Common attributes of native-state structures of proteins, disordered proteins, and amyloid

Previous studies have shown that the large number of common attributes of globular proteins reflect a deeper underlying unity in their behavior (1, 2, 31). At odds with conventional belief, a consequence of our hypothesis is that the gross features of the energy landscape of proteins result from the amino acid aspecific common features of all proteins. This landscape is presculpted by general considerations of geometry and symmetry with ≈1,000 broad minima corresponding to putative native-state structures. These structures comprise the menu of folds, and the role of a sequence is not only to select the native structure from this menu but also to be fit in the environment of other cell products. The key point is that for each of these minima the desirable funnel-like behavior (32, 33) is already achieved at the homopolymer level in the marginally compact part of the phase diagram.

Nature has a choice of 20 aa for the design of protein sequences. The design procedure favors the appropriate native-state structure over the other structures and leads to a funnel-like energy landscape conducive for rapid and reproducible folding of that particular protein. The presculpted free energy landscape greatly facilitates the design process. Indeed, within our model, we find that a crude scheme with just two kinds of amino acids, which take into account the H (propensity to be buried) and polar (P) (desire to be exposed to the water) character of the amino acids (5, 34), is sufficient to carry out a successful design of sequences with a variety of target structures. Note that sequence heterogeneity also can be introduced by assigning different local bending energy penalties to different types of residues.

We turn to an investigation of the design of HP sequences of 48 aa, a length comparable with that of some of the shortest proteins, allowing for design into realistic target structures. We use the same model described in Methods with e_R uniformly chosen to be equal to 0.2 and e_W = −0.4 for H–H pairwise interactions, measured in units in which the local hydrogen bond energy is chosen to be of unit strength. e_W is set to 0 if at least one of the interacting residues is P. Fig. 1 shows the “folded native” states of the de novo designed HP sequences of 48 residues (they are the lowest energy conformations obtained in multiple annealing simulations). The target structures were chosen among tertiary folds adopted by small globular proteins, namely the three-helix bundle, a helix placed on a β-sheet, and a sandwich of β-sheets. Strikingly, the resulting folded structures of the designed sequences bear a high resemblance to real protein native states shown in Fig. 1 d–f.

The design procedure is extremely simple and uses distinct HP patterns for AHs and β-sheets. We find that a chain fragment has a substantially high propensity to form an AH if the H amino acids are separated by two or three P residues as one proceeds along the chain, whereas a β-strand is favored if the H residues are separated by one P residue. Strikingly, exactly the same HP patterns have been used in experiments that allow the successful design of de novo proteins and amyloid-like fibrils (5, 10, 11, 35).

After an initial sequence was produced by simply matching the HP patterns described above with the secondary-structure elements in the target structure, some common-sense tailoring of the sequences ensures that one obtains the desired topology of the ground state. For instance, in the case shown in Fig. 1b, we intentionally assigned only one H residue in the rightmost strand to promote the partial exposure of this strand. Strikingly, nature seems to adopt the same strategy as can be seen in the protein with the Protein Data Bank ID code 1pga shown in Fig. 1 d–f. Nevertheless, the HP sequences of real proteins are not the same as those of the designed sequences. Even though the HP patterns are seen frequently in real native-state protein structures (36), wild-type sequences do not match the patterns exactly.

We find, for instance, few H residues that are exposed in the native structure of 1pga, but this is not the case in our designed structure. An attempt at folding the real HP sequence of 1pga yields a partially folded structure with the AH and one of the β-hairpins formed correctly, whereas the second β-hairpin remains unstructured. This result suggests that more than two types of amino acids may be needed to fold the protein correctly along with the introduction of sequence heterogeneity in the local bending energy, providing a more detailed effective representation of side-chain steric hindrance.

Fig. 2 shows that the free energy landscapes associated with the designed sequences are characterized by several broad minima, one of which corresponds to the folded state shown in Fig. 1 a –c. The effective free energy is computed at the folding transition temperature T_f. (In two-state systems the folding transition temperature is commonly defined as the temperature at which the two states are equally populated. In the presence of more than two states, we resort to the method used here of probing the specific heat maximum, which yields a closely related estimate.)

Interestingly, for the two cases shown in Fig. 1 a and b, we find that there is a competing minimum corresponding to a structure that resembles a mirror image of the folded state (see Fig. 2 a and b). For the case of the β-sandwich (Fig. 2c), the competing minima are structures that are β-sandwiches but with different packing of β-sheets or with unequal numbers of strands on each side. Our simple model, without any side chains, is unable to discriminate between these minima. For the case shown in Fig. 2b, we also find that there is a minimum corresponding to a structure (Bottom Right) that has a somewhat lower energy than the folded state. However, this minimum is not populated at the folding transition temperature. In all three cases, the unfolded state (the upper minimum in the free energy landscape) is characterized by disordered yet compact structures with well formed H contacts but with fewer hydrogen bonds than in the folded state.

Our calculations vividly demonstrate that, in our model, where the menu of folds is predetermined by symmetry and geometry, a simple two-letter code for the amino acids is sufficient for the design process to select interesting native structures from this menu. Our results suggest that the incorporation of 20 types of amino acids with a range of hydrophobicities and other attributes should lead to many sequences adopting the same fold as in experiment. More importantly, the rich repertoire of amino acids allows one to shape sequences that not only fold readily into their native state when in isolation, but also allow specific and varied interactions with other proteins and cell products, promoting solubility within the crowded cellular environment and avoiding deleterious aggregation. Remarkably, similar results have been obtained previously for HP sequences in simple cubic lattice models (38), suggesting that the geometric constraints imposed by hydrogen bonding are mimicked by the lattice geometry constraints. This hypothesis is further confirmed by the observation that secondary structure content is enhanced by compactness (39). The use of more realistic, yet simple, off-lattice models allows one to capture both the role of hydrogen bonding and the tube constraint, which are general properties of any polypeptide chain, in determining a marginally compact phase within which the free energy landscape is presculpted.

Natively unstructured proteins or IUPs (13, 15) are biological molecules that under physiological conditions do not exhibit extensive structural order in solution, but often display local and limited residual structure (19). A key feature of IUPs is their high conformational flexibility, which allows them to interact with different molecular partners and adopt relatively rigid conformations in the presence of natural ligands, thus undergoing a loss of conformational entropy upon binding (16). Note, however, that many IUPs carry out their functionality while remaining in the unstructured state. Furthermore, the conformation in the bound state is determined not only by the amino acid sequence but also by the structure of the interacting partner (17). Our Monte Carlo simulations are performed within a cubic box of side 50.0 Å on a chain of 24 amino acids. The relatively large box size ensures that the entropy loss due to confinement is a relatively small contribution to the overall free energy. The value of the hydrophobicity homopolymer parameter, e_W, is fixed at −0.08 and the curvature energy penalty e_R at 0.3 leading to a ground state of a single straight AH (1): these values have been chosen to allow the homopolymer to ensure that a three-stranded β-sheet (3S) is a local minimum.

It is important to note that for an IUP, the sequence heterogeneity, and more specifically the presence of P residues, leads to no intrinsic ordering under physiological conditions (14, 18). The case considered here is much simpler because we have just one kind of amino acid. Even though the ground state in the absence of any target geometry is ordered, namely a single helix, this simple model system can still be used for IUP modeling by operating at a temperature above the folding transition temperature of the isolated chain. There are local minima present in the free energy landscape, and the “target fold” (or “target structure”) is chosen from among those minima. Our analysis is greatly simplified because we do not include any sequence heterogeneity except for the interaction between the IUP and the target geometry. Our goal is to focus on understanding how this interaction results in the IUP adopting one of the best-fit structures from the menu predetermined at the homopolymer level (1, 2) by geometrical considerations.

The partner of the IUP is represented in a simple coarse-grained framework through three carefully chosen contact points lying on the inner part of the bottom face of the box, each of which has a special affinity to a specific amino acid of the IUP, mimicking a molecular recognition mechanism in the crudest way. The positions of the centers of interaction are chosen based on the geometry of the target fold to maximize the affinity of the IUP to one particular presculpted structure. Also, the bottom wall serves to capture the steric hindrance of the ligand/substrate partner and the associated loss of conformational entropy induced on the IUP. Specific binding centers that are distributed in full three-dimensional space would simplify the design task considerably, but in an unrealistic manner. The range of the contact interaction (r_b) is set to 2.0 Å and the interaction energy of a contact between a binding center and its specific amino acid partner, e_b, is chosen to be three times the energy of a local hydrogen bond. We present the results of simulations run for two different binding center patterns chosen to promote the folding of the IUP into an AH and a 3S.

Plots of the specific heat as a function of temperature (Fig. 3) show two peaks unlike the single peak observed in the absence of the binding. The higher temperature peak is associated with the adsorption transition of the polymer chain to the bottom wall containing the binding pattern, whereas that at the lower temperature marks the folding transition into the target structure. The relative positions of the peaks in the different cases can be understood by recognizing that the folding transition temperature is increased in the presence of the two patterns, because the entropy of the disordered state is reduced by adsorption to the binding substrate with respect to the bulk case, whereas the intrachain energy of the disordered state is not significantly influenced by the presence of the pattern.

Fig. 4 underscores the role of the binding pattern in shaping the energy landscape of the IUP. Contour plots of the effective free energy as a function of the total number of hydrogen bonds and the total number of H contacts are compared at the same temperature, T = 0.2, for three different cases: no binding pattern present, 3S pattern, and AH pattern. In the first case (note that even in the absence of the binding pattern, the IUP is kept confined within the cubic box) the chosen temperature is slightly above the folding transition temperature (see Fig. 3), and the denatured disordered state is the most populated one. The ground state (single AH) is also populated, and the 3S conformation appears as a competitive local minimum as is the case for a completely free chain.

In the cases of 3S and AH patterns, T = 0.2 is below the folding transition temperature so that only the free energy minimum corresponding to the target conformation is populated. The competing conformations (single helix for the 3S, β-sheet for the AH) are entirely absent, being incompatible with the chosen binding patterns. We also found a conformation competing with the 3S similar to a Greek-key motif (data not shown), which fits the contact pattern equally well. However, at the folding temperature the 3S target fold is the global free energy minimum.

Our results fit nicely with the known behavior of IUPs if we identify T = 0.2 with native physiological conditions. Without a pattern, the IUP is mostly denatured, but it gets ordered in the presence of a pattern. The type of ordered structure can change and is controlled by the specificity of the pattern. Within our model the ordered structures are present as local minima even in the absence of the pattern. It has been suggested that the ordered conformation attained after binding to the substrate is visited in a preferential way by the protein even in the absence of the substrate (40). Moreover, some amount of ordering can be induced for IUPs without the presence of the substrate by changing environmental conditions (18). In this respect, one should regard the temperature in our simple approach as an effective parameter mimicking such changes in a crude manner.

Note that the distinction between globular proteins with a well defined native structure and the IUPs, which are natively unfolded, is often not clear-cut, because in many cases only a segment of the whole protein is natively unfolded. In this respect, the chain length used in our simulation, although very short when representing an entire protein sequence, ought to be a more reasonable model of the natively unfolded stretches.

Several neurodegenerative human diseases such as Alzheimer‘s, spongiform encephalopathies, and light-chain amyloidosis involve the deposition of plaque-like material in tissue arising from the aggregation of specific proteins and peptides (20–22, 24, 25). Irrespective of the native conformations of the proteins involved in such pathologies, which might well be rich in α-helical structure in their normal state, all such pathogenic materials are believed to share three basic common features: (i) fibrillar structure as evident from electron microscopic and atomic force microscope images, (ii) birefringence after congo-red staining, and (iii) cross β-structure as determined from x-ray diffraction patterns (20) and solid-state NMR spectroscopy (22), and very recently solved at the atomic level (30). The fibrillar structures may have various morphologies with different underlying molecular structures that can be controlled by subtle variations in the growth conditions (29). Recent experiments have shown that many other proteins not involved in such diseases are also able to aggregate in vitro forming fibrillar structures sharing the same properties (24, 25). Species formed early in the aggregation of such “artificial” fibrils have been even shown to be cytotoxic themselves (23). This finding suggests (24) that the tendency for proteins to aggregate is a generic property of polypeptide chains.

We have found (2) that small homopeptides have an inherent tendency to form amorphous β-sandwiches. To investigate the role of sequence heterogeneity in amyloid formation, we performed the “experiment” of cutting the sequence (Fig. 1a) with the three-helix bundle fold as its native state into six equal small fragments. Each fragment has the same HP sequence of PPHPPHHP, and they form helices when isolated from each other. Fig. 5 shows that when put together, these small peptides aggregate to form a cross-linked “triangular” β-helix arrangement, which is stabilized within our model by the repeated pattern of H residues being placed in the middle of the sides of the triangle. This triangular β-helix arrangement is akin to one of the all-β folds (single-stranded, left-handed parallel β-helix) present in databases of known protein structures. Strikingly, it also was recently proposed as a molecular model for the aggregated disease-causing isoform (PrP^Sc) of the prion protein (26). In other more common structural models for amyloid fibrils, two or more β-sheets are layered in a “sandwich” structure (22, 30). Interestingly, the HP patterns are known to influence amyloid formation (27, 36, 41), and the repeated HP pattern used in our specific example is indeed crucial in stabilizing the triangular β-structure in Fig. 5a. Our results reinforce previous suggestions (24) regarding the generic tendency of multiple chains of amino acids to form aggregated β-structures. We find that three main ingredients, i.e., sterics, hydrophobicity, and backbone hydrogen bonds, are sufficient to cause multiple fragments, irrespective of their native conformations when isolated, to form extensive β-structures, either sandwiches of β-sheets or β-helices. Such structures might easily constitute the building blocks of cross-β amyloid fibrils, with hydrogen bonds parallel to the fibril axis, because of their modularity. Our results also suggest that sequence heterogeneity, at the level of HP residue classes, may help to discriminate the nature of the β-structure into which the fragments assemble.

In a recent report (28), Dobson noted that there is increasing evidence that fibrillar aggregates are not esoteric species associated with a small number of proteins, but instead are a generic form of polypeptide structure that results from the dominance of interactions involving the main chain common to all such molecules. By contrast, the structures of the normally soluble forms of proteins are dominated by the specific packing of the side chains that distinguish one protein sequence from another. One therefore can think of the amyloid diseases as resulting from the “reversion” of the highly evolved biologically functional forms of peptides and proteins into an alternative and unwelcome structural state that exists as a result of the inherent physicochemical nature of polypeptide chains. Our results vividly demonstrate the underlying simplicity of the protein problem, as envisioned by Dobson (28): both the structures of the normally soluble forms of proteins as well as those of fibrillar aggregates result “from the dominance of interactions involving the main chain common to all such molecules,” and the role of side chains of a soluble protein is to select a particular presculpted minimum.