Why does nucleation rate cause the number of microtubules to be proportional to nucleation rate but the length of microtubules to be in

Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
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Chapter1: The Human Body: An Orientation
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Why does nucleation rate cause the number of microtubules to be proportional to nucleation rate but the length of microtubules to be inversely proportional to nucleation rate?

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Microtubules are key elements in maintaining structural integrity, cell signalling, transport and cell divisions of the cell. Microtubulin grow or shrink in size by adding or removing tubulin proteins.  

Microtubules exhibit dynamic instability in the form of slow growth followed faster shortening

Microtubule nucleation starts the in vitro microtubule formation.  The growth of microtubules takes place by addition of GTP-bound αβ-tubulin heterodimers to their ends.

The pure GTP tubulin plays an important role in the assembly of the microtubules in the cell. This depends on exchange between soluble and polymeric tubulin pools. 

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