Energetics and kinetics of substrate analog-coupled staphylococcal nuclease folding revealed by a statistical mechanical approach

Abstract

Protein conformational changes associated with ligand binding, especially those involving intrinsically disordered proteins, are mediated by tightly coupled intra- and intermolecular events. Such reactions are often discussed in terms of two limiting kinetic mechanisms, conformational selection (CS), where folding precedes binding, and induced fit (IF), where binding precedes folding. It has been shown that coupled folding/binding reactions can proceed along both CS and IF pathways with the flux ratio depending on conditions such as ligand concentration. However, the structural and energetic basis of such complex reactions remains poorly understood. Therefore, we used experimental, theoretical, and computational approaches to explore structural and energetic aspects of the coupled-folding/binding reaction of staphylococcal nuclease in the presence of the substrate analog adenosine-3',5'-diphosphate. Optically monitored equilibrium and kinetic data, combined with a statistical mechanical model, gave deeper insight into the relative importance of specific and Coulombic protein-ligand interactions in governing the reaction mechanism. We also investigated structural aspects of the reaction at the residue level using NMR and all-atom replica-permutation molecular dynamics simulations. Both approaches yielded clear evidence for accumulation of a transient protein-ligand encounter complex early in the reaction under IF-dominant conditions. Quantitative analysis of the equilibrium/kinetic folding revealed that the ligand-dependent CS-to-IF shift resulted from stabilization of the compact transition state primarily by weakly ligand-dependent Coulombic interactions with smaller contributions from specific binding energies. At a more macroscopic level, the CS-to-IF shift was represented as a displacement of the reaction "route" on the free energy surface, which was consistent with a flux analysis.

Keywords: protein binding; protein folding; real-time NMR; staphylococcal nuclease; statistical mechanical model.

Fig. 1.

(A) Unified model of ligand binding-coupled folding via IF and CS pathways (fast association/dissociation limit) and its free energy landscape. (B) Schematic representation of our model. The Hamiltonian with respect to the substrate (prAp) (green) binding and His protonation (orange) consists of the specific binding (upper half) and Coulombic (lower half) interactions. The substrate binding and His protonation states were represented by the corresponding grand canonical partition function at the constant chemical potentials of prAp and proton (pH). The charges arising from the other factors were included in the net charge of the SNase molecule. (C) Ribbon diagram of wild-type SNase in a substrate analog (pdTp, green) complex based on a crystallographic structure (Protein Data Bank ID code 1SNC). The N-terminal β-barrel and C-terminal α-helical domains are shown on cyan and magenta background, respectively. The ¹H-¹⁵N resonance shift on prAp binding the native state (N) is mapped onto the SNase structure: 0 < Δδ < 1 SD, 0.21 ppm (white), 1 SD < Δδ < 2 SD (orange), and 2 SD < Δδ (red). The residues in gray remained unassigned in N. The residues contacting with pdTp are represented by stick models. The resonance shift at each assigned residue is shown (Right). (D) A representative structure of SNase in a substrate analog (prAp, green) complex obtained by RPMD simulation at 300 K. The residues contacting with prAp at low (<0.2), intermediate (0.2 to 0.4), and high (0.4<) probabilities are shown in white, orange, and red, respectively. The corresponding probability of contact at each residue is shown (Right). (C and D) The substrate analog binging site, native secondary structures, and sequence segments consisting of residues associated prAp binding defined by the NMR measurements in the native state and replica-permutation molecular dynamics simulation at 300 K are shown above the panels.

Fig. 2.

(A and B) prAp-induced stabilization of SNase against (A) urea and (B) temperature. (A) Urea-induced equilibrium unfolding transition curves were measured by CD in the absence and presence of 180 μM prAp at pH 7.0 and 22 °C. The CD and normalized data are shown by filled and open symbols, respectively. The solid lines show the transition curves obtained by fitting using the two-state model. The green line indicates the difference in native fraction in the absence and presence of 180 μM prAp. (B) Rmsd of an SNase molecule in the absence and presence of a prAp as a function of temperature calculated by using the replica-permutation molecular dynamics simulation of the corresponding system. Error bars represents the SD of the rmsd. (C and D) prAp binding-coupled equilibrium folding (at 2.9 M urea) and prAp binding equilibrium of SNase (at 0 M urea) and fractions of relevant species as a function of prAp concentration. (C) Changes in ellipticity at 225 nm are shown by circles at 0 M and 2.9 M urea at pH 7.0 and 22 °C; the corresponding transition curves represent prAp binding to the prAp-free native state (N) and prAp-coupled folding, respectively. The ellipticity values extrapolated to zero time of the folding kinetics and those fully equilibrated after folding reaction (SI Appendix, Fig. S3) are also shown. (D) Fractions of N/N-prAp (N-prAp: prAp-bound native state), N-prAp, N, and U/D-prAp (U: unfolded state; D-prAp: prAp-bound denatured state) derived from the prAp-coupled equilibrium folding transition curves monitored by ellipticity and fluorescence at 374 nm (SI Appendix, Fig. S1G). (C and D) The solid lines were obtained by the model analysis. Color codes are explicitly shown in each panel.

Fig. 3.

(A) Kinetic traces of prAp binding-coupled folding monitored by Trp fluorescence at 326 nm at various prAp concentrations under denaturing condition (2.9 M urea, pH 7.0, 22 °C). The broken and solid lines were obtained by nonlinear least-squares fitting and by the model analysis, respectively. The kinetic traces were appropriately shifted for clarity as indicated by circles. Color codes are explicitly shown in the panel. (B) PrAp dependence of the apparent rates of the prAp-coupled folding obtained by fitting the ellipticity- and fluorescence-monitored kinetic traces (circles) to a single-exponential function as well as the rates obtained by 2D (filled squares) and 1D NMR (open square); the solid lines represent the prAp dependence of the elementary rate constants of folding (orange) and unfolding (red) (k_DN and k_ND, respectively) and apparent rate (blue) obtained by the model analysis. (C) Comparison of HSQC spectra between the unfolded state (U) (green) and the first data point of prAp-coupled folding kinetics at 120 s after the initiation of the reaction (red). Representative peaks with significant shift (Val23, Val39, and Ile92) are zoomed in the insets. PrAp dependence of the resonance shift of these residues in the denatured species at 120 s of the reaction is shown which corresponded to the binding curve of the transient encounter complex (D-prAp). The black lines are obtained by nonlinear least-squares global fitting to a binding function. (D) Time-dependent change in ¹H resonance in the aromatic side-chain region. A series of the ¹H-NMR spectra in the aromatic side chain region especially for histidine Hε¹ is shown as a function of time after the initiation of the reaction. The side-chain structure of histidine is also shown in the panel. (E) The ¹H-¹⁵N resonance shift between U and the denatured species at 120 s of the reaction is mapped onto the native structure: 0 < Δδ < 1.4 SD, 0.01 ppm (white), 1.4 SD < Δδ < 2 SD (orange), and 2 SD < Δδ (red). The residues in gray remain unassigned in U and D-prAp. The resonance shift at each assigned residue is shown (Right). (F) A snapshot of the SNase structure obtained by the RPMD simulation at 500 K. The prAp molecule is shown in green. The residues contacting with prAp at low (<0.2), intermediate (0.2 to 0.4), and high (0.4<) probabilities are shown in white, orange, and red, respectively. The corresponding probability of contact at each residue is shown (Right). (E and F) The substrate analog binging site, native secondary structures, and sequence segments consisting of residues associated prAp binding defined by the NMR measurements in the native state and RPMD simulation at 300 K are shown above the panel.

Fig. 4.

Free energy diagrams and landscapes of prAp binding-coupled folding of SNase at representative prAp concentrations, obtained by the model analysis. (A) Free energy diagrams at 0 (red), 10 (blue), and 400 μM (green) prAp. (B) Free energy diagrams of the CS and IF pathways at 10 and 400 μM prAp. (C) Folding flux normalized by the concentration of the denatured species (prAp-bound and -free denatured states). J_DN, J_CS, and J_IF indicate the total flux and the flux via the CS and IF pathways, respectively. (D) Relative flux (normalized by the total flux) via the CS and IF pathways. (E) The free energy profile of the prAp-coupled folding along the CS and IF pathways. The corresponding fluxes (arrows) are drawn along the free energy profile of each pathway. The thickness of the arrows represents the flux values. (F) Free energy landscapes as a function of the fractional prAp-bound form (%bound) at 10 and 400 μM prAp. The macroscopic binding/folding route is indicated by the arrow on the free energy landscape. (A and F) The energetic contributions of the specific binding and Coulombic interactions to the stability are shown in pink and light blue, respectively. (E and F) The stability of each species and the kinetic pathway/reaction route are projected onto the bottom plane by color and arrows, respectively. Color codes of the stability are explicitly shown between E and F.

Fig. 5.

Schematic summarizing the CS-to-IF shift of prAp-coupled folding of SNase. Free energy landscapes of the reaction at 10 and 400 μM prAp are shown along with the macroscopic binding/folding route and the energetic contributions of the specific binding (pink) and Coulombic (blue) interactions to the stability (Fig. 4). The shape of the landscapes is simplified to explicitly show the saddle point (%bound in TS_ap). Structural characteristics of prAp-bound forms (D-prAp and N-prAp) are also represented on the basis of the NMR resonance shifts. Residues with the large ¹H-¹⁵N resonance shift between the prAp-bound and -free forms are explicitly shown with the same color codes as those in Figs. 1 and 3 for N-prAp and D-prAp, respectively.