Twisting Transition between Crystalline and Fibrillar Phases of Aggregated Peptides

We study two distinctly ordered condensed phases of polypeptide molecules, amyloid fibrils and amyloidlike microcrystals, and the first-order twisting phase transition between these two states. We derive a single free-energy form which connects both phases. Our model identifies relevant degrees of freedom for describing the collective behavior of supramolecular polypeptide structures, reproduces accurately the results from molecular dynamics simulations as well as from experiments, and sheds light on the uniform nature of the dimensions of different peptide fibrils.

Figure 1

(a),(c) Fibrillar and (b),(d) crystalline phases of peptide $P$ [19]. (a) In the fibrillar phase, no structures are visible by optical microscopy, but (c) atomic force microscopy shows uniform protofilaments. (e) The atomic level structure [10] of the protofilaments shows the significant level of interstrand twist. Panel (b) shows an optical and (d) an atomic force microscopy image of the crystalline phase and the atomic level untwisted structure from (f) [6]. Panel (g) shows the coarse-grained model and the definitions of the geometric parameters used in this Letter.

Figure 2

The twist-dependent free energy $F(\phi )$ was computed from molecular dynamics simulations for different numbers of $\beta$ sheets with corresponding equilibrium atomic coordinates shown in the inset: (i) two, (ii) three, and (iii) four sheets. The lines are a three-parameter global fit of the entire data set to Eq. (1) with $a_T^{\mathrm{bulk}}=4.1\times {10}^{-2}\mathrm{N}/\mathrm{m}$, $k_T^{\mathrm{strand}}=3.3\times {10}^{-18}\mathrm{N}\times \mathrm{m}$, and ${\phi }_0=9.6°$.

Figure 3

(a) The equilibrium twist is shown as a function of filament width. The filamentous state becomes metastable at $W=W^{*}$. For comparison, experimentally determined dimensions of amyloid protofilaments are shown by vertical lines: (1) PI-SH3 domain [20]; (2) lysozyme (D67H) [21]; (3) insulin [22, 23]; (4) apoA1 (L60R) [21]; (5) peptide $P$ [19], present work and Ref. 22; and (6) TTR (V30M) [21]. The experimentally determined widths of microcrystals [Fig. 1d] were in all cases $>10\mathrm{nm}$. Panel (b) shows an atomic force microscopy height map of a sample containing a mixture of fibrils and microcrystals, and the height profile through the cross section that is highlighted with a line is shown in the inset. The height of the microcrystal in (b) is reported as (7) in (a).

Figure 4

(a) The total peptide free energy computed from Eq. (4) as a function of structure width for $ϵ=1$, 3.7, and $7.5\mathrm{kJ}/\mathrm{mol}$ using the values of $a_T^{\mathrm{bulk}}$, $k_T^{\mathrm{strand}}$, and ${\phi }_0$ determined in Fig. 2. Dashed lines represent the fibrillar state, and solid lines represent the microcrystalline state. (b) Experimental observation of the twisting transition with NMR through the measurement of the biphasic incorporation of soluble peptide into supramolecular structures measured from the decrease in intensity of the 1D H spectra acquired between 0 and 35 hours (inset).