A solution of pure $\alpha \beta$ -tubulin dimers is thought to nucleate microtubules by forming a linear protofilament about seven dimers in length. At that point, the probabilities that the next $\alpha \beta$ -dimer will bind laterally or to the end of the protofilament are about equal. The critical event for microtubule formation is thought to be the first lateral association (Figure $Q16-1$ ). How does lateral association promote the subsequent rapid formation of a microtubule?

Step by Step Solution: Step 1. Lateral association occurs between $\alpha \beta$ -tubulin dimers in the linear protofilament. Step 2. This causes a conformational change in the $\alpha \beta$ -tubulin dimer, leading to the formation of a curved protofilament structure. Step 3. The curved protofilament structure can further associate with other $\alpha \beta$ -tubulin dimers to generate a complete ring structure. Step 4. The ring structure can begin to close and form a hollow tubular structure, which allows for more efficient assembly of additional $\alpha \beta$ -tubulin dimers, eventually leading to the rapid formation of a microtubule. Step 5. The microtubule can further undergo structural modifications to generate functional microtubule networks that serve various physiological roles in the cell. Final Answer: Lateral association of $\alpha \beta$ -tubulin dimers in the linear protofilament promotes the rapid formation of a microtubule by generating a curved protofilament structure, which can form a complete ring structure that closes to form a hollow tubular structure, allowing for efficient assembly of additional $\alpha \beta$ -tubulin dimers.