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After several decades of study, the mechanisms of microtubule (MT) growth and dynamic instability remain elusive. Evidence from early cryo EM revealed blunt ends on growing MTs and flared ends on shortening MTs. This suggested an elegant textbook model, in which GTP-tubulin is straight so it can assemble, while GDP-tubulin is intrinsically bent, so it is not stable within the MT lattice. However, further EM studies have reported a range of shapes on growing MT ends: gently curved PF bundles (‘tubulin sheets’) seen in vitro; flared or blunt tips, but not sheets on MTs growing in vivo. Moreover, recent X-ray, SAXS and allo-colchicine binding experiments have additionally challenged the classic model, indicating that both GTP- and GDP-tubulins are bent in solution. In this work we have imaged and quantitatively analyzed the shapes of growing and shortening MTs in vitro and in vivo in 6 species, using cryo EM tomography and rotational sampling. Our evidence suggests that MTs always grow with curved protofilaments (PFs) at their tips, offering a new mechanism of MT assembly, consistent with the latest structural findings about free tubulin shape. To investigate this novel MT growth pathway theoretically, we used Brownian dynamics modeling and found that MTs can elongate with curved PFs when lateral bonds are only slightly stronger than the energy required to straighten PFs. Curved PFs zip and unzip with very high frequency due to Brownian fluctuations. Changes in the lateral bonds of tubulin by only 1-2 kT were sufficient to switch MTs from growth to shortening in the model, providing an attractive mechanism for dynamic instability. A key prediction of the model is that MT growth rate depends linearly on tubulin concentration, while the lengths of curved PFs and overall PF shapes are not sensitive to the free tubulin concentration with negligible correlation between adjacent PFs shapes. We confirmed this prediction experimentally with cryo EM tomography.