We developed a kinetic model for microtubule elongation and altered it to explore models for the polymerase. (A) Cartoon of the cylindrical microtubule (left; pink and green spheres represent α- and β-tubulin, respectively) alongside a two-dimensional representation of the MT lattice (gray boxes, right; the darker boxes represent the microtubule ‘seed’ used to template elongation in our simulations). (B) The model parameterizes all six possible neighbor states for αβ-tubulin in the lattice, but the two that dominate the elongation behavior are the longitudinal (top left) and corner (top right) interactions. (C) A grid search identified parameters capable of recapitulating the concentration dependence of microtubule elongation rates in the presence of GMPCPP. The black line summarizes the trend from experimental observations (Brouhard et al., 2008; Gardner et al., 2011); red dots represent the results from our simulations. Using a kon of 4 × 106 M−1s−1, we obtained a good match to observed growth rates from KDlong = 8 mM and KDcorner = 33 nM. (D) (left) Cartoon illustrating the tethering model, with the polymerase (TOG domains in blue, basic region in red) localized to a curved αβ-tubulin bound at the MT end by pure longitudinal association, (middle) simulated growth rates obtained at increasing association rates for the tethered αβ-tubulin. Enhanced trapping of longitudinally-associated αβ-tubulin through the tethering effect shows catalyst-like activity: growth rates and apparent on-rate constant (slope) both change significantly but the apparent equilibrium for growth (x-intercept) does not. (right) Plot of fold increase in growth rate vs the fold increase in tethered αβ-tubulin association rate, using values at 0.5 μM αβ-tubulin concentration as a reference (black dots; the black line shows the fit of a hyperbolic curve to the growth rates). The model for the polymerase gives a relatively modest change in growth rates compared to the fold-increase in tethered association rate. Simulations with progressively stronger (dark green: 1.7 mM; light green, 0.35 mM) longitudinal interactions show higher maximal polymerase activity. The polymerase activity is related to the population of longitudinally-associated αβ-tubulin at the MT end. (E) Examining an alternative tethering model in which the polymerase promotes incorporation at a ‘corner’ site. This model yields much greater stimulation of elongation (middle) because there is always at least one corner site at the microtubule end. The predicted response also does not appear to saturate with increased tethering effect (right, linear fit). This alternative model does not describe the polymerase action because it fails to produce catalyst-like output.