Constriction of Actin Rings by Passive Crosslinkers

Alexander Cumberworth and Pieter Rein ten Wolde

Phys. Rev. Lett. 131, 038401 – Published 17 July 2023

Abstract

In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared with those of crosslinker-mediated microtubule sliding.

Received 4 March 2022
Accepted 6 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.038401

Physics Subject Headings (PhySH)

Biomechanics Cell division Cell mechanics Elastic forces Protein-protein interactions

Actin Cytoskeleton Filaments Proteins

Physics of Living SystemsPolymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Alexander Cumberworth ^* and Pieter Rein ten Wolde^†

AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands

^*alex@cumberworth.org
^†tenwolde@amolf.nl

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Issue

Vol. 131, Iss. 3 — 21 July 2023

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Images

Figure 1
(a) Diagram of a single overlap of length $L$ formed by two actin filaments. The half helical pitch determines the distance between crosslinking sites $δ_{d}$ rather than the monomer-monomer distance $δ_{s}$ . Filaments slide in increments of $δ_{s}$ , which requires a rotation of $2 π / 13$ . (b) Diagrams of a ring constricting to half its radius. The 2D diagrams use periodic boundary conditions. On the left, the ring is at its maximum radius $R_{\max}$ ; in the middle, it has constricted to three quarters of $R_{\max}$ ; on the right, it has reached its minimum radius $R_{\min} = R_{\max} / 2$ . In the top right, a 3D representation of the topology diagram in the center is given. In this example, the number of filaments in the scaffold ring $N_{sca}$ is 4, while the total number of filaments $N_{f}$ is 6. Note that while $N_{sca}$ is unique, the scaffold ring is not; here, it could instead be defined by filaments 1, 3, 5, and 6.
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Figure 2
Total free energy $Δ Φ$ and total force $F$ as a function of the ring radius. The blue stars indicate the points at which the free energy is minimal, and negative force values indicate a constricting force. In (a), $N_{sca} = 2$ , as per the topology depicted with both 2D periodic boundary conditions (i) and in 3D (ii); the free energies and total forces are then plotted for either a range of $N_{f}$ values [(iii) and (iv)] or a range of $L_{f}$ values [(v) and (vi)]. The constriction force increases linearly with $N_{f}$ . In (b), $N_{f} = 8$ , and the free energies (i) and total forces (ii) are plotted for three values of $N_{sca}$ (see Fig. S1 in the Supplemental Material [19] for associated topology diagrams). Connecting the filaments in series (large $N_{sca}$ ) increases the constriction range, while stacking them in parallel (small $N_{sca}$ ) increases the maximum constriction force. Data for all plots were produced with the parameters given in Table S1 of the Supplemental Material [19].
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Figure 3
Ring-constriction trajectories with $L_{f} = 3.0 μ m$ , $N_{sca} = 2$ , $N_{f} = 5$ , and three different values of $k$ . (a) Progress of radial constriction from its maximum ( $ϕ_{R} = 0$ ) to its equilibrium value ( $ϕ_{R} = 1$ ), where $ϕ_{R} = (R_{\max} - R) / (R_{\max} - R_{eq})$ . (b) Friction coefficient of an overlap in the ring. For numerical details and additional quantities, see Fig. S8(a) in the Supplemental Material [19]; for trajectories with values of $k$ down to $0.1 pN {nm}^{- 1}$ , see Fig. S11 in the Supplemental Material [19]. For the biologically relevant range of $k$ , constriction occurs on experimental timescales [16].
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