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Microtubules are polar structures, and this polarity is reflected in their biased directional growth. Following a convention established previously (G. G. Borisy, 1978, J. Mol. Biol. 124:565--570), we define the plus (+) and minus (-) ends of a microtubule as those equivalent in structural orientation to the distal and proximal ends, respectively, of the A subfiber of flagellar outer doublets. Rates of elongation were obtained for both ends using flagellar axonemes as seeds and porcine brain microtubule protein as subunits. Since the two ends of a flagellar seed are distinguishable morphologically, elongation of each end may be analyzed separately. By plotting rates of elongation at various concentrations of subunit protein, we have determined the association and dissociation rate constants for the plus and minus ends. Under our conditions at 30 degrees C, the association constants were 7.2 X 10(6) M-1 s-1 and 2.25 X 10(6) M-1 s-1 for the plus and minus ends, respectively, and the dissociation constants were 17 s-1 and 7 s-1. From these values and Wegner's equations (1976, J. Mol. Biol. 108:139--150), we identified the plus end of the microtubule as its head and calculated "s," the head-to-tail polymerization parameter. Surprisingly small values (s = 0.07 +/- 0.02) were found. The validity of models of mitosis based upon head-to-tail polymerization (Margolis et al., 1978, Nature (Lond.) 272:450--452) are discussed in light of a small value for s.

Head-to-tail polymerization of microtubules in vitro. Electron microscope analysis of seeded assembly.