Thermodynamics of Deca-alanine Folding in Water

Abstract

The determination of the folding dynamics of polypeptides and proteins is critical in characterizing their functions in biological systems. Numerous computational models and methods have been developed for studying structure formation at the atomic level. Due to its small size and simple structure, deca-alanine is used as a model system in molecular dynamics (MD) simulations. The free energy of unfolding in vacuum has been studied extensively using the end-to-end distance of the peptide as the reaction coordinate. However, few studies have been conducted in the presence of explicit solvent. Previous results show a significant decrease in the free energy of extended conformations in water, but the α-helical state is still notably favored over the extended state. Although sufficient in vacuum, we show that end-to-end distance is incapable of capturing the full complexity of deca-alanine folding in water. Using α-helical content as a second reaction coordinate, we deduce a more descriptive free-energy landscape, one which reveals a second energy minimum in the extended conformations that is of comparable free energy to the α-helical state. Equilibrium simulations demonstrate the relative stability of the extended and α-helical states in water as well as the transition between the two states. This work reveals both the necessity and challenge of determining a proper reaction coordinate to fully characterize a given process.

Figure 1

One-dimensional PMF of Ala₁₀ in vacuum using the distance from the N-terminus carbonyl carbon to the C-terminus carbonyl carbon as the reaction coordinate. Red lines represent calculations using ABF, and blue lines represent calculations using US, with solid lines utilizing the CHARMM36 force field and dashed lines utilizing the CHARMM22/CMAP force field.

Figure 2

Unfolding of Ala₁₀. This “accordion-like” unfolding mechanism of Ala₁₀ was generated using SMD by pulling on the C-terminus C_α while keeping the N-terminus C_α fixed. Three snapshots of the peptide are shown in various stages of the SMD simulations, drawn using the “licorice” representation for all atoms and a cartoon representation for the backbone structure, where the thick ribbon represents those residues which are in an α-helical state. The top image represents the initial, minimized crystal structure of Ala₁₀ used as the starting state. The middle image represents an intermediate state in which the peptide is partially extended while the remaining portion of the peptide is still in an α-helical state. The bottom image represents the fully extended state.

Figure 3

One-dimensional PMF of Ala₁₀ along the end-to-end distance of the peptide calculated using ABF (top) and US (bottom). Top graph: no additional restraints (thick, solid line), no restraints with 50 000 fullsamples (thick, dashed line), 8 Å-radial confinement (thin, dashed line), 10 Å-radial confinement plus antihairpin restraint (thin, dotted-dashed line). Bottom graph: no additional restraints (thick, solid line), 10 Å-radial confinement (thin, dashed line), 10 Å-radial confinement plus antihairpin restraint (thin, dotted-dashed line).

Figure 4

Representative set of compact, low-α-helical content states of Ala₁₀ in water. The Ala₁₀ peptide is shown in the “licorice” representation with the backbone α-helical content represented in orange by a cartoon representation. Water molecules are not shown.

Figure 5

Scatter plot of states from ABF simulations in vacuum (top) and water (bottom). Top graph: scatter plot of states from 50 ns ABF simulation in vacuum using the CHARMM36 force field. Bottom graph: scatter plot of states from 100-ns ABF simulation in water with 10 Å-radial confinement plus antihairpin restraint.

Figure 6

Two-dimensional PMF of Ala₁₀ in vacuum (top) and water (bottom) using end-to-end distance and α-helical content as the two reaction coordinates. Green line represents the least free-energy path from the α-helical state to the extended state. The inset shows the PMF along the least free-energy path, as projected onto the end-to-end distance coordinate.

Figure 7

Histograms of 50 ns equilibrium simulations for an α-helical (top) and extended (bottom) starting states. Green lines represent the previously determined least free-energy path.

Figure 8

One-dimensional PMF of Ala₁₀ in water calculated by integration of the 2D PMF using eq 1.