Recombination Flow Matching Model for Protein Evolution

1. There are many imprecise definations of matrix dimensions, superscipt and subscript. Please see detailed list below:

   1. Line 132, the dimension of $T_i$ is $4\times4$, it cannot be decomposed to a $3\times3$ and a $3\times1$ in line 133.
   2. Eq.(1), $\mathsf{T}_i$ is $4\times4$, it cannot be multiplied by a $3\times3$.
   3. Line 168, the subscript of $\mathsf{T}_t$ is defined in line 182 between (0,1), contradicting to the subscript defined in line 151 which is the i-th residue.
   4. Eq.(8), the superscript of $R^{(t)}$ is time, contradicting to the superscript defined Eq.(7) which is the n-th residue.
   5. Eq.(8), $t-1<0$ according to the interval of t defined in line 182 ($0<t<1$), which is meaningless for corresponding $R^{t<0}$.
   6. Line 237, the subscript of $\mathsf{T}_{sk}$ is defined as k-th segment, contradicting to the subscript defined in line 151 which is the i-th residue.
   7. Line 238, on the right side of the equation defining $\mathsf{T}_{sk}$, it is independant of k, which should be dependant instead.
   8. Eq.(9), the time t appears both subscipt and superscript.
   9. Eq.(9), the superscript s1 represents the selected segment at time $t==1$, contradicting to the defination in line 237 which represents the 1st selected segment.
   10. Eq.(14), the superscript (l-1) represents layer, contradicting to the defination in line 263 which represents time (t-1).

2. The theoritical contribution (by using the same transformation across the selected segments) is not much. The authors may propose other techniques at the same paper. For example, similar to the two strategies in reference "Improved motif-scaffolding with SE(3) flow matching", 1) take the selected segments as input, 2) does not require training but bias the model's generative trajectory to preserve the selected segments.

3. There is no comparsion with other papers on designablility (or RSR). Please comprare with FrameFlow, FrameDiff and VFNDiff.

• Insufficient comparison with SOTA methods like RFDiffusion and Chroma.
• The writing needs improvement.
  • The term "movable" is undefined.
  • "T"/"R" (in Section 4.1) with different font types and sub/super-scripts represents different things, making the manuscript less readable.
  • In Section 4.1, T(s1) denotes the 1-st segment, while in Section 4.2, R(s1) denotes the timestep=1. I find it rather hard to follow.
  • In Figure 2, the training process involves predicting T(s0) given T(s1), should them be exchanged?

Major comments:

1. One of the central claims of the paper is that despite its importance in evolution, recombination is unexplored for protein design methods, and that their method, RFM, is novel as the first model to leverage the critical biological phenomena of recombination into protein design. However, the very premise of this claim falls short to me: while it is true that recombination is critical for evolution on a genome-level, there is much less evidence to suggest that it is one of the major drivers of diversification at the protein level. For example, in Kummerfield and Teichmann 2009, a global analysis of 192 genomes indicates that the linear order of domains in proteins is largely preserved across evolution, and re-arrangements are rare. Across species, the substitution rate greatly outstrips the recombination rate for proteins (see Arenas 2021). The authors provide one citation to back up their claim that recombination is critical to protein evolution (Netzer & Hartl 1997) - but this citation does not even establish this, but instead proposes sequential domain folding as a means to preserve the viability of protein products if recombination does result in novel combinations of domains, without establishing that this is indeed a widespread phenomenon. Considering how much the authors' claim of designing a novel method relies upon their claim of identifying a critical mechanism of evolution that has been so-far underlooked in protein design, the authors should actually establish that recombination at the protein level is indeed a significant driver of protein evolution.

2. Related to the last point, this manuscript conflates the term "recombination" as used by protein engineers, which generally refers to using fragments from existing proteins to design new ones, versus "recombination" as used by evolutionary biologists, which refers to a molecular mechanism. The problem is that the authors rely upon a claim that they're exploiting the latter definition to claim they're doing something novel, whereas they're largely achieving the former definition, which has numerous established papers. Despite claiming to "leverage recombination to generate novel protein structures", the method cannot be said to be even simulating recombination from a biological perspective. For example, there are no species constraints on pools of proteins fragments can be sampled from, no genomic constraints on chromosomal position or sequence constraints on homology, no probabilistic components making double recombination events swapping out just a few hundred KB much rarer compared to swapping out all of a protein sequence past a certain point. Instead, their method more aligns with the former definition used by protein engineers. From this perspective, the authors are missing an entire canon of related works by only focusing on recent generative models - recombining existing protein fragments was a common way to generate functional diversity prior to deep-learning generative models. Bedbrook et al. 2017/2019 design channelrhodopsins assisted by machine learning models this way. Romero et al 2012 purpose active learning algorithms to select sequence fragments from existing libraries to design enzymes. Voigt et al 2002 describes computational algorithms for this purpose. The claim that RFM is the first model that leverages "recombination", at least from a protein engineering perspective, is not true - this is a well-established strategy dating back decades.

3. Especially because this method bears similarity to existing protein engineering methods, the evaluation metrics the authors are using are insufficient. First, the authors use a pdbTM score to claim that the model is generating novel structures. However, it's important for them to keep in mind the point of a novelty evaluation, which is to support the claim that the structures generated by a generative method reflect novel functions beyond proteins present in PDB. Recombination-based design methods generally have the limitation that because they're using templates from existing proteins, it is unlikely that substantially different functions will emerge. Hence, this metric is easily gamed - if I took two protein sequences, chopped each in half, and glued them together, the pdbTM will technically be dissimilar from either source protein, but it's unlikely I'm covering new ground in function space, because I'm just recycling domains from these proteins. Secondly, the scTM score is biased by the fact that the authors are using relatively large chunks of backbones from existing PDB structures. ProteinMPNN itself is trained on PDB, so this raises the question of if scTM is actually a good proxy for designability, or if the model has simply overfit to structure-sequence pairs already seen during training. To generalize these comments - the authors should consider how to adapt metrics recognizing the limitations of their specific method, instead of simply recycling routine protein generation metrics, and I would heavily encourage them to look at the prior literature of recombination-based methods in protein design for this purpose.

Minor comments:

1. Abstract - "current methodologies often face significant limitations in generating both novel protein structures" -> both novel and what? This sentence doesn't parse.

1. The novelty of this algorithm is limited. The architecture of the framework is largely borrowed from previous protein flow matching papers, including protein representations and the setup of training. The addition of recombination loss is marginally novel.
2. The evaluation is not comprehensive. With scTM > 0.5 and no AF confidence reported, it is highly likely that AF models are not at all similar to the design template and yet since part of it is reminiscent of structures in training set (overlapping among AF, MPNN and this work), AF's memorization of fold nonetheless recapitulate the original pattern. It is recommend to adjust the threshold of these metrics and include AF confidence metrics.

1. The paper focuses on generating designable and novel protein structures and does not address the direction of protein functionality at all. Would be interesting to see if this method is generalizable to designing proteins of specific functionality, which might be more relevant to downstream applications.
2. While the rigid-body dynamics employed ensure structural integrity, it might be an oversimplification of the protein evolution process. This might lead to the model not being able to produce diverse protein structures.
3. The authors compared the proposed method with several baselines. However, the comparison seems to be limited to the novelty metric. More comprehensive comparison should be performed.

• The authors don’t sufficiently detail the recombination selection algorithm, or provide an intuitive understanding (beyond an evolutionary explanation) for it being beneficial.