Figure 1.
Schematic representation of the mechanism of facilitated diffusion.
(A) Attraction between two tubulin heterodimers mediated by polyamines. The attraction is mediated by the two C-terminal tails of one tubulin dimer, which, for entropic reasons (separation distance between the two C-termini tails on a tubulin dimer), are likely to share polyamines with two C-terminal tails of another tubulin dimer. (B) In the absence of an attraction force, many collisions between tubulin and nucleus do not result in association, whereas, in the presence of an attraction force, both facilitated diffusion via sliding and an increase of the interaction lifetime favour association to the growing nucleus. (C) In the presence of an attraction force, sliding of tubulin along the cylindrical surface of MT favours tubulin association to the MT ends.
Figure 2.
AFM images of microtubules assembled in the presence of various concentrations of spermidine in buffer M with 30 µM tubulin.
Scan area: 8×8 µm2. (A) Control. (B) 200 µM spermidine. (C) 800 µM spermidine. Microtubules formed in the presence of moderate concentrations of spermidine (<400 µm) had a normal appearance without any tendency for bundling. Higher spermidine concentrations lead to the apparition of shorter MTs and some aberrant structures (oligomers, aggregates, see also Figure 3).
Figure 3.
High resolution AFM images of microtubules in the presence of spermidine in buffer M.
Scan area: 4×4 µm2. (A) 200 µM spermidine. (B) 800 µM spermidine. At moderate spermidine concentrations (<400 µM), long microtubules coexist with free tubulin dimers like in the absence of polyamines. Increasing polyamine concentration leads to the appearance of small tubulin oligomers or aggregates (green circles), microtubule bundles (arrow) and smaller microtubules. Interestingly oligomers or aggregates can also be adsorbed on MT surface (pink circles), as predicted for strong attractions (Regime III).
Figure 4.
Effect of polyamines on the maximum slope of microtubule assembly.
The tubulin concentration (12 µM) was purposely fixed to a value near the critical concentration in buffer M. (A) Both spermidine and spermine promote microtubule assembly at submilimolar concentrations whereas putrescine is unable to improve tubulin polymerization even at large concentrations (>1 mM). However, at high concentrations of spermidine and spermine (>200 µM), tubulin aggregates are formed which lowers the apparent assembly slope leading to a bell-shape profile. (B) SDS page analyses reveal that spermidine gradually increases the pellet mass. As observed by AFM, the increase of the pellet mass is due to microtubule formation at moderate spermidine concentrations (25–200 µM) but, at higher spermidine concentrations (0.5–2 mM), oligomers and (or) tubulin aggregates are also observed and participate to the increase of the pellet mass. The dashed line represents the transition between the zones of microtubule assembly and tubulin aggregation.
Figure 5.
Effect of the competition between monovalent cations and multivalent polyamines on tubulin polymerization (50 mM MES-KOH pH 6.8, 1 mM EGTA, 30 µM tubulin, 2 mM MgCl2, 20% glycerol).
(A) Inhibition of the tubulin assembly with the increase of KCl concentration. (B) Effect of KCl on tubulin assembly in the presence of 100 µM spermidine. The beneficial effect of spermidine is inhibited for KCl concentrations larger than 50 mM. We attribute this phenomenon to the replacement of polyamines by monovalent cations on tubulin surface which then inhibits the attraction between tubulin dimers (see Text S2). (C) To keep a high assembly rate at high ionic strengths, polyamine concentrations can be increased so that polyamine surface density on tubulin surface remains nearly constant. (AFM control revealed the presence of only microtubules under such conditions.) (D) Influence of spermidine on S-tubulin assembly. In the absence of the C-terminal tail, the beneficial effect of polyamine on tubulin assembly disappears.
Figure 6.
Attraction of tubulin dimers onto microtubule mediated by spermidine.
0.3 µM of Cy3-labeled tubulin was allowed to interact with 4 µM of non fluorescent taxol-stabilized microtubules at various concentrations of spermidine (buffer M without GTP and without free taxol). The fluorescence intensity of both pellets and supernatants were then measured after centrifugation at 20,000×g for 10 min. The results show that Cy3-tubulin co-precipitated with microtubules at spermidine concentrations higher than 10 µM (under the conditions tested, we measured that no fluorescent tubulins sedimented in the absence of microtubules).
Figure 7.
Facilitated nucleation mediated by polyamines.
(A) Microtubules were assembled at various concentrations of tubulin with or without 100 µM spermidine at 37°C. (25 mM MES-KOH pH 6.8, 1 mM EGTA, 30 µM tubulin, 2 mM MgCl2, 20% glycerol). The samples were placed in a pre-warmed cuvette to initiate polymerization. (B) Log-log plot of tenth time versus tubulin concentrations extracted from (A). The experimental data are properly fitted by a straight line with a slope of −2.9 in the absence of spermidine. In contrast, in the presence of spermidine, the tenth time is nearly constant over a large range of tubulin concentration (20–40 µM), as represented by the horizontal line. Indeed the shortest nucleation duration is already reached at tubulin concentration larger than CL (∼20 µM) because of facilitated nucleation. For lower concentrations than CL, the tenth time increases sharply when the tubulin concentration decreases, as represented by the linear increase in the log–log plot.
Figure 8.
Scaling properties and nucleus size in the presence of spermidine.
Initial slope of log [(I(t)/I(∞)] versus tubulin concentration. This slope is an interesting indicator of the number of tubulin dimers in the critical nuclei. The mean slope over tubulin concentrations is similar with or without spermidine, 2.36 and 2.32 respectively. Spermidine may then not affect the critical size of the nucleus but this remains to be demonstrated with a valid theory. Inset: examples of log–log plot of [(I(t)/I(∞)]. The slopes were extracted at early times when the curves display a straight line.
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.
Figure 10.
Effect of spermidine on microtubule elongation.
(A) Pseudo-first order rate constant of elongation, Kobs, versus tubulin concentration in buffer M. 100 µM spermidine significantly increases the elongation rates whatever tubulin concentration. Inset: Log-plot of 1−I(t)/I(∞) versus time for 30 µM tubulin. The slope of this curve is −Kobs. The elongations rate is about three times higher with spermidine (except for 40 µM tubulin). (B) A microtubule solution was prepared by incubating 30 µM tubulin at 37°c for 1h in 50 mM MES-KOH pH 6.8, 1 mM EGTA, 2 mM MgCl2, 20% glycerol, 1 mM GTP. At the end of the incubation, 50 µl of a solution containing 30 µM of free tubulin dimers without or with 100 µM spermidine was then added to 50 µl of the microtubule solution. The sudden increase of the free tubulin concentration allows one to observe elongation of the preformed microtubule via light scattering. It turns out that the presence of 100 µM spermidine leads to a significant increase of the elongation rate as indicated by the slope of the assembly curve, which is 2.7 times higher with 100 µM spermidine (see dotted lines). The plateau value which is more rapidly reached in the presence of polyamines also evidences a facilitated elongation.
Figure 11.
Microtubule instability in the presence of polyamines.
To estimate the stability of microtubules, the time course of cold disassembly at 8°C of pre-assembled microtubules (35 µM tubulin) is reported in the presence or absence of 100 µM spermidine. The rate of disassembly is not affected by the presence of 100 µM polyamines whereas it is significantly reduced in the presence of 20 µM taxol, a well known stabilizing agent. These results are thus in agreement with our model since polyamines were not expected to significantly favor microtubule stability and thus should preserve microtubule dynamical instability.
Figure 12.
Influence of spermidine on MAPs-tubulin polymerization.
MAPs-tubulin (12 µM tubulin) was assembled into microtubules as described in materials and methods and then the tubulin content was examined in the supernatant (S) and the pellet (P) after high speed centrifugations. A volume of cold PBS (4°C) equal to that of supernatant was added to pellet. 8 µL of each solution were loaded. The addition of 200 µM spermidine increases the amount of polymerized tubulin even in the presence of MAPs. Furthermore a mixture of taxol and spermidine leads to an additional amount of polymerized tubulin. (M) Molecular weight markers.