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Microtubules (MTs) are tubulin polymers whose dynamic instability is essential for many cellular processes. The propensity of tubulins to polymerize into MTs depends on an associated nucleotide: GTP vs. GDP. However, despite decades of research, it remains unclear how and to what extent the nucleotides affect tubulin conformation and/or inter-tubulin bonds. Using cryo electron tomography, we have recently shown that the tips of growing and shortening MTs both exhibit curved protofilaments (PFs) of very similar curvatures. Based on that observation, we have proposed a Brownian dynamics model and a new mechanism for MT assembly in which MT elongation results from the straightening of curved GTP-bound PFs due to thermal fluctuations and the formation of lateral bonds between tubulins in adjacent PFs. Here we provide both experimental and theoretical evidence supporting that model. We have examined model behavior as a function of its key parameters, such as tubulin bending stiffness, the strengths of lateral and longitudinal bonds, and the concentration of soluble tubulin. Calibrated, the model correctly describes the amount of force that can be generated by a single MT and the dependence of MT assembly rate on soluble tubulin concentration. The shapes and lengths of PFs at growing MT tips are strikingly similar at different tubulin concentrations – a model prediction that we have verified by cryo-electron tomography. Modest changes in lateral bonds between tubulins in simulations are sufficient to drive a switch from assembly to disassembly, whereas the longitudinal bonds largely determine the lengths of curved PFs at the MT tip. This revised view of growing MT tip structure and MT dynamics has important implications for our understanding of MT regulation and the mechanics of MT attachment to kinetochores.