Abstract

Microtubules (MTs) are small hollow tubes that are formed inside every eukaryote cell, and which help in preserving the cell’s structure, internal transport and cell division. Their dynamics show periods of slow growth with shorter periods of quick shrinkage in between.

The MT is made up of filaments that connect laterally to form a tube, an energetically unfavourable construction for the MT. We propose a structural cap to relax this configuration, by having a seam where the MT opens up to form a sheet. We have modelled the sheet as a slab of material that prefers to bend longitudinally and be straight laterally, using a simple finite model. We found that a structure like this, fixed at one side as a circle, has a minimal energy configuration in the shape of a sheet. Furthermore, we found that the configurational energy difference of the whole MT for the closure of a unit of the sheet will be smaller for a long sheet than for a shorter sheet.

The relation between sheet energy and its length is used in a thermodynamical simulation of the growth of the MT, based on the addition and closure of dimers. This model gives, depending on the value of the lateral contact energy, a clear image of how the sheet length behaves in time and sheds some light on how the shrinkage part of MT dynamics might be explained.