Critical Buckling Length versus Persistence Length: What Governs Biofilament Conformation?

We numerically study the length dependence in the bending stiffness of $\alpha$ helices, coiled coils, and a linear chain model. As the length approaches what we named the critical buckling length $l_c$, the chain appears to become increasingly more flexible. This is due to weak nonbonded attractions that eventually lead to buckling instability and alter the chain’s conformational ensemble. For $\alpha$ helices and coiled coils, $l_c$ is much less than their respective persistence lengths, so $l_c$ is the defining length scale for their conformations. These results elucidate the importance of weak nonspecific attractions that are inherent in many biofilaments in physiological conditions.

Figure 1

$\kappa$ vs $L$. (a) Poly-Ala, poly-Leu, and (b) poly-Gly AHs, (c) LZ, and (d) 1D chain ($ϵ$ in units of $\mathrm{kcal}/\mathrm{mol}$). All are from NMA [$n=1,2$, in parentheses, and $n=1$ in (d)], except (c) forced-bending (f.b.) simulation, (d) TMA for $ϵ=440$. Solvent models used are (a),(b),(d) RDIE and (c) ACE2 [14]. Similar plots are obtained for AHs in VAC, with $\kappa$ overall larger (cf. Fig. 4). $\kappa$ further dropped for LZ at 487 Å, but is not plotted since the chain bent slightly during the initial energy minimization.

Figure 2

Whole-chain analysis (NMA and TMA) versus local fluctuation analysis. (a) Deviation from linear elasticity in 1D chain, occurring from shorter $L$ for larger $ϵ$. (b) Symbols: $\kappa$ obtained from local fluctuation analysis, which are independent of $L$. Square: AH (in VAC; open: $L=58.6\AA$, solid: 381 Å). Triangle: 1D chain ($ϵ=440$; open: $L=74\AA$, solid: 119 Å). Dashed horizontal lines and dotted horizontal lines: $\kappa$ obtained from TMA, which decreases with $L$. (c) Sample snapshots of long chains during MD, which do not collapse.

Figure 3

$X\mathrm{\text{−}}Y$ plot ($X\equiv L^{-2}$, $Y\equiv {\omega }_n^2{L}^2$). Solid line: linear fit. The initial rise phase in Fig. 1 was not used in the fit. Only portions near the origin are shown. In (d), lines converge to the origin; hence, $f_c\approx 0$.

Figure 4

$l_c$, $l_p$, and ${\kappa }_0$ of AH and LZ determined from the $X\mathrm{\text{−}}Y$ plots for $n=1$ (Fig. 3). For LZ, labels of the $y$ axes follow those of AH on respective sides.