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From the same source as the previous slide.
The authors write:
"Accordingly, we implemented a 3D finite element model of microtubule walls, which is very similar to the model proposed by Molodtsov et al. (2005a, 2005b). Monomers are represented as homogeneous elastic spheres, and stretching and bending properties are parameterized by linear ‘springs’ of prescribed orientations between neighbouring elements. Longitudinal bonds are set to be 2–5 times stronger than lateral ones. The monomers are impenetrable, and spatial overlap is not permitted. Structural relaxation can be performed either by global conjugate gradient minimization or by a standard molecular dynamics procedure which solves Newtonian equations of motion with hydrostatic damping.
The most important result for the present analysis is that the drastic difference between helical and non-helical configurations disappeared [Figure 6 (this slide)], irrespective of the particular parameter values used. Intuitively, the strongly deformed local configurations at critical buckling are determined by excluded volume interactions in a neighbourhood of a few adjacent dimers. The shape of the buckled zone clearly reflects the lattice geometry. However, the stress distribution, which determines stability, is very similar for helical and non-helical lattices [Figure 6, (this slide)].
Since Brazier buckling is the prototypical critical deformation where local bond orientation might play an essential role, we do not expect that different experiments, such as local indentation by a scanning force microscope tip (de Pablo et al., 2003; Schaap et al., 2006) or uniform radial buckling under osmotic pressure (Needleman et al., 2004, 2005), would lead to different conclusions.
On the basis of these facts and the results described in this section and below, we conclude that helicity is, at most, only weakly coupled to the mechanical properties of microtubules. Consequently, it is not in these mechanical properties we find to be the raison d'être for the helicity of microtubules."
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