Polyamine Sharing between Tubulin Dimers Favours Microtubule Nucleation and Elongation via Facilitated Diffusion
Figure 9
Effects of facilitated diffusion on elongation.
(A) Facilitated diffusion of free GTP-tubulin to the MT ends versus mean MT lengths for different absorption energies (UC). For Uc = −0.1 KBT, the effect of facilitated diffusion can be neglected. For Uc = −1 and −2.5 KBT, diffusion of tubulin to the MT ends is facilitated by sliding. When the MTs are short i.e. at the early stage of MT polymerization, the regime I prevails, which is characterized by an increase of Jfacilitated with MT length. For longer MTs, for example L>0.1 µm for Uc = −1 KBT, the facilitated diffusion is not increasing with L anymore (Regime II). The sharp decrease of Jfacilitated when MT length approaches its maximum length (10 µm) is due to the low free GTP-tubulin concentration near the plateau of the assembly curve. The regime III occurs for Uc = −6 KBT and we can observe a rapid decrease of Jfacilitated with L. It is worth noting that we plotted the average values of the facilitated diffusion to the MT ends versus the average length of the MTs. In other words, it should not be confused with the elongation rate of individual MT. Parameters: Lmaximun = 10 µm, [tubulin] = 15 µM, D3 = D2 = 5.10−12 m2s−1, e = 4 nm. (B) In (A), we assumed that D3 = D2. The benefit of facilitated diffusion was then maximum. If we now consider that D2/D3 = 0.3 or D2/D3 = 0.1 due to hindered diffusion on microtubules, we observe that the transition from regime I to regime II will arise at shorter L values. This partly inhibits the beneficial effect of facilitated diffusion of the elongation rate. D3 = 5.10−12 m2s−1. (C) Simple model of microtubule assembly versus incubation time for three attraction energies, which points out the influence of facilitated diffusion on the MT elongation. For this purpose, it is arbitrary assumed that the mean number of MT nuclei is the same for the three different conditions (see Text S3). It can be though as the last part of the light scattering curve, after the inflexion point, which is more elongation-sensitive. In addition, we assume that the elongation rate is proportional to the difference (Jfacilitated -J0), where J0 is the critical flux of GTP tubulin for which the elongation rate equals the shortening rate. Indeed it is has been shown both experimentally and theoretically that increasing the GTP-tubulin concentration above the critical concentration leads to a linear increase of the mean elongation rate [45]. This figure shows that facilitated elongation of MTs through GTP-tubulin sliding both results in a higher amount of polymerized tubulins and a more abrupt slope near the plateau value. Parameters: J0 = 5000 s−1; e = 4 nm; [tubulin] = 15 µM; D3 = D2 = 5.10−12 m2s−1; a = 12 nm.