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An electrostatic model with weak actin-myosin attachment resolves problems with the lattice stability of skeletal muscle - PubMed

  • ️Sat Jan 01 2011

An electrostatic model with weak actin-myosin attachment resolves problems with the lattice stability of skeletal muscle

D A Smith et al. Biophys J. 2011.

Abstract

The stability of the filament lattice in relaxed striated muscle can be viewed as a balance of electrostatic and van der Waals forces. The simplest electrostatic model, where actin and myosin filaments are treated as charged cylinders, generates reasonable lattice spacings for skinned fibers. However, this model predicts excessive radial stiffness under osmotic pressure and cannot account for the initial pressure (∼1 kPa) required for significant compression. Good agreement with frog compression data is obtained with an extended model, in which S1 heads are weakly attached to actin when the lattice spacing is reduced below a critical value; further compression moves fixed negative charges on the heads closer to the myofilament backbone as they attach at a more acute angle to actin. The model predicts pH data in which the lattice shrinks as pH is lowered and protons bind to filaments. Electrostatic screening implies that the lattice shrinks with increasing ionic strength, but the observed expansion of the frog lattice at ionic strengths above 0.1 M with KCl might be explained if Cl(-) binds to sites on the motor domain of S1. With myosin-myosin and actin-actin interactions, the predicted lattice spacing decreases slightly with sarcomere length, with a more rapid decrease when actin-myosin filament overlap is very small.

Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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Figures

Figure 1
Figure 1

(A) Rhombohedral unit cell of the 2:1 filament lattice for the A-band of striated muscle, showing one myosin filament (open circles) and two actin filaments (solid circles) per unit cell. With a nearest-neighbor myosin-actin spacing d, the myosin-myosin spacing is √3d and the spacing of (1,0) planes is 3d/2. Each myosin filament carries three S1 dimers every 14.3 nm along the filament; only one head of each dimer is shown here. (B) The 2:1 lattice with the S1 dimers replaced by three virtual cylinders parallel to the filaments, which carry the negative charge associated with S1 heads. (C) A perpendicular view of a myosin filament (radius RM) and an actin filament (radius RA) with one S1 head of length lS1, under relaxing conditions with lattice spacing d > dc ≡ RM +RA+lS1. The center of S1 charge is sited on its neck at distance lc from the S1-S2 junction. (D) The same view for d < dc, where a flexible joint at the S1-S2 junction allows the head to attach weakly to that actin site that accommodates it without deformation. The virtual cylinder associated with S1 charge is now at distance d1 from the axis of the myosin filament, and at distance d2 from the actin filament axis. Hence, d = d1 + d2 and lc/lS1 = (d1−RM)/(d−RM−RA).

Figure 2
Figure 2

Contributions to the interaction potential per unit cell as a function of lattice spacing d, for parameters in Table 1 (second column) and full filament overlap (half-sarcomere length = 1050 nm). (A) The total potential V, the actin-myosin contribution VAM+VAS1+ΔVMS1 (Eqs. 4–6), where ΔVMS1 is the change in VMS1 due to myosin-S1 tilting, and the actin-actin and myosin-myosin contributions (Eqs. 9 and 10). The sharp increase in potential for d < dc = 26.8 nm is produced by S1 attaching to actin (Fig. 1D), which moves the virtual cylinders closer to the myosin backbone. (B) The actin-myosin contributions. The actin-myofilament contribution VAM is purely attractive as the filaments are widely separated. Net Coulomb repulsion is supplied by charge on S1, from A-S1 interactions for d > dc, and more powerfully from M-S1 interactions for d < dc as S1 heads tilt toward the backbone.

Figure 3
Figure 3

Published measurements of osmotic pressure Π as a function of lattice spacing in skinned relaxed frog fibers, and fitted curves obtained with the extended electrostatic model (solid lines), using parameter values listed in Table 1. (Dashed lines) Radial stiffness derived from these fits via Eqs. 13 and 14. The values of do are the predicted equilibrium spacings at Π = 0. (A) Data of Umazume and Kasuga (16), assuming an ionic strength I of 0.14 M and a half-sarcomere length L = 1350 nm. (B) Data of Maughan and Godt (17) with I = 0.13 M and L = 1270 nm. (C) Data of Millman and Irving (7) with I = 0.11 M and L = 1300 nm, which show that a pressure bump must exist at a critical spacing dc that lies between 26.8 nm and the zero-pressure spacing (≈28 nm). All fits were made with dc = 26.8 nm. In panels B and C, data at higher osmotic pressures did not allow the same goodness of fit and were discarded.

Figure 4
Figure 4

(A) Predicted lattice spacings as a function of ionic strength and filament charge density, starting from parameter values in the second column of Table 1. The five curves show the effects of multiplying the three charge densities by the same factor f, where f = 0.25, 0.5, 1, 2, and 4 from the lowest curve to the highest. At high ionic strength, the spacings generally stabilize at the critical value dc = 26.8 nm, where myosin heads just touch the actin filament. However, the smallest filament charges (f = 0.25) are insufficient to stabilize the lattice above 0.19 M. (B) The effect of pH changes, as calculated from the second column of Table 1 with a proton affinity of 104.5 M−1. For each type of filament, the number of proton binding sites was determined from isoelectric points of myosin and actin (see main text). As negative charges on filaments are neutralized by lowering the pH, the lattice spacing drops slowly and then rapidly toward the critical spacing of 26.8 nm.

Figure 5
Figure 5

(A) Lattice spacing as a function of half-sarcomere length L, showing data of Matsubara and Elliott (24) for relaxed skinned frog fibers at 0.16 M, and the prediction of the extended model with the parameters of the fifth column in Table 1. (Inset) Behavior near zero filament overlap at 1800 nm; the critical spacing becomes unstable and the equilibrium spacing decreases sharply to 17.5 nm, stabilized only by myosin-myosin and actin-actin interactions. (B) Binding energy per unit cell of the half-sarcomere, showing the total energy (solid line), the actin-myosin contribution (long-dashed line), the actin-actin contribution (medium dash), and the myosin-myosin contribution (short dash). The actin-myosin energy is strictly proportional to filament overlap length, whereas the relative proportions of A-M, A-S1, and M-S1 contributions (Fig. 2B) remain unchanged. Homo-filament energies are independent of the amount of overlap.

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