Pressure-induced protein-folding/unfolding kinetics

Abstract

We use an off-lattice minimalist model to describe the effects of pressure in slowing down the folding/unfolding kinetics of proteins when subjected to increasingly larger pressures. The potential energy function used to describe the interactions between beads in the model includes the effects of pressure on the pairwise interaction of hydrophobic groups in water. We show that pressure affects the participation of contacts in the transition state. More significantly, pressure exponentially decreases the chain reconfigurational diffusion coefficient. These results are consistent with experimental results on the kinetics of pressure-denaturation of staphylococcal nuclease.

Figure 1

Pressure dependence of the PMF between two methane-like solutes in water. The arrow indicates changes with increasing pressures from −.16 to 7.25 kbar.

Figure 2

An illustration of the ground state of the Gō model. Each arrow represents an attractive interaction that exists between two monomers; there are 47 interactions. The nonbonded interaction between two monomers without a connecting arrow is a hard core repulsion term responsible for excluded volume.

Figure 3

Square-well potential with a desolvation barrier representing the hydrophobic-pair potential between pairs of beads participating in native contacts in the Gō model. We parameterize the pressure dependence of the model potential by ɛ⁺ = 1.333 + .2778P, and ɛ⁻ = −1.00 + .1667P, where P is in kbar. At P = 0, the contact-well depth is −1, and the desolvation barrier from the solvent-separated configuration is 1.333. Here the units of energy have been chosen for convenience so that the relevant temperatures are of order one. Energies are shown in units of temperature.

Figure 4

Free-energy curves as a function of the folding order parameter Q, at various temperatures for the square-well potential-energy function with no desolvation barrier (Upper), and with a desolvation barrier corresponding to P = 0 kbar (Lower). T_f for the no desolvation and desolvation models are T_f ∼ 0.74 and T_f ∼ 0.64, respectively.

Figure 5

The specific heat, C_v, of the Gō model vs. temperature for various pressures, and for the potential-energy function without a desolvation barrier (Upper) is contrasted with the folding denaturation curves (Lower). The specific heat for the model with no desolvation barrier is labeled NB, with R_c = 1.8 and R_c = 1.167, where R_c is the width of the attractive square-well potential.

Figure 6

Free-energy curves as a function of the folding order parameter Q at the folding temperature T_f and various pressures (in kbar). Notice that as the pressure is increased, ɛ⁻ decreases, and therefore T_f also decreases.

Figure 7

MFPT (τ_f) as a function of 1/T. Time is measured in number of MC steps. (Inset) The MFPT as a function of P at T = T_f. Error bars reflect one SD from block averages.

Figure 8

Pressure dependence of the chain-reconfigurational correlation time, τ_corr (right side axis); and the reconfigurational-diffusion coefficient, D(Q) (left side axis), for the β-barrel minimalist model.