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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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Related in: MedlinePlus

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.
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pcbi-1000255-g009: 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.

Mentions: This regime occurs at the early stage of MT assembly when the mean MT length (L) is very short (L<λ∼100 nm for UC≈−1.2 KBT using equ. C2 and C3 in Text S3 with e = 4 nm, a = 12 nm, D3 = D2), which corresponds to the elongation step just after nucleation. Provided that MT is shorter than the diffusion length λ, every time a free tubulin touches the MT surface via 3D diffusion, it is able to find its binding sites at the MT extremities via sliding:(2)The diffusion to the MT ends does not apparently depend on the attraction energy but the influence of UC is to set the critical length λ (see equ.C2 and C3 in  Text S3) up to which we quit the Regime I. As λ is longer for stronger attraction, it indicates that regime I is valid for longer MTs under such conditions. It thus results in a highly beneficial effect of facilitated diffusion since the diffusion to the MT ends increases proportionally to L (see Figure 9A). We also note that λ scales like D23/4 (see equ.C2  Text S3). A decrease of D2 due to surface friction (strong attraction) on MT surface could then restrict the domain of validity of Regime I to shorter microtubules. Consequently, facilitated elongation loses part of its effectiveness (see Figure 9B). Let us remark that D2 is a difficult parameter to estimate 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 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.
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2599886&req=5

pcbi-1000255-g009: 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.
Mentions: This regime occurs at the early stage of MT assembly when the mean MT length (L) is very short (L<λ∼100 nm for UC≈−1.2 KBT using equ. C2 and C3 in Text S3 with e = 4 nm, a = 12 nm, D3 = D2), which corresponds to the elongation step just after nucleation. Provided that MT is shorter than the diffusion length λ, every time a free tubulin touches the MT surface via 3D diffusion, it is able to find its binding sites at the MT extremities via sliding:(2)The diffusion to the MT ends does not apparently depend on the attraction energy but the influence of UC is to set the critical length λ (see equ.C2 and C3 in  Text S3) up to which we quit the Regime I. As λ is longer for stronger attraction, it indicates that regime I is valid for longer MTs under such conditions. It thus results in a highly beneficial effect of facilitated diffusion since the diffusion to the MT ends increases proportionally to L (see Figure 9A). We also note that λ scales like D23/4 (see equ.C2  Text S3). A decrease of D2 due to surface friction (strong attraction) on MT surface could then restrict the domain of validity of Regime I to shorter microtubules. Consequently, facilitated elongation loses part of its effectiveness (see Figure 9B). Let us remark that D2 is a difficult parameter to estimate 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