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. 2015 May 5;108(9):2270-81.
doi: 10.1016/j.bpj.2015.03.058.

Mechanical heterogeneity favors fragmentation of strained actin filaments

Enrique M De La Cruz  1 , Jean-Louis Martiel  2 , Laurent Blanchoin  3
Affiliations

Mechanical heterogeneity favors fragmentation of strained actin filaments

Enrique M De La Cruz et al. Biophys J. .

Abstract

We present a general model of actin filament deformation and fragmentation in response to compressive forces. The elastic free energy density along filaments is determined by their shape and mechanical properties, which were modeled in terms of bending, twisting, and twist-bend coupling elasticities. The elastic energy stored in filament deformation (i.e., strain) tilts the fragmentation-annealing reaction free-energy profile to favor fragmentation. The energy gradient introduces a local shear force that accelerates filament intersubunit bond rupture. The severing protein, cofilin, renders filaments more compliant in bending and twisting. As a result, filaments that are partially decorated with cofilin are mechanically heterogeneous (i.e., nonuniform) and display asymmetric shape deformations and energy profiles distinct from mechanically homogenous (i.e., uniform), bare actin, or saturated cofilactin filaments. The local buckling strain depends on the relative size of the compliant segment as well as the bending and twisting rigidities of flanking regions. Filaments with a single bare/cofilin-decorated boundary localize energy and force adjacent to the boundary, within the compliant cofilactin segment. Filaments with small cofilin clusters were predicted to fragment within the compliant cofilactin rather than at boundaries. Neglecting contributions from twist-bend coupling elasticity underestimates the energy density and gradients along filaments, and thus the net effects of filament strain to fragmentation. Spatial confinement causes compliant cofilactin segments and filaments to adopt higher deformation modes and store more elastic energy, thereby promoting fragmentation. The theory and simulations presented here establish a quantitative relationship between actin filament fragmentation thermodynamics and elasticity, and reveal how local discontinuities in filament mechanical properties introduced by regulatory proteins can modulate both the severing efficiency and location along filaments. The emergent behavior of mechanically heterogeneous filaments, particularly under confinement, emphasizes that severing in cells is likely to be influenced by multiple physical and chemical factors.

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Figures

Figure 1
Figure 1
(A–E) The shape, spatial elastic energy, and local shear force of buckling (cofil)actin filaments. Filaments (length 1 μm), with different actin/cofilactin configurations (actin in red, cofilactin in green, illustrated above top panels) are buckled by reduction of the end-to-end distance (Fig. S3) by 1% (black curve), 10% (dark-red curve), 20% (purple curve), and 30% (blue curve). The shape of the filament changes with buckling (A–E, top row); note that the asymmetric configuration in (C) gives rise to asymmetric filament deformation. The total elastic energy stored in the filament configuration (middle row) and the elastic energy gradient (bottom row) for corresponding filaments (illustrated in the top row) is shown. To see this figure in color, go online.
Figure 2
Figure 2
(A) Strain tilts the filament fragmentation-annealing reaction free-energy profile. Filament fragmentation is illustrated as a two-state system with intact (energy illustrated with green line) and severed (energy illustrated with blue line) filaments linked by a transition state (energy illustrated with red line). The spacings between energy states are drawn to scale and reflect relative heights estimated from the severing and annealing rate and equilibrium constants (4). (B) (Red arrows) Compressive forces applied at the two filament-ends during buckling. Note that considerable separation between the ground and transition states exists, even for strained filaments. Thus, the deformations are not irreversible (e.g., to rupture), but exist in a perturbative regime where fragmentation is likely to follow a nativelike pathway. To see this figure in color, go online.
Figure 3
Figure 3
(A–E) Spatial distribution of buckled filament severing rate. The enhancement of filament severing was calculated by considering the contributions from the local elastic energy (Eq. 18; top row) and the energy gradient representing an effective force (Eq. 19; bottom row). The increase in the severing rate constant predicted from the spatial distribution of elastic energy, ksev(Strained)/ksev(Native), coincides with that of ΔG°′Elastic (top row). The distribution considering ΔG°′Elastic as the work done by a pulling force against a filament subunit yields comparable behavior. Note that both the activation energy barrier and force methods of analysis yield essentially identical results, with minor differences observed only in stiff actin filaments with a compliant cofilactin segment (right column). To see this figure in color, go online.
Figure 4
Figure 4
Spatial distribution of elastic energy density, showing severing rate along filaments with a central cofilin cluster. The total energy (top left) and the normalized severing rate constant (bottom left) values are displayed for three cofilin cluster sizes (inset shows color-code for corresponding cofilactin segment length, in micrometers). (Right) Maximal severing rate. To see this figure in color, go online.
Figure 5
Figure 5
(A–E) Contributions of twist-bend coupling to filament energy profiles. Filaments (length, 1 μm), with different actin/cofilactin configurations (actin in red, cofilactin in green, illustrated above top panels), are buckled to an end-to-end distance of 0.7 μm. The two first rows represent the filament shape projected onto the X,Y and X,Z planes, respectively (Fig. S9). (Blue curves) Filaments with the mechanical properties of actin (Table 1); (red lines) filaments with neglected twist-bend coupling elasticity. To see this figure in color, go online.
Figure 6
Figure 6
(A–E) Contributions of filament confinement. Filaments (length, 1 μm), with different actin/cofilactin configurations (actin in red, cofilactin in green, illustrated above top panels) are buckled to an end-to-end distance of 0.7 μm. (Blue curves) Filaments with the mechanical properties of actin (Table 1); (green lines) filament-shape deformations constrained within a rigid cylinder of radius 0.2 μm. To see this figure in color, go online.
Figure 7
Figure 7
(Left) Zero-strain conditions weaken elastic energy and severing. (Color-code: dashed black curve, boundary conditions with both ends constrained; red solid curves, filaments with unconstrained, i.e., green segment, cofilactin ends (s = L); blue, filaments with unconstrained, i.e., red segment, actin ends (s = 0).) For the symmetric actin/cofilin configuration (right), only the condition corresponding to zero strain at s = 0 is shown. Note that the energy and its gradient vanish for the zero strain condition, coherent with the definition of energy (Eq. 1). To see this figure in color, go online.
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