Factors governing fibrillogenesis of polypeptide chains revealed by lattice models

Abstract

Using lattice models we explore the factors that determine the tendencies of polypeptide chains to aggregate by exhaustively sampling the sequence and conformational space. The morphologies of the fibril-like structures and the time scales (τ(fib)) for their formation depend on a balance between hydrophobic and Coulomb interactions. The extent of population of an ensemble of N* structures, which are fibril-prone structures in the spectrum of conformations of an isolated protein, is the major determinant of τ(fib). This observation is used to determine the aggregating sequences by exhaustively exploring the sequence space, thus providing a basis for genome wide search of fragments that are aggregation prone.

FIG. 1.

(a) Spectrum of energies and low energy structures of the monomer sequence $+HHPPHH-$, $H$, $P$, + and − are in green, yellow, blue, and red, respectively. We set $E_{HH}=-1$ and $E_{+-}=1.4$. There are 1831 possible conformations that are spread among 17 possible energy values. The conformations in the first excited state represent the ensemble of $N^{\text{*}}$ structures and the $N^{\text{*}}$ conformation that coincides with the peptide state in the fibril [see Fig. 2(a)] is enclosed in a box. (b) The probability $P_{N^{\text{*}}}$ of populating the structure in the box in (a) as a function of $T$ for $E_{+-}=0,-0.3,0.6,-1$ and −1.4 keeping $E_{HH}=-1$. The arrow indicates $T^{\text{*}}$, where $P_{N^{\text{*}}}=P_{N^{\text{*}}}^{\text{max}}$. Dependence of $P_{N^{\text{*}}}^{\text{max}}$ on $E_{+-}$ for $E_{HH}=-1$ (c), and on $E_{HH}$ for $E_{+-}=-1.4$ (d).

FIG. 2.

(a) The lowest-energy fibril structure for $E_{+-}=-1.4$ and $E_{HH}=-1$. (b) Same as in (a) but with $E_{+-}=0$. (c) Double-layer structure for $E_{HH}=-0.4$ but with $E_{+-}=-1.4$. (d) For $E_{+-}=-1.4$ and $E_{HH}=-0.3$ the fibril structure is entirely altered. (e) Temperature dependence of ${\tau }_{\text{fib}}$ for $E_{+-}=-1.4$ (circles) and $E_{+-}=-0.6$ (triangles). $N=6$ and $E_{HH}=-1$. Arrows show the temperatures at which the fibril formation is fastest.

FIG. 3.

(a) Dependence of ${\tau }_{\text{fib}}$ on $E_{+-}$ for $N=6$ (circles) and $N=10$ (triangles) with $E_{HH}=-1$. The solid curves are fits to $y=c_0+c{(-x)}^{\alpha }$, where $\alpha \approx 0.59$. $c_0=21.32$ and $c=-7.12$ and $c_0=25.14$ and $c=-9.23$ for $N=6$ and 10 , respectively. (b) Dependence of ${\tau }_{\text{fib}}$ on $E_{HH}$ with $E_{+-}=-1.4$ hold constant for $N=6$ (solid circle) and $N=10$ (solid triangles). Lines are fits $y=19.17+7.97x$ and $y=22.69+8.56x$ for $N=6$ and 10 , respectively. For $N=6$ the first point $E_{HH}=-1$ is excluded from fitting. (c) Dependence of ${\tau }_{\text{fib}}$ on $P_{N^{\text{*}}}^{\text{max}}$ for $N=6$ and 10 . Symbols are the same as in (a) and (b) ${\tau }_{\text{fib}}$ is measured in MCS and $P_{N^{\text{*}}}^{\text{max}}$ in percent. The correlation coefficient for all fits $R\approx 0.98$.