A water-explicit lattice model of heat-, cold-, and pressure-induced protein unfolding

Abstract

We investigate the effect of temperature and pressure on polypeptide conformational stability using a two-dimensional square lattice model in which water is represented explicitly. The model captures many aspects of water thermodynamics, including the existence of density anomalies, and we consider here the simplest representation of a protein: a hydrophobic homopolymer. We show that an explicit treatment of hydrophobic hydration is sufficient to produce cold, pressure, and thermal denaturation. We investigate the effects of the enthalpic and entropic components of the water-protein interactions on the overall folding phase diagram, and show that even a schematic model such as the one we consider yields reasonable values for the temperature and pressure ranges within which highly compact homopolymer configurations are thermodynamically stable.

FIGURE 1

Phase diagram for Staphylococcal nuclease from Fourier transform infra-red (FTIR) spectroscopy, small angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC) experiments. Adapted with permission from Ravindra and Winter (3).

FIGURE 2

The phase diagram of a 17-mer homopolymer protein for J_H/J = 0.2, Δυ/υ₀ = 0.348, λ_h = 0, λ_b = 1, and q = 30. The inner line demarcates the region within which the probability of observing the folded state is 87.5% or greater. The other lines similarly demarcate the regions within which the folded probabilities are >75%, 62.5%, 50% (bold), 37.5%, 25%, and 12.5% (outermost).

FIGURE 3

Representative conformations for a 17-mer model protein in the (a) native state, (b) thermally denatured ensemble of states, and (c) high-pressure cold-unfolded state.

FIGURE 4

Contours of 50% folded probability for a 20-mer protein for varying values of the entropic penalty for forming interfacial hydrogen bonds. Simulations were performed with λ_h = 0 and changing λ_b. To retain the same bulk water thermodynamics, the total number of water orientations q increases such that the fraction of bonding configurations for a pair of bonding arms on adjacent molecules (i.e.: (2λ_b + 1)q/q² = (2λ_b + 1)/q) is kept constant, at 0.1. The other model parameters remain constant at J_H/J = 0.2 and Δυ/υ₀ = 0.348.

FIGURE 5

Contours of 50% folded probability for a 20-mer protein for varying values of the enthalpic bonus for interfacial hydrogen bonds J_H/J. The other model parameters are Δυ/υ₀ = 0.348, λ_b = 1, λ_h = 0, and q = 30.

FIGURE 6

Thermal denaturation temperature at zero pressure for proteins of various sizes. J_H/J = 0.2, Δυ/υ₀ = 0.348, λ_h = 0, λ_b = 1, and q = 30 were used for all proteins. The line is a guide to the eye. Irregularities in the trend of decreasing thermal denaturation temperature with protein size are due to the discrete nature of the lattice. Equation 11 connects the structure of the native and denatured states to the thermal denaturation temperature through the change in entropy upon unfolding. The degeneracy of the native, compact state does not increase regularly with protein size. For example, a 9-mer or 16-mer has a square-shaped native state, while other protein sizes have rougher surfaces.

FIGURE 7

A comparison between the thermodynamics of unfolding in (a) our model and in (b) a schematic summary of experimental results. Panel b was adapted with permission from Hawley (1).

FIGURE 8

Contour of 50% folded probability for a model 20-mer with temperature and pressure converted into dimensional quantities using J = 23 kJ/mol and υ₀ = 18 cm³/mol. Parameter values are J_H/J = 0.4 and λ_b = 5, λ_h = 0, q = 110, and Δυ/υ₀ = 0.348.

FIGURE 9

Partial molar volumes of the model hydrophobic solutes in water, in units of υ₀. Data from graphs a, c, and e are at constant P = 0. Data from graphs b, d, and f are at constant T = 0.108. Parameter values are J_H/J = 0.2, λ_b = 3, λ_h = 0, q = 70, and Δυ/υ₀ = 0.348.