental section. The solid line is a fit to a theoretical model, described in the text. (b) The viscoelastic properties obtained from the transformation of this data. The solid and dotted guidelines show $G^{\prime }$ and $G^{″}$, respectively, both scaling with ${\omega }^{3∕4}$ at high frequencies.

Figure 3

The MSDs obtained from experiments using DWS on ionotropic gels of pectin samples with different backbone architectures. Samples of 35 and 48% DM having randomly distributed ion-binding groups (open circles in the schematic polymer structures inset), and a 50% DM sample possessing a blockwise distribution of charged groups are shown. These were formed as described in the experimental section $(●)$ $1.5\%\mathrm{w}∕\mathrm{w}$ polymer, $R=0.4$; $(◻)$ $1\%\mathrm{w}∕\mathrm{w}$ polymer, $R=0.3$; $(엯)$ 0.2% polymer, $R=0.4$).

Figure 4

The MSDs obtained from experiments using DWS on ionotropic gels of pectin samples with 50% ion-binding groups arranged in a blockwise distribution, formed as described in the Experimental section, as a function of concentration.

Figure 5

The concentration dependence of the mean square displacements of tracer particles in a $0.2\%\mathrm{w}∕\mathrm{w}$ gel of the 50% DM, PME generated, pectin. (a) At high frequency and (b) at low frequency.

Figure 6

The frequency dependence of $G^{\prime }$ and $G^{″}$ measured on a $0.2\%\mathrm{w}∕\mathrm{w}$ gel of the 50% DM, PME generated, pectin. The solid line is a theoretical calculation performed as described in the text.