Solvation Thermodynamics of Oligoglycine with Respect to Chain Length and Flexibility

Abstract

Oligoglycine is a backbone mimic for all proteins and is prevalent in the sequences of intrinsically disordered proteins. We have computed the absolute chemical potential of glycine oligomers at infinite dilution by simulation with the CHARMM36 and Amber ff12SB force fields. We performed a thermodynamic decomposition of the solvation free energy (ΔG(sol)) of Gly2-5 into enthalpic (ΔH(sol)) and entropic (ΔS(sol)) components as well as their van der Waals and electrostatic contributions. Gly2-5 was either constrained to a rigid/extended conformation or allowed to be completely flexible during simulations to assess the effects of flexibility on these thermodynamic quantities. For both rigid and flexible oligoglycine models, the decrease in ΔG(sol) with chain length is enthalpically driven with only weak entropic compensation. However, the apparent rates of decrease of ΔG(sol), ΔH(sol), ΔS(sol), and their elec and vdw components differ for the rigid and flexible models. Thus, we find solvation entropy does not drive aggregation for this system and may not explain the collapse of long oligoglycines. Additionally, both force fields yield very similar thermodynamic scaling relationships with respect to chain length despite both force fields generating different conformational ensembles of various oligoglycine chains.

Figure 1

Solvation free energy of rigid/extended (solid) and flexible (dashed) oligoglycines at 310 K as a function of chain length from simulations with the C36 (left) and ff12SB (right) force fields. The vdw, elec, and overall solvation free energy are shown in order from top to bottom. Errors associated with each quantity can be found in Table S1.

Figure 2

Solvation entropy of rigid/extended (solid) and flexible (dashed) oligoglycine as a function of chain from simulations with the C36 (left) and ff12SB (right) force fields using the FD (solid triangle) and EP (open triangle) approaches. The vdw, elec, and overall solvation entropy are shown in order from top to bottom. Error estimates are provided in Tables S2 and S3.

Figure 3

Solvation enthalpy of rigid/extended (solid) and flexible (dashed) oligoglycine at 310 K as a function of chain from simulations with the C36 (left) and ff12SB (right) force fields calculated by the FD (solid triangle) and EP (open triangle) approaches. The vdw, elec, and overall solvation enthalpy are shown in order from top to bottom.

Figure 4

Differences in the average energies of the components contributing to $\Delta H^{\text{sol}}\approx \Delta U^{\text{sol}}$ for flexible Gly₂ (left) and Gly₅ (right). The subscript u denotes the solute/peptide and v denotes the solvent. $\Delta U^b$ is the difference between the average bonded intrapeptide energies (e.g., dihedral, bond, angle energies) of oligoglycine in the final, solvated state and the gas phase.

Figure 5

Thermodynamic decomposition of solvation free energy for rigid/extended (solid) and flexible (dashed) oligoglycines as a function of chain length and force field at 310 K calculated by the FD and EP approaches. (Solid circle) $\Delta G^{\text{sol}}$ calculated by free energy perturbation; (solid and open triangles) $\Delta H^{\text{sol}}$ and $-T\Delta S^{\text{sol}}$ calculated by the FD and EP approaches, respectively. Note that $\Delta H^{\text{sol}}$ and $-T\Delta S^{\text{sol}}$ at 310 K was approximated as their averages at 300 and 320 K.