Phase transition from $\alpha$-helices to $\beta$-sheets in supercoils of fibrillar proteins

The transition from $\alpha$-helices to $\beta$-strands under external mechanical force in fibrin molecule containing coiled-coils is studied and free energy landscape is resolved. The detailed theoretical modeling of each stage of coiled-coils fragment pulling process was performed. The plots of force $(F)$ as a function of moleculeexpansion $(X)$ for two symmetrical fibrin coiled-coils (each $\sim 17$ nm in length) show three distinct modes of mechanical behaviour: (1) linear (elastic) mode when coiled-coils behave like entropic springs $(F < 100 - 125~pN$ and $X > 7 - 8~nm)$, (2) viscous (plastic) mode when molecule resistance force does not increase with increase in elongation length $(F \approx 150~pN$ and $X \approx 10-35~nm)$ and (3) nonlinear mode $(F > 175-200~pN$ and $X > 40-50~nm)$. In linear mode the coiled-coils unwind at 2$\pi$ radian angle, but no structural transition occurs. Viscous mode is characterized by the phase transition from the triple $\alpha$-spirals to three-stranded parallel $\beta$-sheet.The critical tension of $\alpha$-helices is 0.25 nm per turn, and the characteristic energy change is equal to 4.9 kcal/mol. Changes in internal energy $\Delta u$ , entropy $\Delta s$ and force capacity $c_f$ per one helical turn for phase transition were also computed. The observed dynamic behavior of $\alpha$-helices and phase transition from $\alpha$-helices to $\beta$-sheets under tension might represent a universal mechanism of regulation of fibrillar protein structures subject to mechanical stresses due to biological forces.