A simple lattice model that captures protein folding, aggregation and amyloid formation

Abstract

The ability of many proteins to convert from their functional soluble state to amyloid fibrils can be attributed to inter-molecular beta strand formation. Such amyloid formation is associated with neurodegenerative disorders like Alzheimer's and Parkinson's. Molecular modelling can play a key role in providing insight into the factors that make proteins prone to fibril formation. However, fully atomistic models are computationally too expensive to capture the length and time scales associated with fibril formation. As the ability to form fibrils is the rule rather than the exception, much insight can be gained from the study of coarse-grained models that capture the key generic features associated with amyloid formation. Here we present a simple lattice model that can capture both protein folding and beta strand formation. Unlike standard lattice models, this model explicitly incorporates the formation of hydrogen bonds and the directionality of side chains. The simplicity of our model makes it computationally feasible to investigate the interplay between folding, amorphous aggregation and fibril formation, and maintains the capability of classic lattice models to simulate protein folding with high specificity. In our model, the folded proteins contain structures that resemble naturally occurring beta-sheets, with alternating polar and hydrophobic amino acids. Moreover, fibrils with intermolecular cross-beta strand conformations can be formed spontaneously out of multiple short hydrophobic peptide sequences. Both the formation of hydrogen bonds in folded structures and in fibrils is strongly dependent on the amino acid sequence, indicating that hydrogen-bonding interactions alone are not strong enough to initiate the formation of beta sheets. This result agrees with experimental observations that beta sheet and amyloid formation is strongly sequence dependent, with hydrophobic sequences being more prone to form such structures. Our model should open the way to a systematic study of the interplay between the factors that lead to amyloid formation.

Figure 1. Example of experimental beta sheet structure compared to an on-lattice model.

Top: example of a beta sheet in an all-atom structure (1OSP). Note that for clarity only the top sheet of the structure is shown; the hydrophobic downward pointing residues are buried through an another beta sheet. Bottom: example of a designed protein that can fold into its native structure (shown) containing a beta sheet. Note that the designed structure was not explicitly modelled to resemble the experimental structure, but is the result of a stochastic design algorithm (see Methods). Yellow, grey, red and blue residues indicate hydrophobic, polar, negative and positive amino acids respectively.

Figure 2. Folding chacteristics and specificity.

Folding characteristics are shown for a protein sequence that is designed to fold in a specific structure, and a random protein sequence; both sequences contain 35 residues and have a similar amino acid composition (see Methods). (a) Heat capacity versus temperature. A peak in the heat capacity curve can be observed at the folding transition. (b) Number of native contacts versus temperature. (c) Number of hydrogen bonds versus temperature. From the statistics it is clear that the sequence designed to fold shows a much sharper transitions than a random sequence of the same length. Moreover, the number of hydrogen bonds formed is strongly dependent on the sequence. Please refer to the Methods and Supplement for the sequences and structures used.

Figure 3. Fibrils with a cross-beta architecture.

Top and side view of fibrils formed by a grand canonical simulation with a starting configuration of s small fibrillar structure. The peptides have an alternating hydrophobic (yellow) and hydrophilic (grey) sequence composition. The strand and coil states are indicated by green and grey respectively.

Figure 4. Stability of small fibrillar structures containing 10 peptides.

(a) The ensemble average of external (intermolecular) contacts versus temperature for different peptide sequences. External contacts are contacts between different peptides. (b) The ensemble average of hydrogen bonds versus temperature for different peptide sequences. These simulations started from small fibrillar configuration containing 10 peptides with 7 residues and different sequence compositions (see legend). In the temperature regime relevant for folding (), only fibrils that could form a strong hydrophobic core (TFTFTFT) are stable, in this case the hydrophobic residues would point inwards, as shown in Figure 3.

Figure 5. Hydrogen bonds formed between two strands.

The black lines represent hydrogen bonds; residues in green are in the strand state. Hydrogen bonds are allowed to form when neighbouring residues are in a strand state and the side chains are oriented in the same parallel direction.

Figure 6. Facing side chains that interact.

The yellow residues interact due to their orientation: they are directed towards each other.

Figure 7. Parallel side chains that interact.

The yellow residues interact, since they point in the same direction in a parallel fashion.