Wood hemicelluloses exert distinct biomechanical contributions to cellulose fibrillar networks

Hemicelluloses, a family of heterogeneous polysaccharides with complex molecular structures, constitute a fundamental component of lignocellulosic biomass. However, the contribution of each hemicellulose type to the mechanical properties of secondary plant cell walls remains elusive. Here we homogeneously incorporate different combinations of extracted and purified hemicelluloses (xylans and glucomannans) from softwood and hardwood species into self-assembled networks during cellulose biosynthesis in a bacterial model, without altering the morphology and the crystallinity of the cellulose bundles. These composite hydrogels can be therefore envisioned as models of secondary plant cell walls prior to lignification. The incorporated hemicelluloses exhibit both a rigid phase having close interactions with cellulose, together with a flexible phase contributing to the multiscale architecture of the bacterial cellulose hydrogels. The wood hemicelluloses exhibit distinct biomechanical contributions, with glucomannans increasing the elastic modulus in compression, and xylans contributing to a dramatic increase of the elongation at break under tension. These diverging effects cannot be explained solely from the nature of their direct interactions with cellulose, but can be related to the distinct molecular structure of wood xylans and mannans, the multiphase architecture of the hydrogels and the aggregative effects amongst hemicellulose-coated fibrils. Our study contributes to understanding the specific roles of wood xylans and glucomannans in the biomechanical integrity of secondary cell walls in tension and compression and has significance for the development of lignocellulosic materials with controlled assembly and tailored mechanical properties.


Linear biphasic model: analysis of compression-stress relaxation profiles
The composites are assumed to be transversely isotropic in the x,y-plane. This approximation was found to be adequate for describing bacterial cellulose hydrogels given that they are roughly produced in a layer-bylayer fashion. 1,2 In this work we have utilized two models of the linear poroelastic theory: confined and unconfined compression developed by Mow et al. 3 and Cohen et al. 4 , respectively. In our setup, the sides of the hydrogels are not bound by a container wall, and hence water is free to move in a similar manner to unconfined compression setup. The use of sandpaper, however, restricts the lateral expansion of hydrogels, making the balance of stresses within the sold network similar to that described by the confined compression model. In addition, the roughness of the top and bottom plates can facilitate water drainage, making the hydrogels respond in a similar way to the confined compression experiment, 3 where the top plate made of porous material allows water drainage out of the hydrogel. The results of unconfined compression/relaxation modelling were less successful compared to the results obtained using the confined compression/relaxation model. To further refine the confined compression model we have introduced an ad hoc modification to account for the fact that drainage of the fluid occurs through the sides of the hydrogels as well as through the top surfaces in contact with sandpaper. 5,6 According to this model, the normal stress σn(t) resulting from a ramp displacement in the z direction at constant strain rate ! during t0 seconds, followed by a relaxation stage at constant strain is given by And is poroelastic time, t is time, k is the permeability, η is fluid viscosity, h0 is sample thickness, HA and Ez are the aggregate modulus and out-of-plant modulus, respectively. The aggregate modulus is the function of the lateral (in-plane) modulus (EL), where .. and .. are stress and strain in the out-of-plane direction (i.e. The representative fits using the model described in Supplementary

Analysis and discussion regarding anisotropy of the BC-H hydrogels
Zener ratio (a) One of the possible ways of estimating the degree of anisotropy is through evaluating the effective anisotropy ratio a (Zener ratio), which within limits of linear elastic approximation can be defined as:

Supplementary Equation 5
Here we assume that G' >> G" and, hence, G » G' as well as that E can be approximated by Erelax. The a = 1 corresponds to the isotropic material, while for anisotropic materials a > 1. In order to estimate a using Supplementary Equation 5, the Poisson's ratio (ν) is assumed to be 0.3. The resulting values of a are found to be as high as 7 -27 depending on compression ratio and BC-H material. These estimates indicate strong anisotropy.
Modelling was applied to evaluate the poroelastic behavior of hydrogels and the aggregate modulus (HA) was determined. Using the values of HA, we can estimate anisotropy by evaluating effective anisotropy ratio (a2) defined as:

Supplementary Equation 6
In Supplementary

Supplementary Equation 7
All anisotropy ratios (a1, a2, and a3) calculated at a CR around 0.1 are presented in Supplementary Table 3.
The values of a2 are found to be close to 1, indicating that HA and G' show prominent correspondence and may describe the mechanical response of cellulose fibers predominantly oriented in the horizontal direction of the BC and BC-H materials. The a3 values are found to be markedly lower compared to a1 values (19-54 % reduction), which suggests that increase in G' upon compression is partially accounted for by the response of the deformed fibers aligned in the out-of-plane direction of the hydrogel.

Supplementary Figures
Supplementary Figure 1

Supplementary Tables
Supplementary Table 1 ratios (a1, a2, and a3). The anisotropy ratios were calculated at a CR≈0.1 from regular analysis by Method 1, as well as Method 2 where Fn = 0 was targeted to determine a3.