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Polyamine sharing between tubulin dimers favours microtubule nucleation and elongation via facilitated diffusion.

Mechulam A, Chernov KG, Mucher E, Hamon L, Curmi PA, Pastré D - PLoS Comput. Biol. (2009)

Bottom Line: We suggest for the first time that the action of multivalent cations on microtubule dynamics can result from facilitated diffusion of GTP-tubulin to the microtubule ends.The mechanism of facilitated diffusion requires an attraction force between two tubulins, which can result from the sharing of multivalent counterions.The results presented here show that polyamines can be of particular importance for the regulation of the microtubule network in vivo and provide the basis for further investigations into the effects of facilitated diffusion on cytoskeleton dynamics.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Structure-Activité des Biomolécules Normales et Pathologiques, Université Evry-Val d'Essonne, Evry, France.

ABSTRACT
We suggest for the first time that the action of multivalent cations on microtubule dynamics can result from facilitated diffusion of GTP-tubulin to the microtubule ends. Facilitated diffusion can promote microtubule assembly, because, upon encountering a growing nucleus or the microtubule wall, random GTP-tubulin sliding on their surfaces will increase the probability of association to the target sites (nucleation sites or MT ends). This is an original explanation for understanding the apparent discrepancy between the high rate of microtubule elongation and the low rate of tubulin association at the microtubule ends in the viscous cytoplasm. The mechanism of facilitated diffusion requires an attraction force between two tubulins, which can result from the sharing of multivalent counterions. Natural polyamines (putrescine, spermidine, and spermine) are present in all living cells and are potent agents to trigger tubulin self-attraction. By using an analytical model, we analyze the implication of facilitated diffusion mediated by polyamines on nucleation and elongation of microtubules. In vitro experiments using pure tubulin indicate that the promotion of microtubule assembly by polyamines is typical of facilitated diffusion. The results presented here show that polyamines can be of particular importance for the regulation of the microtubule network in vivo and provide the basis for further investigations into the effects of facilitated diffusion on cytoskeleton dynamics.

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Effects of facilitated diffusion on elongation.(A) Facilitated diffusion of free GTP-tubulin to the MT ends versusmean MT lengths for different absorption energies(UC). ForUc = −0.1KBT, the effect of facilitated diffusioncan be neglected. ForUc = −1 and−2.5 KBT, diffusion of tubulin tothe 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 ofJfacilitated with MT length. Forlonger MTs, for example L>0.1 µmfor Uc = −1KBT, the facilitated diffusion is notincreasing with L anymore (Regime II). The sharpdecrease of Jfacilitated when MT lengthapproaches its maximum length (10 µm) isdue to the low free GTP-tubulin concentration near the plateau ofthe assembly curve. The regime III occurs forUc = −6KBT and we can observe a rapid decreaseof Jfacilitated with L. It is worthnoting that we plotted the average values of the facilitateddiffusion to the MT ends versus the average length of the MTs. Inother words, it should not be confused with the elongation rate ofindividual MT. Parameters:Lmaximun = 10µm,[tubulin] = 15µM,D3 = D2 = 5.10−12m2s−1,e = 4 nm. (B) In (A),we assumed thatD3 = D2.The benefit of facilitated diffusion was then maximum. If we nowconsider thatD2/D3 = 0.3orD2/D3 = 0.1due to hindered diffusion on microtubules, we observe that thetransition from regime I to regime II will arise at shorterL values. This partly inhibits the beneficialeffect of facilitated diffusion of the elongation rate.D3 = 5.10−12m2s−1. (C) Simple model ofmicrotubule assembly versus incubation time for three attractionenergies, which points out the influence of facilitated diffusion onthe MT elongation. For this purpose, it is arbitrary assumed thatthe mean number of MT nuclei is the same for the three differentconditions (see Text S3). It can be though as thelast part of the light scattering curve, after the inflexion point,which is more elongation-sensitive. In addition, we assume that theelongation rate is proportional to the difference(Jfacilitated -J0),where J0 is the critical flux of GTPtubulin for which the elongation rate equals the shortening rate.Indeed it is has been shown both experimentally and theoreticallythat increasing the GTP-tubulin concentration above the criticalconcentration leads to a linear increase of the mean elongation rate[45]. This figure shows thatfacilitated elongation of MTs through GTP-tubulin sliding bothresults in a higher amount of polymerized tubulins and a more abruptslope near the plateau value. Parameters:J0 = 5000s−1;e = 4 nm;[tubulin] = 15µM;D3 = D2 = 5.10−12m2s−1;a = 12 nm.
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pcbi-1000255-g009: Effects of facilitated diffusion on elongation.(A) Facilitated diffusion of free GTP-tubulin to the MT ends versusmean MT lengths for different absorption energies(UC). ForUc = −0.1KBT, the effect of facilitated diffusioncan be neglected. ForUc = −1 and−2.5 KBT, diffusion of tubulin tothe 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 ofJfacilitated with MT length. Forlonger MTs, for example L>0.1 µmfor Uc = −1KBT, the facilitated diffusion is notincreasing with L anymore (Regime II). The sharpdecrease of Jfacilitated when MT lengthapproaches its maximum length (10 µm) isdue to the low free GTP-tubulin concentration near the plateau ofthe assembly curve. The regime III occurs forUc = −6KBT and we can observe a rapid decreaseof Jfacilitated with L. It is worthnoting that we plotted the average values of the facilitateddiffusion to the MT ends versus the average length of the MTs. Inother words, it should not be confused with the elongation rate ofindividual MT. Parameters:Lmaximun = 10µm,[tubulin] = 15µM,D3 = D2 = 5.10−12m2s−1,e = 4 nm. (B) In (A),we assumed thatD3 = D2.The benefit of facilitated diffusion was then maximum. If we nowconsider thatD2/D3 = 0.3orD2/D3 = 0.1due to hindered diffusion on microtubules, we observe that thetransition from regime I to regime II will arise at shorterL values. This partly inhibits the beneficialeffect of facilitated diffusion of the elongation rate.D3 = 5.10−12m2s−1. (C) Simple model ofmicrotubule assembly versus incubation time for three attractionenergies, which points out the influence of facilitated diffusion onthe MT elongation. For this purpose, it is arbitrary assumed thatthe mean number of MT nuclei is the same for the three differentconditions (see Text S3). It can be though as thelast part of the light scattering curve, after the inflexion point,which is more elongation-sensitive. In addition, we assume that theelongation rate is proportional to the difference(Jfacilitated -J0),where J0 is the critical flux of GTPtubulin for which the elongation rate equals the shortening rate.Indeed it is has been shown both experimentally and theoreticallythat increasing the GTP-tubulin concentration above the criticalconcentration leads to a linear increase of the mean elongation rate[45]. This figure shows thatfacilitated elongation of MTs through GTP-tubulin sliding bothresults in a higher amount of polymerized tubulins and a more abruptslope near the plateau value. Parameters:J0 = 5000s−1;e = 4 nm;[tubulin] = 15µM;D3 = D2 = 5.10−12m2s−1;a = 12 nm.

Mentions: This regime occurs at the early stage of MT assembly when the mean MT length(L) is very short(L<λ∼100 nm forUC≈−1.2 KBT using equ. C2 and C3in Text S3 with e = 4 nm,a = 12 nm,D3 = D2),which corresponds to the elongation step just after nucleation. Providedthat MT is shorter than the diffusion length λ,every time a free tubulin touches the MT surface via 3D diffusion, it isable to find its binding sites at the MT extremities via sliding:(2)The diffusion to the MT ends does not apparently depend onthe attraction energy but the influence of UC isto set the critical length λ (see equ.C2and C3 in TextS3) up to which we quit the Regime I. As λis longer for stronger attraction, it indicates that regime I isvalid for longer MTs under such conditions. It thus results in a highlybeneficial effect of facilitated diffusion since the diffusion to the MTends increases proportionally to L (see Figure 9A). We also notethat λ scales likeD23/4 (see equ.C2 TextS3). A decrease of D2 due to surfacefriction (strong attraction) on MT surface could thenrestrict the domain of validity of Regime I to shorter microtubules.Consequently, facilitated elongation loses part of its effectiveness (seeFigure 9B). Let usremark that D2 is a difficult parameter toestimate theoretically and to measure experimentally.


Polyamine sharing between tubulin dimers favours microtubule nucleation and elongation via facilitated diffusion.

Mechulam A, Chernov KG, Mucher E, Hamon L, Curmi PA, Pastré D - PLoS Comput. Biol. (2009)

Effects of facilitated diffusion on elongation.(A) Facilitated diffusion of free GTP-tubulin to the MT ends versusmean MT lengths for different absorption energies(UC). ForUc = −0.1KBT, the effect of facilitated diffusioncan be neglected. ForUc = −1 and−2.5 KBT, diffusion of tubulin tothe 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 ofJfacilitated with MT length. Forlonger MTs, for example L>0.1 µmfor Uc = −1KBT, the facilitated diffusion is notincreasing with L anymore (Regime II). The sharpdecrease of Jfacilitated when MT lengthapproaches its maximum length (10 µm) isdue to the low free GTP-tubulin concentration near the plateau ofthe assembly curve. The regime III occurs forUc = −6KBT and we can observe a rapid decreaseof Jfacilitated with L. It is worthnoting that we plotted the average values of the facilitateddiffusion to the MT ends versus the average length of the MTs. Inother words, it should not be confused with the elongation rate ofindividual MT. Parameters:Lmaximun = 10µm,[tubulin] = 15µM,D3 = D2 = 5.10−12m2s−1,e = 4 nm. (B) In (A),we assumed thatD3 = D2.The benefit of facilitated diffusion was then maximum. If we nowconsider thatD2/D3 = 0.3orD2/D3 = 0.1due to hindered diffusion on microtubules, we observe that thetransition from regime I to regime II will arise at shorterL values. This partly inhibits the beneficialeffect of facilitated diffusion of the elongation rate.D3 = 5.10−12m2s−1. (C) Simple model ofmicrotubule assembly versus incubation time for three attractionenergies, which points out the influence of facilitated diffusion onthe MT elongation. For this purpose, it is arbitrary assumed thatthe mean number of MT nuclei is the same for the three differentconditions (see Text S3). It can be though as thelast part of the light scattering curve, after the inflexion point,which is more elongation-sensitive. In addition, we assume that theelongation rate is proportional to the difference(Jfacilitated -J0),where J0 is the critical flux of GTPtubulin for which the elongation rate equals the shortening rate.Indeed it is has been shown both experimentally and theoreticallythat increasing the GTP-tubulin concentration above the criticalconcentration leads to a linear increase of the mean elongation rate[45]. This figure shows thatfacilitated elongation of MTs through GTP-tubulin sliding bothresults in a higher amount of polymerized tubulins and a more abruptslope near the plateau value. Parameters:J0 = 5000s−1;e = 4 nm;[tubulin] = 15µM;D3 = D2 = 5.10−12m2s−1;a = 12 nm.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
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pcbi-1000255-g009: Effects of facilitated diffusion on elongation.(A) Facilitated diffusion of free GTP-tubulin to the MT ends versusmean MT lengths for different absorption energies(UC). ForUc = −0.1KBT, the effect of facilitated diffusioncan be neglected. ForUc = −1 and−2.5 KBT, diffusion of tubulin tothe 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 ofJfacilitated with MT length. Forlonger MTs, for example L>0.1 µmfor Uc = −1KBT, the facilitated diffusion is notincreasing with L anymore (Regime II). The sharpdecrease of Jfacilitated when MT lengthapproaches its maximum length (10 µm) isdue to the low free GTP-tubulin concentration near the plateau ofthe assembly curve. The regime III occurs forUc = −6KBT and we can observe a rapid decreaseof Jfacilitated with L. It is worthnoting that we plotted the average values of the facilitateddiffusion to the MT ends versus the average length of the MTs. Inother words, it should not be confused with the elongation rate ofindividual MT. Parameters:Lmaximun = 10µm,[tubulin] = 15µM,D3 = D2 = 5.10−12m2s−1,e = 4 nm. (B) In (A),we assumed thatD3 = D2.The benefit of facilitated diffusion was then maximum. If we nowconsider thatD2/D3 = 0.3orD2/D3 = 0.1due to hindered diffusion on microtubules, we observe that thetransition from regime I to regime II will arise at shorterL values. This partly inhibits the beneficialeffect of facilitated diffusion of the elongation rate.D3 = 5.10−12m2s−1. (C) Simple model ofmicrotubule assembly versus incubation time for three attractionenergies, which points out the influence of facilitated diffusion onthe MT elongation. For this purpose, it is arbitrary assumed thatthe mean number of MT nuclei is the same for the three differentconditions (see Text S3). It can be though as thelast part of the light scattering curve, after the inflexion point,which is more elongation-sensitive. In addition, we assume that theelongation rate is proportional to the difference(Jfacilitated -J0),where J0 is the critical flux of GTPtubulin for which the elongation rate equals the shortening rate.Indeed it is has been shown both experimentally and theoreticallythat increasing the GTP-tubulin concentration above the criticalconcentration leads to a linear increase of the mean elongation rate[45]. This figure shows thatfacilitated elongation of MTs through GTP-tubulin sliding bothresults in a higher amount of polymerized tubulins and a more abruptslope near the plateau value. Parameters:J0 = 5000s−1;e = 4 nm;[tubulin] = 15µM;D3 = D2 = 5.10−12m2s−1;a = 12 nm.
Mentions: This regime occurs at the early stage of MT assembly when the mean MT length(L) is very short(L<λ∼100 nm forUC≈−1.2 KBT using equ. C2 and C3in Text S3 with e = 4 nm,a = 12 nm,D3 = D2),which corresponds to the elongation step just after nucleation. Providedthat MT is shorter than the diffusion length λ,every time a free tubulin touches the MT surface via 3D diffusion, it isable to find its binding sites at the MT extremities via sliding:(2)The diffusion to the MT ends does not apparently depend onthe attraction energy but the influence of UC isto set the critical length λ (see equ.C2and C3 in TextS3) up to which we quit the Regime I. As λis longer for stronger attraction, it indicates that regime I isvalid for longer MTs under such conditions. It thus results in a highlybeneficial effect of facilitated diffusion since the diffusion to the MTends increases proportionally to L (see Figure 9A). We also notethat λ scales likeD23/4 (see equ.C2 TextS3). A decrease of D2 due to surfacefriction (strong attraction) on MT surface could thenrestrict the domain of validity of Regime I to shorter microtubules.Consequently, facilitated elongation loses part of its effectiveness (seeFigure 9B). Let usremark that D2 is a difficult parameter toestimate theoretically and to measure experimentally.

Bottom Line: We suggest for the first time that the action of multivalent cations on microtubule dynamics can result from facilitated diffusion of GTP-tubulin to the microtubule ends.The mechanism of facilitated diffusion requires an attraction force between two tubulins, which can result from the sharing of multivalent counterions.The results presented here show that polyamines can be of particular importance for the regulation of the microtubule network in vivo and provide the basis for further investigations into the effects of facilitated diffusion on cytoskeleton dynamics.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire Structure-Activité des Biomolécules Normales et Pathologiques, Université Evry-Val d'Essonne, Evry, France.

ABSTRACT
We suggest for the first time that the action of multivalent cations on microtubule dynamics can result from facilitated diffusion of GTP-tubulin to the microtubule ends. Facilitated diffusion can promote microtubule assembly, because, upon encountering a growing nucleus or the microtubule wall, random GTP-tubulin sliding on their surfaces will increase the probability of association to the target sites (nucleation sites or MT ends). This is an original explanation for understanding the apparent discrepancy between the high rate of microtubule elongation and the low rate of tubulin association at the microtubule ends in the viscous cytoplasm. The mechanism of facilitated diffusion requires an attraction force between two tubulins, which can result from the sharing of multivalent counterions. Natural polyamines (putrescine, spermidine, and spermine) are present in all living cells and are potent agents to trigger tubulin self-attraction. By using an analytical model, we analyze the implication of facilitated diffusion mediated by polyamines on nucleation and elongation of microtubules. In vitro experiments using pure tubulin indicate that the promotion of microtubule assembly by polyamines is typical of facilitated diffusion. The results presented here show that polyamines can be of particular importance for the regulation of the microtubule network in vivo and provide the basis for further investigations into the effects of facilitated diffusion on cytoskeleton dynamics.

Show MeSH
Related in: MedlinePlus