Competition between native topology and nonnative interactions in simple and complex folding kinetics of natural and designed proteins

Abstract

We compared folding properties of designed protein Top7 and natural protein S6 by using coarse-grained chain models with a mainly native-centric construct that accounted also for nonnative hydrophobic interactions and desolvation barriers. Top7 and S6 have similar secondary structure elements and are approximately equal in length and hydrophobic composition. Yet their experimental folding kinetics were drastically different. Consistent with experiment, our simulated folding chevron arm for Top7 exhibited a severe rollover, whereas that for S6 was essentially linear, and Top7 model kinetic relaxation was multiphasic under strongly folding conditions. The peculiar behavior of Top7 was associated with several classes of kinetic traps in our model. Significantly, the amino acid residues participating in nonnative interactions in trapped conformations in our Top7 model overlapped with those deduced experimentally. These affirmations suggest that the simple ingredients of native topology plus sequence-dependent nonnative interactions are sufficient to account for some key features of protein folding kinetics. Notably, when nonnative interactions were absent in the model, Top7 chevron rollover was not correctly predicted. In contrast, nonnative interactions had little effect on the quasi linearity of the model folding chevron arm for S6. This intriguing distinction indicates that folding cooperativity is governed by a subtle interplay between the sequence-dependent driving forces for native topology and the locations of favorable nonnative interactions entailed by the same sequence. Constructed with a capability to mimic this interplay, our simple modeling approach should be useful in general for assessing a designed sequence's potential to fold cooperatively.

Fig. 1.

Simulated midpoint free energy profiles and PDB structures of Top7 (A) and S6 (B). P(Q) is normalized conformational population as a function of Q. In the ribbon diagrams, hydrophobic residues are in red; others are in blue. The profiles in red, blue, and green are for db + hϕ models with, respectively, κ²/ε = 0, 1, and 1.1. Profiles for the Gō models are in gray. The arrows indicate threshold Q_U and Q_F values used in our simulations of folding and unfolding kinetics. For Top7 and S6, respectively, Q_U = 0.23 and 0.18, and Q_F = 0.95 and 0.90. The profiles here are very similar to those obtained previously (16) with a slightly weaker excluded-volume repulsion (see Methods).

Fig. 2.

Matching simulated and experimental folded fractions (P_folded). Filled symbols are experimental folded fractions of Top7 (black squares, from ref. 14) and S6 (blue and gray circles, from refs.  and , respectively) as functions of denaturant concentration [GuHCl] (top scales, in M). Curves through open symbols are simulated folded fractions of Top7 (green) and S6 (red) as functions of interaction strength -ε/T (bottom scale) for db + hϕ models with κ²/ε = 0, 1, and 1.1 (from left to right for each set of curves). This figure shows the experimental [GuHCl] scales being fitted to the κ² = 1.1ε models. Fits for other models were attained by moving the -ε/T scale relative to the [GuHCl] scales. Midpoint ε/T value decreases with increasing κ² because nonnative hϕ interactions destabilize the folded structure.

Fig. 3.

Chevron plots for Top7 (A) and S6 (B). Data points in red, blue, and green provide negative logarithm of simulated mean first passage time (MFPT) of folding (filled symbols) and unfolding (open symbols), for db + hϕ models with κ²/ε = 0, 1, and 1.1, respectively. Dependence of model MFPT on ε/T is translated to that on [GuHCl] (in M; see Fig. 2). Black crosses are experimental data for S6 (28) and Top7 (single-exponential rate for [GuHCl]≥4 M and fast-phase rate of the biexponential fit for [GuHCl] < 4 M in ref. ; these data exhibit a trend similar to that of the middle phase in ref. 15). Vertical dashed lines mark [GuHCl] = 0 as well as the onset of severe experimental chevron rollover for Top7 at [GuHCl] = 4 M (14, 15). Black dots in (A) show - ln(A_middle/k_middle + A_slow/k_slow) calculated from the experimental middle- and slow-phase data in ref. ; this quantity corresponds to the negative logarithm of the MFPT contributed by these two phases. We did not include fast-phase data in this calculation because of uncertainties entailed by the negative A_fast values in ref. .

Fig. 4.

Simulated folding relaxation for Top7 for the db + hϕ model with κ² = 1.1ε. Data points in (A) and (B) show relaxation behaviors for selected ε/T values (as marked); curves are single or multiple exponential fits. Data points in (C) show the rates (k_is) from single- (black), two- (red), and three-exponential (blue) fits as functions of -ε/T and [GuHCl] (using the match in Fig. 2).

Fig. 5.

Simulated trajectories, folding intermediates, and kinetic traps of Top7 for the db + hϕ model with κ² = 1.1ε. (A–D) Fractional number of native contact Q (black traces, left scales) and number of nonnative contact N_nonnative (red traces, right scales) as functions of time. Data points at the end of every 5,000 simulation time steps were tracked. Example trajectories were simulated near the transition midpoint at ε/T = 1.16 (A), around the top of the chevron rollover at ε/T = 1.25 (B), and under strongly folding conditions at ε/T = 1.32 (C and D). (E) A typical I₀ conformation sampled during time periods shaded in green in (A) and (B). (F) A trapped structure representative of the I₁ conformations sampled during time periods shaded in gray in (B) and (D). (G) Another trapped structure, representative of the I₂ conformations sampled during time periods shaded in orange in (B) and (C). The N and C termini of the structures are depicted as blue and red spheres, respectively. Six of the seven residues suggested by experiment to stabilize nonnative states (see text) are marked as yellow spheres. Black lines in (F) and (G) indicate examples of significant nonnative contacts involving these residues (chosen from the maps in Fig. 6).

Fig. 6.

Nonnative contact maps of simulated Top7 kinetic traps. Probabilities of nonnative contacts for I₁ and I₂: The upper left map is for I₁, determined from the gray-shaded regime in Fig. 5D; the sampled conformations are typified by Fig. 5F. The lower right map is for I₂, determined from the orange-shaded period in Fig. 5C; the sampled conformations are typified by Fig. 5G. Residues suggested by experiment to be involved in nonnative interactions (see text) are identified by dotted lines. Residue numbering in our contact maps is identical to that in the PDB.