Frozen in Beta

There is growing consensus that protein folding is a stochastic process replete with microscopic heterogeneities (1). This consensus has emerged from an impressive three-way synergy involving advances in theory (2), simulation (3), and in vitro experiments (4). Under folding conditions, the energetics for folding and routes to the folded state are encoded in the topographical details of the underlying free energy landscape. However, the folding process can be waylaid by competing basins of attraction (5). These misfolded states provide interactions that are equivalent to those that are available within the native basin of attraction. Errors can be corrected by backtracking, which helps restart the folding process (6). Of course, backtracking is only feasible if the flux out of the misfolded state is finite. Free energy barriers that are considerably higher than the free energy difference between the misfolded and folded states can cordon-off misfolded metastable states, thereby trapping proteins. Such traps are frozen states and are also known as “glassy states”—a term that derives from the rich literature on atomic, molecular, and polymeric liquids.

Slow cooling of a liquid to a temperature below its freezing point (T_f) leads to a crystalline solid. The same liquid, when cooled rapidly to a temperature <T_f, can become highly viscous. Below a so-called glass transition temperature T_g, all collective motions of the liquid are essentially frozen on experimentally relevant timescales. Static disorder as opposed to crystalline order prevails in the system and the disordered phase is called a “glass”. The frozen disorder that forms will depend on the initial conditions and the cooling schedule. Experiments have documented the existence of glassy states for proteins. These states are unmasked by a variety of methods that include lowering the temperature <T_g, controlling the humidity levels, and using osmolytes to alter the hydration structure around proteins. Theories predict that the relevant criterion for foldability is the gap between the folding temperature T-fold and T_g (5).

Are the glassy states of proteins akin to structural glasses, and are there preferred, perhaps convergent structures that are encoded as frozen states on protein energy landscapes? Alternatively, is static disorder a characteristic hallmark of frozen structures of proteins, thus placing them in the same category as spin glasses (7)? Computer simulations have played an important role in the development of theories to describe the physics of glass-forming liquids. Simulations, whether they are based on molecular-dynamics or importance-sampling Monte Carlo-based methods, yield information regarding the thermodynamically relevant configurations.

To distinguish metastable glassy states from globally stable states, one needs a formalism to connect the configurations extracted from simulations to the topographical features of the underlying energy landscape. This often calls for a method that discretizes configuration space to enable the identification of metastable states and compare the residence times within these states to transit times between states. Configurational mapping is a well-established method (8) for the study of glass-forming liquids. Each point in configuration space is mapped, via steepest descent, to a nearby local minimum, which is referred to as an “inherent” structure. Configurations that map to the inherent structure define its basin of attraction. Enumerating the set of inherent structures and quantifying their weights helps achieve the desired discretization of configurational space. Further, given a set of inherent structures, one can study the dynamics within each basin and connect the slowest relaxations to T_g and to the dynamical properties of glass-forming systems (Fig. 1).

Figure 1.

Schematic of a rugged free energy landscape. Here, c1 and c2 denote two collective conformational coordinates. The ordinate denotes the free energy relative to the native basin. The metastable states are depicted as local minima. To see this figure in color, go online.

Configurational mapping is not practicable for characterizing glassy states of proteins. The extent of sampling obtainable with a single or small number of trajectories is insufficient to make configurational mapping meaningful. There is also the added complexity of having to rely on steepest descent for identifying inherent structures. This is computationally expensive, and generates a noisy distribution of inherent structures when using explicit representations of solvent molecules. Is there a way out of this sampling conundrum? The design and successful deployment of Markov state models (MSMs) (3) has opened the door to an alternative approach for discretizing protein conformational space. Each Markov state represents a cluster of conformations. Transitions between distinct conformations within the cluster are rapid when compared to transitions between clusters.

In this issue of the Biophysical Journal, Weber et al. (9) leverage their MSM builders to identify and characterize glassy states for a set of model proteins. The folding pathways have been previously characterized for each of the proteins using MSMs. To uncover the dynamically frozen glassy states, Weber et al. (9) adapted a method (10) whereby a biasing suppressor field or s-field is applied to suppress protein motions. When this field is positive, protein dynamics are suppressed, and when the field is negative, protein dynamics are enhanced. Weber et al. document the sampling of expanded, unfolded states for negative values of s. When s = 0, the native state is the dominant basin of attraction, although it is reasonably fluid—as quantified by p_ii, the probability for remaining within the native state. For positive values of s, Weber et al. (11) demonstrate a sharp transition to dynamically inactive, frozen states. Although the transition is sharp, it is continuous, which is consistent with the finite sizes of proteins. Surprisingly, for seven of the 16 proteins studied by Weber et al., the frozen states are rich in β-sheets. This feature prevails despite very different folded states for the different proteins. For the remaining nine systems, the glassy states are compact and unstructured, which is indicative of static disorder.

What is the biological relevance of being frozen in β-sheet-rich structures? Weber et al. (9) speculate that their findings might have a bearing on the nucleation of β-sheet- rich aggregates. Although this is an intriguing hypothesis, it is worth noting that amyloid formation is a concentration-dependent phenomenon. At protein concentrations where amyloids form, they are expected to be the thermodynamic ground state. Importantly, the existence of a saturation concentration for aggregation implies that nucleation requires the crossing of a concentration threshold. Hence, the relevance of a unimolecular misfolded glassy state is not entirely clear. The consensus, supported by a growing body of experimental data and chemical kinetics analysis, indicates that amyloid formation proceeds through nucleation within liquidlike oligomeric states with no real evidence for frozen conformations serving as templates for amyloid growth (11,12). Additional evidence has been presented for secondary processes such as fragmentation and surface catalyzed aggregation (13). However, the proposal of an intramolecular amyloid state is in accord with the idea of an aggregation competent, unimolecular N^∗ state (14).

Might there be other areas of relevance for β-sheet-rich frozen states? Protein misfolding is expected to be a recurrent theme within the cellular milieu. Chaperones assist in maintaining protein homeostasis by recognizing and sequestering misfolded proteins (15). The widely held view is that chaperones recognize exposed hydrophobic patches on misfolded proteins. The observations of Weber et al. raise the intriguing possibility that chaperones may have evolved to recognize generic, frozen, β-sheet-rich misfolded structures, thus suggesting the existence of a recognition code for misfolded proteins.

What’s next? An exciting result invariably opens the door to new questions and new lines of investigation. A set of questions that readily comes to mind include the following: Might there be rules to distinguish protein sequences that form glassy states rich in β-sheet versus those that form unstructured ones? Might heterotypic interactions with other proteins and macromolecules serve as a proxy for the s-field within the cellular milieu and drive proteins into specific misfolded states such as the β-sheet-rich structures identified by Weber et al.? And is there an experimentally accessible equivalent of the s-field that can be deployed in vitro?

With regard to the last question, it appears that force, as deployed in atomic force microscopy and optical tweezer experiments, might be a useful proxy for the s-field. As for answers to the remaining questions and many more that the study of Weber et al. will invariably throw up, it makes sense that synergistic advances in theory, simulation, and experiment will pave to road to answers or at least to the refinement of questions.