Dynamic allostery of protein alpha helical coiled-coils

Abstract

Alpha helical coiled-coils appear in many important allosteric proteins such as the dynein molecular motor and bacteria chemotaxis transmembrane receptors. As a mechanism for transmitting the information of ligand binding to a distant site across an allosteric protein, an alternative to conformational change in the mean static structure is an induced change in the pattern of the internal dynamics of the protein. We explore how ligand binding may change the intramolecular vibrational free energy of a coiled-coil, using parameterized coarse-grained models, treating the case of dynein in detail. The models predict that coupling of slide, bend and twist modes of the coiled-coil transmits an allosteric free energy of approximately 2kBT, consistent with experimental results. A further prediction is a quantitative increase in the effective stiffness of the coiled-coil without any change in inherent flexibility of the individual helices. The model provides a possible and experimentally testable mechanism for transmission of information through the alpha helical coiled-coil of dynein.

Figure 1

(a) Mean conformations of ADP·Vi and apo dynein-c molecules. (b) Distribution of stalk tip positions. Figure reprinted from Burgess et al. (2004a) with permission from Elsevier.

Figure 2

Model of coiled-coil alpha helices as two classical flexible rods with paths r_±1(s) and radii ρ.

Figure 3

Allosteric free energy ΔΔG against clamping κ=k₁/k₀=k₋₁/k₀ showing the effect of the clamping on the allosteric free energy for the model of rigid parallel rods. The values of the parameters used are those given for dynein in appendix E.

Figure 4

Allosteric free energy ΔΔG against the Young's modulus of each rod Y showing the effect of bending on the allosteric free energy for the model of parallel flexible rods free to slide and bend. The values of the parameters used are those given for dynein in appendix E.

Figure 5

Allosteric free energy ΔΔG against clamping κ=k₁/k₀=k₋₁/k₀ showing the effect of the clamping on the allosteric free energy for the model of flexible parallel rods free to slide and bend. The values of the parameters used are those given for dynein in appendix E.

Figure 6

Diagram showing the geometry of two rods coiled round each other. α is the angle between the central axis and the path length along an individual rod. h is the helical pitch of the two rods coiled round each other. The distance between the centres of the rods is 2ρ.

Figure 7

Allosteric free energy ΔΔG against the shear modulus of each rod μ showing the effect on the allosteric free energy for coiled geometry for slide and bend fluctuations.

Figure 8

Allosteric free energy ΔΔG against the Young's modulus of each rod Y showing the effect on the allosteric free energy for coiled geometry for slide and bend fluctuations.

Figure 9

Allosteric free energy ΔΔG against clamping κ=k₁/k₀=k₋₁/k₀ showing the effect of clamping on the allosteric free energy for coiled geometry for slide and bend fluctuations.

Figure 10

Allosteric free energy ΔΔG against the shear modulus of each rod μ showing the effect on the allosteric free energy for coiled geometry for slide, bend and twist fluctuations. Solid line is κ=100, dashed is κ=500 and dotted is κ=1000.

Figure 11

Allosteric free energy ΔΔG against Young's modulus Y showing the effect on the allosteric free energy for coiled geometry for slide, bend and twist fluctuations.

Figure 12

Allosteric free energy ΔΔG against clamping κ=k₁/k₀=k₋₁/k₀ showing the effect of the clamping on the allosteric free energy for coiled geometry for slide, bend and twist fluctuations.

Figure 13

Allosteric free energy ΔΔG against the shear modulus of each rod μ showing the effect on the allosteric free energy for coiled geometry for slide, bend and twist fluctuations. Solid line is Y∼10³ MPa and dashed line is Y∼10⁴ MPa.

Figure 14

Allosteric free energy ΔΔG against the length in units of number of turns l₀/h (where h is the pitch h=2π/γ₀ which we fix) for coiled geometry for slide, bend and twist fluctuations.

Figure 15

(a) Diagram showing the coil in figure 6 unrolled. ρ is the radius of the circle that the centre of one rod travels in the coil structure. Therefore the circumference is 2πρ which makes the vertical side. The horizontal side is in the direction of the arc length of the centre of the coil s ($\hat{\mathit{z}}$ if there is no bend) and the pitch h. The individual rod arc length, s₁ is along the diagonal in the unrolled geometry. (b) Diagram showing the coil of the two rods in figure 6 end on. Again ρ is the radius the centre of one rod travels. The arc length s₁ sin α marked is the component of individual rod arc length s₁ along the vertical side of the unrolled geometry in (b). ϕ is the global twist angle defined as the angle between the line joining the centres of the two rods and the x-axis.

Figure 16

Diagram to show geometry of the lowest normal mode (bend) used to calculate the Young's modulus Y of an alpha helix from the NMA using AMBER.

Figure 17

Diagram to show geometry of the lowest twist normal mode used to calculate the shear modulus μ of an alpha helix from the NMA using AMBER (a) The lowest twist mode of rod of length l. The straight groove (dashed line) becomes twisted (solid line). (b) Looking at the rod end on (radius ρ). The twist is described by the angle ϕ and the displacement of end atom is δ.