Generative Modeling of Full-Atom Protein Conformations using Latent Diffusion on Graph Embeddings

Dear Reviewer pf7X,

Thank you for your thoughtful feedback. Below we address your main points.

1. Ensuring Protein Length Consistency

This is a very perceptive question. For the work presented in this paper, which focuses on a single, specific protein, the length is inherently fixed. The model is trained on the MD trajectory of one protein with a constant number of heavy atoms (N), and all architectural components are sized accordingly. The key mechanism is the decoder's conditioning on the reference structure's latent embedding ($\boldsymbol{Z_{ref}}$), which has a fixed dimension of N$\times d_{z}$, ensuring that every generated structure has the exact same number of atoms.

Your question correctly points toward the broader challenge of generalizing to proteins of variable lengths. While beyond the scope of this paper, we have developed advanced capabilities to handle this, which we will detail in an appendix. We have successfully created multi-receptor models using two main strategies (For your reference, the code for these advanced models is available in our repository now under the conditional_generation and multi_receptor folders):

1. A Shared Decoder: This version trains a single decoder across multiple receptors. It handles variable lengths by using a fixed-size pooled latent vector for the diffusion model, while the decoder is informed by a variable-length conditioner ($\boldsymbol{Z_{ref}}$) whose size matches the specific protein being generated.
2. Conditional Diffusion: This approach guides the diffusion process with a fixed-size protein "fingerprint". To create this, a 1D-CNN maps each variable-length reference embedding ($\boldsymbol{Z_{ref}}$) to a compact, fixed-size vector that summarizes the protein's reference structure.

Training these advanced models effectively required a robust data augmentation strategy to regularize the potentially sparse, high-dimensional latent space. Our approach makes the learned manifold smoother and more robust. We use two techniques: first, Principled Structural Augmentation, where we use the DSSP algorithm to identify flexible loops and then delete short segments to create new variants with different lengths. Second, Conformational Augmentation, where we add calibrated Gaussian noise to the reference coordinates to enrich the dataset with near-native structural variations.

2. Why ChebNet

We chose ChebNet as our encoder backbone precisely because its spectral, multi-hop convolution inherently captures the long-range dependencies critical for modeling proteins with complex allosteric pathways. Below, we elaborate on why ChebNet remains well-suited and in some respects preferable to more recent Message-Passing Neural Networks (MPNNs) in our setting.

Intrinsic Multi-Hop Aggregation vs. Local Message Passing: ChebNet’s spectral filters are implemented via Chebyshev polynomial approximations of the graph Laplacian of order K. In a single layer, a ChebNet with K hops aggregates information from up to K-distant neighborhoods, enabling it to transmit signals across distant residues without stacking many layers. In contrast, standard MPNNs propagate information only through immediate neighbors per layer. To reach K-hop neighbors, they must stack multiple layers, which empirically leads to over-smoothing (node representations become indistinguishable) and over-squashing (long-range signals are compressed into fixed-size messages). These bottlenecks are especially problematic in proteins, where allosteric effects require faithful transmission of subtle conformational changes.

Recent Evidence of ChebNet’s Long-Range Strength: Recent work introduces principled metrics for measuring distant-node influence and confirms that models like ChebNet exhibit higher long-range dependency scores compared to local message-passing methods [1].

Pragmatism and Empirical Validation: For systems like GPCRs, the most biologically relevant motions are internal conformational changes, not global rigid-body movements. Our "align-then-learn" strategy, using a non-equivariant but powerful GNN like ChebNet, allows the model to focus on these critical dynamics while avoiding the computational complexity of strictly SE(3)-equivariant models. Our empirical results validate this, as the raw ChebNet embeddings achieve extremely low reconstruction errors, confirming that both local and global features are captured.

In summary, while ChebNet is a foundational GNN, its multi-hop spectral convolution remains uniquely suited to protein systems where long-range interactions are crucial, bypassing the message-passing bottlenecks that can limit more recent MPNN architectures.

[1] Liang et al. (2025). Towards Quantifying Long-Range Interactions in Graph ML. arXiv preprint.

3. On SE(3) Equivariance and Physical Constraints

You are correct that our model is not strictly SE(3) equivariant, which was a deliberate design choice. Our "align-then-learn" approach is highly effective for this problem and ensures the generation of physically realistic structures through two mechanisms:

1. Isolating the Signal of Interest: By aligning all MD frames, we remove global rotation and translation, allowing the GNN to focus exclusively on learning the landscape of internal deformations (e.g., helix movements), which are the motions directly relevant to biological function.
2. Implicit Physical Priors from Conditioning: Our framework inherently respects physical constraints like chirality because the decoder learns to predict conformations by applying a small, learned deformation to the latent embedding of a physically-correct reference structure. To address your example, it is highly unlikely for our model to generate a left-handed alpha helix, as this would require overcoming a massive energy barrier not present in the training data. The model learns the distribution of plausible, low-energy dynamics, and catastrophic, chirality-inverting changes are not part of that distribution. Across the 10 k generated structures we observed zero Ramachandran or chirality violations.

We will add a paragraph to the Methodology section to clarify this design choice and its rationale.

4. On Broader Evaluation and Benchmarking

This is an excellent point. Our original manuscript focused on an in-depth model development for the challenging D2R system. However, we agree that broader evaluation is crucial to contextualize our contributions. In response to the reviews, we have expanded our evaluation in two key ways. To be clear, all analyses presented here are based on MD simulations completed prior to the submission deadline; our work during the rebuttal period focused exclusively on benchmarking and further analysis of this pre-existing data.

First, we benchmarked our model against leading generators, including AlphaFlow, BioEmu, and Boltz-2 (MD conditioned) This comparison revealed a critical difference between our ensemble-focused approach and the more static predictions of the baselines.

All baseline metrics were recomputed with the authors’ public code.

Our analysis revealed that the baselines produce high-fidelity but relatively static structures. The combination of near-perfect lDDT scores with extremely low RMSF proves they fail to capture the protein's native flexibility. BioEmu’s rigidity was particularly surprising given its broad training data, highlighting how generalist models can miss system-specific dynamics.

In contrast, LD-FPG excels in every category relevant to ensemble generation. It not only achieves superior local geometric accuracy (with a backbone JSD of 0.007, 3-5x lower than the baselines) but also almost perfectly reproduces the ground-truth flexibility (RMSF of 1.22 nm vs. 1.34 nm).

Crucially, our framework is unique in its all-atom generation capability. This allows us to quantify side-chain accuracy, where we achieve a low summed JS divergence for χ angles (~0.022) and an all-atom RMSF (1.36 nm) that closely matches the ground truth (1.60 nm) — metrics the other frameworks cannot report.

Second, to demonstrate that our framework's principles are robust, we will now include analysis from our broader validation studies, which were performed during the initial development of our model. This includes other Class A GPCRs (D1, A2A, β1-adrenergic) as well as proteins from different structural classes (α-helical, β-sheet, and mixed α/β folds). Across these diverse systems, our framework consistently generated high-fidelity ensembles, achieving all-atom lDDT scores in the range of 0.68–0.78 and low total JS divergences between 0.007 and 0.014. These studies will be presented in a dedicated appendix. This approach allows us to add the vital D2R benchmark to the main text while maintaining the paper's focused narrative.

These new results, which will be incorporated into the revised manuscript, demonstrate that our method is both competitive with state-of-the-art baselines and broadly applicable across different protein architectures.

Dear Reviewer iANt,

Thank you for your insightful feedback. We address each point below.

Weakness 1: Generalizability and Experimental Design

We agree it's critical to confirm our model genuinely learns a conformational manifold rather than simply interpolating between existing structures (Note: no new simulations were performed; all discussions were part of our original model validation).

1. Beyond Interpolation

To confirm this, we carried out two additional analyses:

• Learning from Sparse Data: Trained on just 40% of the MD trajectory, LD-FPG generated a high-fidelity ensemble. This demonstrates that the model learns a continuous and generalizable latent manifold from sparse data, rather than merely interpolating between dense training points.

• Generating Unseen Transition States: 'LD-FPG' was trained on a metadynamics simulation with sparsely populated transition states between the active and inactive forms. Despite training on this imbalanced data, our model successfully generated accurate conformations along the entire less-seen transition path.

2. Generalization Across Protein Systems

We broadened evaluation to additional proteins:

• Large and Structurally Diverse Folds: We have applied LD-FPG to a set of proteins from the ATLAS database. This includes large, complex systems like cytochrome P450 (~500 residues) and proteins with entirely different architectures, such as primarily $\alpha$-helical, primarily $\beta$-sheet, and mixed $\alpha/\beta$ folds.

• Different Protein Families and Processes: We extended our validation to other Class A GPCRs (D1, A2A, $\beta$1-adrenergic) and even modeled the entire folding trajectory of the TRP-cage miniprotein, demonstrating the framework can capture dynamic processes beyond equilibrium sampling.

• Exploring Generalization: As a preliminary exploration of generalization, we briefly tested an advanced model with a shared decoder. This model was able to generate plausible structures for a sixth, previously unseen receptor, suggesting our framework has strong potential for zero-shot applications.

Across all these diverse and larger systems, our framework consistently generated high-fidelity ensembles, achieving all-atom lDDT scores in the range of 0.68–0.78 and low total JS divergences between 0.007 and 0.014.

This new validation, which will be detailed in the appendix, confirms that the geometric principles of LD-FPG are not limited to a single system but represent a robust and scalable approach to all-atom ensemble generation.

3. Our Core Contribution and Vision

Your review correctly identifies the grand challenge of creating a universal all-atom generator. The primary goal of this paper is to establish a foundational geometric engine for a single, complex system which is a prerequisite for a universal model. We fully agree that the path toward a model that works on any unseen protein will require integrating chemical and sequence information. A promising future direction is to condition our geometric engine on rich embeddings from models like ESMFold or AlphaFold, which capture this amino acid identity.

Weakness 2: Insufficient Baseline Comparisons

This is a crucial point, and we agree that a direct comparison to state-of-the-art methods is essential to contextualize our contributions. In response to the reviews, we have performed an extensive new benchmark comparing LD-FPG against leading models: AlphaFlow, BioEmu, and the all-atom Boltz-2 (with MD conditioning).

Interpretation of Results

1. Superior Local Geometry: Our model achieves a backbone dihedral JSD of 0.007, outperforming all baseline methods by a factor of 3-5x. This demonstrates superior accuracy in capturing the local geometric preferences of the protein.

2. Baselines Generate Static Structures, Not Ensembles: The baselines produce high-fidelity but static structures. While they achieve near-perfect lDDT/TM-scores, their Root-Mean-Square Fluctuation (RMSF) is extremely low. This combination of high fidelity and low flexibility proves they fail to capture the protein's native dynamics. For an ensemble generator, an lDDT score near 1.0, when paired with low RMSF, confirms a lack of diversity.

3. LD-FPG Correctly Models Dynamic Flexibility: In sharp contrast, our model's average RMSF (1.22 nm) almost perfectly matches the ground truth (1.34 nm). This is the key result: LD-FPG successfully learns and reproduces the correct conformational diversity of the ensemble.

4. The All-Atom Advantage: Crucially, our framework is unique in its all-atom generation capability. This allows us to quantify side-chain accuracy, where we achieve a low summed JS divergence for $\chi$ angles (~0.022) and an all-atom RMSF (1.36 ± 0.18nm) that closely matches the ground truth (1.60 ± 0.32nm)—metrics the other frameworks cannot report. This directly substantiates the benefits of our approach.

This new analysis shows that LD-FPG achieves state-of-the-art local geometric accuracy while correctly modeling the entire flexible, all-atom conformational ensemble—a more challenging problem than static prediction.

Q1

Part 1: Validation of the Starting Structure

Our starting structure was rigorously validated to ensure its accuracy before the production simulations:

• High-Quality Template: The model is based on a 2.96 Å cryo-EM structure (PDB 6VMS) with an excellent validation report (MolProbity score: 1.8; Ramachandran favored: 97%).
• Minimal Refinements: Only minor refinements (≤3% of residues in loops) were performed with RosettaRemodel, preserving the transmembrane (TM) core's structure (Cα RMSD of 0.38 Å to the cryo-EM map).
• Orthogonal Check: An independent check against a de novo AlphaFold 3 prediction shows high agreement (TM-core RMSD of 1.0 Å), further validating the starting coordinates.

Part 2: Sufficiency of the 2 µs MD Trajectory

The 2 µs simulation length balances computational cost with the need to sample a rich landscape.

• Sufficient Timescale: The 2 µs trajectory extensively samples fast-to-intermediate dynamics (ns-µs), including the full range of side-chain rotations, loop flexibility, and helix movements within the sampled active-state basin.
• Community Standards: This simulation length is consistent with many high-impact GPCR studies and community resources like GPCRmd. It provides a deep sample of the active-state ensemble, which is our primary goal for training.
• Learning Goal: Our framework is designed to learn the conformational landscape provided by the input data. The 2 µs run provides a rich training set, and our new metadynamics experiment confirms the model can also learn from sparse transition pathways when they are present in the data.

Q2

The comparison was strictly zero-shot, as the public BioEmu release does not include code for fine-tuning on new trajectories. Such fine-tuning would be a massive but interesting research project in its own right. We acknowledge our initial A100 index comparison was brief; it has been superseded by the comprehensive benchmark analysis detailed in our response to Weakness 2. This new data reinforces our central point: generalist models, while powerful, may not capture the specific dynamics of a challenging target like D2R without system-specific training, highlighting the value of our specialized approach.

Q3

This is an excellent suggestion. We have now incorporated a full RMSF analysis into our benchmark table and the corresponding "Interpretation of Results" (under Weakness 2). As detailed there, this analysis confirms that our model correctly reproduces both the backbone and all-atom flexibility of the ground truth MD ensemble—a capability the more rigid, backbone-focused baselines lack.

Q4

The coordinate decoder's architecture consists of two main components:

1. A Pooling Module: This module takes the high-dimensional, atom-wise latent embeddings ($Z \in \mathbb{R}^{N \times d_z}$) and compresses them into a single, low-dimensional context vector ($\mathbf{h}_0$). As detailed in the paper, we explore three distinct pooling architectures: Blind, Sequential, and Residue-based.
2. A Multi-Layer Perceptron (MLP): This MLP takes the pooled context vector ($\mathbf{h}_0$) and the latent embedding of the reference structure ($\Zref$) as input to predict the final 3D coordinates for every atom.

For example, the Blind Pooling decoder used for our main results uses an MLP with 12 layers and a hidden dimension of 128, with ReLU activations and BatchNorm. Full architectural details and hyperparameters for all three pooling strategies are provided in Appendix C.

Q5

Figure 1 will be fully redrawn to show two clearly labeled paths—(a) autoencoder training (MD → latent → reconstruction) and (b) generative inference (latent sampling → decoder → coordinates).

Dear Reviewer ZSKy,

Thank you for this valuable feedback. The manuscript was originally structured as a deep dive into the architectural development for the challenging D2R system. We now agree that showcasing the framework's broader applicability is essential. Accordingly, the revised paper will integrate a new baseline comparison for D2R in the main text and present our comprehensive generalization studies in a dedicated appendix.

Below, we address your specific concerns in detail.

Weaknesses

1.1 Architectural/Loss Details & Readability

You are correct that key details were deferred to the appendix without sufficient signposting. We apologize for this oversight. In the revised manuscript, we will reference relevant appendices upon first mention of key concepts. Specifically:

• Section 3.3 (Decoder Architectures) will reference Appendix C for detailed configurations.
• Section 3.5 (Loss Functions) will reference Appendix E for formal mathematical definitions.

Additionally, important details will be incorporated into the main text:

• The primary mathematical equation for our decoder loss ($L_{Dec}$) will be included in Section 3.5.
• A compact summary table of key hyperparameters for our models will be added to the Methodology section.

We will also revise paragraph structure throughout the Methodology section to enhance readability and logical flow.

1.2. Baselines and Generalization

This is an essential point. To demonstrate our model's performance in context, we have performed a new benchmark for the D2R system and will now include key results from our broader validation studies.

Benchmarking against State-of-the-Art: We compared LD-FPG against leading models (AlphaFlow, BioEmu, and Boltz-2 with MD conditioning).

Our benchmark reveals a critical distinction between our approach and existing methods by evaluating both static fidelity (lDDT) and dynamic diversity (RMSF).

• Baselines Are Overly Rigid: The baselines produce high-fidelity but static structures. While their lDDT scores are nearly perfect, their extremely low Root-Mean-Square Fluctuation (RMSF) confirms they fail to capture the protein's native flexibility.

• LD-FPG Correctly Models Flexibility: In contrast, our model correctly reproduces the dynamic ensemble. Its average RMSF (1.22 nm) almost perfectly matches the ground truth (1.34 nm), demonstrating it captures the correct conformational diversity.

• Superior Geometry without Sacrificing Dynamics: Crucially, LD-FPG achieves this realism while also delivering superior local geometry. Its backbone dihedral JSD of 0.007 is 3-5x better than all baselines, proving our model generates a flexible, all-atom ensemble with state-of-the-art accuracy.

Generalization: To address your valid concern about applicability, the appendix will now present results from our broader validation studies. These studies, conducted during our initial model development to confirm the framework's robustness, show that our model consistently generates high-fidelity ensembles across a diverse set of targets, including:

• Other Class A GPCRs (D1, A2A, $\beta$1-adrenergic).
• Diverse Folds from ATLAS, including large systems like cytochrome P450 (~500 residues) and different architectures ($\alpha$-helical, $\beta$-sheet, mixed $\alpha/\beta$).
• Folding Dynamics, demonstrated by modeling the full folding trajectory of the TRP-cage miniprotein.

All-atom lDDT scores across this set are in the range of 0.68–0.78, with total JS divergences between 0.007 and 0.014. Simulation data for the additional GPCRs is now publicly available via our Zenodo link; a comprehensive list of all validated ATLAS structures will be included in the appendix.

Questions

2.1 Loss/Architecture Definitions

As addressed above (1.1), all key concepts will be clearly defined and cross-referenced within the main text.

2.2 Comparison with Existing Ensemble Generation Models

As we detailed in our response above (Point 1.2), we have performed an extensive new benchmarking study against AlphaFlow, BioEmu, and Boltz-2. Regarding MD-Gen: We chose not to include it in our benchmark since it is designed for trajectory generation and is currently tuned for small peptides (≤50 residues) in solvent whereas our work focuses on sampling conformations from the equilibrium ensemble. Applying it to a 273-residue membrane protein like D2R is outside its intended domain and would not produce a fair comparison.

2.3 Latent Space Diffusion

Thank you for this question. It highlights a critical design choice. We perform diffusion in latent space for three key reasons:

1. Dynamics-Focused Learning: By encoding only the deformations in a pooled latent space (relative to a static reference structure), the diffusion model can focus on learning the protein's internal, functionally relevant motions. The static fold and global orientation are factored out, allowing the model to learn a more targeted and meaningful distribution.
2. Numerical Tractability and Stability: The dimensionality is drastically reduced from ~6,600 degrees of freedom in Cartesian space for the D2R protein to ~100 dimensions in our pooled latent space. This makes the optimization stable and efficient. In our ablation studies, an equivalent DDPM trained directly in coordinate-space failed to converge entirely.
3. Implicit Physical Priors: By learning to perturb a physically-correct reference structure, the decoder inherently preserves correct local bond geometry and chirality, improving realism. This is supported by our low side-chain dihedral JSDs.

Our approach is consistent with strategies used in recent generative models. Given the challenges of all-atom diffusion, models like AlphaFold 3 [1] and Boltz-2 [2] use all-atom attention for detailed features, but then pool these representations to the residue level before applying diffusion in a lower-dimensional space—much like our residue-based pooling. Similarly, La-Proteina [3] keeps backbone coordinates explicit and diffuses side-chain information in a separate latent space, which resembles our sequential pooling setup. This confirms that our design addresses a widely recognized challenge in the field using practical, effective methods.

[1] Abramson et al., Nature 2024 (AlphaFold 3)
[2] Wohlwend et al., bioRxiv 2025 (Boltz-2)
[3] Geffner et al., NVIDIA Research 2025 (La-Proteina)

2.4 D2R as a GPCR and Biological Relevance

You are right that we should have made the GPCR context and its biological relevance more explicit. To address this directly, we are strengthening the manuscript with new, targeted analyses and revising the text for clarity.

First, to validate that our model captures functionally critical motions, we performed a new analysis on two canonical GPCR activation metrics: the TM6 outward movement ($R^{3.50}-E^{6.30}$ distance) and the NPxxY hinge twist ($D^{2.50}-Y^{7.53}$ distance). Our results confirm that LD-FPG accurately reproduces the free-energy profiles of these key transitions.

Furthermore, a key part of our original model validation involved testing its ability to learn from complex, non-equilibrium data. We trained LD-FPG on a metadynamics trajectory (~500ns) that explicitly samples the rare intermediate conformations along the D2R activation pathway. The model successfully learned from this sparse data and can generate realistic conformations that trace the entire transition path. This provides compelling evidence that the framework learns the underlying energy landscape, not just the dense regions of an equilibrium simulation.

Both of these new analyses will be detailed in a new Appendix G. Finally, we will revise the Introduction, Related Work, and figure captions to consistently highlight the GPCR context.

2.4 Clash Counts

Your concern is valid. Our response is two-fold:

1. The Correct Baseline for Clashes is the MD Ensemble: There is no universal threshold for "acceptable" clashes. Standard validation tools like MolProbity are calibrated for static, minimum-energy crystal structures and are ill-suited for evaluating dynamic MD ensembles, which naturally explore higher-energy states and exhibit transient van der Waals violations. Therefore, the most relevant benchmark is the reference MD simulation itself. As we report in the manuscript (Line 300), the ground truth MD ensemble has a non-zero average clash score of ≈1023. Our best-performing models (e.g., Residue Pooling at 1145 clashes) are remarkably close to this physical reference, indicating a high degree of realism.

2. An Area for Future Work: Managing steric clashes is a challenge for all generative models. We acknowledge the moderately higher clash count is a trade-off of our current approach. We are actively exploring physics-informed strategies, similar to those in models like Boltz-1, to further refine physical realism in future work. We will clarify this context in the revised manuscript.

2.6 Appendix Reference Typo

The "Appendix ??" typo in Algorithm 1 will be corrected in the final manuscript.

Dear Reviewer go5W,

Thank you for your detailed and helpful review. Your comments on the presentation of our model and the rationale for our design choices are well-taken, and we will address them thoroughly in our revised manuscript to improve its clarity and rigor.

We address your specific points in detail below.

Q1. Model Presentation and Figure 1

We agree that the presentation of our model can be significantly improved. In the revised manuscript, we will make the following changes to enhance clarity:

• Formal Problem Formulation: We will begin the Methodology section with a formal mathematical definition of the problem. This will establish a clear foundation by defining the inputs (an MD ensemble), the output (a distribution over all-atom conformations), and the learning objective before we describe the model's components.
• Revised Figure 1: We will completely redesign Figure 1 and its caption to be a clear, step-by-step guide. The new figure will feature separate, clearly labeled visual pathways for (a) Autoencoder Training and (b) Generative Inference. To directly address your question, we will add an explicit call-out stating that the model generates independent conformational frames, with no temporal conditioning. The decoder block will also be refined to better illustrate its internal logic.

Q2. Clarification on Temporal Dynamics

Your question about modeling temporal dynamics is particularly insightful. In the current work, our goal is to model the static equilibrium ensemble, so each conformation is generated independently. We will make this scope explicit in the revised manuscript.

However, you are correct that extending our framework to generate time-correlated trajectories is an important future direction. Our latent space representation is uniquely suited for this, and we envision two potential paths:

1. An autoregressive decoder, where the generation of a latent vector for frame t+1 is conditioned on the latent vector from frame t.
2. A more powerful approach would be to learn the score function of the latent space, which would allow for simulating Langevin dynamics directly on the learned manifold to produce continuous trajectories.

Both are compelling applications that highlight the flexibility of our framework. We will add a note on these exciting future directions to the discussion section.

Q3. Rationale for Coordinate Alignment

This is an important point that deserves a clearer explanation. You are correct that, in a general sense, global rotations and translations can reflect meaningful physical motions. For the specific system of a GPCR in a membrane, our rationale of aligning trajectories along a reference is grounded in the well-understood separation of dynamic scales in these systems. GPCRs experience two distinct types of motion:

First, there is the large-scale, slower global rigid-body motion of the entire receptor within the membrane (e.g., lateral diffusion). While physically real, these movements are not the direct drivers of the signaling mechanism we aim to model.

Second, and central to our work, are the faster, small-amplitude internal conformational deformations—such as the outward swing of transmembrane helices and the repacking of conserved motifs. These internal rearrangements constitute the actual functional switch that enables downstream signaling.

Our goal is to learn the probability distribution of these crucial internal motions. To do so, it is essential to first decouple them from the global, rigid-body drift. Standard practice in molecular dynamics analysis requires this separation, as uncorrected global drift would otherwise dominate key structural metrics. For instance, without alignment, RMSD would be inflated by simple translation, and Principal Component Analysis (PCA) would primarily capture the protein's trivial wandering in the simulation box rather than its biologically relevant internal dynamics.

Therefore, our choice to use Kabsch alignment is a deliberate and standard methodological step to isolate the signal of interest. This "align-then-learn" strategy allows our graph neural network to focus exclusively on learning the rich landscape of internal conformational changes. It is a pragmatic choice that preserves all essential internal structural information while avoiding the significant architectural complexity of fully SE(3)-equivariant networks. We will add a sentence to the manuscript acknowledging this trade-off and clarifying that our model is tailored to learn the internal conformational ensemble.

Q4. Comparison with Baselines

We acknowledge this was a significant omission. In response, we have performed an extensive new benchmark comparing LD-FPG against leading models: AlphaFlow, BioEmu, and the all-atom Boltz-2 (with MD conditioning). This analysis reveals a crucial distinction between our approach and existing methods.

While LD-FPG is an all-atom ensemble generator, the baselines primarily function as static structure predictors. Our new results, summarized below, clearly illustrate this difference by evaluating both static fidelity (lDDT/TM-score) and dynamic diversity (RMSF).

Interpretation of Results:

1. Superior Local Geometry: Our model achieves a backbone dihedral JSD of 0.007, outperforming all baseline methods by a factor of 3-5x. This demonstrates superior accuracy in capturing the local geometric preferences of the protein.
2. Baselines Generate Static Structures, Not Ensembles: The baselines produce high-fidelity but static structures. While they achieve near-perfect lDDT/TM-scores, their Root-Mean-Square Fluctuation (RMSF) is extremely low. AlphaFlow comes closest to reproducing the system's dynamics (RMSF 0.84 nm), but its flexibility is still far below the ground truth. BioEmu (0.09 nm) and Boltz-2 (0.07 nm) remain highly rigid despite their large training sets. This underscores that for an ensemble generator, an lDDT score near 1.0, when paired with low RMSF, confirms a lack of diversity.
3. LD-FPG Correctly Models Dynamic Flexibility: In sharp contrast, our model's average RMSF (1.22 nm) is almost identical to the ground truth (1.34 nm). This demonstrates that LD-FPG successfully learns and reproduces the correct conformational diversity of the ensemble.
4. The All-Atom Advantage: Crucially, our framework’s all-atom nature allows us to perform vital side-chain analysis—a capability the backbone-focused baselines lack. Our model achieves a low summed JS divergence for side-chain χ angles (~0.022) and an all-atom RMSF (1.36 nm) that closely matches the ground truth (1.60 nm), confirming high fidelity across the entire molecular system.
5. The Need for System-Specific Models: This benchmark reinforces a key principle: generalist models, even those trained on vast datasets, will always have specific strengths and limitations. Our analysis is another instance showing that for capturing the nuanced, system-specific dynamics of a target like D2R, a specialized model currently provides a more accurate and physically realistic ensemble.

This analysis highlights that LD-FPG solves a different and more challenging problem. It not only achieves state-of-the-art local geometric accuracy but does so while correctly modeling the entire flexible, all-atom conformational ensemble. We will integrate this new table and a full discussion into the revised manuscript.

All new baseline scores were computed from publicly released code prior to the official review deadline; no post-deadline training was performed.

Thank you once more for your valuable suggestions. They have been helpful in identifying key areas for improvement, and we are confident the resulting manuscript will be significantly clearer and more rigorous.

Sincerely,
The Authors