Inference-Time Steering Across Scaffolds and Epitopes for Sample-Efficient De Novo Nanobody Design

Inference-Time Steering Across Scaffolds and Epitopes for Sample-Efficient De Novo Nanobody Design

arXiv:2610.13844v1 [cs.LG] 9 Oct 2026

Mason Minot, Simon Friedensohn, Cédric R. Weber Alloy Therapeutics Allschwil, Switzerland mason.minot@alloytx.com

Abstract Generative molecular design typically relies on over-generation and post-hoc filtering. Inference-time steering methods like Feynman-Kac (FK) steering improve efficiency by biasing trajectories toward high-reward candidates, yet they optimize within a single fixed configuration. In de novo nanobody design, upfront commitment to conditioning choices like scaffold identity or target epitope creates a bottleneck. Since yield varies across these conditions, steering unpromising setups wastes compute. We recast generative condition selection as an inferencetime resource-allocation problem. We propose two dynamic budget allocators: a joint Global Sequential Monte Carlo (SMC) formulation that steers and allocates compute across configurations concurrently, and a decoupled approach adapting Batched Successive Elimination (BaSE). Empirically, these dynamic allocators increase the yield of designable candidates per GPU-hour nearly 5× without sacrificing diversity across distinct therapeutic targets and generative configurations.

1

Introduction

Diffusion and flow matching have made in silico molecular design accessible [1–3]. However, current methods rely on over-generation followed by computationally expensive post-hoc scoring and filtering pipelines (e.g., evaluating binding energy or interface confidence). Because the yield of viable candidates is often highly variable across different targets and configurations, campaigns expend a large portion of their computational budget evaluating true negatives, creating a bottleneck. To reduce this waste, inference-time steering methods like Feynman-Kac (FK) steering [4, 5] integrate scoring functions directly into the sampler without requiring model fine-tuning. By estimating denoised backbones via Tweedie’s formula [6] and evaluating them against intermediate reward functions, FK algorithms sample from a reward-tilted distribution by actively cloning promising trajectories and culling low-scoring ones. While recent works apply FK steering to protein design [2, 7, 8], they optimize within a single generative configuration and leave specialized, scaffold-driven formats largely unexplored. This poses a challenge for modalities like nanobodies (VHHs). Generative methods typically design sequences and conformations for the antigen-binding loops, known as complementarity-determining regions (CDRs), onto a fixed, user-specified framework [9, 10]. However, framework identity dictates paratope geometry, stability, immunogenicity, and generative yield [11, 12]. The scaffold must therefore be treated as a variable rather than a constant. Consequently, trajectory success remains bottlenecked by upfront choices of the scaffold, target epitope, or hotspot conditioning, whose viability is unknown a priori. This presents a budgetallocation problem [13–15]. Steering exacerbates this issue, as relocating costly oracle evaluations into the generation loop means that committing to an unproductive configuration wastes budget and leaves viable conditions under-sampled. Accepted at the NeurIPS 2026 AI for Drug Discovery workshop.

A

B

Figure 1: Overview of the inference-time steering and allocation pipeline. (A) Illustration of the resource allocation and steering trajectory progressing from the initial noisy state xT to the final generated structure x0 . (B) Breakdown of the intermediate resampling step. At timestep t, Tweedie’s formula is used to predict the denoised backbone x̂0|t from the noisy sample xt . The inverse folding model BoltzIF generates sequences for the designed CDRs. These are refolded with ESMFold2; the (i) ipTM is then computed and used to update particle weights, wt ∝ exp (ipTM/τ ).

2

Methods

2.1

Fixed-Scaffold Nanobody Generation

We formalize nanobody design as a conditional generation task, employing BoltzGen [1] to sample 3D CDR coordinates conditioned on a fixed scaffold. While standard generation samples candidates uniformly from the learned distribution qθ (x0 ), our goal is to shift this distribution toward highquality, designable binders. Formally, we aim to approximate a reward-tilted target distribution over the full generative trajectory from initial noise at time T to the final structure at time 0: ptarget (x0:T ) ∝ qθ (x0:T ) exp(Φ(x0:T )/τ ) (1) where qθ (x0:T ) is the joint distribution of the unsteered generative trajectory, Φ(x0:T ) is the reward path functional, and τ is a temperature parameter controlling the reward strength. Candidate backbones generated from this distribution are evaluated for post-hoc designability by sampling 8 sequences per backbone using ProteinMPNN [16], refolding each complex with AlphaFold2-Multimer (AF2-M) [17], and scoring against AlphaProteo designability criteria [18] (Appendix A.4). We employ an in-loop oracle (discussed below) that is orthogonal to our validation pipeline to prevent generation from over-optimizing for a single evaluator’s biases. 2.2

Feynman-Kac Steering via In-Loop ipTM

Because exact sampling from ptarget is intractable, we apply Feynman-Kac (FK) steering over a parallel population of N interacting particles. We interleave standard denoising steps with guidance events that evaluate particle quality, discarding unpromising states and replicating successful ones. At guidance event m (diffusion timestep tm ), each particle’s denoised terminal estimate x̂0,m = fθ (xtm , tm ) is scored by an immediate in-loop reward R(x̂0,m ). This scalar value is obtained by generating CDR sequences via BoltzIF, refolding the complex with ESMFold2 [19], and computing the interface predicted Template Modeling score (ipTM) (Figure 1B). For independent steering baselines and the Successive Halving (SH) allocator, we adopt a memoryless immediate potential, i assigning particles instantaneous normalized weights wm scaled by temperature τ and tracking the Effective Sample Size (ESSm ) to monitor population collapse: exp(R(x̂i0,m )/τ ) 1 i wm = PN , ESSm = PN (2) j i 2 j=1 exp(R(x̂0,m )/τ ) i=1 (wm ) 2

Figure 2: Impact of inference-time steering on terminal quality and structural diversity. (A, B, C) Oracle correlation (terminal ESMFold2 vs. terminal AF2-M) across three target-scaffold pairs, with marginal showing steering shifts toward higher ipTM. (D) CDR-H3 structural diversity of passing designs (Cα RMSD); while steering narrows diversity within a run, it explores distinct structural basins across independent runs. Numbers denote total passing designs. (E) Structural examples of PD-L1 (7eow) candidates showing oracle agreement (top) and divergence (bottom). We evaluate two resampling triggers: a fixed-cadence policy occurring at predetermined intervals tied to network time, and an adaptive policy dynamically triggered by weight degeneracy (ESSm ≤ 0.5N ). Implementation details are provided in Appendix A.1. 2.3

Condition Allocation Algorithms

Steering individual trajectories fails to address the condition selection bottleneck. Because generative yield varies unpredictably across scaffolds and epitopes, standard baselines often waste compute on unpromising setups. To solve this, we introduce two dynamic allocation paradigms, both initialized with a uniform prior that distributes the starting computational budget equally across all candidate configurations: • Joint Steering and Allocation via Global SMC: Rather than steering K isolated populations for K candidate configurations (scaffolds or epitopes), we introduce a Global Sequential Monte Carlo (SMC) allocator that maintains a single, joint system of N particles (Algorithm 1). As ipTM values are bounded in [0, 1] and scaffold lengths are comparable, the allocator evaluates raw in-loop ipTM. We leave condition-specific score re-calibration to future work. Unlike the memoryless methods, this approach targets a cumulative reward path. i At each shared guidance event m, the immediate reward increment gm = R(x̂i0,m ) is added to particle i’s historical log-weight and normalized globally across the entire population:   N X gi gj j i i log wm = log wm−1 + m − log exp log wm−1 + m (3) τ τ j=1 Consequently, no explicit budget is assigned. During global systematic resampling over the i accumulated weights {wm }, the computational budget emerges dynamically as unpromising particles are extinguished and successful ones replicate across condition boundaries. • Decoupled Allocation via Successive Halving (SH): We formulate condition selection as a multi-armed bandit problem using the Batched Successive Elimination (BaSE) framework (Algorithm 2)[13, 15]. Configurations (arms) are steered independently, with the total computational budget allocated across successive rounds. We modify standard BaSE (detailed in Appendix A.3) by: (1) distributing per-round budgets evenly among surviving arms, (2) ranking arms by the 90th percentile of their terminal validation scores (AF2-M ipTM), and (3) enforcing a deterministic 50% elimination rate at the end of each round. To isolate the effects of dynamic allocation from inference-time steering, we additionally evaluate ablation variants, specifically an unsteered SH approach and an SMC algorithm utilizing a fixed resampling cadence. Additional information and ablation results are detailed in the Appendix.

3

Results and Discussion

3.1

Steering Increases Yield Without Sacrificing Structural Diversity

3

Figure 3: Generation of BHRF1 binders across 4 epitope-conditioning approaches. (A) Terminal AF2-M ipTM distributions across baseline, unallocated, and dynamic allocation methods. Dashed lines denote group medians (grey: Vanilla). (B) Budget allocation across targeted epitopes and the unconditional (Hotspot off) baseline (1,728 backbones per method across 3 replicates of 576). (C) Designable backbone yield. Segments detail absolute counts and condition-specific success rates. (D) Compute breakdown (GPU-hours) and efficiency (designable backbones per GPU-hour). (E) Structural visualization of targeted BHRF1 epitopes.

Steering on fixed-scaffold nanobody generation was assessed for three distinct tar- Table 1: Compute efficiency and success rate of gets: PD-L1, BHRF1, and IL-7Rα. Both inference-time steering. Designable backbones per endfixed-cadence and adaptive (ESS) steer- to-end GPU-hour and pass rate (%) across three targets. Steered ing shifted generated candidate distributions toward higher ipTM compared to Target (Scaffold) Vanilla Fixed ESS the unsteered (vanilla) baseline for both Designable / GPU-h terminal ESMFold2 and post-hoc AF2-M PD-L1 (7eow) 10.6±0.9 16.9±0.6 14.4±0.5 oracles (Figure 2). We also found steerIL-7Rα (7xl0) 9.4±0.3 17.8±1.2 15.3±1.3 ing improves the rate of designable backBHRF1 (7eow) 4.8±0.3 7.0±2.8 6.3±0.8 bones yielded per GPU-hour (Table 1). A Pass Rate (%) breakdown of generation and evaluation PD-L1 (7eow) 14.9±1.2 42.7±1.1 36.7±1.2 compute (Figure 5) and an assessment IL-7Rα (7xl0) 22.9±0.7 62.2±4.0 53.7±4.4 of the impact of the number of inverse BHRF1 (7eow) 9.7±0.6 20.2±8.1 18.1±2.2 folded sequences evaluated per backbone in identifying passing designs (Figure 6) are presented in the Appendix. While steering collapses paired CDR-H3 Cα RMSD, a measure of backbone diversity, within individual trajectories, this loss of variation is localized to single runs (Figure 2D). Across independent seeds, steering recovers structural variation by exploring distinct, high-reward conformational basins. Thus, steering does not inherently sacrifice global diversity; rather, it highlights the need to distribute compute across multiple starting conditions to sample the viable paratope space. However, over-optimizing on an in-loop metric exposes generation to reward hacking. While the terminal ESMFold2 oracle and the post-hoc AF2-M validation oracle generally correlate, this agreement is imperfect (Figure 2A,B,C). Structural overlays of PD-L1 candidates (Figure 2E) serve to highlight instances of agreement and divergence, emphasizing that satisfying the in-loop metric does not guarantee terminal validation success. 3.2

Dynamic Allocation Maximizes Yield Across Configurations

To evaluate resource allocation across candidate conditions, each method was evaluated on a fixed computational budget distributed across three independent replicates. For BHRF1, this totaled 1,728 designs per method across four epitope configurations (576 per replicate; Figure 3; Table 2); for PD-L1, this totaled 2,880 designs per method across six scaffolds (960 per replicate; Figure 4; Table 3). PDB identifiers for scaffolds refer to the source complex structures from which the nanobody frameworks were extracted. Initialized with a uniform starting budget across all conditions, both the SMC and SH allocators successfully shifted terminal ipTM higher. Additionally, adaptive global SMC steering achieved nearly a 5× increase in designable backbones per GPU-hour over the vanilla baseline (rising from 1.41 to 6.82 for BHRF1, and 2.21 to 10.81 for PD-L1). Decoupled SH steering 4

similarly yielded a 2.4–3.1× throughput improvement. The increase in yield did not sacrifice global conformational diversity across independent runs (Appendix Figures 8, 10). To isolate the distinct contributions of trajectory steering and condition allocation, we evaluated several algorithmic ablations (Appendix Figures 7 and 9). Applying the SH allocation framework to unsteered trajectories improved yield over the vanilla baseline, indicating that iterative condition selection alone provides benefits. However, unsteered SH yielded fewer passing designs than steered SH, demonstrating that the budget allocation and inference-time steering are additive. Furthermore, we evaluated a fixed-cadence SMC allocation policy. While the fixed-cadence approach successfully outperformed both the vanilla and steered-unallocated baselines, the adaptive SMC policy (triggered dynamically by ESS weight degeneracy) produced the highest throughput overall. 3.3

Oracle Divergence and the Hierarchy of Reward Hacking

While joint SMC allocation maximizes raw yield in the PD-L1 binder design experiment, our use of orthogonal oracles for steering and evaluation exposes a vulnerability to reward hacking. SMC allocated 53% of its particles to the 8z8v-derived framework because of high ESMFold2 ipTM, but yielded zero terminal AF2-M passes due to pose divergence (Figure 4). Decoupled SH mitigates this issue by using orthogonal terminal validation scores for rank cuts. Therefore, SH is preferable when serial rounds are feasible, whereas SMC is suited for settings where in-loop rewards are reliable or offline validation is costly. Importantly, both metrics remain in silico surrogates; high ipTM scores do not guarantee in vitro affinity (KD ) or stability, leaving optimization vulnerable to model-specific artifacts.

Figure 4: Dynamic scaffold allocation and the impact of oracle divergence. Generation of PDL1 binders across six distinct scaffolds. (A) Terminal AF2-M ipTM distributions across baseline, unallocated, and dynamic allocation methods. (B) Budget allocation per scaffold (2, 880 backbones per method across 3 replicates of 960 each). (C) Designable backbone yield, detailing absolute counts and scaffold-specific success rates. (D) Compute breakdown (GPU-hours) and efficiency (designable backbones per GPU-hour). (E, F) Oracle correlation (terminal ESMFold2 vs. AF2-M ipTM) for 7eow and 8z8v. (G) Structural overlays showing oracle agreement (7eow) and divergence (8z8v).

4

Conclusion

Dynamic resource allocation paired with inference-time steering converts static scaffold and epitope constraints into active optimization variables, increasing in silico nanobody yield without sacrificing structural diversity. While global SMC maximizes throughput, decoupled multi-armed bandits offer robustness against in-loop reward hacking. Because intermediate confidence metrics remain surrogates, adapting these allocators to wet-lab-correlated oracles represents a primary direction for future work.

5

5

Acknowledgements

We would like to thank Mike Schmidt and Piotr Bobrowicz for their scientific support and critical review of the mansucript. We also thank Esteban Gea for his assistance with the computational infrastructure used in early experiments.

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[11] Cécile Vincke, Remy Loris, Dirk Saerens, Sergio Martinez-Rodriguez, Serge Muyldermans, and Katja Conrath. General strategy to humanize a camelid single-domain antibody and identification of a universal humanized nanobody scaffold. Journal of Biological Chemistry, 284(5):3273–3284, 2009. doi: 10.1074/jbc.M806889200. [12] Martin A. Rossotti, Kasandra Bélanger, Kevin A. Henry, and Jamshid Tanha. Immunogenicity and humanization of single-domain antibodies. The FEBS Journal, 289(14):4304–4327, 2022. doi: 10.1111/febs.15809. [13] Zohar Karnin, Tomer Koren, and Oren Somekh. Almost optimal exploration in multi-armed bandits. In Proceedings of the 30th International Conference on Machine Learning, volume 28 of Proceedings of Machine Learning Research, pages 1238–1246. PMLR, 2013. [14] Lisha Li, Kevin Jamieson, Giulia DeSalvo, Afshin Rostamizadeh, and Ameet Talwalkar. Hyperband: A novel bandit-based approach to hyperparameter optimization. Journal of Machine Learning Research, 18(185):1–52, 2018. [15] Zijun Gao, Yanjun Han, Zhimei Ren, and Zhengqing Zhou. Batched multi-armed bandits problem. Advances in Neural Information Processing Systems, 32, 2019. [16] Justas Dauparas, Ivan Anishchenko, Nathaniel Bennett, Hua Bai, Robert J Ragotte, Lukas F Milles, Basile IM Wicky, Alexis Courbet, Rob J de Haas, Neville Bethel, et al. Robust deep learning–based protein sequence design using proteinmpnn. Science, 378(6615):49–56, 2022. [17] Richard Evans, Michael O’neill, Alexander Pritzel, Natasha Antropova, Andrew Senior, Tim Green, Augustin Žídek, Russ Bates, Sam Blackwell, Jason Yim, et al. Protein complex prediction with alphafold-multimer. biorxiv, pages 2021–10, 2021. [18] Vinicius Zambaldi, David La, Alexander E. Chu, Harshnira Patani, Amy E. Danson, Tristan O. C. Kwan, Thomas Frerix, Rosalia G. Schneider, David Saxton, Ashok Thillaisundaram, Zachary Wu, Isabel Moraes, Oskar Lange, Eliseo Papa, Demis Hassabis, Pushmeet Kohli, Rob Fergus, and Jue Wang. De novo design of high-affinity protein binders with AlphaProteo. arXiv preprint arXiv:2409.08022, 2024. doi: 10.48550/arXiv.2409.08022. [19] Salvatore Candido, Thomas Hayes, Alexander Derry, Roshan Rao, Zeming Lin, Robert Verkuil, Bryan Z Wu, Jin Sub Lee, Elise S Bruguera, Jehan A Keval, et al. Language modeling materializes a world model of protein biology. bioRxiv, pages 2026–06, 2026. [20] Nathaniel R Bennett, Brian Coventry, Inna Goreshnik, Buwei Huang, Aza Allen, Dionne Vafeados, Ying Po Peng, Justas Dauparas, Minkyung Baek, Lance Stewart, et al. Improving de novo protein binder design with deep learning. Nature Communications, 14(1):2625, 2023.

7

A

Extended Methods and Implementation Details

A.1

Theoretical Considerations and Steering Implementation

Base Measure As noted in the main text, Feynman-Kac steering reweights base samples toward ptarget (x0:T ) ∝ qθ (x0:T ) exp(Φ(x0:T )/τ ), where the path functional Φ(x0:T ) accumulates per-event immediate potentials Rt along particle genealogies. This potential tilt acts at discrete intermediate resampling events rather than solely at terminal generation. Specific to BoltzGen, the base measure qθ reflects the deployed design sampler. Because this sampler is sharpened and under-noised relative to the exact reverse SDE assumed by standard Feynman-Kac guarantees, steering converges to the reward-tilted deployed sampling distribution. Consequently, a given temperature τ acts more aggressively than in an exact continuous-time process. Network Guidance events are placed on a schedule uniform in network time c(σ) =   Time 1 σ 4 log σdata rather than raw diffusion steps, ensuring the schedule remains invariant to the overall step budget. Because c(σ) non-linearly stretches the noise schedule, guidance events cluster toward the lower-noise stages of the trajectory. Steering Parameters Steering parameters were empirically optimized for each experiment. For standard unallocated steered runs and steered SH runs, we utilize a population of N = 16 particles, a value chosen empirically following a sweep of 8, 16, 32, and 64 particles. In joint allocation experiments, the total particle count is scaled to K × 16, where K represents the total number of candidate conditions (scaffolds or epitopes). The steering temperature, τ ∈ [0.1, 0.25], was determined via a grid search. Between 6 and 12 guidance events were applied per trajectory, with the exact number tailored to the specific experimental setup. Furthermore, based on an initial parameter sweep ranging from 40% to 60%, steering was consistently initiated at the 60% mark of the diffusion trajectory. We opt for systematic resampling over multinomial. Finally, for all experiments, per-event reward increments are computed using the immediate potential mode [7], where the instantaneous Tweedie estimate evaluates the current reward. Following an initial sweep across immediate, difference, sum, and max potentials [4], the immediate mode was selected due to higher empirical yield. However, because instantaneous immediate potentials do not construct a standard telescoping Feynman-Kac path functional, standard convergence guarantees do not apply. The realized target distribution instead depends on the algorithmic context: for independent steering and Successive Halving (SH) baselines, the weights are memoryless and reflect only the instantaneous immediate potential, whereas the Global SMC allocator recursively accumulates these immediate increments to target an additive path functional. A.2

Global SMC Scaffold Allocation

To address the configuration bottleneck, we treat the scaffold or epitope label k as a coordinate of the particle state z = (k, xt ). Let qk (x0:T ) be scaffold k’s frozen generative law and ω be a prior over scaffolds. A joint population of N particles targets the reward-tilted joint distribution: π(k, x0:T ) ∝ ωk qk (x0:T ) exp(Φ(x0:T )/τ )

(4)

P

where Φ(x0:T ) = m R(x̂0,m ) is the additive reward path functional. Although the per-event increments are evaluated using the memoryless immediate potential mode, the weight recursion of the Global SMC algorithm accumulates these instantaneous rewards, yielding a target distribution proportional to their cumulative sum. By formulating the label as a component of the state, we deploy standard Sequential Monte Carlo (SMC) on the augmented space. Unlike independent steering, the weight recursion normalizes over a global denominator coupling all N particles across all K candidate conditions (Equation 3). Emergent Budget Allocation. This serves as the primary allocation mechP global normalization i anism. The component mass ρk = i:ki =k wm converges to the label marginal of the target joint distribution. No explicit computational budget is assigned. During global systematic resampling, the per-scaffold budget emerges dynamically as the integer count bk ≈ N ρk . Scaffolds with consistently low in-loop rewards transition to an absorbing state of bk = 0, while highly designable scaffolds duplicate. 8

Algorithm 1 Global SMC scaffold allocator. P Require: scaffolds {1, . . . , K} with initial counts bk , k bk = N ; steps T ; potential mode setting the exponent g; fixed temperature τ ; scaffold prior ω; warmup events W ; stop fraction η; draw rule D RAW 1: log w i ← log ωki − log bki , then normalize; m ← 0; 2: for t = 1 to T do 3: advance every active particle by one denoising step with local resampling disabled 4: if t is a shared reward event then 5: m←m+1 ▷ weight-event clock 6: g i ← potential-mode exponent of particle i ▷ g i = R(x̂i0,m ) for immediate
P 7: ∆ ← log j exp log wj + g j /τ ;
8: log wi ← log wi
+ g i /τ − ∆ ▷ persistence and global normalization i 9: if D RAW m, {w } and m > W and t/T ≤ η and t < T then 10: draw N ancestors by one global systematic resample over {wi }, particles ordered by scaffold label 11: regroup ancestors by scaffold label; log wi ← − log N ▷ mass → multiplicity 12: end if 13: end if 14: end for 15: return joint population, emergent counts bk = |{i : k i = k}|, and terminal weights {w i }

9

A.3

Successive Halving (SH) Schedule

The decoupled allocation approach adapts the Batched Successive Elimination (BaSE) framework [15, 13]. Allocation is implemented across multiple rounds, where available configurations (arms) are evaluated by steering a small batch of particles. We implement this as a specific case of BaSE with three structural modifications. First, rather than utilizing a confidence-bound threshold for elimination, our algorithm removes the confidence width (δ = 0). This reduces the elimination step to an unconditional rank-based cut that prunes the bottom 50% of configurations at the end of each round. Second, configurations are ranked using the 90th percentile of their terminal validation scores (q = 0.90) rather than the mean. Finally, while theoretical bounds favor a geometric or minimax budget schedule, we distribute the computational budget uniformly across rounds, as our experiments indicated this can provide greater robustness to the varying quality and composition of the initial panel. Algorithm 2 Outer-loop successive-halving allocator over generative configurations. Arms are ranked by terminal validation scores of completed designs. Importance weights are never compared across configurations. An equal-budget schedule (Bm = Btotal /M ) is used and δ = 0; a positive elimination width recovers standard batched successive elimination [15]. Require: arms A (configurations); rounds M ; survival fraction κ; round budgets B1 , . . . , BM with P m Bm = Btotal designs; quantile q; elimination width δ 1: Sk ← ∅ for every arm k ▷ running score pool 2: for m = 1 to M do 3: for all k ∈ A do ▷ split Bm evenly over surviving arms generate Bm /|A| fresh designs from arm k via the memoryless, independent FK sampler 4: 5: score each with the terminal validation oracle and add the scores to Sk 6: end for 7: if m < M then ▷ eliminate 8: sk ← Quantileq (Sk ) ▷ over the current round’s pooled designs 9: sort A by sk , best first 10: drop the arms ranked below ⌈κ|A|⌉ whose gap maxj sj − sk is at least δ 11: end if 12: end for 13: return every generated design and the surviving arm(s)

10

A.4

Post-Hoc Designability Validation

Generated nanobody candidates are evaluated using a post-hoc structural validation pipeline adapted from the Proteina Complexa framework [3], which builds upon the AlphaProteo designability criteria [18]. For each generated nanobody backbone, we sample eight sequences using ProteinMPNN [16], restricting sequence redesign exclusively to the design residues (i.e., the CDRs) while maintaining the fixed scaffold sequence. These redesigned sequences are folded in complex with the target using the ColabDesign implementation of AlphaFold2-Multimer (AF2-M). Figure 6 details the impact of the number of inverse folding sequences sampled. Following previous structural verification protocols [20], we enable target templating and utilize the initial guess feature, which initializes the AF2 pair representation using the pairwise distances extracted from the generative model’s 3D backbone. To determine designability, we evaluate each folded structure across three metrics: inter-chain predicted alignment error (ipAE), complex predicted local distance difference test (complex pLDDT), and the self-consistent root-mean-square deviation of the binder (binder scRMSD). A generated backbone is classified as designable if any sequence among its eight ProteinMPNN variants satisfies the following AlphaProteo thresholds: 1. ipAE < 7 Å 2. complex pLDDT > 90 3. binder scRMSD < 1.5 Å

11

Table 2: Epitope-conditioning arms for the BHRF1 (PDB 2WH6) experiment. Epitope

Nominated hotspot residues (PDB numbering)

Ep1 [18] Ep2 [10] Ep3

Phe65, Thr74, Glu77, Asp82, Ser85, Arg93 Val86, Ile90, Arg93 Glu77, His78, Leu81

Hotspot off

none nominated

Table 3: Properties and generative parameters of the evaluated nanobody scaffolds. Scaffold / Sourcea

FR Identityb

CDR-H3 Len.

Insertionsc

8coh sonelokimab 7eow 7xl0

85.0 % 90.0 % 85.0 % 87.5 %

19 17 21 15

3/3/7 3/4/4 3/3/7 3/3/6

8z8v isecarosmab

91.2 % 88.8 %

8 8

3/3/3 3/2/2

a PDB identifiers denote the source complex structure from which the

nanobody framework backbone was extracted. Named entries (e.g., sonelokimab, isecarosmab) correspond to clinical nanobody frameworks. b Per-position identity of FR1+FR2+FR3 to human germline IGHV323. c Number of residues inserted by BoltzGen for H1 / H2 / H3. 1,152 backbones per method × target Vanilla Steered, fixed

Steered, ESS Refold + Analysis

40

GPU-hours

30 26.4 14.9

20

26.4

14.9

21.5

21.5

11.6

11.8

26.4 10

21.5 14.9 14.2

13.9

1.8

1.4

0

14.5

PD-L1 – 7eow

14.1

1.6

IL7RA – 7xl0

BHRF1 – 7eow

Figure 5: Steered and baseline compute overhead breakdown by generation method and target for three targets. Total GPU-hours expended for 1,152 backbones per target across steering policies. Solid bars represent direct steered/vanilla trajectory generation, while hatched bars account for in-loop and terminal refolding, inverse folding, and post-hoc filtering compute.

12

IL7RA — 7xl0

PD-L1 — 7eow

BHRF1 — 7eow

Expected designability pass rate (%)

60 80

25 50

70 Steered, fixed 62.2%

60

Steered, fixed 42.7% 20

40 Steered, ESS 53.7%

Steered, fixed 20.2% Steered, ESS 18.1%

Steered, ESS 36.7%

50 15

30

40 30

10

20 Vanilla 22.9%

20

Vanilla 9.7%

Vanilla 14.9%

5

10 10 0

0 1

2

3

4

5

6

7

8

MPNN sequences folded per backbone

0 1

m

2

3

4

5

6

7

8

MPNN sequences folded per backbone

1

m

2

3

4

5

6

7

8

MPNN sequences folded per backbone

m

Figure 6: Expected designability pass rate vs. MPNN sequence budget (Unallocated). The expected pass rate (y-axis) is the fraction of backbones yielding ≥ 1 successful design out of m folded sequences (x-axis, m = 1..8). 1,152 backbone designs per (target, scaffold, method) tuple.

A Quality

B Allocation Vanilla

Vanilla

Steered, unallocated

Steered, unallocated

SMC fixed

SMC fixed

531

SMC ESS

SMC ESS

464

SH unsteered

SH unsteered

432

C Yield 432

432

500

1,728

432

whisker: mean±SD over 3 replicates · dots: replicate AP rates

±2.5pp

428 (25%) 432

0.1

0.2

0.3

0.4

0.5

AF2-M ipTM

0.6

0.7

0.8

0.9

Ep1

250

750

144

144

1,728

432

144

144

1,728

1000

1250

1500

Designs allocated per epitope

Ep3

1,728

339

816

500

1,728

576

1008

0

Ep2

606

624

1,728

432

868

SH

SH

432

1750

400

Designable backbones per epitope

432

22 (6%)

±5.1pp

300

222 (26%)

±1.3pp

240 (14%)

±1.9pp

109 (6%)

100

0

29 (7%)

197 (11%)

200

69 (4%)±0.6pp

39 (9%)

36 (8%) 27 (6%)

57 (13%)

Vanilla

Steered unalloc.

37 (6%) 29 (5%)

131 (25%)

±1.8pp

118 (7%) 183 (39%)

66 (8%)

206 (20%)

45 (7%)

SMC fixed SMC ESS

SH unsteered

SH

Hotspot off (no intended epitope)

Figure 7: Ablation benchmark for BHRF1 binder generation across epitope-conditioning approaches. (A) Terminal AF2-M ipTM distributions across baselines, dynamic allocation methods, and ablation variants (SMC fixed resampling cadence and SH unsteered). Dashed lines denote group medians (grey: Vanilla). (B) Computational budget allocation across targeted epitopes (Ep1–Ep3) and the unconditional baseline (Hotspot off). Total design budget is held constant at 1, 728 trajectories per method across 3 replicates with 576 designs each. (C) Designable backbone yield evaluated under post-hoc structural validation criteria. Bar segments specify absolute counts and condition-specific success rates per epitope.

13

Figure 8: CDR-H3 structural diversity for BHRF1 epitope allocation. Cα RMSD of passing designs across baseline, unallocated steering, and dynamic allocation methods (including SMC and SH ablation variants). Lighter violins denote diversity within a single run, whereas darker violins indicate diversity across multiple runs, highlighting that while steering restricts structural diversity within individual trajectories, it successfully explores diverse productive basins across independent runs. Circles denote the mean, and the numbers at the bottom denote the total passing designs per method.

A Quality

B Allocation

C Yield whisker: mean±SD over 3 replicates · dots: replicate AP rates

Vanilla

Vanilla

480

480

480

480

480

480

2,880

±7.7pp

±5.0pp

800

SMC fixed

SMC fixed

SMC ESS

SMC ESS

SH unsteered

SH unsteered

480

480

480

480

1,009

480

480

2,880

1,871

1,350

2,880

1,529

1,008

528

816

2,880

144144 240 2,880

698 (24%)

Designable backbones per scaffold

Steered, unallocated

Steered, unallocated

624 (22%) 29 (2%)

600

±1.8pp

486 (17%)

400

±4.8pp

248 (9%)

595 (59%)

672 (50%)

200

44 (5%)

133 (5%) ±0.1pp

SH

SH

0.1

0.2

0.3

0.4

0.5

AF2-M ipTM

0.6

0.7

0.8

1,008

0

528

500

1000

432

1500

144 240

2000

Designs allocated per scaffold

7eow

528

2,880

2500

3000

8coh

194 (40%)

0

7xl0

Steered, unallocated

420 (42%)

161 (16%)

87 (18%)

Vanilla

±0.9pp

225 (8%)

32 (7%)

SMC fixed SMC ESS

isecarosmab

SH unsteered

SH

sonelokimab

8z8v

F D PD-L1 – 7eow

E PD-L1 – 8z8v

Figure 9: Ablation benchmark for PD-L1 binder generation and scaffold allocation. Evaluation across six candidate scaffolds (extracted from complex structures 7eow, 8coh, 7xl0, 8z8v, and clinicalstage frameworks isecarosmab and sonelokimab). (A) Terminal AF2-M ipTM distributions across baselines, dynamic allocation methods, and ablation variants (SMC global fixed cadence and SH unsteered). Dashed lines denote group medians (grey: Vanilla). (B) Computational budget allocation per scaffold, holding total trajectory count constant at 2, 880 designs per method across 3 replicates of 960 designs each. (C) Designable backbone yield under post-hoc structural validation criteria. Bar segments specify absolute counts and scaffold-specific success rates. AF2-Multimer ipTM AF2-Multimer ipTM 1.0

0.6 0.4 0.2 0.0

Pearson r = 0.07 Spearman ρ = 0.19 n = 544

0.8

ESMFold2 ipTM

ESMFold2 ipTM

1.0

Pearson r = 0.39 Spearman ρ = 0.49 n = 416

0.8

0.6 0.4 0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.0

0.2

0.4

0.6

14

0.8

1.0

CDR-H3 Diversity — PD-L1 Scaffold Allocation — 7eow 2.0

within run across runs mean

H3 Cα RMSD (Å)

1.5

1.0

0.5

0.0 87

194

136

216

161

420

Vanilla

Steered unalloc.

SMC fixed

SMC ESS

SH unsteered

SH

Figure 10: CDR-H3 structural diversity for PD-L1 Scaffold allocation. Cα RMSD of passing designs for the 7eow scaffold across baseline, unallocated steering, and dynamic allocation methods (including SMC and SH ablation variants). Lighter violins denote diversity within a single run, whereas darker violins indicate diversity across multiple runs, highlighting that while steering restricts structural diversity within individual trajectories, it successfully explores diverse productive basins across independent runs. Circles denote the mean, and the numbers at the bottom denote the total passing designs per method.

15

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