The effects of pK(a) tuning on the thermodynamics and kinetics of folding: design of a solvent-shielded carboxylate pair at the a-position of a coiled-coil

Abstract

The tuning of the pK(a) of ionizable residues plays a critical role in various protein functions, such as ligand-binding, catalysis, and allostery. Proteins harness the free energy of folding to position ionizable groups in highly specific environments that strongly affect their pK(a) values. To investigate the interplay among protein folding kinetics, thermodynamics, and pK(a) modulation, we introduced a pair of Asp residues at neighboring interior positions of a coiled-coil. A single Asp residue was replaced for an Asn side chain at the a-position of the coiled-coil from GCN4, which was also crosslinked at the C-terminus via a flexible disulfide bond. The thermodynamic and kinetic stability of the system was measured by circular dichroism and stopped-flow fluorescence as a function of pH and concentration of guanidine HCl. Both sets of data are consistent with a two-state equilibrium between fully folded and unfolded forms. Distinct pK(a) values of 6.3 and 5.35 are assigned to the first and second protonation of the Asp pair; together they represent an energetic difference of 5 kcal/mol relative to the protonation of two Asp residues with unperturbed pK(a) values. Analysis of the rate data as a function of pH and denaturant concentration allowed calculation of the kinetic constants for the conformational transitions of the peptide with the Asp residues in the doubly protonated, singly protonated, and unprotonated forms. The doubly and singly protonated forms fold rapidly, and a ϕ-value analysis shows that their contribution to folding occurs subsequent to the transition state ensemble for folding. By contrast, the doubly charged state shows a reduced rate of folding and a ϕ-value near 0.5 indicative of a repulsive interaction, and possibly also heterogeneity in the transition state ensemble.

Figure 1

(A) Ribbon diagram of the coiled-coil dimer of GCN4-p1 (30). The buried Asp¹⁶ is shown in ball-and-stick representation. (B) Expanded diagram based on the crystal structure of Deng et al. (30), showing hydrogen-bonded interactions of Asp¹⁶. The sphere indicates a water molecule. (C) Alternative conformation of Asp¹⁶ as seen in the crystal structure of a GCN4/cortexillin hybrid coiled-coil peptide (38). (D) A six-state model that describes the coupled folding and ionization equilibria of cross-linked GCN4-D. F⁻² represents the folded coiled-coil conformations in which the two buried Asp residues are deprotonated, and FH⁻ and FH₂ are the single- and double-protonated forms. U⁻², UH⁻, and UH₂ are the corresponding unfolded states. K₀, K₁, and K₂ are equilibrium constants for unfolding of each species. K_a is the ionization constant for the buried aspartate (Asp¹⁸) in the unfolded state; K_b and K_c are ionization constants for each Asp¹⁸ in the SS-linked GCN4-D dimer. Numbers next to the arrow refer to elementary rate constants for each transition.

Figure 2

Unfolding equilibrium of GCN4-D as a function of denaturant concentration and pH monitored by far-UV CD. The mean residue ellipticity at 222 nm, [θ]₂₂₂, measured at 10°C (A) and 25°C (B) is plotted versus GuHCl concentration at different pH values. (Solid lines) Global fit to a six-state model (Fig. 1D), using the kinetically derived parameters as constraints (Table 1).

Figure 3

(A) Semilogarithmic plots of the observed folding/unfolding rate constant of GCN4-D at 10°C versus GuHCl concentration (chevron plot). Rate constants for folding (solid symbols) and unfolding (open symbols) were measured by stopped-flow fluorescence at pH 4.8 (squares), 5.2 (triangles), 5.7 (circles), and 6.2 (diamonds). (Solid lines) Modeling of the kinetic data using numerical analysis according to a six-state kinetic scheme. In this simulation, the rate of diffusion of hydrogen ions is arbitrarily set to 10¹² s⁻¹. (B) Plot of observed unfolding rates versus pH, obtained at a final GuHCl concentration of 3.50 (▵), 3.75 (□), and 4.00 M (○). (Solid lines) Fit of the observed unfolding rates to the six-state kinetic scheme, using the kinetic parameters obtained from simulating the chevron plot in panel A. (C) Plot of fraction of folded GCN4-D versus GuHCl concentration, measured by circular dichroism at pH 4.8 (■), pH 5.2 (▴), pH 5.7 (●), and pH 6.2 (♦). (Solid lines) Theoretical curves computed on the basis of kinetic parameters obtained from simulating the kinetic data in Fig. 2a. (D) Plot of elementary folding and unfolding constants as a function of GuHCl concentration for the neutral, −1 charged, and −2 charged species (dashed lines). (Solid lines) Theoretical chevron plot for the neutral, −1 charged, and −2 charged species, assuming 100% population, computed on the basis of kinetic parameters obtained from simulating kinetic data in panel A. (Dashed lines) Elementary rate constants as a function of GuHCl concentration.

Figure 4

(A) Plots of calculated populations (mole fraction) of the folded states (FH₂, FH⁻, and F⁻²) versus pH in the absence of denaturant. The unfolded states (dotted line) have negligible population under these conditions. Populations were calculated from the kinetic parameters in Table 1. (B) Flux of molecules through the three parallel channels in the six-state scheme (Fig. 1D), defined as the product of folded population in each charge state and the corresponding unfolding rate constant, normalized with respect to the total flux. (C) Schematic free-energy profiles for the conformational transitions of the three charge states of GCN4-D. A preexponential factor A = 1 × 10⁶ s⁻¹ was used for calculating the free energy of the folding transitions state, ΔG^‡_f = −RT·ln(k_f/A).