Title: ProtInvTree: Deliberate Protein Inverse Folding with Reward-guided Tree Search
Venue: NeurIPS 2025
Accepted: yes
Keywords: protein design
Abstract: Designing protein sequences that fold into a target 3D structure—known as protein inverse folding—is a fundamental challenge in protein engineering. While recent deep learning methods have achieved impressive performance by recovering native sequences, they often overlook the one-to-many nature of the problem: multiple diverse sequences can fold into the same structure. This motivates the need for a generative model capable of designing diverse sequences while preserving structural consistency. To address this trade-off, we introduce ProtInvTree, the first reward-guided tree-search framework for protein inverse folding. ProtInvTree reformulates sequence generation as a deliberate, step-wise decision-making process, enabling the exploration of multiple design paths and exploitation of promising candidates through self-evaluation, lookahead, and backtracking. We propose a two-stage focus-and-grounding action mechanism that decouples position selection and residue generation. To efficiently evaluate intermediate states, we introduce a jumpy denoising strategy that avoids full rollouts. Built upon pretrained protein language models, ProtInvTree supports flexible test-time scaling by adjusting the search depth and breadth without retraining. Empirically, ProtInvTree outperforms state-of-the-art baselines across multiple benchmarks, generating structurally consistent yet diverse sequences, including those far from the native ground truth. The code is available at https://github.com/A4Bio/ProteinInvBench/.

ProtInvTree: Deliberate Protein Inverse Folding with Reward-guided Tree Search

Abstract

Designing protein sequences that fold into a target 3D structure-known as protein inverse folding-is a fundamental challenge in protein engineering. While recent deep learning methods have achieved impressive performance by recovering native sequences, they often overlook the one-to-many nature of the problem: multiple diverse sequences can fold into the same structure. This motivates the need for a generative model capable of designing diverse sequences while preserving structural consistency. To address this trade-off, we introduce ProtInvTree , the first reward-guided tree-search framework for protein inverse folding. ProtInvTree reformulates sequence generation as a deliberate, step-wise decision-making process , enabling the exploration of multiple design paths and exploitation of promising candidates through self-evaluation, lookahead, and backtracking. We propose a two-stage focus-and-grounding action mechanism that decouples position selection and residue generation. To efficiently evaluate intermediate states, we introduce a jumpy denoising strategy that avoids full rollouts. Built upon pretrained protein language models, ProtInvTree supports flexible test-time scaling by expanding the search depth and breadth without retraining. Empirically, ProtInvTree outperforms state-of-the-art baselines across multiple benchmarks, generating structurally consistent yet diverse sequences, including those far from the native ground truth. The code is available at https://github.com/A4Bio/ProteinInvBench/ .

1 Introduction

Proteins are 3D folded linear chains of amino acids that perform essential biological functions, such as metabolic control, transmitting signals, and regulating cellular processes [21, 5]. Designing sequences of amino acids that fold into a desired protein structure, also known as protein 'inverse folding' (IF) [58], is a crucial task with great potential for protein engineering and synthetic biology [27, 62, 8]. Recent deep learning approaches typically recover the native sequence conditioned on a target structure through the following three paradigms: autoregressive generation , which models sequence dependencies step-by-step [22, 23, 44, 20, 10]; one-shot prediction , which directly maps structure to sequence in a single forward operation [13, 32, 15]; and iterative refinement , which progressively improves an initial design through multiple passes [61, 11, 12, 63]. Despite of achieving impressive recovery performance, these methods often overlooked the inherently one-to-many nature of the problem [38, 33, 16], where multiple distinct amino acid sequences are capable of folding into the

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same protein backbone structure. As a result, rather than predicting a single native sequence, it is often desirable to generate a diverse set of sequences while preserving structural consistency.

This goal, however, reveals an inherent trade-off: while diversity prefers broad exploration of the sequence space, structural consistency strictly requires a feasible subspace that has good local residue compatibility and global foldability. To address this challenge, we advocate for a deliberate, step-wise design process that progressively explores the solution space of feasible sequences. Inspired by the dual process theory in cognitive science [25, 43, 40], where System 1 is characterized by fast, automatic, and heuristic-driven responses, while System 2 involves slow, deliberate, and analytical reasoning, we propose to model the protein design process as a deliberate and iterative decisionmaking process that should (1) explore multiple alternatives at each design step rather than one single candidate, (2) dynamically assess and revise each design step through lookahead and backtracking to optimize the overall designed sequence, and (3) maintain a structured decision history to support effective credit assignment and multi-step planning.

To this end, we propose ProtInvTree , a training-free framework for structure-based protein design that formalizes the design process as a sequence of branching decisions and leverages Monte Carlo Tree Search (MCTS) during generation. Specifically, we iteratively perform the design process, sampling multiple decisions at each step and looking ahead to compute reward signals that evaluate the quality of current choices, thereby guiding the overall sequence design. At each decision step, we introduce a two-stage focus-and-grounding action mechanism that first selects the positions in the sequence to modify ( focus ) and then generates new residues at these positions ( grounding ). Moreover, we employ fast, jumpy denoising as an evaluation mechanism, efficiently estimating trajectory quality without costly forward model rollouts. Through these designs, ProtInvTree is capable of making globally optimal decisions rather than settling for locally optimal ones, which allows it to design novel yet plausible sequences that may deviate significantly from the native sequence (as shown in Fig. 1). Additionally, the explicit exploration of design paths may offer potential insights into the interpretability of protein sequences. To our knowledge, this is the first work to apply a tree-search framework to structure-based protein sequence design.

Empirically, we comprehensively evaluate ProtInvTree across fixed-backbone and de novo protein design tasks. We demonstrate that ProtInvTree outperforms state-of-the-art baselines and excels in the design of plausible proteins with high structural consistency. Besides, it achieves Pareto-optimal trade-offs in both the scTMscore-diversity and scTMscore-novelty. Notably, we observe that existing approaches aggressively optimizing for sequence recovery achieve limited novelty at the same scTMscore level. Further analyses reveal that increasing planning depth and expansion width can effectively improve structural consistency, demonstrating that the paradigm of test-time scaling can effectively unlock the potential of pretrained protein language models (PLMs).

In summary, our contributions are as follows:

We propose ProtInvTree , the first test-time reward-guided tree search framework for protein inverse folding. It formulates protein design as a deliberate, step-wise decision process, enabling exploration of multiple trajectories and exploitation of promising candidates.

We introduce a two-stage focus-and-grounding mechanism decoupling position selection and residue generation and a fast, jumpy denoising strategy for efficient reward evaluation.

We demonstrate that ProtInvTree achieves state-of-the-art performance across multiple benchmarks, with a test-time scaling capability that improves both structural consistency and sequence diversity without retraining or fine-tuning.

2 Related Works

2.1 Protein Inverse Folding

Recently, AI algorithms have spurred a major revolution in modeling protein inverse folding, enabling accurate sequence design conditioned on target structures. Existing approaches can be broadly categorized into the following three paradigms based on their generation strategies.

Autoregressive models generate sequences residue-by-residue, conditioned on both the 3D structure and previously generated tokens. Pioneering models like GraphTrans [22] and GVP [23] introduced SE(3)-invariant graph encoders with attention or geometric modules. Later, models such as GCA [44], ESM-IF [20], and ProteinMPNN [10] incorporated global context and fine-grained pairwise distance modeling. These models offer accurate recovery but suffer from slow inference on long sequences.

One-shot models bypass iterative steps by directly predicting full sequences from structure. PiFold [13] introduced an efficient graph encoder with an MLP decoder, achieving significant speedups and improved accuracy on long proteins. Uni-IF [15] generalizes this to multiple molecule types. These models are highly efficient but face challenges in maintaining global structural consistency.

Iterative refinement methods address this by first generating a full sequence and then improving it through multiple steps. AlphaDesign [12] and LMDesign [61] use confidence-aware predictors and pretrained sequence models for guided refinement. KWDesign [11] combines sequence and structure pretraining with an uncertainty-aware update mechanism. Recent works such as BridegIF [63] and GraDe-IF [57] apply diffusion to enhance diversity and structural compatibility. Fast nonautoregressive diffusion models like PMPnnDiff [54] accelerate inference while preserving accuracy.

Despite notable advances in protein inverse folding, most efforts focus on training-time improvements, while the inference phase remains underexplored. As large protein foundation models emerge, harnessing test-time computation to boost sequence quality and diversity becomes crucial for incentivizing their full potentials. To this end, we propose a novel paradigm based on tree-structured generation, which departs fundamentally from the three existing categories of approaches.

2.2 Test-time Scaling and MCTS

Test-time scaling refers to increasing computational resources during inference to enhance model output without modifying its parameters. This approach has gained significant attention in the field of large language models (LLMs), where performance is improved by generating multiple samples and using reward models for best-solution selection [41, 53, 4]. Various test-time search methods have been proposed [26, 46], including random sampling [49], self-consistency, and tree-search methods [56, 17, 59, 36]. Among them, MCTS, a heuristic search algorithm designed for decisionmaking tasks [55, 50, 7, 9, 39], has emerged as a powerful technique for structured exploration in the output space of large language models. It enables deliberate reasoning by simulating multiple generation trajectories, selectively expanding promising paths, and integrating reward feedback to guide inference toward high-quality outputs. Inspired by these advances, we are the first to extend the paradigm of test-time scaling to PLMs. Our proposed framework, ProtInvTree, leverages rewardguided tree search to perform deliberate, step-wise protein sequence generation, enabling test-time scaling for improved structural consistency and diversity.

3 Preliminaries

Problem Definition. The protein inverse folding problem seeks to determine the amino acid sequence x that folds into a given target structure c . Here, x = [ x 1 , x 2 , . . . , x L ] represents the sequence of L residues, where x i ∈ { 1 , 2 , . . . , 20 } denotes the type of the i -th residue. The structure c = [ c 1 , c 2 , . . . , c n ] ∈ R n × 4 × 3 specifies the Cartesian coordinates of the backbone atoms (N, Cα , C, and optionally O) for each residue c i . The inverse folding problem can be formally expressed as:

where θ is the learnable parameter. Given that homologous proteins invariably exhibit similar structures, the solution for a given structure is not unique [16]. Hence, an ideal model should be capable of learning the underlying mapping from protein backbone structures to their corresponding sequence distributions p θ ( x | c ) .

Iterative Denoising. Recently, diffusion models [19, 42, 37, 35, 30] have demonstrated remarkable capabilities in the field of life science [1, 2, 47, 51, 48, 31] and have achieved notable success in protein inverse folding [12, 61, 11, 63]. These methods, including iterative refinement models, formulate the task as an iterative denoising process that refines the sequence step by step. Following this paradigm, we adopt this strategy to progressively construct the sequence. Formally, starting from an initially corrupted sequence x 0 , the model iteratively denoises the sequence into a complete design x T through a series of conditional reverse transitions, where x 0 and x T differ from the definition in diffusion modeling:

where x t represents the intermediate sequence at step t , with a subset of amino acids remaining unfilled (e.g., represented by [MASK] tokens), and c denotes the target backbone structure. Each reverse step p θ ( x t +1 | x t , c ) refines the current sequence while preserving the structural context.

4 ProtInvTree: Deliberate Protein Inverse Folding Framework

In this section, we propose a reward-guided tree-search framework for deliberate protein inverse folding. We first formulate the iterative denoising as a tree-based Markov decision process (MDP), enabling structured exploration over multiple trajectories (Section 4.1). Then we describe the MCTS procedure employed to identify diverse and high-quality sequences that are consistent with the target backbone structure (Section 4.2). Finally, we introduce two designs of the action and reward components (Sections 4.3 and 4.4), which define how the sequence is updated at each step and how intermediate states are evaluated during the search process. We present the detailed algorithm to formalize the entire framework in the appendix.

4.1 Tree-based MDP Formulation

As described in Section 3, while the step-wise denoising process is effective, it lacks the ability to incorporate intermediate feedback, track uncertainty, and revise previous decisions. To overcome these limitations, we reformulate the iterative denoising process as a tree-based Markov decision process for structured, feedback-aware generation. In this tree structure, each node represents a state s t , each branch corresponds to an action a t , and each node is assigned a value that reflects the reward r t at that state. Specifically, we define the concepts in the tree search framework as follows:

Here, the state s t consists of the target backbone structure c and a partially generated sequence x t . The action a t corresponds to the selection of positions in the sequence and modification of new residues, as detailed in Section 4.3. The reward r t is computed by a reward function R ( s t , a t ) , which evaluates the structural consistency of the modified sequence, as described in Section 4.4. The policy model π ( a t | s t ) generates the next partial sequence x t +1 based on the current state s t . It is parameterized by a structurally modulated protein language model (PLM). A trajectory in the multi-step Markov decision process is defined as a sequence of state-action-reward transitions:

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where each transition corresponds to an incremental update of the sequence. By reformulating the sequence design process from a linear chain into a tree structure, our framework enables deliberate planning over multiple generation trajectories, facilitates the incorporation of intermediate feedback from structural evaluations, and supports systematic revision of prior design decisions.

4.2 Reward-guided Tree Search

In our approach, the reward-guided tree search process operates as an iterative procedure. As illustrated in Figure 2, it comprises four key steps: selection, expansion, evaluation, and backpropagation. The details of each step are described as below.

Selection. The selection process begins at the root node s 0 and identifies the leaf node with the highest exploration potential, determined by the UCT (Upper Confidence Bounds applied to Trees) [28] score. The UCT score is computed as follows:

where w is a hyperparameter that balances exploitation (i.e., node value V ( s t ) ) and exploration (i.e., visit count N ( s t ) ), and p denotes the parent node of s t .

Expansion. After selecting the node with the highest UCT score, it is expanded by generating multiple child nodes. Conditioned on the current state s t , which consists of the target structure c and current sequence x t , the policy model samples K candidate sequences for the next step:

Each candidate sequence x ( k ) t +1 constitutes a new child state s ( k ) t +1 = ( c , x ( k ) t +1 ) , which is added to the search tree as an expansion of the selected node. The details of the candidate construction process by policy model are described in Section 4.3.

Evaluation. Each expanded node is evaluated to determine its value V ( s t +1 ) . As described in Equation 12, we first perform rollouts that complete the state s t +1 via sampling m fully generated sequences, and then assess them with a reward model, assigning the average reward r t +1 as the node value V ( s t +1 ) . The details of the reward function and evaluation process are provided in Section 4.4.

Backpropagation. After evaluating the expanded nodes, their values are backpropagated along the traversal path to update the visit counts and value scores of the ancestor nodes s j (0 ≤ j ≤ t ) . The updates are performed using the following equations:

where N old ( s j ) and V old ( s j ) represent the previous visit count and value score of node s j , respectively, and r t +1 is the reward obtained during the evaluation step.

The four stages described above are performed iteratively until the terminal state is reached. We define two termination conditions for MCTS as follows: (1) The maximum number of MCTS iterations, M , is reached. (2) A terminal node is encountered with a reward exceeding a predefined threshold, indicating strong structural consistency and high-quality design. Once the tree search is complete, the optimal path is selected greedily by prioritizing nodes with the highest scores.

4.3 Focus-and-Grounding Action

To generate candidate transitions from each intermediate state s t , we propose a two-stage Focusand-Grounding action mechanism (see illustration in Fig. 2b). At each denoising step, the model explicitly decomposes the sequence updating process into identifying where to modify (Focus) and determining what token to generate at the selected position (Grounding).

Formally, the Focus operation F ( · ) defines a position selection distribution p ϕ ( i | s t ) over all positions, from which the topK t positions with the highest probabilities are selected:

where L denotes the sequence length and i indicates the targeted position for refinement. Conditioned on the focused positions { i 1 , . . . , i N } , the Grounding operation defines a distribution over amino acid types, specifying the generated token:

where each p ψ ( x i | s t , i ) predicts the residue x i ∈ V for position i , and V denotes the amino acid vocabulary. The overall policy is factorized as the product of the Focus and Grounding distributions:

In practice, the selected position set { i 1 , . . . , i N } is a random subset of sequence positions (more selection strategies comparison is provided in appendix), and each token x i is generated by a structurally modulated PLM conditioned on the backbone structure c and the partial sequence context. This two-stage action design enables precise localization of modifications, ensuring structural coherence and enhancing search efficiency throughout the generation process.

4.4 Jumpy Denoising for Fast Reward

In the MCTS procedure, evaluating a node far from a leaf node is challenging, as the intermediate nodes are not fully expanded. This is typically addressed in one of two ways: employing forward dynamics models to simulate complete trajectories, which is computationally expensive, or approximating node values via bootstrapping methods, which are faster but less accurate. Effectively integrating these evaluation strategies into ProtInvTree remains an open challenge.

To address this, we introduce a Jumpy Denoising strategy to accelerate the evaluation process, which is a rapid, single-step DDIM-based [42] sampling process:

where J ( · ) approximates the reverse denoising distribution p ( x T | x t +1 , c ) . Here, x t +1 is obtained through action a t at step t . We define the reward function R ( s t , a t ) as the structural consistency feedback obtained by comparing the folding results from the sampled sequence ˜ x T and the input structure c , formulated as:

where f is the protein folding algorithm. TMScore ( · , · ) is a widely used metric for measuring protein structure similarity. This jumpy denoising strategy significantly reduces computational overhead while maintaining a reliable approximation of the final reward.

5 Experiments

5.1 Experimental Setup

Datasets. We conduct experiments on both CATH v4.2 and CATH v4.3 [34], where proteins are categorized based on the CATH hierarchical classification of protein structure, to ensure a comprehensive analysis. Following the standard data splitting [22, 20], CATH v4.2 dataset consists of 18,024 proteins for training, 608 proteins for validation, and 1,120 proteins for testing; CATH v4.3 dataset consists of 16,153 proteins for training, 1,457 proteins for validation, and 1,797 proteins for testing. We also include a set of de novo proteins collected from the CASP15 competition to provide a more realistic assessment. Following the previous work ProtInvBench [14], we download the public TS-domains structures from CASP15 which consists of 45 structures, namely TS45 .

Evaluation Metrics. For evaluation metrics, we use sc-TMscore [60] and RMSD [6] to evaluate structural consistency. We define diversity as the average proportion of differing residues across all pairs of generated sequences and define novelty as 1 -recovery . Details of all metrics are provided in the appendix. Following previous studies [22, 20], we report them on three settings, namely short proteins (length ≤ 100 ), single-chain proteins (labeled with 1 chain in CATH), and all proteins.

Baselines. We compare ProtInvTree with several state-of-the-art baselines, categorized into three groups: (1) autoregressive models, including StructGNN [22], GraphTrans [22], GCA [45], GVP [24], and ProteinMPNN [10]; (2) the one-shot model, PiFold [13], UniIF [15]; (3) iterative models, including AlphaDesign [12], LM-Design [61], KW-Design [11].

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Implementation Details. All experiments are conducted on NVIDIA-A100 GPUs with 80G memory. We choose ESM-3 [18] as our policy model because it is the first protein foundation model that directly supports inverse folding without task-specific fine-tuning. The Jumpy Denoising strategy also leverages it, which is capable of filling in arbitrary mask ratios. Building on this capability, we focus on unleashing the potential of PLMs through test-time scaling . To ensure fast structural feedback for reward computation, we use ESMFold [29] to predict the 3D structures of candidate sequences. For ProtInvTree, we set the maximum number of MCTS iterations M to 50. The selection numbers K t at each step follow a cosine schedule. In the UCT algorithm, the weight w balancing the exploration and exploitation is set to 0.01.

5.2 Benchmarking Fixed Backbone Protein Design

Structural Consistency. We benchmark the fixed backbone protein design task in CATH4.2 and CATH4.3 datasets, reporting the sc-TMscore and RMSD in Tables 1 and 2. ProtInvTree demonstrates superior performance over previous methods. We highlight the following: (1) Although iterative refinement models have significantly outperformed previous autoregressive and one-shot baselines, the proposed tree-based generation framework (ProtInvTree) further achieves substantial improvements, demonstrating the effectiveness of branching exploration over linear refinement. (2) ProtInvTree enhances inference based on the frozen ESM-3 model, requiring no additional trainable parameters, yet achieving the strongest performance. Compared to plain ESM-3 run for the same number of denoising steps (no tree search), ProtInvTree improves the sc-TMscore by 18.3% (short), 17.6% (single-chain), and 7.8% (all) in CATH 4.2. (3) We further evaluate RMSD as an independent structural metric, which consistently supports the effectiveness of ProtInvTree.

Balance between Structural Consistency and Diversity & Novelty. Figure 3 illustrates the Pareto frontier between structural consistency (measured by sc-TMScore) and two key sequence-level objectives: diversity (left) and novelty (right). We highlight our primary findings as follows: (1) ProtInvTree achieves Pareto-optimal performance in both the diversity-scTMscore and novelty-scTMscore

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spaces, outperforming all baselines across the trade-off frontier. (2) Compared to ESM-3 , we observe that ProtInvTree also achieves significantly higher diversity and novelty even at comparable levels of structural consistency. (3) Notably, when at comparable sc-TMScore levels, the baselines of AlphaDesign, PiFold, and KW-Design exhibit progressively higher diversity and lower novelty . This highlights a fundamental distinction between the two metrics: diversity measures variation within the set of generated sequences, whereas novelty reflects deviation from the native (ground-truth) sequence. As shown in Fig. 4, baseline methods optimized with a recovery loss tend to converge around local optima near the ground-truth sequence, as illustrated in case (a); by contrast, our method can escape this regime and explore multiple diverse and structurally consistent solutions, including those far from the ground-truth sequence, as shown in case (c).

5.3 De Novo Proteins Design

Evaluating models on the TS45 dataset allows us to gain a better understanding of the potential of AI models in designing de novo proteins and reveals that different models exhibit non-trivial differences in generalizability. We present the quantitative results in Table 3, which reveal the following: (1) ProtInvTree outperforms all baseline methods in terms of both sc-TMscore and RMSD, highlighting its superior ability to maintain structural consistency and achieve accurate geometric reconstruction. (2) We additionally compare ProtInvTree with ESM-3 [18] to assess the effectiveness of our overall framework beyond the pretrained language model itself. Despite sharing the same pretrained model, ProtInvTree achieves substantially better results, suggesting that test-time reward-guided planning plays a key role in unlocking the full potential of pretrained PLMs.

5.4 Analysis: Diving Deep into ProtInvTree

Test-time Scaling Analysis. To understand how test-time computation scales with performance, we investigate the effect of two key planning hyperparameters in our framework: the number of candidate expansions and planning depth , as shown in Fig. 5. We observe that, as the expansion number and planning depth increase, sc-TMscore gradually improves, although the average time cost also rises moderately. This indicates that scaling test-time computation can effectively enhance sequence quality through more deliberate search. However, as the number of planning depths further increases, the sc-TMscore tends to be saturated, as the search converges to high-confidence regions, the diversity of refinable sequences becomes limited, and further refinements yield diminishing structural gains. Moreover, the diversity in both settings decreases as the expansion number and planning depth increase, revealing the trade-off between structural consistency and sequence diversity.

Computational Efficiency The analysis of test-time computational efficiency is critical, particularly for methods that involve large pretrained models and structure prediction. We provide a detailed analysis of the compute-performance trade-off. Specifically, for each given backbone, we generate 10 designs and compute the average generation time for each design. We fix the depth and scale the expand number from 2 to 6, as shown in Table 4. We also scaled the number of sampling iterations for ESM-3 to assess its performance-efficiency trade-off. The resulting sc-TMScore and average inference time per design are summarized in Table 5. We observe that, although inference

time increases with a larger expand number or planning depth, the performance-efficiency trade-off remains superior to simply scaling the base ESM-3 sampler.

Case Study. To facilitate understanding of the entire workflow of our proposed ProtInvTree, we visualize a reward-guided search tree in Figure 6. Each node represents a partially generated sequence with its predicted reward r , reflecting structural consistency. The tree showcases how ProtInvTree performs branching exploration guided by reward scores. Two high-reward sequences, S1 and S2 , emerge from different trajectories, with high diversity and novelty, yet achieve high structural rewards ( r = 0 . 99 , r = 0 . 98 ). We further compare their predicted 3D structures with the ground truth structure in Figure 7. Its high sc-TMScore and low RMSD demonstrate ProtInvTree 's ability to generate diverse sequence candidates while maintaining structural consistency. This case illustrates how the reward-guided tree search enables efficient exploration of the solution space and selection of structurally faithful, non-trivial designs beyond native recovery.

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6 Conclusion

We present ProtInvTree, a novel reward-guided tree-search framework for protein inverse folding that explicitly addresses the trade-off between structural consistency and sequence diversity. By reformulating sequence design as a step-wise, decision-making process, ProtInvTree enables the exploration of diverse design trajectories through self-evaluation, lookahead, and backtracking. ProtInvTree shows superior performance across multiple benchmarks, achieving state-of-the-art structural consistency while generating diverse and novel sequences beyond the native ground truth. Future work will focus on extending our framework to a broader range of protein-related tasks beyond fixed-backbone inverse folding. One limitation of the proposed ProtInvTree is the computational efficiency, particularly for methods that involve large pretrained models and structure prediction. Another potential limitation is its current lack of experimental validation in real-world biological settings. We will seek collaborations with experimental laboratories to test the viability and functional relevance of the designed sequences.

Acknowledgments

This work is partially supported by the program of The Robotic AI-Scientist Platform of Chinese Academy of Sciences.

S1&GT  sc-TMScore:0.99; RMSD:0.33

S2&GT  sc-TMScore:0.98; RMSD:0.38

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A Algorithms

The overall workflow of the ProtInvTree is provided in Algorithm 1.

Algorithm 1 ProtInvTree: Reward-Guided Tree Search for Protein Inverse Folding

Input: Backbone structure c , ground truth sequence x gt , initial sequence x 0 , folding model f ( · ) , PLM policy π θ , reward function R ( · , · ) , max iterations M , tree depth T , expansion number per node K , reward threshold τ

Output: A set of generated sequences S = { x ∗ i } Z i =1 , where Z denotes the number of generated sequences.

B Evaluation Metrics

In the main paper, we report evaluation results using four metrics: sc-TMscore, RMSD, novelty, and diversity. The descriptions of these metrics are detailed as follows.

sc-TMScore. The structural similarity is the ultimate standard for measuring the quality of the designed sequence. However, the structures of designed protein sequences needed to be predicted by other algorithms, such as AlphaFold [1], RoseTTAFold [3], OmegaFold [52] and ESMFold [29]. The protein folding algorithm itself has a certain inductive bias and will cause some prediction errors, which will affect the evaluation. To overcome the inductive bias, we adapt the self-consistent TM-score (sc-TMscore) metric:

where f is the protein folding algorithm and TMScore ( · , · ) is a widely used metric [60] for measuring protein structure similarity. Since the structures of the designed sequence and reference sequence are predicted by the same protein folding algorithm, the model's inductive bias is expected to be canceled out when calculating the TM-score. This approach results in a more robust metric, called the sc-TMScore, that is less affected by the inductive bias of the protein folding algorithm.

RMSD. The standard dissimilarity measure for protein structures is the root mean square deviation (RMSD) of representative atom positions such as α -carbons. RMSD is calculated as the square root

of the average squared distance between corresponding atoms in two 3D structures:

where v = f (˜ x ) and w = f ( x ) are the predicted 3D structures of the designed sequence ˜ x and the reference sequence x , respectively, obtained using a structure prediction algorithm f . Here, v i and w i denote the 3D coordinates of the i -th atom in each structure, and n is the total number of atoms considered (typically backbone or α -carbon atoms). RMSD provides a fine-grained comparison of atomic positions after optimal rigid-body alignment of the two structures. However, it is sensitive to local deviations, such as flexible loops or inaccurate predictions in side-chain packing, and may not fully reflect the overall fold similarity. As a result, RMSD is typically used in conjunction with other metrics such as TM-score to provide a more comprehensive assessment of structural quality.

Novelty. We define novelty as the complement of sequence recovery, reflecting the extent to which the generated sequences deviate from the native ground truth:

where recovery is the fraction of amino acids in the predicted sequence that exactly match the ground-truth sequence at each position, defined as:

Diversity. The average fraction of amino acids that differ between pairs of sequences:

̸

where d H is the Hamming distance. We note that sequence diversity alone is not a sufficient measure of an IF method's quality, as it can be increased arbitrarily at the expense of sample quality (e.g. as measured by structural consistency).

C Analysis of the Planning Components

We investigate how explicit planning componentsintermediate feedback , uncertainty tracking , and backtracking -affect test-time protein design quality. We compare our MCTS-based planner (ProtInvTree) against two commonly used test-time strategies: Best-ofN and Beam Search sampling.

ESM-3 : base model without any planning or feedback;

Best-ofN : generates N independent candidates and returns the one with the highest reward;

Beam Search : incrementally expands partial solutions while keeping only the topB (beam width) candidates, iterating step-by-step with intermediate feedback until a complete sequence/design is found;

ProtInvTree (ours) : Monte Carlo Tree Search with intermediate feedback, uncertainty tracking, and backtracking.

Table 6 summarizes the results and the presence of each planning component. We find that (1) Intermediate feedback (Beam Search) improves convergence over purely independent sampling (Best-ofN ), indicating that partial evaluations guide more promising local expansions. (2) Uncertainty tracking further boosts reliability by prioritizing candidates with stable scores, reducing variance in final structures. (3) Backtracking enables recovery from suboptimal branches and better global exploration, yielding the best overall accuracy.

D Selection Strategies Comparison

To analyze the impact of different position selection strategies in the Focus-and-Grounding action mechanism, we evaluate several variants for computing the position distribution p ϕ ( i | s t ) , which determines the set of positions { i 1 , . . . , i K t } to be modified at each denoising step.

Specifically, we compare the following approaches:

Random sampling: Positions are selected uniformly at random from the sequence.

Autoregressive sampling: Positions are visited sequentially from left to right in an autoregressive manner.

Entropy-based selection: Positions with the lowest predictive entropy, representing the model's most confident predictions, are prioritized for update.

We integrate each strategy into the Focus module F ( s t ) , keeping the Grounding step unchanged. Table 7 summarizes the quantitative results, showing that all three strategies achieve competitive performance, with random sampling performing surprisingly well despite of its simplicity. This may be because exploring a broader space in the early stages helps avoid premature convergence and encourages greater sequence diversity, which ultimately benefits overall generation quality.

E Structure Complexity Effects

We also provide additional breakdowns across fold classes and protein lengths, revealing meaningful differences in performance and novelty trends. Table 8 summarizes the breakdown by fold class and length-based results are given in Table 1.

F Broader Impacts

Inverse protein folding models, positioned at the intersection of bioinformatics and computational biology, offer significant potential for advancing both basic research and real-world applications. By enabling the design of protein sequences that reliably fold into desired three-dimensional structures, these models can drive progress across diverse domains. Broader impacts include facilitating structure-based drug discovery, enabling the rational design of enzymes with novel functionalities, and advancing synthetic biology through the creation of custom proteins with tailored properties.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes ProtInvTree, a framework for inverse protein folding which generates diverse and structurally consistent designs for a given backbone using reward-guided tree-search applied to existing structure-conditioned design models. The framework is comprised of four steps; selection, expansion, evaluation, and backpropagation. The selection step uses UCT to select the node with the highest potential for exploration. In the expansion step, the pre-trained ESM-3 model is used to predict the amino acid identities at selected positions in the backbone. This yields a number of child nodes. In the evaluation step, ESM-3 is used to predict the full sequence as a \"look-ahead\" for the current designs. These are fed to ESMFold to predict the three-dimensional structures which in turn are used to compute the reward of the current designs. In the backpropagation step, the computed rewards are used to update the visited nodes. These steps repeat until a termination criteria is met. ProtInvTree is comprehensively evaluated on popular benchmarks where it achieves state-of-the-art performance in multiple metrics simultaneously.\n\nSTRENGTHS AND WEAKNESSES:\n__Strengths__:\n\n1. Well-written and well-structured paper - it was a pleasure to read and easy to follow.\n2. Impressive performance across diverse metrics, comfortably beating state-of-the-art inverse folding models.\n3. Comprehensive and succinct related works. \n4. Conceptually simple yet effective ideas.\n5. Comprehensive benchmarking which goes beyond simply maximizing sequence recovery but considers pareto-optimal solutions regarding structural consistency, novelty, and diversity.\n\n__Weaknesses__:\n\n1. No mention of computational cost at inference time which to me is significant omission. I think this is an important detail, particularly since protein folding is an active part of the pipeline as well as extensive use of a billion+ parameter model. An analysis of the cost of creating, e.g., 10 designs for a given backbone for ProtInvTree vs. ESM-3 and other models would be particularly beneficial. If the model is expensive at inference, that can perhaps be excused by the absence of model training. Experiments or at least discussions of the computational cost would be a valuable if not necessary addition to an otherwise great paper which would, potentially, further support the model’s utility. \n2. Few ablation studies to support modeling choices. Only a single model configuration is presented despite relying on two pre-trained models; ESM-3 and ESMFold. The inclusion of alternatives and their effect on downstream performance would shine light on where the performance is coming from. See related questions.\n3. This also applies to hyperparameter configurations, where it would be interesting to see model behavior using, e.g., different schedules for selection numbers, different balancing parameter in the UCT algorithm, different termination strategies. Without experiments supporting the chosen hyperparameters, they seem arbitrary. I appreciate the study in section 5.4 and would appreciate seeing something similar for the remaining parameters. Presumably, increasing both depth and expansions numbers leads to increased computational costs. I think this should be addressed as well.\n4. No code in the supplementaries.\n5. No mention of statistical significance, despite the checklist saying so.\n6. Very limited discussion on model limitations.\n\nQUESTIONS:\n1. L118: Shouldn’t $n$ be $L$?\n2. L214: What is DDIM? \n3. More of a comment than a question, but I find it curious and partly non-satisfactory that equation 10 essentially implies that using some different model for inverse folding is part of the proposed inverse folding model.\n4. In equation 8, how are the tokens chosen? Are they sampled or do you apply argmax to the distribution over amino acids?\n5. L197 and L201: Why is $N$ used? Shouldn’t it be $K_t$ after the top-$K_t$ positions have been selected?\n6. L201: Curious that random ends up being optimal. Have you considered other approaches than the ones included in the supplementaries, or do you believe that “random” is optimal?\n7. L205: If the positions are randomly sampled, then calling it “precise localization of modifications” is somewhat misleading. I suppose that the approach does *enable* it, but in actuality it’s “random localization of modifications”, which I acknowledge does not sound as convincing.\n8. Section 5.1: \n    1. Did you explore other hyperparameter configurations? E.g., different values of $M$, different schedules for $K_t$, different values for the balancing parameter $w$? An ablation study or sweep over various configurations would be a valuable addition to the paper or the supplementaries.\n    2. Did you explore other PLMs or folding models? Is ESMFold accurate enough, or would a higher-fidelity folding model improve performance? \n    3. Why is it not possible to use a different structure-conditioned model than ESM-3? This model essentially plays the role of inverse folding in that a partially masked sequence and a structure is used to design a sequence. Something like MIF-ST or SaProt might work as well - or even just models like KWDesign or ProteinMPNN. The relative performance gap between base models and the ProtInvTree-version of them would be interesting to observe and would support the framework's utility.\n9. The termination number is set to 50. How many iterations are typically required before the algorithm terminates? Is it due to reaching this number, or is the structural consistency goal often met? An analysis of this would be very interesting. \n10. In the same vein, how many nodes end up being generated? How many structures are predicted to arrive at a given design? This feeds back into my earlier questions regarding the compute cost. Are we talking a handful of structures or hundreds/thousands?\n11. Figure 4: Noverty→Novelty\n\nLIMITATIONS:\nI do not think that the model limitations have been adequately addressed. \n\nIn the conclusion it is mentioned that a potential limitation is the lack of experimental validation. While this is true, I’d be very curious to hear about modeling limitations. E.g., the computational cost of relying on a 1.4B model which is extensively used is arguably a limitation, as is the computational burden of relying on online protein folding and the quality of the predicted structures. Similarly, the Jumpy Denoising process is, as far as I can tell, an inverse folding process in and of itself. Having both protein folding and inverse folding as often-repeated operations by other pre-trained models necessarily means that these models do most of the heavy lifting. However, I believe this can be ameliorated by ablation studies as mentioned in both the weaknesses and questions sections.\n\nThere must also be other limitations that I am not aware of and I believe it would be highly valuable to the paper to address these properly.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-07"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors proposed ProtInvTree, a test-time framework using MCTS to optimize sequences generated for a target structure. In the framework, ESM-3 is used as a policy for generating candidate mutations in a focus and grounding step-wise methodology, and ESMFold is used to calculate the reward function. Given the step-wise sequence generation, a jumpy denoiser is also proposed to allow the reward calculation in intermediate steps. The proposed methodology is evaluated against other state-of-the-art inverse folding methods, showing better performance, especially in refoldability metrics such as sc-TMScore and RMSD.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. A test-time methodology for optimizing the sequence candidates generated for a target backbone is proposed, applying a structure-informed protein language model and tree search.\n2. For evaluating intermediate steps during the generation step, a jumpy denoising strategy is proposed.\n3. The proposed methodology improves sc-TMScore when compared to other baseline inverse folding methods.\n\nWeaknesses:\n\n1. The main concern is regarding the fairness of the evaluation in the manuscript: (i) it is not clear if the same folding model is used both as the reward function and to calculate the scTMScore for evaluation; (ii) it would be more fair to evaluate multiple sequences generated also from baseline methods.\n2. There is no information about computational efficiency in the manuscript. For applying test-time methods, computational efficiency and performance are crucial to evaluate which applications are worthy of using the proposed methodology.\n3. There is not enough information for the reader to reproduce the work. For example, there is no information about the training of the jumpy denoiser in section 4.4. The code is also not available.\n\nQUESTIONS:\nComments:\n\n1. It would be helpful to compare the differences between the proposed method with Evoplay [1] and other works using MCTS for protein design in the Related Work section. \n\n[1] Wang et al, “Self-play reinforcement learning guides protein engineering”, Nature Communications, 2023.\n\n2. The term “suboptimal” in Tables 1/2/3 seems not appropriate in this case. It implies that the model with the best result is optimal. This term should be rewritten.\n\n3. (Lines 257-258) The sentence “Compared to ESM-3 alone, when both methods set the same number of iterative steps” is unclear to me. Does it mean trying to optimize iteratively the sentences generated by ESM-3 without using the MCTS framework?\n\n4. Figure 3: Why are there not the same number of points in both graphs for ESM-3 and ProtinvTree?\n\n5. (Lines 259-260) “While the improvement in scTMscore is expected due to its use as the reward function during search”. Does this sentence mean that ESMFold is both used to calculate the reward function and used to calculate the sc-TMscore? This would be a leakage. In the reviewer’s understanding, the more robust way would be to use another folding model, like AF2 or RF2, to calculate the sc-TMscore.\n\n6. (Line 269-270) Can you clarify the sentence “Notably, when at comparable sc-TMScore levels, the baselines of AlphaDesign, PiFold, and KW-Design exhibit progressively higher diversity and lower novelty”? Should I check this pattern in Fig. 3?\n\n7. (Lines 291-292) “Although the average time consumed also rises to some extent”. To what extent? One of the most critical parts for test-time scaling is computational efficiency, but there are no ablations or numbers regarding this in the manuscript. This is crucial for the reader so that it can be evaluated in which situations the proposed model can be applied.\n\n8. The example in Fig. 7 would be more informative if it showcased an example in which the sc-TMScore is increased by applying the proposed method when compared to baseline methods (even if it is a cherry-picked example).\n\n9. Is the code available? There is no mention of the code availability throughout the manuscript.\n\n10. For the reviewer, it is still not clear if the sequence in a state s_t contains all the amino acid identities and these are mutated depending on the positions sampled, or if there are positions masked that are being filled. From Fig. 2(b) it seems that there are masked positions that are being filled, but it is not clear in the writing. Also, this affects the MCTS termination conditions, as I expected the MCTS to be terminated when the full sequence is generated (no need of the denoiser to calculate the reward function).\n\n11. Is the jumpy denoiser described in section 4.4 trained by the authors? There is no mention of that.\n\n12. In the manuscript, the authors used ESM-3 as their inverse folding method, but any other protein inverse folding could be combined with the proposed MCTS and jumpy denoiser framework. Did the authors test other models as the inverse folding method?\n\nMinor Comments:\n\n1. Figure 1: The ground-truth sequence should have the highest sc-TMScore value from my understanding.\n\n2. Acronyms like PLMs and MCTs are defined multiple times throughout the manuscript.\n\n3. (lines 175-176) Is equation 11 the right equation for V(s)?\n\n4. Writing: “Following the previous work [10]”: maybe explicitly mention the reference [10].\n\n5. Figure 4: There is a typo for the word “Noverty”.\n\nLIMITATIONS:\nThe authors have discussed the positive impacts of their work in Appendix D; however, it would be important to also add the potential negative societal impact of their work.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-28"}

comments: SUMMARY:
The paper proposes ProtInvTree, a training‑free inference framework that frames protein inverse folding as a reward‑guided Monte‑Carlo Tree Search (MCTS) problem. At each step, a residue position is first chosen to modify and then residues are sampled from a frozen protein language model (e.g., ESM‑3). Intermediate states are evaluated with a jumpy denoising shortcut that avoids full rollouts, using ESMFold to estimate a TM‑score‑based reward. The rewards are then backpropagated normally as in MCTS.

STRENGTHS AND WEAKNESSES:
- Strengths
    - The integration of MCTS into the inverse folding problem is intuitive and executed reasonably.
    - Results in Table 1-3 demonstrate the method’s effectiveness across multiple benchmarks, achieving SoTA performance.
    - Figure 3 shows the method’s effectiveness in balancing diversity and consistency.
- Weaknesses
    - Comparisons to other test-time scaling methods are lacking. Specifically, the author should compare MCTS to simpler methods like beam search and best-of-N to demonstrate the need for a more complex MCTS approach.
    - The explanations for the Jumpy Denoising strategy are unclear.
    - MCTS also brings additional computational costs, which should be noted and discussed.

QUESTIONS:
- What is J(.) in Equation 10, and how does it save computation compared to standard decoding?
- What’s DDIM in line 214?
- Line 135: MPD → MDP

LIMITATIONS:
Yes, but I suggest the author also address the computational cost in the limitations section.
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-01

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents ProtInvTree, a reward-guided tree search framework for protein inverse folding. It reformulates sequence generation as a step-wise decision process using Monte Carlo Tree Search, enabling exploration of diverse sequences consistent with a target structure. Key innovations include a two-stage focus-and-grounding mechanism for position and residue selection, and a jumpy denoising strategy for efficient evaluation. Built on pretrained models without retraining, ProtInvTree achieves state-of-the-art performance in terms of structural consistency, diversity, and novelty. Experimental validation is pending.\n\nSTRENGTHS AND WEAKNESSES:\n### **Strengths**\n\n**Quality:**\nThe paper proposes ProtInvTree, a reward-guided MCTS framework for protein inverse folding that operates entirely at test time. Built on top of pretrained models (ESM-3), it delivers strong performance across benchmarks (CATH 4.2/4.3, TS45) without additional training. The method achieves state-of-the-art structural consistency while improving sequence diversity and novelty. Jumpy denoising offers an efficient approximation for reward evaluation.\n\n**Clarity:**\nThe paper is clearly written, with intuitive diagrams and a detailed description of the method. \n\n**Significance:**\nTest-time compute scaling is a key strength. The method enables more deliberate search at inference without retraining.\n\n**Originality:**\nApplying MCTS to protein sequence design is novel. The focus-and-grounding mechanism and jumpy denoising strategy are also original contributions.\n\n\n### **Weaknesses**\n\n* The claimed benefits of planning (intermediate feedback, uncertainty tracking, backtracking) are not directly validated. There is no comparison to beam search or other simpler baselines that lack these features.\n* Figure 5 shows a drop in diversity with deeper planning, but the paper does not analyze how **novelty** changes under the same conditions. This limits insight into when and how the method converges toward native-like sequences.\n* The test-time compute–performance trade-off is not quantified in practical terms (e.g., runtime vs. accuracy).\n* There is no experimental or functional validation of designed sequences.\n\nQUESTIONS:\nA)\n1. **Intermediate Feedback and Uncertainty**: Section 4.1 emphasizes the benefits of incorporating intermediate feedback, tracking uncertainty, and enabling backtracking via tree-based search. Could you provide empirical evidence to isolate these contributions? For example, how much do they improve performance over simpler strategies?\n\n2. **Beam Search Baseline**: Have you considered comparing ProtInvTree to a **beam search baseline** that does not include backtracking or uncertainty estimation? Including such a baseline would clarify whether the proposed advantages of tree search are essential or incremental.\n\n3. **Ablation of Planning Features**: Can you ablate specific planning features—e.g., removing backtracking, removing jumpy denoising, or using greedy selection—to assess their individual impact on structural consistency, diversity, and novelty?\n\n4. **Uncertainty Quantification**: How is uncertainty explicitly tracked and used during search in your implementation? If applicable, showing how this improves exploration or stability would help justify its inclusion.\n\n\n\nB)\n1. **Novelty Collapse Analysis**: Have you evaluated how novelty changes alongside diversity as planning depth and expansion width increase (e.g., in Figure 5)? Including novelty plots would clarify whether deeper search also leads to convergence toward native sequences.\n\n2. **Failure Mode Characterization**: It would strengthen the work to systematically identify conditions under which ProtInvTree collapses to native-like sequences. Could you analyze thresholds (e.g., depth ≥ X or expansion ≥ Y) beyond which the method fails to explore novel solutions?\n\n3. **Parameter Sensitivity Study**: Consider conducting a controlled sweep over planning parameters to map the diversity–novelty–consistency landscape. This would help practitioners tune the method for different design goals (e.g., conservative vs. exploratory designs).\n\n4. **Recovery-Oriented Trade-off**: Would adding an explicit recovery-based reward term bias the search toward the native sequence? A comparison with and without such terms could reveal how tightly ProtInvTree adheres to or diverges from native recovery.\n\n5. **Structure Complexity Effects**: Does the convergence behavior vary across protein types (e.g., different lengths, fold classes, or disorder levels)? Reporting such breakdowns might uncover structure-specific tuning needs.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}