Author response:
The following is the authors’ response to the original reviews.
Public Reviews:
Reviewer #1 (Public review):
Summary:
The authors aim to study mutational paths connecting WW domains with different binding specificities. Their approach combines an unsupervised sequence generative model based on RBMs with a path-sampling algorithm. The key result is that most intermediate sequences along the designed transition paths retain measurable binding activity in wet-lab assays, whereas paths containing the same mutations introduced in a randomized order are largely non-functional. This difference is attributed to epistatic interactions captured by the RBM model.
Strengths:
Exploring mutational paths in high-dimensional protein sequence space is a challenging problem. The computational framework used here is state-of-the-art and is strengthened by systematic experimental characterization of binding activity. The study is comprehensive in scope, including multiple transition paths both within and across WW specificity classes, and the integration of modeling with high-throughput experimental validation is a clear strength.
Weaknesses:
A major concern is whether the stated goal of specificity switching is fully achieved. Along the sampled transition paths, most intermediate variants appear to retain specificity close to either the initial or the final class, rather than exhibiting gradually shifting specificity. For example, in Figure 4G (Class I to Class II/III), binding appears largely binary, with intermediates behaving similarly to one of the endpoints. A similar pattern is observed in Figure 3H for the Class I to Class IV transition, where binding responses are close to 0 or 1. In this sense, the specificity-switching objective is only partially realized by assigning two endpoints with different specificity. This raises a broader conceptual question: is it possible that different WW specificities evolved from a common ancestor without passing through intermediates that exhibit mixed or intermediate specificity? If so, then inferring specificity-switching pathways purely from extant natural sequences may be fundamentally challenging.
We have added a sentence in the introduction to underline these points, in particular: Is the specificity switch happening through abrupt or more gradual specificity changes? Does it correspond to a bottleneck in sequence space?
Reviewer #2 (Public review):
This is an extremely important work that shows how one can use generative models to construct specificity-switching mutational paths in complex fitness landscapes. The experimental evidence is very clear, and the theoretical tools are innovative.
The work will likely have a deep impact on future research aimed at understanding how evolution navigates fitness landscapes as well as reconstructing ancestral sequences.
The manuscript is extremely clear and well written, the experimental evidence is strong, and the methods are clearly described, so I do not have major issues to raise. A few minor issues are listed below.
(1) I consider the WW domain as an 'easy' case from the point of view of generative modelling. The domain is rather short, epistatic effects are not very strong (e.g. Boltzmann learning usually converges very quickly to a very paramagnetic state), and the resulting models are well interpretable (e.g. the hidden units of the RBM correlate well with subclasses).
This is not always (not often?) the case, however. In more complex proteins, the learning procedures can be slower and the resulting models less interpretable. Just for completeness, perhaps the authors could comment on the generality of the results and what they would expect for other systems based on their experience.
We have added a sentence in conclusion to discuss the application of our framework to more complex and longer proteins.
(2) In Section 3.3, the authors say that direct paths connecting Class I and Class IV behave similarly to indirect paths, despite having lower scores according to the RBM. How generic is this? Does it also happen for other classes? This might be an important point to address, as direct paths are easier to sample.
We have added a sentence in conclusion to emphasize the need for a more exhaustive study of non-direct vs direct paths.
(3) The path shown in Figure 4 goes through a region of non-functionality around sequences 18-19. It seems that the sample path is basically exploring the functional regions for Class I and Class II/III separately, trying to approach the other class, but then it can't really make the switch.
By contrast, the path going from Class I to Class IV seems able to perform the functional switch in a single step (20-21) without losing too much of the function.
Perhaps the authors could better comment on this? Is this a limitation of the sampling method, or a fundamental biological fact?
We now better stress and discuss the comparison between Class I to Class IV paths and Class I to Class II paths in the conclusion.
(4) On page 12, it is stated that the temperature was chosen to 1/3 to maximize the score. This is important and should be mentioned earlier (I didn't notice it until that point).
We have added a sentence in Section 3.2 on the lowering of the sampling temperature to 1/3 to obtain high-scores sequences.
(5) On page 13, it is stated that: "However, the scores of the ancestral sequences along the phylogenetic pathways assigned by the RBM are significantly lower than the ones of the RBM-designed sequences. This result is expected as ASR reconstruction does not take into account epistasis, differently from RBM, and we expect ASR sequences to generally be of lesser quality."
I was very surprised by this result. My own experience with ASR shows that, on the contrary, sequences found by ASR (via maximum likelihood) tend to have high scores in the (R)BM, and tend to be more stable than extant sequences. I attribute this to the fact that ASR typically finds a "consensus" sequence that maximizes the contribution to the score coming from the fields (the profile), which is typically dominant over the epistatic signal, resulting in a bigger score. Maybe the authors did not use maximum likelihood in the ASR? Some clarification might be useful here.
We have updated Figure 5 with shuffled and ASR sequences, and added Suppl Figure 7 to compare the score of the consensus sequences and the ones of the most ancestral nodes along the path in the ASR reconstruction with the natural scores.
Recommendations for the authors:
Reviewer #1 (Recommendations for the authors):
I suggest that the authors either more clearly acknowledge that smooth specificity switching is not fully demonstrated or reconsider the use of "specificity switching" in the title. An alternative framing could emphasize the study of mutational paths connecting different specificity classes, without implying a transition in specificity.
One of the main questions motivating our study was precisely to investigate where along the path and how the transition in specificity happens, i.e. through intermediate that exhibit mixed or intermediate specificity (which we had defined as ‘smooth’) or more abruptly.
For class I-IV paths, we observe a smooth specificity switch with some cross-specificity of the sequences designed in the switching-specificity region, with low but significant binding responses not only towards class I and IV ligands (the extant sequences specificity class) but also to ligand of class II. On the contrary, in the paths from class I to class II-III, we observe the abrupt switch, at the predicted specificity boundary, with sequences with a clear response to one or the other peptide. This abrupt switch requires the change of several amino acids determining the specificity class, and binding is loss when this change is incomplete.
We understand that the term “smooth” to design the cross-reactivity of the few sequences in the predicted ‘switching boundary zone’ could be misleading, so we have removed it from the abstract.
Moreover, we have added a sentence in introduction to motivate the study of where and how the specificity transition takes place, and two sentences in conclusion about the identification of where the specificity switching take place along the path, and to underline the difference between the paths from class I to class IV and the ones from class I to class II/III.
It is striking that all scrambled paths are non-functional. Given that sequences adjacent to the end states differ by only a few mutations, one might expect at least some of these variants to remain functional, as small numbers of mutations often do not abolish activity. The authors should discuss this result in greater depth and more clearly explain how it uniquely supports the role of epistatic interactions.
The sampling of the scrambled paths is not strictly random. Along the scrambled path the mutations are inserted in the reverse order; the scrambled paths are therefore chosen to maximize the sequence divergence between the unscrambled sequences (in which the mutation is predicted to be functional by the path sampling algorithm) and the one in which it is tested in the scrambled path. The fact that the background matters is a clear sign of epistasis.
We have better explained this important point in Section 3.3, where we introduce scrambled paths.
Specificity class annotations are inferred using RBM latent weights. However, as shown in Figure 2E, the boundaries between classes in latent space are not sharply defined. It would strengthen the analysis to validate these class assignments using alternative representations, such as clustering in the latent space of a VAE or embeddings from protein language models, to assess whether the inferred class boundaries are robust and consistent.
Beyond RBM weights, the boundaries between clusters have been assessed by inferring two different RBMs (which we call class specific RBM) on class specific MSA, such models validated the robustness of the boundaries. Most importantly, we have shown that the classification is consistent with experiments.
To further answer this comment, we have added Suppl. Figures 7 and 8, showing that a simple PCA approach, as well as VAE agree with our clustering.
In Figure 3C and Figure 3F, variants 18 and 19 appear to represent transition states located in regions of latent space with little or no training data. Intuitively, such variants would be expected to have a lower probability than variants 22, which lie in a high-density region of the RBM model. However, this expectation is not reflected in Figure 3C. A similar issue appears in Figure 4. The authors should carefully re-examine these results and clarify whether this behavior arises from the model, the scoring procedure, or a potential error.
We confirm that variants 18 and 19 in mutational path between classes I-IV have larger scores than the class IV wild-type domain. We have attributed the low score of this class IV wild-type (the extant sequence) to its smaller structural stability, as discussed in Sec 3.3 and with Supplementary Figure 3.
The key point here is that the scores of Natural sequences are spread, as shown with the histogram in Fig. 5 (green distribution), corresponding to more or less stable natural protein. The RBM model (with a low sampling temperature favoring higher RBM scores) is able to generate artificial sequences far away in sequence space (i.e. with high Hamming distance with respect to natural one), while keeping high scores. The functionality of designed proteins with high RBM scores has been demonstrated in previous work by some of us, e.g. [Malbranke et al PLoS Comp Bio 2026], [Huot, Monasson, Cocco Cell system 2026], [Fernandez-de-Cossio-Diaz Nature Communication 2026], building up on similar results for BM models [Russ et al Science 2020].
We have now clarified the point of the sampling at low temperature earlier in the manuscript in Section 3.2.
Reviewer #2 (Recommendations for the authors):
(1) In Figure 2 F-G, maybe a histogram of the scores of natural sequences could be added for comparison.
We have added the histogram of scores of natural sequences in figure 5, where we discuss the scores of the generated sequences for the different paths.
(2) In Section 3.4, "(Wild type 1YWI or formin binding protein)" is not clear; there might be a typo. Please check
We do refer to Formin-binding protein 1, also known as FNBP1. We have reformulated the corresponding sentence.
(3) On page 16 at the end of section 4, the authors could consider citing "Integrating experimental feedback improves generative models for biological sequences" by Calvanese et al. among the active learning methods.
Thanks for suggesting to cite this very relevant work. We have added the reference.
(4) Reference 78 is stated "in preparation (2019)", I guess this is a mistake and could be fixed.
The reference has been updated.
