Deformation geometry of cellulose fibril arrays constraining the stretching and growth of plant cell walls

There are several ways in which the nanoscale array of cellulose fibrils in one layer of a plant cell wall can rearrange to permit the cell wall to expand under external uniaxial tension or, in the case of primary cell-walls, the biaxial turgor pressure that drives growth. Here, seven such deformation modes were identified and their scale-independent geometry was described: fibril rotation, regular shear, interdigitated sliding, fibril stretching, fibril respacing and the formation and straightening of waves. The distinction between regular shear and interdigitated sliding was introduced to capture a continuous range of sliding modes at fibril interfaces. Combinations of these nanoscale deformations were examined to find out how their relative magnitude must vary to satisfy cell-scale geometric constraints. When the cellulose fibrils were transversely oriented, respacing, wave formation or both were needed for elongation. When the tissue restrained twist to zero, the deformation modes became co-ordinated, readjusting as the cellulose orientation became more axial during elongation. Regular shear, possibly facilitated by expansin activity, could then control the width of the elongating cell-wall. Each deformation mode fortuitously contributed most elongation at the microfibril orientation where it was most efficiently driven by the local force vector.