Microtubules confined to the two-dimensional cortex of elongating plant cells must form a parallel yet dispersed array transverse to the elongation axis for proper cell wall expansion. Some of these microtubules exhibit free minus-ends, leading to migration at the cortex by hybrid treadmilling. Collisions between microtubules can result in plus-end entrainment (“zippering”) or rapid depolymerization. I am developing computational models of cortical microtubule organization. We are elucidating the relative importance of plus-end entrainment and catastrophe-inducing collisions; how catastrophe-inducing boundaries (e.g., upper and lower cross-walls) can tune the orientation of an ordered array to a direction transverse to elongation; how changes in dynamic instability parameters, such as in mor1-1 mutants, can impede self-organization, in agreement with experimental data; increased entrainment, as seen in clasp-1 mutants, conserves self-organization, but delays its onset and fails to demonstrate increased ordering; and how branched nucleation at acute angles off existing microtubules results in distinctive sparse arrays. Our simulations are leading us to several testable predictions, including the effects of reduced microtubule severing in katanin mutants. Further, although the cell-wide self-organization is being studied by several research groups in addition to ours, less emphasis has been placed on explaining the interactions mechanistically from the molecular scale. I am developing models for microtubule-cortex anchoring and collision-based interactions between microtubules, based on a competition between crosslinker bonding, microtubule bending and microtubule polymerization. We are addressing how a higher probability of entrainment at smaller collision angles and at longer unanchored lengths of plus-ends; and the source of observed differences between collision resolutions in various cell types, including Arabidopsis cells and Tobacco cells.