During the last 10 years, the energy-landscape theory has moved from outsider status to central paradigm of protein folding. For many proteins, the theory predicts the same kind of kinetics as activation barrier models [18], namely:

Landscape theory makes a key prediction that can be tested by very fast folding of engineered proteins: that the entropy and enthalpy contributions can cancel under ideal folding conditions (Fig. 2) [3]. In this picture, when all stresses against folding (denaturants, ‘bad’ sidechains, high temperature, etc.) are removed, the protein folds ‘downhill’ without any barriers greater than 1–2RT (‘type-0’ folding scenario). When stresses are applied, the cancellation is less perfect and the protein must cross a barrier (‘type-1’ folding scenario). Without a barrier, the activation energy disappears from Eq. (2.1), and the prefactor can be observed directly, without resorting to extrapolated Arrhenius plots [14].

Let us consider how downhill folding arises from the energy-landscape picture of folding. Fig. 2a shows a 3-D projection of a ‘folding funnel’. A folding funnel is a plot of the enthalpy against configurational entropy. Both decrease as more native contacts are made during folding: the enthalpy because favorable contacts are made during folding, the configurational entropy because the protein becomes more compact and less flexible. From the funnel picture, the free energy of reaction

1. Landscape theory, combined with linear response theory, predicts that downhill folding shows up gradually when a protein is engineered to fold increasingly fast [14]. This is illustrated in Fig. 2b. The natural protein ensemble explores the free energy surface on the time scale of the prefactor km (short blue arrows), but it must be activated to cross over the barrier, which occurs with much slower rate coefficient k (long blue arrow) [7]. The slower process washes out the faster process; only the rate k can be measured, yielding reaction kinetics with a single exponential decay exp[−kt]. In terms of classical transition-state theory, we would say that the activated protein is in equilibrium with the native and denatured states because km is so much faster than k. As the native bias increases and the barrier decreases, k approaches km, and the equilibrium assumption of transition state theory breaks down. In that case, protein population diffusing with rates on the order of km can be observed directly. This has been observed experimentally for α-helical and β-sheet proteins especially engineered for a strong native bias (e.g., Fig. 3a). The time scale km−1 was found to be ∼1 μs for a five-helix bundle [14], and ∼3.5 μs for a triple stranded β-sheet [24]. The latter is in good agreement with the folding rate for isolated β-hairpins [4,25]. Experiments by Gai and coworkers show that a 3-helix bundle can fold even faster, setting an upper limit of 0.5 μs on k−1 for that case (Fig. 1) [26]. The merger of the activated and prefactor time scales, when full downhill folding is achieved, has recently been observed for lambda repressor [7], as has the transition from type-0 to type-1 folding when denaturant is added or the temperature is raised (Fig. 2b) [21].

2. According to Eq. (2.1), folding is an orderly process with a single rate coefficient k. Downhill folding on a multidimensional rough free-energy landscape need not be so orderly: different proteins can take different paths and the protein population is not herded through a single ‘mountain pass’ (transition state). Although the prefactor km roughly describes the time scale for downhill folding ‘at the speed limit’, such fast folding is no longer necessarily described by a single exponential function exp[−kt]. Nonexponential decays indicative of such a heterogeneous folding process were observed by Sabelko et al. and later Osváth et al. for downhill formation of a compact globular state during refolding of phosphoglycerate kinase from a cold denatured state (Fig. 3b) [27,28]. In that work, use was made of the principle, illustrated by the red arrows in Fig. 2, that the folding barrier moves towards the native state when the native state is stabilized. This shift can be used to map cold denatured populations of proteins into the barrier region from where they fold downhill. The kinetics can be fitted to a stretched exponential function exp[−(kt)β] with β=0.5–0.9 (Fig. 3b). Maximum stretching occurs at the temperature of maximal stability, and single exponential activated kinetics occur under more denaturing conditions, in agreement with a transition from downhill (type-0) to barrier-limited (type-1) folding when the native state is destabilized [3]. More recently, the downhill phase of a λ6–85 mutant folding to the native state has also been found to fit a stretched exponential, with β≈0.7 (Fig. 3a) [21]. The experimental observations could be roughly reproduced with a 1-dimensional free energy surface, but a surface with at least two reaction coordinates provided better agreement. It should not come as a surprise that one coordinate is not sufficient to describe folding: protein folding is neither as simple as organic molecule bond breaking/making (where a single reaction coordinate often suffices), nor is it as cooperative as water freezing (where one reaction coordinate, called ‘order parameter’, also suffices, despite the very many molecular coordinates involved).

3. Other types of experiments also have set limits on km. Single molecule FRET experiments have been able to set an upper limit on km−1 of ca. 200 μs, compatible with the direct measurement in 1 [29,30]. The original experimental estimate of the folding speed limit (1 μs, close to the direct observation discussed above) was made by Eaton and coworkers based on 40 μs contact formation rates in denatured cytochrome c, extrapolated to denaturant-free solution [31]. Several groups have carried out extensive measurements of loop formation, an elementary process which sets a lower limit on folding times of 10–100 ns, depending on loop length [32–34]. Good models for the loop length dependence exists; the one by Szabo, Schulten and Luthey-Schulten seems to fit the size-dependence best [35]. Measurements of secondary structure formation by several groups have pushed the lower limit of helix formation to 50 ns, and for β-hairpins to 700 ns, as absolute limits on the folding rate [4,36]. Muñoz and coworkers observed collapse, another limiting factor for folding on the 100-ns timescale [37]. Real proteins of course have to do all those things (form secondary structure, form loops, collapse, etc.) to fold, and even in the best designed protein small barriers (∼1RT, too low for activated rate theory to work) remain as discussed earlier. This is why the measurements on downhill-folding proteins yield minimal folding times longer than 0.5 μs.

4. Another prediction of the energy-landscape model is that different rates are obtained by different spectroscopic probes during downhill folding. This is illustrated in Fig. 4. When there is a barrier, protein populations are small in the region along x where probes such as infrared, circular dichroism, fluorescence, or NMR spectroscopy switch from their denatured to their native signatures. Thus the observed signals are a linear combination of only the folded and unfolded state signals, and they are probe-independent. When landscape roughness is the only barrier left, kinetics are no longer homogeneous, and different results are observed with different probes. This has been confirmed for peptides whose free energy surface computed by MD is rough and flat [38], as well as for designed downhill folders [21]. When there is no substantial barrier in the energy landscape, the residual ‘roughness’ can be quantified directly. Direct measurements on a small peptide yield values of δ2G≈0.7(kT)2, which agrees with the roughness computed from replica-exchange molecular dynamics simulations [4,38]. Fitting a Langevin model to experimental data for a five-helix bundle also yields δ2G≈0.7(kT)2 [7].

5. A thermodynamic criterion for a more extreme type of downhill folding than the ‘type-1 under stress/type-0 without stress’ scenario of energy-landscape theory has been proposed by Muñoz and coworkers [39]. In the original energy-landscape picture, proteins in presence of a stress (e.g., high temperature, or an unfavorable mutation) will fold over a small barrier, and type-0 folding can occur only when the stress is reduced (e.g., by lowering the temperature towards the point of minimum free energy). If instead the protein retains a single well that simply shifts along x towards the denatured state when a stress is applied, two separate thermodynamic states never occur (Fig. 2c) [40]. As a result, different spectroscopic probes will not match during denaturation even at high stress, the denaturation transition will be much less steep, and ‘baselines’ before and after the unfolding transition will be substantial. Data on the small protein BBL fit this kind of picture [39]. It may turn out that very small proteins and peptides with only a few hydrophobically buried residues can follow such a single well scenario, while larger downhill-folding proteins such as engineered λ6–85 make a type-0–type-1 transition when stress is applied.

6. A final kinetic consequence of downhill folding is the unusual folding Arrhenius plot (lnkf vs. 1/T) observed in very fast folding proteins (Fig. 5). As mentioned earlier, proteins folding over a barrier usually exhibit a maximum in the folding rate, giving the Arrhenius plot a ‘parabolic’ appearance, in contrast to the straight line of negative slope expected for most small molecule reactions. This is attributed to the hydrophobic effect, which acts as a major driving force during folding. When hydrophobic amino acid side chains are in contact with water, the water molecules become more ordered; polar/charged side chains induce less order, as seen in neutron scattering experiments. Burial of hydrophobic sidechains thus lowers the free energy of the protein–solvent system, inducing a rapid collapse of the polypeptide chain under conditions favoring the native state. In very fast folders, the formation of secondary structure and diffusion processes establishing the correct fold compete with collapse, leading to a loss of this ‘parabolic’ signature [7]. Fig. 5 shows that both very negative and very positive slopes show up, and that these slopes are extremely sensitive to single-point mutations.

It used to be thought that proteins must fold over a linear sequence of many barriers before reaching the native state [41]. Then it was recognized that some proteins could fold in a single step over just one barrier [42]. Then the possibility of parallel processes was recognized [43]. Now it appears that engineered proteins can relax downhill to the native state without even a single barrier much greater than RT≈2–3 kJ mol⁻¹ [14].

Yet natural proteins do have folding barriers greater than 3 kJ mol⁻¹. If the folding barrier is not required by the physics of folding, why is it usually there? The real paradox is not why proteins fold so rapidly, but why they fold so slowly. Why do not all small proteins fold in a few microseconds? The answer may tell us something about protein function, which, unlike the fundamental physical interactions of hydrogen bonding, hydrophobicity, etc., is subject to continuing evolutionary pressure. Here are some possible reasons why natural proteins fold so slowly.

1. In order to function, most proteins must avoid aggregation. It has been proposed that folding barriers help prevent aggregation [16]. Aggregation occurs when proteins misfold into non-native structures and associate into clusters and eventually fibers consisting of stacked β-sheets. Recent work has shown that proteins acquire local extended structure (the type found in beta sheets) upon heat denaturation, even in the monomeric state [15]. Thus the propensity for forming β-sheet aggregates is already built into the sequence, and not even a property that emerges only at higher protein concentration.

Fast folders would be particularly prone to such aggregation because rapid folding also implies rapid unfolding, even with improved protein stability. For example, a protein that folds in 1 μs and has an equilibrium constant of 5000 unfolds on average every 5 ms. In the absence of a barrier at intermediate reaction coordinate x, partial unfolding will occur even more often. Such fast folders would be vulnerable to the protein degradation machinery. In contrast, a free barrier at intermediate x would exclude large populations of partially unfolded proteins.

The prediction is therefore that downhill folders should be more prone to aggregation, despite the fact that they are thermodynamically more stable than native states. This apparently paradoxical prediction has been observed experimentally [14]. Slow-folding mutants of the 5-helix bundle λ6−85 that destabilize the native state show no propensity for aggregation up to nearly millimolar concentrations. Mutants that stabilize the native state and speed up folding near the speed limit show a strong propensity for aggregation, as illustrated in Fig. 4b.

2. In order to function, proteins must also have sequences that support the function: binding sites, flexible backbones to accommodate substrate diffusion into the protein or conformational changes upon binding, and loops that mediate protein–protein interactions are just a few examples of function-specific features of the sequence. Amino acid side chains necessary for function may decrease hydrophobicity, destabilize secondary structure, require a larger decrease in conformational entropy upon folding, or introduce non-native interactions into the folding process. In general terms, these factors increase the ‘energetic frustration’ of proteins, producing proteins in Fig. 1 that fold at sub-optimal rates for a given complexity of the fold. Two examples of such effects are discussed next, although much work remains to be done to see how widespread the evolutionary competition between folding and function really is.

The WW domain binding module provides a good example of how a long binding loop can affect folding kinetics [10]. The wild-type Pin WW domain has a large loop connecting β-strands 1 and 2. The loop binds to proline-rich PPXP motifs, enabling signal transduction. A mutation analysis of the loop has shown that it forms in the rate-limiting step of folding [44]. Wild-type Pin WW domain is not a particularly fast folder for its small size, requiring about 75 μs to fold. When the large Pin loop is replaced by the smaller FBP WW domain loop, the relaxation rate speeds up to 3.5 μs. At the same time, a functional assay shows that the binding function of the module has been drastically decreased by altering its amino acid composition [10]. The simplest explanation of these observations is that the large loop is needed to recognize the PPXP motif, but slows down folding because a more difficult conformational search is required to form the proper loop geometry. The smaller replacement loop less capable of binding, but forms more efficiently.

An example of how a binding pocket affects the folding rate is provided by the 8-helix bundle myoglobin (Fig. 6), the first protein to have its X-ray crystal structure determined. The protein contains two sub-domains. The ‘functional’ one consists of the CDEF helices; in the folded apo-protein, there is a large cavity with two histidine and other polar residues, which bind the iron and haem group that fits into the cavity. The ‘structural’ sub-domain consists of the ABGH helices, which are tightly packed together by hydrophobic residues. Topologically, the two sub domains are very similar 4-helix bundles, and there is no reason why their folding rates should differ from one another. Stopped-flow circular dichroism and hydrogen exchange NMR experiments have shown that the CDCEF helices form native-like structure in ∼1 s [45]. Fluorescence-detected temperature-jump experiments have shown that the ABGH core forms from the cold denatured state in ∼7 μs, much closer to the expected downhill speed limit of ∼1 μs [46]. The simplest explanation of these observations is that the ABGH core is optimized for fast folding and provides a scaffold for the CDEF to loosely fold, so it can bind the haem group that finally stabilizes the pocket in the CDEF sub-domain. This explanation makes a straight-forward prediction: it should be possible to redesign the CDEF core with larger and more hydrophobic sidechains, trading off folding speed for reduced haem binding ability. Indeed, it has been shown by Wright and coworkers that substitution of one of the two iron-binding histidines by a phenylalanine speeds up folding of the CDEF sub-domain by a factor of 2.5, while reducing haem binding affinity [11]. It remains to be seen whether more extensive redesign can bring the folding time into the μs regime, while resulting in total loss of haem binding.

3. A significant fraction of proteins is not even folded in vitro under ‘physiological’ conditions (usually meaning something like 25 °C, 50 millimolar phosphate, pH 7). Some of these proteins are extreme cases where folding occurs only as part of the protein's binding function. The ‘fly fishing’ mechanism has been proposed to explain how folding concurrent with binding can enhance specific binding interactions, therefore enabling protein function [47].

For many ‘unfolded’ proteins, there may be yet another explanation: The cellular matrix, via a multitude of nonspecific interactions, can have a stabilizing effect on the folding thermodynamics of proteins at the verge of stability. For example, it is well known that cosmotropes such as glycerol or sugars can stabilize the native state [48], inducing folding in vitro. Similarly, the cellular matrix is full of carbohydrates, glycosylated proteins and other molecules that could shift the folding equilibrium.

The cellular matrix could also act by crowding (still allowing the unfolded chain to explore interstitial spaces, but excluding expanded conformations of the protein), or even by confining the protein [49], thereby disfavoring the higher entropy unfolded state. For proteins that already fold in vitro, such as lysozyme, crowding may also hinder slow folding processes such as the formation of disulfide bridges [23]; however, disulfide bridge formation, proline isomerization, and other slow processes are not obligatory for folding, in the sense that the sidechains which cause them can generally be engineered out of proteins.

The free-energy landscapes of proteins are sculpted by evolution subject to physics, which dictates the nature of the interactions between parts of the protein and between the protein and its local environment:

As we learned from Anfinsen [2], the amino acid sequence is the principal determinant of protein structure for small proteins, laying the foundation for the native local minimum via hydrophobicity, hydrogen bonding, and many other weak backbone/sidechain interactions. The solvent environment in vivo or in vitro modulates the stabilities of local minima, and of interconversion barriers connecting local minima on the free-energy landscape. Usually this environmental modulation relative to simple aqueous solvent is small (a few RT), but the resulting effects can be dramatic: a seemingly small modification of sequence or environment may cause proteins to unfold, aggregate, fold to a new state, or accelerate folding dramatically, as in the engineered downhill folders.

This sensitivity is both biological and physical in origin. On the biological side, proteins have generally evolved for function and against aggregation, leaving the minima sub-optimally shallow and barriers sub-optimally high as far as folding of the isolated protein is concerned: natural proteins tend to be energetically frustrated, not topologically limited. Physics dictates that protein populations and rates depend exponentially on the free energy (Kab=exp[ΔGab/RT] is the thermodynamic equivalent of Eq. (2.1)). Therefore, small changes in free energy can have a large effect on protein populations and their dynamics. In fact, when we talk about a pathway ‘opening up’ and another ‘closing’, what we really mean is that the free energy of these pathways has been shifted a little bit. The free-energy landscape of natural proteins is full of such pathways, hence the bewildering array of folding behaviors; hence also our ability to landscape the landscape and engineer downhill folders.

Several ways in which evolution and physics affect sequence and environment have been discussed here. Physics dictates fundamental interactions such as the need for hydrophobic contacts or location of backbone hydrogen bonds, which in turn set limits on the foldable sequences, and how the solvent environment interacts with the protein. Evolution dictates the need for function (including suppression of aggregation when required for function), which is possible only with certain combinations of sidechains that facilitate binding, catalysis, or protein flexibility. The physical requirements of foldability and the evolutionary requirement of function can clash.

Proteins engineered to fold downhill are a prime example. From them, we have learned that activation barriers are not an obligatory physicochemical feature of protein folding. The weak interactions that guide folding can cooperate sufficiently in engineered proteins to abolish significant free-energy barriers. Ironically, what is usually referred to as “cooperative folding” among two states connected by an activation barrier, results from insufficient cooperation between the guiding forces for folding in natural proteins. We generally found that replacement of functional loops, removal of residues that may create flexibility for binding function, or replacement of residues by more hydrophobic residues at the expense of function, provides a successful route for designing highly stabilized downhill folders. This can be accompanied by an increased tendency to aggregate.

Highly stable downhill folders can do more than just prove that the origin of folding barriers must not be sought in physical chemistry alone, but also in protein evolution. They could serve as optimal starting points for the design of new protein functions because the compromises of their former natural function have been largely removed.