Here we first review evidence regarding the native state. Perhaps the most informative observations from a quantitative perspective are those of Hanley et al. regarding the alga Micrasterias denticulata (15) and those of Haigler regarding celluloses formed by the bac­terium Acetobacter xylinum (16). In both instances, a long-period helical form is observed.

A micrograph of Micrasterias denticulata provides an excellent demonstration of the regularity of the periodicity. It is shown in Figure 6.1, where the period of about 1200 nm is evident. Panel A shows the micrographs of the fibril, while panel B provides the authors’ rationalization of the appearance of linear segments connected by highly deformed segments within which the 180° turning occurs. The linear segments are about 600 nm each, so that a helical twist of 180° occurs over 600 nm, and two linear segments totaling about 1200 nm corresponding to the full period wherein a complete turn of 360° occurs.

A similar periodicity has been observed by Haigler in her pioneering studies of the struc­tures of bacterial celluloses from Acetobacter xylinum and their response to different pertur­bations of their growth environment (16). The period consistently observed is about 600 nm,

which has also been reported for celluloses formed by A. xylinum (17). A key point is that the long period of the helical biological structure appears to depend on lateral dimensions. The lateral dimensions of Micrasterias denticulata fibrils are approximately 10 by 20 nm, whereas the lateral dimensions of bacterial cellulose microfibrils are approximately 6-7 nm. Thus, one would expect that the period of the nanofibrils in higher plant cell walls, which have lateral dimensions of the order of 3-5 nm, would be significantly less than 600 nm.

The conclusion regarding the period of higher plant fibrils has been confirmed by the most recent comprehensive molecular modeling studies carried out for hydrated aggregates of cellulose molecules (14). It is also confirmed by atomic force microscopic images of maize parenchyma cell walls shown in Figure 6.2. Here we see that the fibrils appear to vary in width as indicated by the arrows. The variation in width is indicative of an ellipsoidal cross section as

suggested by the ellipsoidal polyhedral model proposed by Ding and Himmel (18). The sep­aration of the narrower sections along an individual fibril appears to be of the order of 200­250 nm. The lateral dimensions of the ellipsoidal polyhedron are approximately 3 by 5 nm.

Before discussing the implications of the molecular modeling studies and patterns of fibril aggregation, it is helpful to clarify the questions regarding symmetry and helical organization with the aid of geometric models of the constrained crystallographic structures and the unconstrained structures manifesting the long-period helical twist. These are illustrated in Figure 6.3, which shows scaled representation of nanofibrils of different sizes. In panel A, they are represented as they would be if they were describable in terms of the symmetry of space groups as implicit in the crystallographically determined structures. They range in cross-sectional size from 2 by 2 nm, which approximates the most elementary fibrils observed, to 20 by 20 nm fibrils representative of algae such as Valonia and Cladophera as well as the tunicate Halocynthia. The length dimension has been scaled to be 300 nm presented in 4 nm intervals to aid in visualization. The geometry of fibrils was defined by the requirement of translational symmetry along three non-coplanar linear axes in Cartesian space. Note that the angles between axes will not be 90° for many crystallographic space groups, although linear translational symmetry in three dimensions is foundational in space group theory (19). Panel B in contrast shows the same fibrils as transformed to reflect a helix with a period of 1200 nm. The figure in panel B represents a 90° turn of the end of each fibril over 300 nm to display the effect of a 360° turn over 1200 nm.

It is immediately obvious that assumptions underlying crystallographic analyses are ap­proximations, the implications of which cannot be ignored. For this reason, we need to adopt new terminology to avoid confusion. We suggest no longer using the terms crystal or crystalline, but rather use the term “aggregate” to indicate ordered fibrils. We regard them as highly ordered biological structures that do not meet the classical criteria for crystallinity illustrated in panel A of Figure 6.3. However, since they are periodic at the molecular level as well, we anticipate that they will diffract X-rays in a pattern that approximates that expected from the structures depicted in panel A of Figure 6.3.

The central problem for crystallographic analyses is that the helical twist in fibrils elimi­nates the possibility of constructing a reciprocal space, and such a construction is essential for the interpretation of diffractometric data. Given this observation, one must ask why it has been ignored for approximately 100 years since crystallinity in cellulose was first proposed and diffractometric studies were undertaken. We suggest that a key obstacle has been trans­formation of native celluloses in the course of isolation. Before reviewing the matter further,
it is useful to begin consideration of the native state in living plants by reviewing the results of the molecular modeling program.