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This and the next image are from:
Why is the microtubule lattice helical? by Viktória Hunyadi, Denis Chrétien, Henrik Flyvbjerg and Imre M. Jánosi, Biology of the Cell, Vol. 99, pp. 117-128, 2007
ABSTRACT: Microtubules polymerize from identical tubulin heterodimers, which form a helical lattice pattern that is the microtubule. This pattern always has left-handed chirality, but it is not known why. But as tubulin, similar to other proteins, evolved for a purpose, the question of the title of this artcile appears to be meaningful. In a computer simulation that explores the ‘counterfactual biology’ of microtubules without helicity, we demonstrate that these have the same mechanical properties as Nature's microtubules with helicity. Thus only a dynamical reason for helicity is left as potential explanation. We find that helicity solves ‘the problem of the blind mason’, i.e. how to correctly build a structure, guided only by the shape of the bricks. This answer in turn raises some new questions for researchers to address.
From the paper cited above:
"Local buckling is not to be confused with Euler buckling, which refers to the elastic instability of a thin rod subject to longitudinal compressing forces (Landau and Lifshitz, 1986). Local buckling can be demonstrated simply by bending a drinking straw: as its overall curvature increases, its cross-section changes from circular to increasingly elliptic until a kink forms and the tube collapses [see Figure 5 (this slide)]. This phenomenon is referred to as the Brazier effect in the engineering literature (Brazier, 1927). Brazier buckling is a rather complex phenomenon (Calladine, 1983). It depends not only on macroscopic properties, such as flexural and bending rigidities, geometry, deformation history or internal pressure; in real materials, local (microscopic) parameters, such as residual stresses or structural irregularities (buckling seeds), can play an equally important role.
We carried out a series of buckling simulations with different parameters in the elastic sheet model (Jánosi et al., 1998). In general, we observed the well-known characteristics of local buckling: an increasing bending force leads to significant eccentricity of the cross-section together with a gradual decrease of global rigidity until the tube collapses. We obtained the same critical eccentricity, 0.790, for all values of the model parameters. This result agrees well with the theoretical value estimated by Reissner (1961), who solved the non-linear local buckling problem for an infinitely long thin-walled tube, giving also a correction to the linear solution of Brazier (1927).
We found that wall anisotropy has a dramatic effect on how cylindrical shells buckle. A non-helical lattice develops a sharp kink, similar to a straw, as demonstrated in Figure 5 (lower panel of this slide). In contrast, a helical lattice buckles in a way that leaves its sides smooth, as illustrated in Figure 5 (upper panel of this slide). At this point, however, the sheet model becomes unrealistic as a model for real microtubules, because its wall is infinitely thin; the strong local deformation requires us to consider the effects of finite wall thickness."
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