  The efficient and controlled assembly of complex structures from
macromolecular building blocks is a critical open question in both biological
systems and nanoscience. Using molecular dynamics simulations we study the
self-assembly of tubular structures from model macromolecular monomers with
multiple binding sites on their surfaces [Cheng et al., Soft Matter 8,
5666-5678 (2012)]. In this work we add chirality to the model monomer and a
lock-and-key interaction. The self-assembly of free monomers into tubules
yields a pitch value that often does not match the chirality of the monomer
(including achiral monomers). We show that this mismatch occurs because of a
twist deformation that brings the lateral interaction sites into alignment when
the tubule pitch differs from the monomer chirality. The energy cost for this
deformation is small as the energy distributions substantially overlap for
small differences in the pitch and chirality. In order to control the tubule
pitch by preventing the twist deformation, the interaction between the vertical
surfaces must be increased without resulting in kinetically trapped structures.
For this purpose, we employ the lock-and-key interactions and obtain good
control of the self-assembled tubule pitch. These results explain some
fundamental features of microtubules. The vertical interaction strength is
larger than the lateral in microtubules because this yields a controlled
assembly of tubules with the proper pitch. We also generally find that the
control of the assembly into tubules is difficult, which explains the wide
range of pitch and protofilament number observed in microtubule assembly.
