LIMO: Latent Inceptionism for Targeted Molecule Generation

Peter EckmannKunyang SunBo ZhaoMudong FengMichael K. GilsonRose Yu

article2022ICML59 citations

Presents a gradient-based reverse-optimization framework that pairs a variational autoencoder with sequential property predictors to rapidly generate drug-like molecules with high target binding affinities at a fraction of the computational cost of reinforcement learning methods.

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Early-stage drug discovery is a multi-billion-dollar process that often takes years, largely because researchers must screen enormous chemical libraries to find drug-like molecules that bind tightly to disease-related proteins. Existing machine learning methods, such as reinforcement learning and sampling-based models, struggle to efficiently optimize computationally expensive properties like physics-based binding affinity. The article presents Latent Inceptionism on Molecules (LIMO), a generative modeling framework designed to rapidly generate novel, drug-like compounds with high binding affinities to target proteins.

LIMO works by mapping molecules into a continuous representation using a variational autoencoder and predicting properties from the decoded molecular output rather than directly from the latent space. It then uses gradient-based optimization to backpropagate directly into the latent space to generate optimized molecules, followed by filtering and fine-tuning steps to ensure drug-likeness. The framework was evaluated across standard benchmarks and applied to de novo molecule design targeting two human proteins: human estrogen receptor (ESR1), which has known drug binders, and acetyl-CoA acyl transferase 1 (ACAA1), an enzyme with no known binders.

Key findings show that LIMO operates 6 to 8 times faster than leading reinforcement learning approaches and 12 times faster than sampling methods, completing optimization tasks in roughly one hour. In docking-based binding affinity tests, LIMO achieved superior target binding compared to all baselines, reaching the nanomolar range for both proteins. Furthermore, rigorous molecular dynamics simulations revealed a generated ESR1 candidate with an exceptionally strong predicted dissociation constant of 6·10⁻¹⁴ M, well beyond the affinity of existing cancer drugs such as tamoxifen and raloxifene. LIMO also effectively maintained high structural diversity and demonstrated the unique capability to optimize molecular properties while keeping specific chemical substructures fixed.

These findings suggest that LIMO can significantly compress early drug discovery timelines and lower computational costs by rapidly producing diverse, high-affinity leads for novel and validated disease targets alike. The primary limitation of the study is that binding affinities are derived from computational simulations rather than physical laboratory experiments, meaning false positives can occur despite promising physics-based validation. Moving forward, researchers and drug discovery teams should integrate automated validation tools into the design pipeline and synthesize top-performing candidates to confirm their biological activity through physical laboratory testing.

University of California, San Diego latent inceptionism targeted molecule generation de novo drug design

arXiv: 2206.09010

Paper: Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules, Rafael Gómez-Bombarelli et al. (2016). This foundational paper establishes continuous latent space molecular representation and optimization via variational autoencoders, providing the fundamental generative paradigm upon which LIMO builds.
Paper: Junction Tree Variational Autoencoder for Molecular Graph Generation, Wengong Jin et al. (2018). It introduces variational autoencoding over molecular graphs and chemically valid substructures, demonstrating core latent-space property optimization concepts essential for understanding LIMO.
Paper: DeepDTA: deep drug–target binding affinity prediction, Hakime Öztürk et al. (2018). This work formulates deep learning models for continuous drug-target binding affinity prediction, establishing the target-based scoring principles that LIMO optimizes.
Paper: MoleculeNet: a benchmark for molecular machine learning, Zhenqin Wu et al. (2017). It provides standard molecular machine learning benchmarks and property evaluation frameworks that define the baseline metrics and validation protocols used in LIMO.

Paper: Sample Efficiency Matters: A Benchmark for Practical Molecular Optimization, Wenhao Gao et al. (2022). This study establishes a standardized benchmark to rigorously evaluate the sample efficiency and practical search performance of generative molecular optimization methods like LIMO.
Paper: MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space, Yanru Qu et al. (2024). It extends structure-based drug design into continuous parameter space to generate geometrically valid 3D binding poses alongside high target affinity.
Paper: E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking, Yangtian Zhang et al. (2023). It advances protein-ligand binding pose prediction using end-to-end equivariant deep learning networks to overcome docking inaccuracies.
Paper: DrugOOD: Out-of-Distribution Dataset Curator and Benchmark for AI-Aided Drug Discovery - a Focus on Affinity Prediction Problems with Noise Annotations, Yuanfeng Ji et al. (2023). It investigates and benchmarks out-of-distribution generalization and noisy labels in drug-target affinity prediction, directly addressing the validation challenges faced by affinity-driven molecular generators.

Cover for LIMO: Latent Inceptionism for Targeted Molecule Generation

Abstract

Generation of drug-like molecules with high binding affinity to target proteins remains a difficult and resource-intensive task in drug discovery. Existing approaches primarily employ reinforcement learning, Markov sampling, or deep generative models guided by Gaussian processes, which can be prohibitively slow when generating molecules with high binding affinity calculated by computationally-expensive physics-based methods. We present Latent Inceptionism on Molecules (LIMO), which significantly accelerates molecule generation with an inceptionism-like technique. LIMO employs a variational autoencoder-generated latent space and property prediction by two neural networks in sequence to enable faster gradient-based reverse-optimization of molecular properties. Comprehensive experiments show that LIMO performs competitively on benchmark tasks and markedly outperforms state-of-the-art techniques on the novel task of generating drug-like compounds with high binding affinity, reaching nanomolar range against two protein targets. We corroborate these docking-based results with more accurate molecular dynamics-based calculations of absolute binding free energy and show that one of our generated drug-like compounds has a predicted KD (a measure of binding affinity) of 6 · 10−14 M against the human estrogen receptor, well beyond the affinities of typical early-stage drug candidates and most FDA-approved drugs to their respective targets. Code is available at https://github.com/Rose-STL-Lab/LIMO.

Keywords

latent inceptionism targeted molecule generation de novo drug design molecular optimization deep generative models variational autoencoder molecular representation gradient ascent ligand-protein interactions

1. Introduction
2. Related Work
3. Methodology
3.1. Variational Autoencoder
3.2. Property Predictor
3.3. Reverse Optimization
3.4. Refinement
4. Experiments
4.1. Experimental Setup
4.2. QED and Penalized logP Maximization
4.3. logP Targeting
4.4. Similarity-constrained Penalized logP Maximization
4.5. Substructure-constrained logP Extremization
4.6. Single-objective Binding Affinity Maximization
4.7. Multi-objective Binding Affinity Maximization
5. Discussion and Conclusions
Acknowledgements
References
A. Experiment description and baselines
A.1. Tasks
A.2. Molecule metrics
A.3. Fine-tuning algorithm
A.4. Baselines
A.5. Experimental details
A.6. Autodock-GPU
A.7. Absolute binding free energy
B. Additional experiments
B.1. Random generation of molecules
B.2. Justification of multi-objective optimization

Knowls

Knowl 1 — LIMO’s stacked latent-space generation architecture
model/method
Latent Inceptionism on Molecules (LIMO) generates molecules by combining a variational autoencoder (VAE) with a separate molecular-property predictor. The VAE encoder maps a SELFIES molecular string $x$ to a continuous latent vector $z\in\mathbb{R}^{m}$ , and the VAE decoder maps $z$ to a differentiable, real-valued molecular representation. A property predictor then consumes the decoder output rather than $z$ directly. After the predictor is trained, LIMO treats $z$ as an optimizable variable and backpropagates the desired property objective through the decoder and predictor. This stacked decoder–predictor design is intended to make property prediction easier than learning a direct latent-space-to-property mapping while retaining efficient gradient-based optimization.
Knowl 2 — SELFIES VAE representation and valid molecular decoding
model/method
A molecule is represented as a length- $n$ SELFIES string $x=(x_1,\ldots,x_n)$ whose symbols belong to a vocabulary $S=\{s_1,\ldots,s_d\}$ . The VAE decoder produces, for every position $i$ , a probability vector $y_i\in[0,1]^d$ over the $d$ SELFIES symbols. The discrete output is obtained by selecting the most probable symbol at each position:

$\hat{x}_i=s_{d_i^*},\qquad d_i^*=\arg\max_{1\leq j\leq d}y_{i,j}.$

Because SELFIES is designed so that every SELFIES string corresponds to a chemically valid molecule, decoding the continuous representation into a SELFIES string preserves chemical validity. The VAE learns a latent space in which molecules can be sampled and optimized; random molecules are generated by sampling $z\sim\mathcal{N}(0_m,I_m)$ and decoding it.
Knowl 3 — Property prediction from decoded molecular representations
model/method
LIMO freezes the trained VAE before fitting a property predictor $g_\theta$ . Let $f_{\mathrm{dec}}$ be the VAE decoder and let $\pi$ be a ground-truth molecular-property function, such as logP, QED, synthetic accessibility, or docking-based binding affinity. Training examples are obtained by sampling latent vectors $z\sim\mathcal{N}(0_m,I_m)$ , decoding them, and evaluating the resulting molecules with $\pi$ . The predictor is trained with mean-squared error:

$\ell_0(\theta)=\left\|g_\theta\!\left(f_{\mathrm{dec}}(z)\right)-\pi\!\left(f_{\mathrm{dec}}(z)\right)\right\|_2^2.$

Training the predictor after the VAE has been completed avoids requiring expensive property labels for the full generative-model dataset, permits generated molecules to provide diverse property-training examples, and allows new properties to be added without retraining the VAE. The predictor receives the decoder’s intermediate molecular representation, not the latent vector itself.
Knowl 4 — Gradient-based reverse optimization with optional substructure preservation
algorithm
After training, LIMO freezes the decoder $f_{\mathrm{dec}}$ and property predictors $g_1,\ldots,g_k$ , then initializes a trainable latent vector from $z\sim\mathcal{N}(0_m,I_m)$ . For properties to be maximized, it minimizes the weighted objective

$\ell_1(z)=-\sum_{i=1}^{k}w_i\,g_i\!\left(f_{\mathrm{dec}}(z)\right),$

where $w_i$ are property weights selected by random grid search. The Adam optimizer updates $z$ through the differentiable decoder–predictor composition. Property-minimization or targeting objectives are implemented by changing the objective direction or weights.

For substructure-constrained optimization, a binary mask $M\in\{0,1\}^{n\times d}$ marks SELFIES positions and symbols that must remain fixed. An input molecule containing the desired substructure is reconstructed as $\hat{x}_{\mathrm{start}}=f_{\mathrm{dec}}(f_{\mathrm{enc}}(x_{\mathrm{start}}))$ . LIMO adds the penalty

$\ell_2(z)=\lambda\sum_{i=1}^{n}\sum_{j=1}^{d}\left[M_{i,j}\left(f_{\mathrm{dec}}(z)_{i,j}-\hat{x}_{\mathrm{start},i,j}\right)\right]^2,$

where $\lambda=1000$ in the experiments. The combined objective preserves the masked molecular substructure while allowing the remaining molecular positions to change.
Knowl 5 — Drug-likeness filtering after multi-objective optimization
model/method
After reverse optimization, LIMO removes molecules that fail simple drug-likeness and synthesizability criteria. A molecule is retained only if its quantitative estimate of drug-likeness satisfies $\mathrm{QED}>0.4$ , its synthetic accessibility score satisfies $\mathrm{SA}<5.5$ , and it contains no ring with fewer than 5 or more than 6 atoms. The ring restriction supplements SA because very small and very large rings can be difficult to synthesize without being adequately penalized by the SA score. The authors also used an auxiliary greedy refinement procedure for some tasks: repeatedly test replacing eligible carbon atoms with N, O, Cl, or F, retain the best valid improving replacement, and stop when a complete pass yields no improvement.
Knowl 6 — Experimental configuration for molecular optimization
experimental setup
Optimization experiments use the approximately 250,000 purchasable drug-like molecules in ZINC250k; random-generation experiments use the approximately 2-million-molecule ZINC-derived MOSES dataset. The shared VAE latent dimension is 1024. Its 64-dimensional symbol embedding feeds four batch-normalized fully connected layers with ReLU activations, using width 2,000 in the first layer and 1,000 thereafter; the decoder has the same layer dimensions and uses position-wise softmax outputs. The VAE is trained for 18 epochs with Adam at learning rate $10^{-4}$ , using an ELBO whose reconstruction and KL terms are weighted 0.9 and 0.1, respectively. Each property predictor has three 1,000-unit ReLU fully connected layers; it is trained for 5 epochs, followed by 10 reverse-optimization epochs with latent-space learning rate 0.1. There are 100,000 predictor-training examples for ordinary properties and 10,000 for binding affinity because docking is expensive.

The optimized properties are logP, penalized logP, QED, SA, and docking-based binding affinity. Binding-affinity experiments target human estrogen receptor ESR1 using crystal structure PDB 1ERR and human peroxisomal acetyl-CoA acyl transferase 1 (ACAA1) using PDB 2IIK. LIMO receives only the protein structure and binding-site information, not known binders. AutoDock-GPU supplies docking affinities, RDKit supplies ordinary molecular properties, and comparisons use JT-VAE, GCPN, MolDQN, MARS, and GraphDF. Experiments run on two GTX 1080 Ti GPUs, four CPU cores, and 32 GB of memory.
Knowl 7 — Fast QED and penalized-logP maximization
data/table
On 100,000 generated molecules, LIMO matches or approaches the strongest benchmark scores while requiring substantially less total generation-and-evaluation time. The reported top-three scores are:
- JT-VAE: penalized logP $5.30,4.93,4.49$ ; QED $0.925,0.911,0.910$ ; 24 hours; no output-length limit.
- GCPN: penalized logP $7.98,7.85,7.80$ ; QED $0.948,0.947,0.946$ ; 8 hours; length limit.
- MolDQN: penalized logP $11.8,11.8,11.8$ ; QED $0.948,0.943,0.943$ ; 24 hours; length limit.
- MARS: penalized logP $45.0,44.3,43.8$ ; QED $0.948,0.948,0.948$ ; 12 hours; no length limit.
- GraphDF: penalized logP $13.7,13.2,13.2$ ; QED $0.948,0.948,0.948$ ; 8 hours; no length limit.
- LIMO with prediction directly on $z$ : penalized logP $6.52,6.38,5.59$ ; QED $0.910,0.909,0.892$ ; 1 hour; length limit.
- LIMO with prediction on the decoded representation: penalized logP $10.5,9.69,9.60$ ; QED $0.947,0.946,0.945$ ; 1 hour; length limit.
On an unseen set of 1,000 generated molecules, the coefficient of determination between predicted and actual properties is $R^2=0.04$ for direct prediction from $z$ and $R^2=0.38$ for the stacked decoder–predictor architecture. Replacing the fully connected encoder and decoder with eight-layer, 512-hidden-unit LSTMs reduced performance; the maximum QED observed in that variant was 0.3.
Knowl 8 — LogP targeting, similarity-constrained optimization, and fixed-substructure editing
empirical result
For targeting the range $-2.5<\mathrm{logP}<-2.0$ , LIMO places 10.4% of generated molecules in the target range and achieves diversity 0.914, where diversity is one minus mean pairwise Morgan-fingerprint Tanimoto similarity. The corresponding success/diversity values are JT-VAE 11.3%/0.846, GCPN 85.5%/0.392, MolDQN 9.66%/0.854, and GraphDF 0% with diversity unavailable. LIMO generates 33 molecules per second within the target range.

For similarity-constrained penalized-logP maximization, the experiment starts from the 800 ZINC250k molecules with the lowest penalized logP, performs 1,000 latent gradient-ascent steps per molecule, and selects the best candidate satisfying a minimum Morgan-fingerprint Tanimoto similarity $\delta$ . LIMO’s mean improvement and success rate are $10.1\pm2.3$ and 100% at $\delta=0.0$ ; $5.8\pm2.6$ and 99.0% at $\delta=0.2$ ; $3.6\pm2.3$ and 93.7% at $\delta=0.4$ ; and $1.8\pm2.0$ and 85.5% at $\delta=0.6$ . LIMO has the largest improvement at the two least restrictive similarity levels and remains competitive at higher similarity constraints.

In a separate fixed-substructure experiment, LIMO successfully increased or decreased logP from two ZINC250k starting molecules while preserving a specified substructure. This demonstrates optimization around a fixed scaffold rather than merely enforcing whole-molecule similarity.
Knowl 9 — Single-objective docking-affinity generation
data/table
LIMO was evaluated by generating 10,000 molecules per method for ESR1 and ACAA1 and reporting the three lowest predicted dissociation constants $K_D$ in nanomolar; lower $K_D$ means higher computed affinity. LIMO produced the strongest docking scores with the shortest runtime:
- GCPN: ESR1 $6.4,6.6,8.5$ nM; ACAA1 $75,83,84$ nM; 6 hours.
- MolDQN: ESR1 $373,588,1062$ nM; ACAA1 $240,337,608$ nM; 6 hours.
- GraphDF: ESR1 $25,47,51$ nM; ACAA1 $370,520,590$ nM; 12 hours.
- MARS: ESR1 $17,64,69$ nM; ACAA1 $163,203,236$ nM; 6 hours.
- LIMO: ESR1 $0.72,0.89,1.4$ nM; ACAA1 $37,37,41$ nM; 1 hour.
Although single-objective optimization generated very favorable docking scores, the resulting molecules often contained problematic polyenes or rings with at least 8 atoms. The authors regarded these structures as concerns for reactivity, toxicity, or synthesis, motivating simultaneous optimization of affinity, QED, and SA.
Knowl 10 — Multi-objective affinity optimization and molecular-dynamics corroboration
empirical result
For each protein target, LIMO generated 100,000 molecules while simultaneously optimizing docking affinity, QED, and SA, then applied the drug-likeness and ring filters. The two best retained ligands for each target had the following reported properties; $K_D$ values are in nM, QED is higher-is-better, SA is lower-is-better, and ABFE values are more rigorous than docking values.
- ESR1 LIMO molecule 1: docking $K_D=4.6$ , QED 0.43, SA 4.8, ABFE $6\times10^{-5}$ nM, Lipinski pass, 0 PAINS alerts, $Fsp^3=0.16$ , MCE-18 90.
- ESR1 LIMO molecule 2: docking $K_D=2.8$ , QED 0.64, SA 4.9, ABFE 1000 nM, Lipinski pass, 0 PAINS alerts, $Fsp^3=0.52$ , MCE-18 76.
- ESR1 GCPN molecules: docking $K_D=810$ and $2.7\times10^4$ nM, with QED 0.43 and 0.80 and SA 4.2 and 3.7; their ABFE values were not reported.
- For comparison, tamoxifen had docking $K_D=87$ nM and experimental ABFE-derived $K_D=1.5$ nM; raloxifene had docking $K_D=7.9\times10^6$ nM and experimental $K_D=0.030$ nM.
- ACAA1 LIMO molecule 1: docking $K_D=28$ , QED 0.57, SA 5.5, ABFE $4\times10^4$ nM, Lipinski pass, 0 PAINS alerts, $Fsp^3=0.52$ , MCE-18 52.
- ACAA1 LIMO molecule 2: docking $K_D=31$ , QED 0.44, SA 4.9, no ABFE binding detected, Lipinski pass, 0 PAINS alerts, $Fsp^3=0.81$ , MCE-18 45.
- ACAA1 GCPN molecules both had docking $K_D=8500$ nM, with QED 0.69 and 0.54 and SA 4.2 and 4.3.
The authors inspected docked three-dimensional poses and found that representative LIMO ligands fit the target pockets with favorable interactions. They then used molecular-dynamics-based absolute binding free-energy calculations on promising ligands. For each ligand, five docking poses were evaluated, their free energies were combined into an overall binding free energy, and the reported value was averaged over two independent runs. One of two ESR1 candidates was assigned $K_D=6\times10^{-5}$ nM, equivalent to $6\times10^{-14}$ M, by ABFE. This result is computational and was not experimentally confirmed.

Coverage note — The detailed greedy carbon-to-heteroatom fine-tuning pseudocode and the auxiliary MOSES random-generation benchmark were not expanded into separate knowls because they are secondary refinement/diversity analyses rather than load-bearing components of LIMO’s targeted optimization contribution.

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Citation

MLA

Eckmann, P., et al. “LIMO: Latent Inceptionism for Targeted Molecule Generation”. International Conference on Machine Learning, vol. 162, 2022, pp. 5777–92, https://proceedings.mlr.press/v162/eckmann22a.html.

APA

Eckmann, P., Sun, K., Zhao, B., Feng, M., Gilson, M., & Yu, R. (2022). LIMO: Latent Inceptionism for Targeted Molecule Generation. International Conference on Machine Learning, 162, 5777–5792. https://proceedings.mlr.press/v162/eckmann22a.html

Chicago

Eckmann, P., K. Sun, B. Zhao, M. Feng, M. Gilson, and R. Yu. 2022. “LIMO: Latent Inceptionism for Targeted Molecule Generation”. International Conference on Machine Learning 162: 5777–92. https://proceedings.mlr.press/v162/eckmann22a.html.

Harvard

Eckmann, P. et al. (2022) “LIMO: Latent Inceptionism for Targeted Molecule Generation”, International Conference on Machine Learning. PMLR, pp. 5777–5792. Available at: https://proceedings.mlr.press/v162/eckmann22a.html.

Vancouver

1. Eckmann P, Sun K, Zhao B, Feng M, Gilson M, Yu R (2022) LIMO: Latent Inceptionism for Targeted Molecule Generation. In: International Conference on Machine Learning. PMLR, pp 5777–5792

BibTeX

@InProceedings{pmlr-v162-eckmann22a,
  title = 	 {{LIMO}: Latent Inceptionism for Targeted Molecule Generation},
  author =       {Eckmann, Peter and Sun, Kunyang and Zhao, Bo and Feng, Mudong and Gilson, Michael and Yu, Rose},
  booktitle = 	 {Proceedings of the 39th International Conference on Machine Learning},
  pages = 	 {5777--5792},
  year = 	 {2022},
  editor = 	 {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
  volume = 	 {162},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {17--23 Jul},
  publisher =    {PMLR},
  pdf = 	 {https://proceedings.mlr.press/v162/eckmann22a/eckmann22a.pdf},
  url = 	 {https://proceedings.mlr.press/v162/eckmann22a.html},
  abstract = 	 {Generation of drug-like molecules with high binding affinity to target proteins remains a difficult and resource-intensive task in drug discovery. Existing approaches primarily employ reinforcement learning, Markov sampling, or deep generative models guided by Gaussian processes, which can be prohibitively slow when generating molecules with high binding affinity calculated by computationally-expensive physics-based methods. We present Latent Inceptionism on Molecules (LIMO), which significantly accelerates molecule generation with an inceptionism-like technique. LIMO employs a variational autoencoder-generated latent space and property prediction by two neural networks in sequence to enable faster gradient-based reverse-optimization of molecular properties. Comprehensive experiments show that LIMO performs competitively on benchmark tasks and markedly outperforms state-of-the-art techniques on the novel task of generating drug-like compounds with high binding affinity, reaching nanomolar range against two protein targets. We corroborate these docking-based results with more accurate molecular dynamics-based calculations of absolute binding free energy and show that one of our generated drug-like compounds has a predicted $K_D$ (a measure of binding affinity) of $6 \cdot 10^{-14}$ M against the human estrogen receptor, well beyond the affinities of typical early-stage drug candidates and most FDA-approved drugs to their respective targets. Code is available at https://github.com/Rose-STL-Lab/LIMO.}
}

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LIMO: Latent Inceptionism for Targeted Molecule Generation

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Knowls

Knowl 1 — LIMO’s stacked latent-space generation architecture

Knowl 2 — SELFIES VAE representation and valid molecular decoding

Knowl 3 — Property prediction from decoded molecular representations

Knowl 4 — Gradient-based reverse optimization with optional substructure preservation

Knowl 5 — Drug-likeness filtering after multi-objective optimization

Knowl 6 — Experimental configuration for molecular optimization

Knowl 7 — Fast QED and penalized-logP maximization

Knowl 8 — LogP targeting, similarity-constrained optimization, and fixed-substructure editing

Knowl 9 — Single-objective docking-affinity generation

Knowl 10 — Multi-objective affinity optimization and molecular-dynamics corroboration

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