Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix-Coil Transition and Helix-Helix Assembly in a Deca-Alanine Peptide

Abstract

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state over extended states and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into quasi-chemical components consisting of a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part that is well described by a Gaussian. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the extended coil states. Analysis of enthalpic effects shows that it is the favorable hydration of the peptide backbone that favors the unfolded state. Protein intramolecular interactions favor the helix state and are decisive in favoring folding. In the pairing of two helices, the cavity contribution outweighs the short-range attractive protein-water interactions. However, long-range, protein-solvent attractive interactions can either enhance or reverse this trend depending on the mutual orientation of the helices. In helix-helix assembly, change in enthalpy arising from change in attractive protein-solvent interactions favors disassembly. In helix pairing as well, favorable protein intramolecular interactions are found to be as important as hydration effects. Overall, hydrophilic protein-solvent interactions and protein intramolecular interactions are found to play a significant role in the thermodynamics of folding and assembly in the system studied.

Figure 1

Quasichemical organization of the excess chemical potential. The λ_SE = 3 Å envelope defines the solvent excluded (SE) volume and λ_G = 5 Å defines the envelope for which the conditional solute–solvent binding energy P(ε|ϕ) is Gaussian. For chemistry coupled (uncoupled), the solute–solvent interaction is present (absent). In eq 1 we follow G-packing to the hydrated solute; in eq 2 we follow SE-packing. Figure adapted from ref with permission from Elsevier.

Figure 2

Hydration free energies of the helix and {C₀,…,C₉} coil states. The horizontal axis has no meaning and is used solely to differentiate multiple coil states with similar μ^ex values. (One could plot the data versus R_g or R_c, but the physical picture that the less compact structure has a more negative free energy is independent of these considerations.) The radius of the symbol is equal to twice the standard error of the mean (2σ). The C₀ state is the smallest circle in the collection of unfolded states; the standard error is about half compared to the other estimates because we had 4 times more data for C₀ (Sec. S.I).

Figure 3

Components of the potential of mean force in bringing two helices together. The helices are shown in green and the parallel (blue △) and antiparallel (red ○) arrangements are indicated by the arrows. W_solv is the solvent contribution (open symbols), and W_solv + ΔU (eq 3) is the net PMF (filled symbols). For r ≲ 8 Å, there is steric overlap between the helices and ΔU rises rather sharply. Data including these values of ΔU are thus not shown.

Figure 4

SE packing, revised chemistry, and long-range (eq 2) contributions to the free energy of helix–helix complexation. The data is presented relative to two helices infinitely apart. At contact (r ≈ 9.5 Å) the packing effects outweigh the local chemistry effects, but this trend can be easily reversed by long-range interactions.

Figure 5

Van der Waals (solid line) and electrostatic (open symbols, dashed lines) contributions to the free energy. The long-range contribution to free energy is uniquely decomposable^, into electrostatic and van der Waals contributions because P(ε|ϕ) = P(ε_vdw|ϕ) × P(ε_elec|ϕ), where ε = ε_vdw + ε_elec, i.e., the individual binding energy distributions are uncorrelated.