Protein stability is determined by single-site bias rather than pairwise covariance.

Scientists have long believed that the secret to a stable, functional protein lies in the complex web of interactions between its amino acid residues. In protein design, the goal is to mimic these natural patterns. Specifically, designers try to replicate the way certain residues "co-evolve" or move in tandem to maintain structure. However, a new study from the Barrick lab challenges this assumption. It suggests that when we try to optimize for these pairwise correlations, we might actually be making proteins less stable.

The researchers find that thermodynamic stability is driven primarily by single-site biases. These are the inherent preferences of a specific position for a particular amino acid. Pairwise coupling of residues, the study finds, does not drive stability. While these correlations are essential for biological activity, such as enzyme catalysis, they appear to act as a counterweight to structural stability. This discovery reveals a fundamental tension in protein evolution. A protein must balance being rock-solid in its shape with being flexible enough to perform its job.

The limitations of co-evolutionary design

Current protein design strategies often rely on capturing the statistical correlations found in Multiple Sequence Alignments (MSAs). These alignments are massive databases of related protein sequences. They reveal which residues tend to change together over evolutionary time. By using these correlations, designers hope to reconstruct the cooperative networks that hold a protein together.

Common approaches like Direct Coupling Analysis (DCA) use Potts models. These are statistical frameworks from physics used to describe how individual components in a system influence one another. Designers use them to infer both single-site biases and pairwise couplings. The prevailing logic is that including both types of information will lead to more "natural" proteins. Yet, as the authors observe, simple "consensus" designs often produce remarkable results. These designs ignore pairings and focus only on the most common amino acids at each site. They often produce proteins that are more stable than natural ones. This creates a theoretical gap. If pairwise correlations are so vital for structure, why do models that ignore them perform so well?

Decoupling site bias from residue pairing

To resolve this, the authors developed a method to surgically separate single-site biases from pairwise correlations. They used a Potts model to infer two distinct types of energy coefficients. They used large datasets, including a DNA-binding homeodomain (HD) family with 19,221 sequences and several enzyme families.

The team's approach involved creating several distinct "energy functions" to guide a Monte Carlo search. This is a stochastic optimization process used to find low-energy configurations. Their workflow followed these stages:

1. Coefficient Inference: They fitted MSAs using a pseudolikelihood optimization procedure. This extracted single-site energies ($h_i$) and pairwise coupling energies ($j_{i,k}$).
2. Energy Function Construction: They built specialized energy functions ($\epsilon_{seq}$) to test different combinations. Crucially, they created an "H-optimized" function ($\epsilon_{seq}^H$) that used only single-site energies. This effectively purged the design of any pairwise bias. They also created an "HJ-optimized" function ($\epsilon_{seq}^{HJ}$) that included both.
3. Sequence Generation: They used simulated annealing to generate 1,000 independent sequences for each category. This ensured the sequences captured the intended mathematical biases.

As shown in, this allowed them to generate "H-optimized" sequences that maximized individual site preferences. They also generated "HJ-optimized" sequences that maximized the cooperative dance between pairs.

Stability follows the single-site signal

The results of this decoupling were striking. The authors report that H-optimized sequences were significantly more stable than their HJ-optimized counterparts. In the HD family, H-optimized sequences achieved a mean folding free energy of $-14.0 \text{ kcal/mol}$. In contrast, extant natural proteins averaged only $-3.91 \text{ kcal/mol}$ .

This represents a massive increase in the energy required to unfold the protein.

The paper finds that stability correlates strongly with the single-site energy score ($H(seq)$). It reports a Pearson correlation coefficient of $\rho_{GH} = +0.80$ [Figure 4a]. Conversely, the correlation between stability and pairwise coupling ($J(seq)$) was actually negative ($\rho_{GJ} = -0.44$). The authors performed a partial correlation analysis to control for mathematical links between $H$ and $J$. They demonstrate that the apparent importance of pairwise coupling is an indirect effect. Once you account for the single-site bias, the coupling signal disappears .

This trend held across multiple unrelated enzyme families. These included adenylate kinase (AK) and dihydrofolate reductase (DHFR). In all cases, the H-optimized designs showed higher denaturation midpoints than the HJ or consensus designs .

The activity-stability trade-off

If H-optimization is superior for stability, why hasn't evolution abandoned pairwise correlations entirely? The answer, the authors suggest, lies in function.

While maximizing single-site biases makes a protein structurally "stiff," it can limit catalytic ability. The study finds that HJ-optimized sequences exhibit much higher turnover numbers ($k_{cat}$) across all tested enzyme families [Figure 6d–f]. Turnover number refers to how many substrate molecules an enzyme converts per unit of time. For the HD family, maximizing correlations led to a much higher DNA-binding affinity [Figure 6a–c]. Specifically, HJ-optimized HDs had a $K_d$ of 343 nM, while H-optimized versions reached 8.9 nM. Note that for the HD family, H-optimization actually yielded higher binding affinity.

Regardless, for the enzymes, the trade-off is clear. Maximizing pairwise correlations improves enzyme turnover. However, this often occurs alongside reduced thermodynamic stability. This suggests a profound biological trade-off. Pairwise correlations likely provide the flexibility required for an enzyme to bind a substrate. Designing for maximum stability by stripping away these correlations is a viable engineering route. But it may come at the cost of biological utility.

Assessing the design roadmap

The findings are robust across different protein architectures. However, practitioners should note two key caveats. First, the authors report that some H-optimized enzyme designs exhibited limited solubility or poor expression. Extreme stability optimization might push a protein into a regime that is difficult to manufacture. Second, H-optimized enzymes showed lower "$m$-values." This is a parameter describing the sharpness of the folding transition. Lower values may indicate lower folding cooperativity or the presence of partially folded intermediates.

For engineers looking to build hyperstable scaffolds, the verdict is clear. Prioritize single-site amino acid preferences. If your goal is to create a rigid structural component, ignore the co-evolutionary "noise" of residue pairs. However, if you are designing a functional catalyst, you cannot simply optimize for stability. You must carefully reintroduce specific pairwise couplings to restore the catalytic machinery. This may require sacrificing some thermodynamic margin. Code and data for these models are reportedly available; see the paper for the canonical links to the Barrick lab repositories.

Figures from the paper