Funnel-like protein energy landscapes emerge from functional evolution under thermal fluctuations

Function Can Drive Form

Proteins perform their vital biological roles by folding into precise, three-dimensional shapes. For decades, biophysicists have operated under the "energy landscape" paradigm. This is the idea that a protein's amino-acid sequence creates a funnel-shaped energetic map. This map guides the molecule smoothly from a chaotic, unfolded coil toward a single, stable native structure. However, a fundamental evolutionary question remains. If natural selection primarily acts on biological function—such as an enzyme's ability to bind a molecule—how did these efficient, funnel-shaped landscapes emerge? Did evolution explicitly select for "foldability," or is the ability to fold a secondary consequence of something else?

Recent research suggests that proteins do not need to evolve specifically to fold easily. Instead, when evolution selects for a specific biological function under the influence of natural thermal fluctuations, the protein naturally develops a "funnel" shape. This helps it fold reliably. This implies that the sophisticated architecture of protein folding is not necessarily a direct target of evolution. Instead, it may be a thermodynamic byproduct of maintaining function in a noisy environment.

The Gap Between Function and Foldability

In the standard model of protein folding, the "native state" is the low-energy configuration where the protein is most stable. To ensure a protein reaches this state efficiently, evolution must minimize "frustration." Frustration refers to conflicting energetic interactions that create traps in the energy landscape. A frustrated landscape is rugged and "glassy." In this state, a protein gets stuck in many different, incorrect shapes instead of sliding down a smooth funnel toward the correct one [Figure 1(a)].

Historically, researchers have struggled to determine if the selection for a local functional motif (a specific arrangement of amino acids) is sufficient to organize the global structure of a protein. While some studies using abstract mathematical models suggested that functional selection could promote foldability, they often lacked a physical connection to actual protein structures. They could not definitively show whether a sequence optimized for a local shape would spontaneously develop the global, funnel-like energetic organization seen in real-world proteins.

Organizing the Landscape Through Thermal Noise

To bridge this gap, the authors utilized a two-dimensional lattice protein model. Rather than simulating millions of atoms, they represented the protein as a 20-residue chain on a square grid. They used a four-letter amino-acid alphabet consisting of two hydrophobic (water-fearing) and two polar (water-loving) types. This simplification allowed them to explore "sequence space"—the astronomical number of possible amino-acid combinations. They used a multicanonical Monte Carlo method to do this. This technique allows for an efficient random walk across the entire spectrum of protein fitness.

The researchers defined "fitness" in a very specific way. Fitness is the equilibrium probability that a prescribed local structure (the active site) is realized at a given environmental temperature $T$. Crucially, they did not include "foldability" or "stability" in their definition of fitness. The mechanism follows three logical steps:

1. Local Constraint: Selection favors sequences that can form a specific, functional local motif, such as a binding pocket .

2. Thermal Fluctuation: Because the environment has a temperature $T$, the protein is constantly vibrating and shifting. To maintain a high probability of function, the protein cannot rely on a single, perfect shape. It must ensure the functional motif is preserved even as the rest of the chain fluctuates.
3. Global Organization: To prevent non-functional shapes from becoming too stable and "stealing" the protein's time, the sequence must evolve to make the functional state energetically dominant over a wide range of configurations.

The Temperature Threshold for Folding

The study reveals that the emergence of the protein "funnel" depends on the environmental temperature. The authors report that at intermediate temperatures (specifically $T = 1.0$ in their model), high-fitness sequences spontaneously acquire funnel-like energy landscapes [Figure 4(a)]. In these sequences, the energy decreases systematically as the number of "native contacts" (interactions shared with the target structure) increases.

Furthermore, the authors find that these high-fitness sequences exhibit a "two-state" free-energy landscape [Figure 4(c)]. This means there is a clear separation between the unfolded ensemble and the folded native ensemble. They are separated by a free-energy barrier. This is the hallmark of a reliable, cooperative folder. Interestingly, despite the massive variety of possible sequences, the authors observe that high fitness is achieved by only a very limited number of distinct native conformations [Figure S2].

In stark contrast, the results change entirely when the environmental temperature is low ($T = 0.1$). At low temperatures, high fitness can be achieved by sequences with "glass-like" energy landscapes [Figure 5(a)]. These landscapes are rugged and lack any systematic organization toward a native state. Because the thermal noise is so low, a sequence can achieve high fitness simply by having the functional motif present in its absolute lowest-energy state. It does not need any global structural organization to support it.

Limitations of the Lattice Model

While the findings are conceptually powerful, the researchers are transparent about the model's boundaries. First, the protein is quite small, consisting of only 20 residues. In real biology, much larger proteins have more complex topological constraints. The authors note that the free-energy barrier observed in their model is relatively modest. This is a direct consequence of this short chain length.

Second, the model uses a simplified four-letter amino-acid alphabet. While this captures the essential physics of hydrophobicity and polarity, it cannot account for the intricate side-chain interactions that fine-tune real protein folding. Finally, the study analyzes equilibrium landscapes rather than explicit folding kinetics (the actual speed and pathway of folding). It shows that the capacity for a funnel exists, but it does not simulate the actual journey a protein takes as it folds.

The Verdict: A Thermodynamic Necessity

The evidence points to a compelling conclusion. Foldability is likely a thermodynamic consequence of functional selection in fluctuating environments. If you want a protein to perform a job consistently while being shaken by thermal noise, you cannot just optimize a single shape. You must organize the entire energetic landscape to favor that shape.

This work provides a theoretical link between several major principles of biophysics. It suggests that the "scaffold" of a protein—the large mass of amino acids surrounding a tiny active site—is not just passive support. Instead, it is a necessary energetic stabilizer required to keep the active site functional under thermal stress. For practitioners in protein design, the takeaway is profound. You may not need to design a whole fold. You may only need to design a function that survives the heat.

Figures from the paper