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Stress generation and filament turnover during actin ring constriction.

Zumdieck A, Kruse K, Bringmann H, Hyman AA, Jülicher F - PLoS ONE (2007)

Bottom Line: We present a physical analysis of the dynamics and mechanics of contractile actin rings.In particular, we analyze the dynamics of ring contraction during cytokinesis in the Caenorhabditis elegans embryo.We show that on a microscopic level contractile stresses can result from both the action of motor proteins, which cross-link filaments, and from the polymerization and depolymerization of filaments in the presence of end-tracking cross-linkers.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.

ABSTRACT
We present a physical analysis of the dynamics and mechanics of contractile actin rings. In particular, we analyze the dynamics of ring contraction during cytokinesis in the Caenorhabditis elegans embryo. We present a general analysis of force balances and material exchange and estimate the relevant parameter values. We show that on a microscopic level contractile stresses can result from both the action of motor proteins, which cross-link filaments, and from the polymerization and depolymerization of filaments in the presence of end-tracking cross-linkers.

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Stress generation in a bundle of treadmilling filaments and passive cross-linkers in the absence of motor proteins.(A) Three stages of the treadmiling of a pair of anti-parallel filaments. The arrows at the filament ends indicate that monomers are added at the plus ends and removed from the minus ends. As a consequence of treadmilling, in the absence of cross-linkers, the centers of mass of the filaments move relative to each other. At the same time, fixed subunits along the filaments do not move. Stresses can be generated if filaments are linked by passive cross-linkers, which have the ability to bind to filaments and also stay attached to depolymerizing filament ends (end-tracking cross-linkers). No stress is generated if monomers are cross-linked along filaments since these monomers do not move (left). As soon as one depolymerizing filament end is linked to the second filament by a cross-linker (middle), both filaments are physically moved relative to each other by depolymerization forces. This leads to a stress profile along the filament pair with positive (contractile) stress (middle and right). This process therefore contributes to contractile average bundle stress if many filament pairs are interacting in a filament bundle. Note that this is different from stress generation by motors, where anti-parallel filaments do not contribute to stress. (B) Stress profiles for a pair of treadmiling filaments that are arranged in parallel. Again, if a depolymerizing end of one filament is linked to the second filament, relative sliding occurs which is driven by filament depolymerization. The resulting stress is positive (contractile).
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pone-0000696-g004: Stress generation in a bundle of treadmilling filaments and passive cross-linkers in the absence of motor proteins.(A) Three stages of the treadmiling of a pair of anti-parallel filaments. The arrows at the filament ends indicate that monomers are added at the plus ends and removed from the minus ends. As a consequence of treadmilling, in the absence of cross-linkers, the centers of mass of the filaments move relative to each other. At the same time, fixed subunits along the filaments do not move. Stresses can be generated if filaments are linked by passive cross-linkers, which have the ability to bind to filaments and also stay attached to depolymerizing filament ends (end-tracking cross-linkers). No stress is generated if monomers are cross-linked along filaments since these monomers do not move (left). As soon as one depolymerizing filament end is linked to the second filament by a cross-linker (middle), both filaments are physically moved relative to each other by depolymerization forces. This leads to a stress profile along the filament pair with positive (contractile) stress (middle and right). This process therefore contributes to contractile average bundle stress if many filament pairs are interacting in a filament bundle. Note that this is different from stress generation by motors, where anti-parallel filaments do not contribute to stress. (B) Stress profiles for a pair of treadmiling filaments that are arranged in parallel. Again, if a depolymerizing end of one filament is linked to the second filament, relative sliding occurs which is driven by filament depolymerization. The resulting stress is positive (contractile).

Mentions: The polymerization and depolymerization of filaments can also generate forces [24], [25]. In a filament bundle this can contribute to stress generation if end-tracking cross-linker are present [26]. Such proteins can bind along filaments and stay bound to depolymerizing filament ends for some time, Fig. 4A. Such forces might be important for cytokinesis in particular in the absence of myosin II motors [27]. We can extend our description to include filament treadmilling and the role of end-tracking cross-linkers. Treadmilling leads to spontaneous motion of filaments with respect to the surrounding fluid, even in the absence of interactions with other filaments. In the presence of end-tracking cross-linkers, treadmilling can induce relative sliding between filaments of the same and opposite orientation, see Fig. 4. Simulating this dynamics analogously to the case of motor-induced filament sliding, we find again cases of stable homogenous bundles and cases where homogeneous bundles are unstable and complex dynamics emerges. The critical value of the interaction strength α̅′ mediated by end-tracking cross-linkers depends on the treadmilling velocity v and the interaction strength of filaments of opposite orientation. Remarkably, even in a homogenous bundle the interaction between anti-parallel filaments now leads to a net contractile stress, see Fig. 4.


Stress generation and filament turnover during actin ring constriction.

Zumdieck A, Kruse K, Bringmann H, Hyman AA, Jülicher F - PLoS ONE (2007)

Stress generation in a bundle of treadmilling filaments and passive cross-linkers in the absence of motor proteins.(A) Three stages of the treadmiling of a pair of anti-parallel filaments. The arrows at the filament ends indicate that monomers are added at the plus ends and removed from the minus ends. As a consequence of treadmilling, in the absence of cross-linkers, the centers of mass of the filaments move relative to each other. At the same time, fixed subunits along the filaments do not move. Stresses can be generated if filaments are linked by passive cross-linkers, which have the ability to bind to filaments and also stay attached to depolymerizing filament ends (end-tracking cross-linkers). No stress is generated if monomers are cross-linked along filaments since these monomers do not move (left). As soon as one depolymerizing filament end is linked to the second filament by a cross-linker (middle), both filaments are physically moved relative to each other by depolymerization forces. This leads to a stress profile along the filament pair with positive (contractile) stress (middle and right). This process therefore contributes to contractile average bundle stress if many filament pairs are interacting in a filament bundle. Note that this is different from stress generation by motors, where anti-parallel filaments do not contribute to stress. (B) Stress profiles for a pair of treadmiling filaments that are arranged in parallel. Again, if a depolymerizing end of one filament is linked to the second filament, relative sliding occurs which is driven by filament depolymerization. The resulting stress is positive (contractile).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC1936222&req=5

pone-0000696-g004: Stress generation in a bundle of treadmilling filaments and passive cross-linkers in the absence of motor proteins.(A) Three stages of the treadmiling of a pair of anti-parallel filaments. The arrows at the filament ends indicate that monomers are added at the plus ends and removed from the minus ends. As a consequence of treadmilling, in the absence of cross-linkers, the centers of mass of the filaments move relative to each other. At the same time, fixed subunits along the filaments do not move. Stresses can be generated if filaments are linked by passive cross-linkers, which have the ability to bind to filaments and also stay attached to depolymerizing filament ends (end-tracking cross-linkers). No stress is generated if monomers are cross-linked along filaments since these monomers do not move (left). As soon as one depolymerizing filament end is linked to the second filament by a cross-linker (middle), both filaments are physically moved relative to each other by depolymerization forces. This leads to a stress profile along the filament pair with positive (contractile) stress (middle and right). This process therefore contributes to contractile average bundle stress if many filament pairs are interacting in a filament bundle. Note that this is different from stress generation by motors, where anti-parallel filaments do not contribute to stress. (B) Stress profiles for a pair of treadmiling filaments that are arranged in parallel. Again, if a depolymerizing end of one filament is linked to the second filament, relative sliding occurs which is driven by filament depolymerization. The resulting stress is positive (contractile).
Mentions: The polymerization and depolymerization of filaments can also generate forces [24], [25]. In a filament bundle this can contribute to stress generation if end-tracking cross-linker are present [26]. Such proteins can bind along filaments and stay bound to depolymerizing filament ends for some time, Fig. 4A. Such forces might be important for cytokinesis in particular in the absence of myosin II motors [27]. We can extend our description to include filament treadmilling and the role of end-tracking cross-linkers. Treadmilling leads to spontaneous motion of filaments with respect to the surrounding fluid, even in the absence of interactions with other filaments. In the presence of end-tracking cross-linkers, treadmilling can induce relative sliding between filaments of the same and opposite orientation, see Fig. 4. Simulating this dynamics analogously to the case of motor-induced filament sliding, we find again cases of stable homogenous bundles and cases where homogeneous bundles are unstable and complex dynamics emerges. The critical value of the interaction strength α̅′ mediated by end-tracking cross-linkers depends on the treadmilling velocity v and the interaction strength of filaments of opposite orientation. Remarkably, even in a homogenous bundle the interaction between anti-parallel filaments now leads to a net contractile stress, see Fig. 4.

Bottom Line: We present a physical analysis of the dynamics and mechanics of contractile actin rings.In particular, we analyze the dynamics of ring contraction during cytokinesis in the Caenorhabditis elegans embryo.We show that on a microscopic level contractile stresses can result from both the action of motor proteins, which cross-link filaments, and from the polymerization and depolymerization of filaments in the presence of end-tracking cross-linkers.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.

ABSTRACT
We present a physical analysis of the dynamics and mechanics of contractile actin rings. In particular, we analyze the dynamics of ring contraction during cytokinesis in the Caenorhabditis elegans embryo. We present a general analysis of force balances and material exchange and estimate the relevant parameter values. We show that on a microscopic level contractile stresses can result from both the action of motor proteins, which cross-link filaments, and from the polymerization and depolymerization of filaments in the presence of end-tracking cross-linkers.

Show MeSH
Related in: MedlinePlus