Peptide binding landscapes: Specificity and homophilicity across sequence space in a lattice model

Peptide aggregation frequently involves sequences with strong homophilic binding character, i.e., sequences that self-assemble with like species in a crowded cellular environment, in the face of a multitude of other peptides or proteins as potential heterophilic binding partners. What kinds of sequences display a strong tendency towards homophilic binding and self-assembly, and what are the origins of this behavior? Here, we consider how sequence specificity in oligomerization processes plays out in a simple two-dimensional (2D) lattice statistical-thermodynamic peptide model that permits exhaustive examination of the entire sequence and configurational landscapes. We find that sequences with strong self-specificities have either alternating hydrophobic and hydrophilic residues or short patches of hydrophobic residues, both which minimize intramolecular hydrophobic interactions in part due to the constraints of the 2D lattice. We also find that these specificities are highly sensitive to entropic and free energetic features of the unbound conformational state, such that direct binding interaction energies alone do not capture the complete behavior. These results suggest that the ability of particular peptide sequences to self-assemble and aggregate in a many-protein environment reflects a precise balance of direct binding interactions and behavior in the unbound (monomeric) state.

Figure 1

Illustration of peptide binding scenarios on a two-dimensional square lattice: (a) peptide binding to peptide, (b) peptide binding to linear peptide (i.e., fibrillar peptide partner), and (c) linear peptide binding to linear peptide (i.e., binding of two fibrillar peptides). H and P circles represent hydrophobic and hydrophilic amino acid residues, respectively. In (a,b), peptides initially exist in an ensemble of partially folded states promoted by intramolecular H-H interactions (H-H contacts); upon binding in a linear arrangement, intermolecular H-H (H-H contacts) interactions promote affinity.

Figure 2

Average folding energy of all sequences with $N=6,8,10$, and 14 with respect to temperature. An effective folding temperature for the entire sequence ensemble, $T_{\mathrm{fold}}$, is determined from the midpoint of the folding energy using ${\langle E\rangle }_{\mathrm{fold}}\left(T_{\mathrm{fold}}\right)=\left[{\langle E\rangle }_{\mathrm{fold}}\left(T\to 0\right)+{\langle E\rangle }_{\mathrm{fold}}\left(T\to \infty \right)\right]/2$.

Figure 3

Illustrative energy level diagrams for the bound free energy, folded free energy, and binding affinity of two selected sequences that have (a) good and (b) poor specificity. Here we consider a low temperature $(T=0.1)$ that makes the levels easier to distinguish visually. Each line represents a potential binding partner $S\prime$ for target sequence $S$. In case (a), the specificity is positive and defined as the gap between the self-binding and next highest affinities. In case (b), the specific is negative and defined as the gap between the self-binding and lowest affinity.

Figure 4

Self-binding and folding free energies of all $2080(\mathrm{P}/\mathrm{H}{)}_{12}$ sequences. The red line represents the point at which $A_{\mathrm{bound}}=2A_{\mathrm{fold}}$ or where $\mathrm{Affinit}{\mathrm{y}}_{\mathrm{self}}=0$ as seen in Eq. (5).

Figure 5

Illustration of the number of HH pairs. Each line shows a HH contact possible in at least one configuration on the 2D lattice; these are pairs of H residues separated by an even number of amino acids.

Figure 6

Folding free energies compared to the number of hydrophobic residues and the number of HH pairs, for all $2080(\mathrm{P}/\mathrm{H}{)}_{12}$ sequences.

Figure 7

The relationship of the self-binding affinity to the number of H residues $\left(N_{\mathrm{H}}\right)$, shown for three scenarios: (a) peptide-peptide binding, (b) peptide addition to a fibril, and (c) association of two fibril ends (see Fig. 1). Points represent every ${(\mathrm{P}/\mathrm{H})}_{12}$ sequence. Panel (a) illustrates that binding between two monomeric peptides is strongly influenced by factors other than sequence composition (i.e., $N_{\mathrm{H}}$), in contrast to binding events involving fibrils.

Figure 8

Binding landscapes for the ${(\mathrm{H}/\mathrm{P})}_{12}$ model for the three binding scenarios of Fig. 7. Binding affinities are shown in the left column and bound-state free energies in the right; the former accounts for the unfolding free energies of the peptides, whereas the latter includes only the bound-state partition sum in Eq. (2). Each row and column represents a given sequence, and colors then indicate strength of interaction (lower and more favorable free energies in darker gray). Sequences are sorted by their self-binding affinities (the diagonal lines), so that the most favorable interactions occur in the top left corners and the diagonal in the left panels lightens in color from top left to bottom right. The sequence orders are identical among adjacent plots in each row: (a,b), (c,d), and (e,f). After sorting, only the first 400 sequences are shown.

Figure 9

The relationship between self-binding specificities and self-binding affinities of all ${(\mathrm{P}/\mathrm{H})}_{12}$ sequences, for the three binding scenarios of Fig. 1. The $y$ axis is inverted to present sequences in (a) with both good affinity and good specificity in the third quadrant. Percentages indicate the fraction of sequences in each quadrant.

Figure 10

Frequency of triple consecutive hydrophobic residues in a sequence, $f\left(\mathrm{HHH}\right)$, with respect to the number of hydrophobic residues, $N_{\mathrm{H}}$ . Sequences with both good affinity and specificity for the peptide-peptide scenario [as defined in Fig. 9] are shown as red circles, while all other sequences are shown as blue circles. The area of each circle is proportional to the number of sequences at each point.

Figure 11

Self-binding affinity and specificity in peptide-peptide binding for the sequence space $(\mathrm{A}/\mathrm{C}/\mathrm{H}/\mathrm{P})-{(\mathrm{H}/\mathrm{P})}_{10}-\left(\mathrm{A}/\mathrm{C}/\mathrm{P}/\mathrm{H}\right)$, that is, for a modified HP model in which there are four different types of end residues. Percentages indicate the fraction of the sequence space falling within each quadrant.

Figure 12

Self-binding affinity and specificity plots for sequences with distinct termini chemistry and an odd length $(N=13)$.