Helix Folding in One Dimension: Effects of Proline Co-Solvent on Free Energy Landscape of Hydrogen Bond Dynamics in Alanine Peptides

Abstract

The effects of proline co-solvent on helix folding are explored through the single discrete coordinate of the number of helical hydrogen bonds. The analysis is based on multi-microsecond length molecular dynamics simulations of alanine-based helix-forming peptides, (ALA)n, of length n = 4, 8, 15 and 21 residues, in an aqueous solution with 2 M concentration of proline. The effects of addition of proline on the free energy landscape for helix folding were analyzed using the graph-based Dijkstra algorithm, Optimal Dimensionality Reduction kinetic coarse graining, committor functions, as well as through the diffusion of the helix boundary. Viewed at a sufficiently long time-scale, helix folding in the coarse-grained hydrogen bond space follows a consecutive mechanism, with well-defined initiation and propagation phases, and an interesting set of intermediates. Proline addition slows down the folding relaxation of all four peptides, increases helix content and induces subtle mechanistic changes compared to pure water solvation. A general trend is for transition state shift towards earlier stages of folding in proline relative to water. For ALA5 and ALA8 direct folding is dominant. In ALA8 and ALA15 multiple pathways appear possible. For ALA21 a simple mechanism emerges, with a single path from helix to coil through a set of intermediates. Overall, this work provides new insights into effects of proline co-solvent on helix folding, complementary to more standard approaches based on three-dimensional molecular structures.

Keywords: alanine peptides; helix folding; hydrogen bond dynamics; proline co-solvent.

Figure 1

Molecular structures of simulated systems. (A) Proline zwitterion with NH₂⁺ N-terminus and COO⁻ C-terminus, neutral overall. (B) ALA5 helix (C) ALA8 helix. (D) ALA15 helix. (E) ALA21 helix. Alanine peptides include N-terminal acetyl blocking group and C-terminal amide blocking group and are neutral overall. The hydrogen bonds considered here involve CO of residue i and HN of residue i + 4, starting with acetyl C=O to HN of Ala 4, and end with Ala (n − 3) C=O to H₂N of amide blocking group, with n = 5, 8, 15, 21. Standard hydrogen bonds are shown in blue; some distorted hydrogen bonds present at termini shown in orange.

Figure 1

Molecular structures of simulated systems. (A) Proline zwitterion with NH₂⁺ N-terminus and COO⁻ C-terminus, neutral overall. (B) ALA5 helix (C) ALA8 helix. (D) ALA15 helix. (E) ALA21 helix. Alanine peptides include N-terminal acetyl blocking group and C-terminal amide blocking group and are neutral overall. The hydrogen bonds considered here involve CO of residue i and HN of residue i + 4, starting with acetyl C=O to HN of Ala 4, and end with Ala (n − 3) C=O to H₂N of amide blocking group, with n = 5, 8, 15, 21. Standard hydrogen bonds are shown in blue; some distorted hydrogen bonds present at termini shown in orange.

Figure 2

Hydrogen bonding microstate population comparison between aqueous solution (0 M) [16] and 2 M proline solution (2 M). Results averaged over independent trajectories, two for ALA5 and ALA8, and five for ALA15 and ALA21. (A) ALA5 (B) ALA8 (C) ALA15 (D) ALA21. Statistical errors are about 5–10% of values. Logarithmic scale is used.

Figure 3

Global maximum weight paths in the space of helical hydrogen bond counts. State populations shown as circles with free energies, $∆G_i=-RT\ln {\displaystyle \frac{p_i}{p_{max}}}$, with R the gas constant, T = 298 K, $p_i$ the population of state i and $p_{max}$ the maximum population for a given peptide. GMWPs are shown by arrows and the bottlenecks marked by asterisk, “*”. (A) ALA5 GMWP is $0\to 3$, same as bottleneck. (B) ALA8 GMWP is $0\to 4\to 6$, with $0\to 4$ bottleneck. (C) ALA15 GMWP is $0\to 7\to 13$, with bottleneck $7\to 13$. (D) ALA21 GMWP is $0\to 6\to 7\to 8\to 11\to 12\to 13\to 14\to 18\to 19$, with bottleneck $0\to 6$.

Figure 4

Coarse-grained kinetic models of dimensionality N = 2 based on hydrogen bond microstate transitions in 2 M proline. Notation for coarse-grained state descriptions: #s—number of microstates belonging to aggregate state; e.g., [0, 1]—state consisting of NHB = 0 and NHB = 1 microstates; h—helix; c—coil. (A) ALA5 model based on discretization with lag time ${\tau }_l=2.0 \mathrm{ns}$. (B) ALA8 model with ${\tau }_l=8.0 \mathrm{ns}$. (C) ALA15 model with ${\tau }_l=100 \mathrm{ns}$. (D) ALA21 model with ${\tau }_l=80 \mathrm{ns}$.

Figure 5

Coarse-grained kinetic models for ALA5 of dimensionality N = 3, 4 in 2 M proline, based on transitions between four microstates, NHB = 0, 1, 2, 3, 4 and lag time ${\tau }_l=2.0 \mathrm{ns}$ (A) ODR dimension N = 3. (B) ODR dimension N = 4. More details are in SI Table S7a.

Figure 6

Coarse-grained kinetic models for ALA8 of dimensionality N = 3, 4 in 2 M proline, based on transitions between seven microstates, NHB = 0, 1, …, 6 and lag time ${\tau }_l=8.0 \mathrm{ns}$. (A) ODR dimension N = 3. (B) ODR dimension N = 4. More details are in SI Table S7b.

Figure 7

Coarse-grained kinetic models for ALA15 of dimensionality N = 3, 4 in 2 M proline, based on transitions between fourteen microstates, NHB = 0, 1, …, 13 and lag time ${\tau }_l=100 \mathrm{ns}$. (A) ODR dimension N = 3. (B) ODR dimension N = 4. More details are in SI Table S7c.

Figure 8

Coarse-grained kinetic models for ALA21 of dimensionality N = 3, 4 in 2 M proline, based on transitions between twenty microstates, NHB = 0, 1, …, 19 and lag time ${\tau }_l=80 \mathrm{ns}$. (A) ODR dimension N = 3. (B) ODR dimension N = 4. More details are in SI Table S7d.

Figure 9

Average diffusion (A) and friction (B) coefficients for helix propagation in the four studied peptides. The values are averaged over the set of possible microstate transitions from $i$ to $i+1$. Values for individual transitions are in Figure S1.