Energetic coupling between amino acid residues is difficult to discern from the static folded structure of a protein alone. Double-mutant cycle (DMC) is a direct perturbative technique to assess the degree to which the consequences of mutations at two different sites are correlated. DMC compares the sum of effects of two single mutations on two sites (one at a time) and the effect of double mutations on both of the sites. Often, as in Noivirt-Brik et al. 1, the effect of interest is the free energy of folding, ΔG (native state more stable for more negative ΔG). If ΔΔG(m₁), ΔΔG(m₂), and ΔΔG(m₁, m₂) are, respectively, the changes in ΔG resulting from two single mutations and from the double mutations (ΔΔG equals ΔG of the mutant minus that of the wild type), coupling is quantified by an 'interaction free energy' ΔΔG_int = ΔΔG(m₁, m₂) – [ΔΔG(m₁) + ΔΔG(m₂)]. The two sites are energetically independent if the mutational effects are additive (ΔΔG_int = 0). Otherwise they are coupled, wherein the native state is either stabilized (ΔΔG_int < 0) or destabilized (ΔΔG_int > 0) by coupling. Energetic coupling may also be estimated using a bioinformatics approach based on evolutionary assumptions. This indirect method has also identified likely long-range interactions, for example in PDZ domains 2.

The existence of long-range coupling should not be surprising. After all, the folded state of a protein may be viewed as an elastic solid 3. As such, the vibrational dynamics of distant sites can be coupled and a 'pathway of energetic connectivity' 2 inside the folded protein is physically plausible. Without discounting such folded-state mechanisms, Noivirt-Brik et al. 1 tackled another possibility, focusing mainly on the unfolded (denatured) state. Because native stability is determined by the balance between the folded and unfolded states, interactions in the unfolded states can have an impact on coupling. This possibility was overlooked when unfolded states were envisaged to be devoid of significant contact interactions (Figure 1a), a picture rooted in a simplistic view of cooperative, two-state-like folding. However, it is physically reasonable to expect, for instance, that two hydrophobic residues can associate in the unfolded state even if they are not in contact in the folded structure. This idea is embodied in the well-studied hydrophobicpolar (HP) model, which aims to capture essential protein physics by using only two residue types (Figure 1b). The HP model 4 illustrates the same principle as that deduced from the model with four residue types used by Noivirt-Brik et al. 1. Figure 1b shows two residues (red and blue) exposed in the folded structure, but they can contact other residues as well as each other in the unfolded state.

Does the model in Noivirt-Brik et al. 1 and that shown in Figure 1b reasonably mimic reality? Ample evidence supports the existence of non-native interactions in protein unfolded states 5. As early as 1990, the hydrophobicity of an exposed residue in the Cro repressor from bacteriophage λ was found to correlate negatively with the stability of the protein. Dubbed the 'reverse hydrophobic effect' to contrast it with the usual role of hydrophobicity in stabilizing the folded state, the phenomenon was rationalized by the proposal that the residue is partially buried; that is, it has non-native contact(s) in the unfolded state 6. The variation in the denaturant dependence of native stability (equilibrium m-value, defined as the rate of decrease in native stability with respect to increase in denaturant concentration) of staphylococcal nuclease observed in earlier site-directed mutagenesis experiments also indicated variable hydrophobic burial in the unfolded state. Recent experiments suggested that non-native ionic interactions are present as well in the unfolded states of the amino-terminal domain of ribosomal protein L9 (see 5 and references therein).

Lattice models have been successful in accounting for some of these phenomena. An early HP square-lattice model study elucidated how mutations can lead to substantial changes in m-value, as found for staphylococcal nuclease experimentally 4. Figure 1b shows three HP model mutants that exhibit reverse hydrophobic effect (ΔΔG < 0). From their ΔΔG values, ΔΔG_int for the model DMC was determined to be significantly negative (green curve in the left plot of Figure 1b). This result indicates a long-range coupling (between the red and blue residues) underpinned by non-native interactions in the unfolded state of the HP model.

As illustrated by these examples and similar analyses by Noivirt-Brik et al. 1, lattice models are a powerful investigative tool. Common notions about protein energetics are sometimes fuzzy. Their precise ramifications are often obscure owing to a lack of discipline from an explicit consideration of chain connectivity and conformational entropy 7. Lattice models account for these key ingredients, albeit in a simplified fashion. By virtue of their computational tractability, lattice models can clarify the logic between assumptions and testable consequences, generate new hypotheses, and ask 'what if' questions to advance conceptual understanding.

It goes without saying that lattice models are limited. Learning from both their strengths and limitations, concrete progress often requires comparative evaluation of models embodying different physical ideas. Notably, extensive analyses over the past decade have shown that traditional lattice protein models – the HP model included – fold much less cooperatively than real, two-state proteins 7. In the light of this knowledge, it is instructive to explore whether the predictions about long-range coupling obtained by Noivirt-Brik et al. 1 and from the HP model are robust.

Contact interactions such as that in the model used by Noivirt-Brik et al. 1 and the HP model do not fully capture protein energetics. More subtle physical chemistry has enabled higher native specificity and more cooperative folding to be achieved in natural proteins. Hence, the probabilities of non-native interactions and the long-range coupling they engender in real proteins are likely to be lower than those stipulated by these models. This point is illustrated in Figure 1b using a class of energy functions E = (1 - s) E_HP + sE_Gō interpolating between the HP model (E_HP) and a Gō model (E_Gō) that favors only native interactions (formulated originally by Nobuhiro Gō and co-workers in 1975; see reference to Gō in 7). Here, s is the weight of Gō energy and thus a parameter for native specificity. As the strength of favorable non-native interactions decreases with increasing s, the associated long-range coupling diminishes. Could all non-native interactions be 'designed out' by evolution?

Experiments on reverse hydrophobic and other effects of non-native interactions suggested otherwise. There are physical limits to evolutionary and artificial protein design. Unlike Gō models, non-native interactions are present in some real proteins that fold cooperatively 510. (Conversely, Gō models are often insufficiently cooperative 7.) From a modeling standpoint, a mixture of HP- and Gō-like components (with s somewhere between 0 and 1) may best capture the balance between physical constraints and the drive toward native specificity. A continuum version of such a modeling construct has successfully predicted non-native interactions in the unfolded and folding transition states of the SH3 domain of the protein kinase Fyn 10. As an illustration of the method, Figure 2 applies the same model to obtain putative non-native interactions in several other proteins 689.

The main point of the study of Noivirt-Brik et al. 1 – that non-native interactions are the origin of some long-range coupling – is thus on a firm physical and molecular biological footing. A deeper question is whether non-native interactions are mere annoying necessities imposed by physics, a feature that should be designed out if possible by evolution, or whether they can serve biological purposes? With our increasing appreciation of the regulatory functions of intrinsically disordered proteins 11, there is no reason to believe that biology would not exploit every opportunity presented by physics. A case in point is that non-native conformations can have 'promiscuous' biological functions different from the dominant function of a protein, and that selection for promiscuous functions can speed up evolution considerably 12. In this case as well, simple lattice modeling has afforded the pertinent biophysical principles (see accompanying article of 12). More discoveries lie ahead as protein scientists broaden our sight beyond well-ordered folded native structures.