Schematic representation of how bending and stretching affects energy in the model. In each graph, the standard free-energy change (Δ

*G*°) is measured on the

*Y* axis. (

*A*) Subunit curling and torsion. The preferred curling angle,

*θ*, is 0° for tubulin-GTP and 22° is the preferred

*θ* for tubulin-GDP. The preferred torsion angle,

*φ*, is 0° for both tubulin-GTP and tubulin-GDP. These preferences are described by direction cosines, and the actual dimer position is similarly described (see Methods). The angle between the preferred orientation (

*shaded arrow*) and the actual orientation (

*bold black arrow*) is Φ. The relationship between Φ and

*E*_{curl} obeys a Hookean spring law, where energy is minimized at the preferred orientation (Φ = 0°) and energy increases with increased deviation from this preferred orientation (Φ > 0°). Note that Φ measures deviation of an actual orientation from a preferred orientation, so that, e.g., a tubulin-GDP held in a straight conformation would have Φ = 22°, the same value for Φ as a tubulin-GTP would have when held curled to 22°. Although not explicitly shown in the figure, curling may also occur at the centroid of the

*α*-tubulin monomer to relieve mechanical stress propagated throughout the microtubule lattice by curling events at the

*β*-tubulin monomers. (

*B*) Longitudinal strain. Longitudinal strain (

*E*_{longstrain}) is minimized when longitudinal stretching (

*d*) is zero. Energy follows a Hookean spring law, where energy increases with longitudinal stretching squared. (

*C*) Lateral strain. Lateral stretching energy (

*E*_{latstrain}) is minimized when lateral stretching (

*S*) is zero. Energy follows a Hookean spring law, where energy increases with longitudinal stretching squared.

*S* is a derived position descriptor for the purpose of evaluating energetics;

*θ*,

*φ*, and

*D* give a complete description of dimer positions in the microtubule lattice.

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