Establishing the entatic state in folding metallated Pseudomonas aeruginosa azurin

Abstract

Understanding how the folding of proteins establishes their functional characteristics at the molecular level challenges both theorists and experimentalists. The simplest test beds for confronting this issue are provided by electron transfer proteins. The environment provided by the folded protein to the cofactor tunes the metal's electron transport capabilities as envisioned in the entatic hypothesis. To see how the entatic state is achieved one must study how the folding landscape affects and in turn is affected by the metal. Here, we develop a coarse-grained functional to explicitly model how the coordination of the metal (which results in a so-called entatic or rack-induced state) modifies the folding of the metallated Pseudomonas aeruginosa azurin. Our free-energy functional-based approach directly yields the proper nonlinear extra-thermodynamic free energy relationships for the kinetics of folding the wild type and several point-mutated variants of the metallated protein. The results agree quite well with corresponding laboratory experiments. Moreover, our modified free-energy functional provides a sufficient level of detail to explicitly model how the geometric entatic state of the metal modifies the dynamic folding nucleus of azurin.

Fig. 1.

The free-energy profile of zinc metallated azurin at temperature T = 1.91. The bold line represents the free-energy profile when the metal–ligand interactions were simply treated as contacting positions carrying electrostatic interactions during the folding event (●). Dashed lines connect the corresponding positions of the free-energy profile of the metallated enzyme treated with the coordinate contribution of the histidine and glycine metal–ligand interactions H_{int_coord} (□). (Inset) The primary coordination sphere: the coordinating ligands, His-46 (orange) and Gly-45 (green) are shown relative to the canonical loop (gray).

Fig. 2.

The free-energy profile for metallated-azurin (A) and apo-azurin (B) (adapted from ref. 22) as a function of temperature. The dashed line in A follows the trajectory of the metallated folding nucleus as function of temperature. From right to left the corresponding temperatures for the folding barriers are ∼1.86 (‡_early), ∼1.96 (‡_middle), and ∼2.06 (‡_late).

Fig. 3.

The local fluctuations around the native structure of members of the transition-state ensemble as measured by the mean square deviation (MSD) of residues as function of temperature [i.e., T = 1.86 (‡_early), 196 (‡_middle), and 2.06 (‡_late) represented as black, red, and blue, respectively] and residue sequence number. The fluctuation of a given residue constituting the fold barrier is given by the convariance matrix B, where B_ij = a⁻²〈(r_i − 〈r_i〉)(r_j − 〈r_j〉)〉 and a is a scaling factor equal to 3.8 Å. The cofactor is represented by the set of triangles in the right lower corner. (Inset) Formation of the primary coordination sphere: the five copper ligands, His-46 (orange), Gly-45 (green), Cys-112 (cyan), His-117 (red), Met-121 (purple), and the cofactor (yellow).

Fig. 4.

Nonlinear extrathermodynamic free-energy relationships. (Upper) Experimental, ln k_obs versus GuHCl (M); adapted from ref. . (Lower) Theoretical chevron plots, ln k_obs versus temperature, for 14 metallated-azurin variants provide an overview of the energetic consequences of mutations on the folding barrier along with the relative position of ‡. An expanded view of the individual theoretical chevron plot is shown in SI Fig. 7.

Fig. 5.

A direct comparison of theoretical and experimental φ-values. x represents φ_experimental at 0 M and φ_theoretical at T = 1.86 (‡_early), ○ represents φ_experimental at 2 M and φ_theoretical at T = 1.96 (‡_middle), and ▵ represents φ_experimental at 4 M and φ_theoretical at T = 2.06 (‡_late). The correlation coefficient between the calculated and experimental values is 0.77.