Protein folding guides disulfide bond formation

Abstract

The Anfinsen principle that the protein sequence uniquely determines its structure is based on experiments on oxidative refolding of a protein with disulfide bonds. The problem of how protein folding drives disulfide bond formation is poorly understood. Here, we have solved this long-standing problem by creating a general method for implementing the chemistry of disulfide bond formation and rupture in coarse-grained molecular simulations. As a case study, we investigate the oxidative folding of bovine pancreatic trypsin inhibitor (BPTI). After confirming the experimental findings that the multiple routes to the folded state contain a network of states dominated by native disulfides, we show that the entropically unfavorable native single disulfide [14-38] between Cys14 and Cys38 forms only after polypeptide chain collapse and complete structuring of the central core of the protein containing an antiparallel β-sheet. Subsequent assembly, resulting in native two-disulfide bonds and the folded state, involves substantial unfolding of the protein and transient population of nonnative structures. The rate of [14-38] formation increases as the β-sheet stability increases. The flux to the native state, through a network of kinetically connected native-like intermediates, changes dramatically by altering the redox conditions. Disulfide bond formation between Cys residues not present in the native state are relevant only on the time scale of collapse of BPTI. The finding that formation of specific collapsed native-like structures guides efficient folding is applicable to a broad class of single-domain proteins, including enzyme-catalyzed disulfide proteins.

Keywords: disulfide proteins; early collapse; enzyme-catalyzed folding; native-like interactions; nonnative interactions.

Fig. 1.

(A) Ribbon diagram of the native structure of the 58 residue BPTI containing three disulfide bonds (marked in yellow) between residues Cys₅ and Cys₅₅ [5–55], Cys₁₄ and Cys₃₈ [14–38], and Cys₃₀ and Cys₅₁ [30–51], respectively. The antiparallel β-sheet is in red. (B) Simplified representation of the secondary tructure of BPTI and the three native disulfide bonds in BPTI. (C) Variables ${\beta }_O$ and ${\beta }_R$ mimicking the redox conditions. Small ${\beta }_O$ (${\beta }_R$) represent strongly oxidizing (reducing) condition. The star with ${\beta }_O$ = 1.0 and ${\beta }_R$ = 1.5 is used in most of the simulations. These values are a mixture of mildly oxidizing and reducing condition. (D) Distribution of fraction of native contacts obtained from high-temperature simulations.

Fig. S1.

The mean values of the three structural parameters $\langle d_{\alpha }\rangle$, $\langle {\theta }_{\alpha }^k\rangle$, and $\langle n_{\alpha }\rangle$ obtained from equilibrium simulations at $k_B$T = $0.9\mathit{ϵ}$ for BPTI containing with different combination of S–S bonds. Here, $d_{\alpha }$ is the distance between the two cysteines in native state, ${\theta }_{\alpha }^k$ ($k=\mathrm{1,2}$) is the orientation angle defined in Fig. S2, and $n_{\alpha }$ is the number of residues within a spherical shell with radius R (Fig. S3). The label α = 1, 2, and 3 refer to the three disulfide bonds [5–55], [14–38], and [30–51], respectively. For example, for [5–55] (Left), these values are obtained from the simulations of BPTI mutants containing [5–55], N′, $N_{SH}^{SH}$, and N.

Fig. S2.

Definition of the orientation angle ${\theta }_1$ and ${\theta }_2$. The indices i − 1, i, i + 1 and j − 1, j, i + 1 are the two different peptide segments such that i and j are the two cysteines that can form a disulfide bond in the native state; ${\theta }_1$ is the angle between the vector connecting the cysteine residues i and j (i < j) and the covalent bond connecting $Cy{s}^i$ and the neighboring $C_{\alpha }^{i-1}$. A similar definition holds for ${\theta }_2$.

Fig. S3.

The definition of the number of residues ($n_{\alpha }$) within a spherical shell with radius R, drawn from O, the center of the α^th S–S bond.

Fig. 2.

The folding pathway, represented as a network of native-like states, connecting the fully unfolded state (R) to the folded (N) state with three disulfide bonds. For ${\beta }_O$ = 1.0 and ${\beta }_R$ = 1.5, the early event produces predominantly [14–38]. Subsequently, there is a bifurcation in the pathway with this intermediate rearranging to [5–55] and [30–51]. The percentages indicate the dominant route to N from R. Representative structures of all of the relevant states are shown. The numbers in parentheses were obtained from simulations with ${\beta }_O$ = 2.0 and ${\beta }_R$ = 4.0, which mimics the redox conditions used by Weissman and Kim (24). In red are the fluxes through the various native intermediates to the native state obtained from simulations that consider native and nonnative disulfide bond formation. The qualitative agreement between the two simulations is striking.

Fig. 3.

(A) Dependence of the mean first passage time (black line) for forming [14–38] as the oxidizing condition is changed from being strong (small ${\beta }_O$) to weak (large ${\beta }_O$). The red line gives the yield of [14–38]. (B) Time-dependent decay, $P_u^{\alpha }\left(t\right)$, of the three native single disulfide species. (Inset) $ln{P}_u^{\alpha }\left(t\right)$; the lines are linear fits.

Fig. S4.

(A) A trajectory showing the time-dependent changes during the [14–38] → [30–51] transition. The distance $d_{14-38}$ increases (red) abruptly around $t\approx$ 9$\times$ 10³τ and is accompanied by a decrease in $d_{30-51}$ (blue). During the transition, Q remains low (scale is on the right), which is also illustrated by the snapshot below. (B) Same as A except the trajectories and conformations are for the [14–38] → [5–55] transition. Note that the scales for the distance as well as Q are different in A and B. (C) Distribution of the radius of gyration for the ensemble of R′ structures sampled during the [14–38] → [30–51] transition, an example of which is shown in A. (D) Same as C except the distribution is for the [14–38] → [5–55] transition.

Fig. S5.

Distribution of $R_g$ using an ensemble of unfolded conformations generated at high temperature. The set of initial conformations with $R_g>$ 20 Å and fraction of native contacts $Q<$ 0.1 (Fig. 1D) is used to initiate oxidative refolding. The initial conformations are devoid of any disulfide bonds.

Fig. 4.

(A) An example of one of 2,000 oxidative folding trajectories showing the route to the folded state from a fully reduced starting conformation with low Q. The blue curve shows the decrease in the radius of gyration, $R_g$ (scale is on the right). The gray lines show formation of various disulfide species labeled on the left. Snapshots (a–h) show some of the conformations sampled in the trajectory. (B) Plot of the distance between the distance between residues 14 and 38, $d_{14-38}$, as a function of the fraction, $Q_{\beta }$, of contacts in the β-hairpin shows that the hairpin (formed between β-strands from Ile18 to Asn24, and from Leu29 to Tyr35) is fully structured before [14–38] formation. (C) Distribution of $Q_{\beta }$ when $d_{14-38}$ = 5.7 Å (the distance at which [S–S] bond forms) for the first time in a folding trajectory.

Fig. S6.

A second folding trajectory is shown to illustrate that except for changes in the value of the first passage time, the behavior is similar to the one shown in Fig. 4A. Some of the sampled conformations (a–h) are explicitly shown. This figure, together with the one in Fig. 4A, shows that structures similar to the native state of BPTI are populated in the folding process relatively early.

Fig. 5.

(A) Illustration of the dynamics of rearrangement from N′ to ${\mathrm{N}}_{SH}^{SH}$ using distance between the different Cys residues. The colors are illustrated in the figure. In this transition, BPTI samples both the nonnative species [30–51, 5–14] (structure on the left) and [30–51, 5–38] (conformation on the right). (B) Same as A except this trajectory describes the N* $\to$ ${\mathbf{N}}_{SH}^{SH}$ transition.

Fig. S7.

Distributions of the radius of gyration ($R_g$) for the three native two-disulfide intermediates calculated from simulations emphasizing only native-like interactions. The distributions are narrow and are roughly peaked at the value of $R_g$ corresponding to the native state, thus confirming the near native structures in these intermediates.

Fig. 6.

Time for forming [14–38] relative to the wild-type as function of λ (defined in Eqs. S1 and S2). The stability of the β-hairpin increases (decreases) as λ increases (decreases). The relative times are given for two variants. One of them (black line) is for the WT (λ = 1.0) and the other blue is for a pseudo mutant, in which disulfide bonds other than [14–38] cannot form. The red curves show the yield of [14–38] for the WT.

Fig. S8.

Kinetics of formation of three single-disulfide bonds for type I model (A), type II model (B), and type III model (C). The three models are described in detail in the main text. The mean first-passage time values, quoted in the main text, are obtained using single exponential fits shown as solid lines in A–C.

Fig. S9.

Folding pathways for an in silico mutant created by setting $E_{SS}=0$ (Eq. S1) for only the [14–38] disulfide bond. Although the mutant does fold clearly, the resulting pathways bear no resemblance to the ones found for the wild type (Fig. 2).

Fig. S10.

Kinetics of formation of [14–38] (black) and the entropically favored nonnative [5–14] (red). We also show the decay of $R_g$ in blue (scale on the right). The results show that both the native [14–38] and the nonnative [5–14] only form after considerable compaction of the polypeptide chain. In addition, even with nonnative interactions [14–38] forms slightly ahead of [5–14] with substantially greater yield. The simulations were performed using ${\beta }_O=1.0$ and ${\beta }_R=1.5$.