Molecular Dynamics Simulation of the $\alpha$-Helix to $\beta$-Sheet Transition in Coiled Protein Filaments: Evidence for a Critical Filament Length Scale

The alpha-helix to beta-sheet transition ($\alpha \mathrm{\text{−}}\beta$ transition) is a universal deformation mechanism in alpha-helix rich protein materials such as wool, hair, hoof, and cellular proteins. Through a combination of molecular and theoretical modeling, we examine the behavior of alpha-helical coiled-coil proteins with varying lengths under stretch. We find that the occurrence of the $\alpha \mathrm{\text{−}}\beta$ transition is controlled by the length of constituting alpha-helical proteins. In the asymptotic limit, short proteins with less than 26 amino acids or 3.8 nm length reveal interprotein sliding, whereas proteins with greater lengths feature an $\alpha \mathrm{\text{−}}\beta$ transition, leading to a significant increase in the protein’s stiffness, strength, and energy dissipation capacity at large deformation. Our study elucidates the fundamental physics of this mechanism and explains why the $\alpha \mathrm{\text{−}}\beta$ transition typically occurs in protein filaments with long alpha-helical domains.

Figure 1

Model for studying the strength of coiled-coil proteins under shear loading. (a) Upper: Schematic of the structure and loading condition of the coiled-coil ($AA=\mathrm{\text{amino}}$ acid residue). Lower: Example molecular structure of the 2B segment in the vimentin protein (PDB ID 1gk4). (b) Force-strain behavior of two coiled-coil proteins with different lengths (PDB ID 1gk4, where the modulus in the $L$ region is 0.3 GPa average diameter 2.4 nm, and in the $E$ region reaches 8.9 GPa average diameter 1.1 nm; PDB ID 1 ajy, short). The shaded area reflects the energy dissipated during unfolding. (c) Dissipated energy during the entire stretching process, for coiled-coil proteins with different lengths.

Figure 2

Simulation snapshots of two coiled-coil proteins under shear (proteins with PDB ID 1ajy [(a), (c)] and 1gk4 [(b), (d)]). (a) and (b) Structure under applied strain during stretching of the proteins (H bonds are shown as dashed lines). (c) and (d) Number of amino acids associated with alpha-helix and beta-sheet secondary structures as a function of strain. (e) Structure spectrum for structure of the protein 1gk4 under stretching. (f) Structure spectrum of the protein 1gk4 during equilibration. The color bar distinguishes 7 structures: Alpha helix (AH), 3–10 helix (3H), Phi helix (PH), Isolated bridge (IB), Coil (C), Turn (T), beta sheet (BS).

Figure 3

(a) Theoretical analysis of the critical condition for the $\alpha \mathrm{\text{−}}\beta$ transition, where the shaded area in the middle represents the critical condition. The left side of the critical point corresponds to sliding and unfolding of the alpha-helices without occurrence of the $\alpha \mathrm{\text{−}}\beta$ transition, while the right side corresponds to the regime in which the $\alpha \mathrm{\text{−}}\beta$ transition occurs. (b) Percentage of $\alpha \mathrm{\text{−}}\beta$ transition occurrence for various coiled-coil proteins (simulation). Each point reflects the percentage of the transition within the simulation ensemble. The fitted curve is a sigmoid function $p=A_2+(A_1-A_2)\{1+\exp [(n-n_0)/dx]{\}}^{-1}$, with $A_1=0.083$, $A_2=0.967$, $n_0=38.835$, and $dx=0.465$. The fit enables us to identify the transition point from the simulation data, leading to $N_{\mathrm{cr}}=38.7$ (probability 50%). (c) Critical number of amino acids $N_{\mathrm{cr}}$ as a function of pulling speed (continuous curve is power law fit to the simulation data; asymptotic limit $N_{\mathrm{cr}}=26$).