Coarse-grained sequences for protein folding and design

Abstract

We present the results of sequence design on our off-lattice minimalist model in which no specification of native-state tertiary contacts is needed. We start with a sequence that adopts a target topology and build on it through sequence mutation to produce new sequences that comprise distinct members within a target fold class. In this work, we use the alpha/beta ubiquitin fold class and design two new sequences that, when characterized through folding simulations, reproduce the differences in folding mechanism seen experimentally for proteins L and G. The primary implication of this work is that patterning of hydrophobic and hydrophilic residues is the physical origin for the success of relative contact-order descriptions of folding, and that these physics-based potentials provide a predictive connection between free energy landscapes and amino acid sequence (the original protein folding problem). We present results of the sequence mapping from a 20- to the three-letter code for determining a sequence that folds into the WW domain topology to illustrate future extensions to protein design.

Fig. 1.

Comparison of thermodynamic data for the new optimized sequences of proteins L and G to that of original L/G sequence. (a) Heat capacity C_v vs. temperature T for the original nonoptimal L/G, L, and G sequences. The new L and G sequences show increased cooperativity. (b) Fraction of chains in the native state, P_Nat, vs. temperature, T, for the L/G, L, and G sequences. At the folding temperature, T_f, the distribution of population between the folded and unfolded states is equal, that is, P_Nat(T_f) = 0.5.

Fig. 2.

Thermodynamic measures of the formation of native-state secondary structure. (a) Average native-state similarity of the α helix 〈χα〉 vs. temperature T. Stability of the α helix is reduced for new L and G sequences compared with original L/G sequence. (b) Average native-state similarity of the first (N-terminal) β-sheet region 〈χβ₁〉 vs. temperature T. Stability of β₁ region is reduced for new L and G sequences relative to original L/G sequence. Note that the stability is reduced further for G than for L. (c) Average native-state similarity of the second (C-terminal) β-sheet region 〈χβ₂〉 vs. temperature T. Stability of β₂ region is similar for L/G and G sequences but reduced for the L sequence.

Fig. 3.

Projection of free-energy surfaces onto order parameters χβ₁ and χβ₂. (a) Free-energy contour plot for protein L as a function of native-state similarity of the second (C-terminal) β-sheet region χβ₂ and first (N-terminal) β-sheet region χβ₁ at the folding temperature. Note the minimum free-energy path connecting the unfolded and folded ensembles proceeds through a transition state in which the β₁ region is native and the β₂ region is largely disrupted. (b) Free-energy contour plot for protein G as a function of native-state similarity of the second (C-terminal) β-sheet region χβ₂ and first (N-terminal) β-sheet region χβ₁ at the folding temperature. For G, the minimum free-energy path connecting the unfolded and folded ensembles proceeds through a transition state in which the β₂ region is native-like and the β₁ region is disrupted. Contour lines are spaced k_BT apart.

Fig. 4.

Kinetic data with fits for proteins L and G. (a) Fraction of unfolded states P_unfold as a function of time t for protein L at the folding temperature. The best fit of the data is to a single exponential. (b) Fraction of unfolded states P_unfold as a function of time t for protein G at the folding temperature. The best fit for these data is to a double exponential. Fit parameters are given in Table 4.

Fig. 5.

Minimalist model of the native state topology for Pin WW domain (Right) and the NMR solution structure (Left), showing the very similar arrangement of secondary and tertiary structure.