Part 1: CytoFlow Architecture Introduction

Our dry lab constructed an end-to-end antimicrobial peptide intelligent development platform, CytoFlow, covering the entire process from molecular design, activity prediction, sequence optimization to production processes.

It consists of three major models: CytoEvolve (antimicrobial peptide evolution model, inputs AMP sequences and outputs improved variants), CytoGuard (antimicrobial peptide activity evaluation model, inputs AMP sequences and outputs MIC), and CytoGrow. The system framework is shown below:

Part 2: Experimental Level Design and Optimization

2.1 CytoGrow

CytoGuard and CytoEvolve can be considered models designed to improve LL-37 antimicrobial peptide quality.

CytoGrow, on the other hand, is a model aimed at increasing LL-37 yield, consisting of three major models: Grow-Medium (medium composition optimization model), Grow-Yeast (Saccharomyces cerevisiae growth kinetics model), and Grow-Glucose (glucose consumption model).

2.1.1 Grow-Medium

Abstract

Grow-Medium establishes a hybrid intelligent optimization framework of quadratic response surface + Gaussian process residuals + dual acquisition function Bayesian optimization for optimizing the culture medium formulation for Saccharomyces cerevisiae. We used two methods for optimization. The Mean method yielded an improved medium composition of glucose 54.49 g/L, peptone 9.82 g/L, KH2PO4 3 g/L, with predicted corresponding OD value of 0.408 (20.9% improvement over the basic medium result OD=0.3375), showing small improvement but high reliability. The UCB method predicted glucose 41.39 g/L, peptone 23.58 g/L, KH2PO4 3 g/L conditions to achieve OD value 0.424 (25.6% improvement over the basic medium result OD=0.3375), showing larger improvement but requiring further experimental validation.

Problem

Dataset Description

• Source: Actual wet lab experimental data
• Target variable: OD value (optical density, reflecting microbial growth)
• Independent variables:
• Glucose concentration (G): 20-70 g/L
• Peptone concentration (T): 6-30 g/L
• KH2PO4 concentration (K): 0-5 g/L
• Data scale: 228 experimental points, 3 replicates each
• Basic Medium OD: 0.3375(G=20, T=20, K=0)
• Experimental Average OD: 0.3410
• Highest Experimental OD: 0.401 (G=54, T=10, K=3)

Optimization Objective

Find the optimal concentration combination of glucose, peptone, and potassium dihydrogen phosphate to maximize OD value.

Method

Initially, we attempted a hybrid modeling approach of quadratic response surface + Gaussian process residuals.

Quadratic Response Surface (Trend Term)

where feature matrix $𝐗$ contains:

Parameter estimation: $\mathit{\beta }=({𝐗}^T𝐗+\lambda 𝐈{)}^{-1}{𝐗}^T𝐲$, where $\lambda ={10}^{-8}$ is the regularization parameter.

Gaussian Process Residual Modeling (Rasmussen & Williams, 2006)

Residual definition:

Kernel function: Anisotropic RBF kernel

Hyperparameter settings:

• ${\sigma }_f=max({10}^{-6},\text{std}(r))$ (signal amplitude)
• ${\sigma }_n=max({10}^{-6},0.02\times \text{range}(y))$ (noise amplitude)
• ${\ell }_1={\ell }_2={\ell }_3=1.0$ (length scales)

Prediction Formulas

Mean prediction:

Variance prediction:

Experiments & Results

For the initial optimization strategy, we used grid search, first defining the search space:

• G ∈ [30, 70] g/L
• T ∈ [6, 30] g/L
• K = 3 g/L (fixed)
• Grid resolution: 121×121 = 14,641 points

For the second method, we set the acquisition function: Upper Confidence Bound (UCB)

, where $\kappa =2.58$ (99% confidence)

Results

Mean argmax @ (G=54.33, T=9.80, K=3): OD_mean=0.408 UCB argmax @ (G=41.33, T=23.60, K=3): OD_mean=0.424

Through grid search, both Mean and UCB found optimized configurations and predicted corresponding OD values.

The figures below show visualization of two extrema predicted by Mean and comparison of biomass(OD value) across different medium compositions:

The following figures show model validation and analysis: sensitivity analysis of the three parameters and model fitting quality analysis:

Conclusion

Through hybrid modeling combining parametric (quadratic response surface) and non-parametric (GP) methods, and dual acquisition functions considering both conservative optimistic (UCB) and deterministic exploitation (Mean) strategies, we optimized existing medium compositions and predicted their OD values. Optimal formulation discovered: Glucose 41.4g/L + Peptone 23.6g/L + KH2PO4 3g/L, predicted OD 0.424, 25.6% improvement over best experimental observation. Through modeling and computational prediction, we provided clear medium formulation recommendations for subsequent experiments, reducing trial-and-error costs. Moreover, this method is generalizable—the established optimization framework can be extended to other microbial medium optimization problems.

2.1.2 Grow-Yeast

Abstract

To monitor Saccharomyces cerevisiae growth and obtain biomass at any time point, we established S. cerevisiae growth kinetics models using Logistic and Gompertz models. The Logistic model showed the best fitting performance for biomass data (R²=0.9937, RMSE=0.3462).

Problem

Data Source

The project uses standardized yeast fermentation experimental data, including:

• Time series: 0-48 hours, 14 measurement time points
• Biomass indicator: OD₆₀₀ optical density values (3 parallel experiments)
• Substrate concentration: Glucose concentration (g/L, 3 parallel experiments)

Considering practical situations, wet lab experiments on S. cerevisiae growth cannot be precise to every minute and second. However, in practical applications, such as calculating S. cerevisiae efficiency ratios, we may need S. cerevisiae biomass at different time points. Being able to obtain S. cerevisiae biomass at any moment becomes particularly important. Therefore, our dry lab designed the Grow-Yeast model, using limited data to transform discrete points into continuous curves for obtaining biomass at different time points.

Method

Biomass Growth Models

Logistic Growth Model (Verhulst, 1838)

The Logistic model describes biological growth limited by environmental resistance:

where: - $X(t)$: Biomass at time t - $X_0$: Initial biomass - $X_{max}$: Maximum biomass - $\mu$: Maximum specific growth rate

Characteristics: S-shaped growth curve, suitable for describing complete growth processes

Gompertz Growth Model (Gompertz, 1825)

The Gompertz model is suitable for describing processes with gradually declining growth rates:

Characteristics: Asymmetric S-shaped curve with more gradual growth rate decline

Experiments & Results

Data Preprocessing

1. Statistical calculations:
2. Mean: $\overline{x}=\frac{1}{n}{\sum }_{i=1}^n{x}_i$

3. Sample standard deviation: $s=\sqrt{\frac{1}{n-1}{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}$

4. Data quality assessment:

5. Coefficient of variation: $CV=\frac{s}{\overline{x}}\times 100\%$

6. Data completeness check and outlier identification

7. Phase division:

8. Exponential growth phase: 0-15 hours
9. Stationary phase: 15-48 hours

Visualization of Raw Experimental Data

This figure uses dual Y-axis design, simultaneously displaying biomass growth (OD₆₀₀, green) and glucose consumption (red) over time. Shaded regions identify different fermentation phases, clearly showing the transition between exponential growth and stationary phases.

Experimental Results

The figure below shows the fitting performance of Logistic and Gompertz models on biomass data, including:

• Experimental data points (dark dots): Observed values with standard deviation error bars
• Fitted curves: Different colors represent different model fitting results
• Fitting quality indicators: R² values shown in legend for direct comparison

The figure below shows fitting using the best-performing Logistic model:

Model validation:

2.1.3 Grow-Glucose

Abstract

To monitor glucose consumption during S. cerevisiae growth and obtain glucose remaining at any time, we established glucose consumption kinetics models using modified exponential decay and Logistic decay models. The modified exponential decay model showed the best fitting performance for biomass data (R²=0.955).

Problem

Data Source

The project uses standardized yeast fermentation experimental data, including:

• Time series: 0-48 hours, 14 measurement time points
• Substrate concentration: Glucose concentration (g/L, 3 parallel experiments)

Problem Description

Similar to Grow-Yeast, we hope to obtain glucose remaining at any time point. Glucose remaining and when glucose is depleted are crucial for our project, as S. cerevisiae only begins producing LL-37 after glucose depletion. Therefore, our dry lab designed the Grow-Glucose model, using limited data to transform discrete points into continuous curves for obtaining glucose remaining at different time points.

Method

1. Modified Exponential Decay Model

Considering different consumption rate differences in fermentation phases:

where: - $S_0$: Initial substrate concentration - $k_1$: Early consumption rate constant - $k_2$: Late consumption rate constant - $t_{switch}$: Transition time point

2. Logistic Decay Model

Describing S-shaped characteristics of substrate consumption:

where: - $S_{min}$: Minimum substrate concentration - $k$: Consumption rate constant - $n$: Shape parameter

Experiments & Results

The figure below shows fitting performance of modified exponential decay and Logistic decay models on glucose consumption:

The figure below shows fitting using the best-performing modified exponential decay model:

Part 3: Molecular Level Design and Optimization

3.1 CytoGuard Model

Abstract

CytoGuard is an innovative deep learning framework specifically designed to predict the biological activity of Antimicrobial Peptides (AMPs). This model integrates feature representations from multiple pre-trained protein language models (ESM-2, Ankh, ProtT5) and captures high-order structural dependencies in sequences through Hypergraph Neural Networks (HGNNs). The model employs dynamic k-mer selection mechanisms and attention fusion strategies, achieving excellent performance on the test set: Spearman correlation coefficient of 0.8543, Pearson correlation coefficient of 0.9105, RMSE of 0.1806, and R² of 0.8153.

Problem

Antimicrobial peptides, as essential components of the innate immune system, have tremendous potential in combating bacterial resistance (Hancock & Sahl, 2006; Mahlapuu et al., 2016), with LL-37, as the only human-derived antimicrobial peptide, holding exceptional research potential. What properties does LL-37 possess, and how can we evaluate whether this is a "good" antimicrobial peptide? Traditional methods naturally involve constructing antimicrobial peptide expression systems, from strain selection, cultivation to separation and purification, or direct chemical synthesis. The obtained antimicrobial peptides then require antimicrobial activity determination through inhibition zone experiments or dilution plating methods. Evaluating other physicochemical properties requires even more experiments. Traditional experiments are time-consuming, labor-intensive, and costly (Fjell et al., 2012). In today's era of rapid computational development, can we design a computational pipeline to learn from existing antimicrobial peptide data and predict the activity and physicochemical properties of unseen antimicrobial peptides? The answer is affirmative, but existing machine learning methods face the following challenges:

1. Sequence Complexity: Antimicrobial peptide sequences vary in length with complex amino acid combinations
2. Feature Representation: Traditional feature engineering struggles to capture deep semantic information in sequences
3. Structural Dependencies: Lack of modeling for high-order structural relationships in sequences
4. Data Sparsity: Relatively limited high-quality annotated data

To address these challenges and efficiently and accurately predict the properties of unknown antimicrobial peptides, we designed the CytoGuard antimicrobial peptide activity prediction model.

Method

Process Flow

Multi-Model Embedding Representation

Given an antimicrobial peptide sequence $S=\{s_1,s_2,\dots ,s_L\}$, where $L$ is the sequence length, we extract features using three renowned pre-trained protein language models (Rives et al., 2021; Lin et al., 2023; Elnaggar et al., 2022):

ESM-2 Embedding:

Ankh Embedding:

ProtT5 Embedding:

where $d_{\text{esm2}}=1280$, $d_{\text{ankh}}=768$, $d_{\text{prott5}}=1024$.

Through feature extraction with protein large language models, we achieve high-dimensional feature extraction of antimicrobial peptides, with each model aligned in dimensions for subsequent data processing.

Before feature extraction, we fine-tune on a 10K deduplicated antimicrobial peptide dataset to improve model performance on antimicrobial peptides. We also tested non-fine-tuned models; see the Experiment section for comparison.

Attention Mechanism Multi-Model Fusion

We employ an attention mechanism (Bahdanau et al., 2015; Vaswani et al., 2017) to fuse multiple embedding representations:

Projection Layer:

Attention Weight Calculation:

Fused Features:

Hypergraph Construction and TF-IDF Weighting

For a given $k$ value, we construct hypergraph $𝒢=(𝒱,ℰ,𝐖)$ (Feng et al., 2021):

Node Set: $𝒱=\{v_1,v_2,\dots ,v_L\}$, corresponding to each position in the sequence.

Hyperedge Set: $ℰ=\{e_1,e_2,\dots ,e_{L-k+1}\}$, each hyperedge $e_i$ connects positions $\{i,i+1,\dots ,i+k-1\}$.

Edge Weights (based on TF-IDF) (Salton & Buckley, 1988):

where:

Hypergraph Laplacian Matrix:

Algorithm pseudocode:

Hypergraph Attention Mechanism

CytoGuard employs multi-head hypergraph attention mechanism:

Query, Key, Value Transformation:

Attention Score Calculation:

Output:

The hypergraph Laplacian matrix serves as a structural bias term, guiding the attention mechanism to focus on important connections in the hypergraph structure.

Algorithm pseudocode:

Dynamic k-mer Selection

To adaptively select optimal k-mer combinations, we designed a dynamic k-mer selection mechanism:

Global Feature Extraction:

k-mer Weight Calculation:

where $\tau$ is the temperature parameter, $\mathit{\beta }\in {ℝ}^{|K|}$, $K=\{2,3,4,5\}$.

Loss Function Design

CytoGuard employs a combined loss function with three components:

Mean Squared Error Loss:

Mean Absolute Error Loss:

Ranking Loss:

Total Loss:

where ${\lambda }_1=0.5$, ${\lambda }_2=0.3$, ${\lambda }_3=0.2$.

Experiments & Results

Dataset

The dataset is divided into training, test, and validation sets, all containing AMP and non-AMP sequences. AMP sequences are primarily sourced from PepVAE with their minimal inhibitory concentration (MIC) labels against E.coli, totaling 3,265 AMPs with annotated MIC values. Non-AMPs are 3,265 amino acid sequences without antimicrobial activity selected from Uniprot. Additionally, we collected nearly 10K deduplicated antimicrobial peptide sequences from APD3 (Wang et al., 2016), DRAMP, DBAASP (Pirtskhalava et al., 2021), etc., for fine-tuning pre-trained protein language models.

Comparison of Fine-tuned vs Non-fine-tuned Protein Language Models

Blue line represents fine-tuned, green line represents non-fine-tuned

Training Process Comparison

Training convergence speed comparison shows fine-tuned models converge faster than non-fine-tuned:

CytoGuard Model Results

Final performance on test set:

Metric	Value	Interpretation
Spearman Correlation	0.8543	Predicted rankings highly consistent with true values
Pearson Correlation	0.9105	Strong linear correlation
RMSE	0.1806	Small root mean square error
MAE	0.0786	Very small mean absolute error
R²	0.9053	Explains 90.5% of variance

Model performance visualization:

Multi-Model Fusion Effect - Ablation Study

Model Combination	Spearman	RMSE
ESM-2 only	0.7892	0.2134
Ankh only	0.7456	0.2301
ProtT5 only	0.7123	0.2456
ESM-2 + Ankh	0.8234	0.1934
All three	0.8543	0.1806

Selection Strategy Comparison - Comparative Experiment

Strategy	Spearman	RMSE
Fixed k=3	0.8201	0.2012
Fixed k=4	0.8156	0.2034
Uniform weights	0.8334	0.1887
Dynamic selection	0.8543	0.1806

Attention Visualization

Through attention weight visualization, we discovered:

1. Multi-head attention captures sequence patterns at different levels
2. Dynamic k-mer weights tend to select combinations of $k=3$ and $k=4$
3. Hypergraph structure effectively models local sequence dependencies

Uncertainty Estimation

Model output includes prediction uncertainty, providing confidence assessment for practical applications:

• High confidence predictions: uncertainty $<0.1$
• Medium confidence predictions: $0.1\le$ uncertainty $<0.2$
• Low confidence predictions: uncertainty $\ge 0.2$

Conclusion

CytoGuard significantly improves antimicrobial peptide activity prediction accuracy through innovative hypergraph attention mechanisms and multi-model fusion strategies. The excellent performance achieved on the test set demonstrates the method's effectiveness, outperforming previous deep learning approaches for AMP prediction (Veltri et al., 2018; Chung et al., 2020). This work provides new technical solutions for computational biology and drug discovery fields, with important theoretical value and practical significance.

Future work will focus on further improving the model's generalization ability and computational efficiency, and exploring applications in broader protein function prediction tasks.

3.2 CytoEvolve Model

Abstract

The CytoEvolve model is a deep reinforcement learning-based antimicrobial peptide sequence optimization framework for improving and optimizing antimicrobial peptide sequences to enhance their antimicrobial activity. The framework primarily includes: (1) an attention mechanism-based policy network (Mutator) integrated with Diffusion architecture for selecting amino acid mutation sites; (2) a fine-tuned Ankh protein language model for generating amino acid substitutions; (3) CytoGuard for evaluating antimicrobial activity. By optimizing policy network parameters through the REINFORCE algorithm, the system can iteratively improve peptide sequences to maximize predicted antimicrobial activity scores. The framework employs experience replay mechanisms and early stopping strategies, effectively balancing exploration and exploitation, achieving effective evolution from existing AMPs, signal peptides, or random sequences to highly active antimicrobial peptides.

Model Workflow

Problem

Wet lab experiments revealed that the original LL-37's antimicrobial duration is only about 8 hours, with slightly insufficient antimicrobial activity. Facing this dilemma, we hope to obtain LL-37 variants that can improve the deficiencies of the original sequence. However, traditional experimental methods often involve manual mutation induction with low success rates and high time costs (Das et al., 2021). While computational design has low costs, it also faces the following challenges:

1. Vast sequence space: For a peptide of length L, the number of possible sequences is 20^L, with the search space growing exponentially
2. Difficult activity prediction: The nonlinear relationship between antimicrobial activity and sequence is complex, making it difficult to establish accurate structure-activity relationships
3. High experimental validation costs: Biological experimental validation is time-consuming and expensive, requiring computational methods to pre-screen candidate sequences
4. Multi-objective optimization: Need to simultaneously consider multiple properties including antimicrobial activity, cytotoxicity, and stability

To address existing dilemmas and challenges, our dry lab designed the CytoEvolve model to generate more stable LL-37 variants with higher antimicrobial activity.

Method

Modeling Analysis

Let the antimicrobial peptide sequence be $𝐬=(s_1,s_2,...,s_L)$, where $s_i\in 𝒜$ represents the amino acid at position i, and $𝒜$ is the set of 20 natural amino acids. The optimization objective can be expressed as:

where $f(𝐬)$ is the antimicrobial activity evaluation function. Due to direct optimization difficulties, we transform it into a Markov Decision Process (MDP):

• State space $𝒮$: Current peptide sequence
• Action space $𝒜$: Selection of mutation sites and amino acid substitutions
• Reward function $R(s,a)$: Activity score based on CytoGuard predictor
• Policy function ${\pi }_{\theta }(a|s)$: Probability distribution of selecting actions given state

Policy Network (Mutator)

The policy network is designed based on attention mechanisms to learn optimal mutation site selection strategies:

where $𝐩\in [0,1{]}^L$ represents the probability distribution for each site being selected for mutation.

Network structure includes:

• Embedding layer: $𝐄=\text{Embedding}(\text{input-id})$, dimension $(L,L)$
• Attention mechanism:

• Probability output: $𝐩=\text{Softmax}(𝐀[:,:,0])$

Sequence Generation Model

We employ a Discrete Diffusion Model (Austin et al., 2021; Sohl-Dickstein et al., 2015) for iterative sequence generation. The model gradually transforms the original sequence $s_0$ into pure noise (e.g., fully masked sequence) $s_T$ through a predefined forward process over T time steps.

The core is a trained denoising network $f_{\theta }$ that learns to reverse this process: given a noisy sequence $s_t$ at any time step $t$, it predicts the most likely original sequence $s_0$. The model's optimization objective is to minimize prediction loss:

where t is uniformly sampled from {1,...,T}, and $s_t$ is the sequence after t steps of noise addition from $s_0$.

The generation process starts from a fully random or masked sequence $s_T$ and gradually recovers a structurally clear target sequence $s_0$ through T iterative applications of the denoising network $f_{\theta }$.

Diffusion Steps: T=200 Noise Schedule: Cosine Schedule Max Length: $L_{max}=41$

Activity Evaluation (CytoGuard)

The CytoGuard predictor is based on hypergraph neural networks, constructing k-gram features as hypergraph structures:

where: - Node set $𝒱$: Ankh embedding representations of amino acid residues - Hyperedge set $ℰ$: k-gram subsequences (k=2,3,4)

Hypergraph convolution operation:

where: - $𝐁\in \{0,1{\}}^{|𝒱|\times |ℰ|}$: Incidence matrix - ${𝐃}_v$, ${𝐃}_e$: Node and hyperedge degree matrices - ${𝐖}_1^{(l)}$, ${𝐖}_2^{(l)}$: Learnable weight matrices

TF-IDF weights enhance important k-gram contributions:

REINFORCE Algorithm (Williams, 1992)

We optimize policy network parameters $\theta$ using policy gradient methods:

In implementation, gradient estimation is:

where: - ${\ell }_i$: Log-likelihood of the i-th sample - $r_i$: Corresponding reward value

Experience Replay Mechanism

To improve sample efficiency, we introduce experience replay buffer $𝒟$:

During each training step, the loss function combines current batch and historical experience:

Buffer management strategy: 1. Deduplication: Remove duplicate sequences 2. Sorting: Sort by score in descending order 3. Truncation: Keep top $M_{max}=200$ high-scoring samples

Main Reward Function

Reward function designed based on CytoGuard predicted logMIC values:

where $\hat{y}$ is the predicted normalized antimicrobial activity.

Sequence Diversity Penalty

To avoid repeatedly generating identical sequences, we introduce history penalty mechanism:

Experiments & Results

Hyperparameter Configuration

• Learning rate: $\alpha ={10}^{-3}$
• Batch size: 16
• Training steps: 10
• Iterations per step: 8
• Early stopping threshold: 20 steps without improvement

Loss Function and Optimizer

Custom negative log-likelihood loss:

Optimizer uses Adam algorithm (Kingma & Ba, 2015):

Here is the pseudocode for Reinforcement Learning and Diffusion Model algorithms.

Experimental Results

Facing the challenges of high experimental validation costs and time-consuming biological experiments, dry and wet labs collaborated. The dry lab further validated and screened generated sequences, narrowing candidates to the four best-performing variants, while the wet lab used D2P methods for synthesis and validation, further reducing experimental costs.

Finally, the dry lab's LL-37 variants labeled as Variant-1 and Variant-2 showed stronger antimicrobial activity compared to the original LL-37 sequence. However, from experimental data, Variant-2's duration was lower than Variant-1 and the original LL-37 sequence, showing strong initial antimicrobial activity but reduced activity at 3 hours.

Conclusions

CytoEvolve constructed an end-to-end antimicrobial peptide (AMP) optimization framework, with its core being the first organic combination of Discrete Diffusion Models for sequence generation with Reinforcement Learning. The framework utilizes the diffusion model's powerful generative capabilities to explore vast sequence spaces, creating diverse candidate peptides; simultaneously, a hypergraph neural network-based activity predictor serves as a reward function, efficiently guiding and optimizing sequence generation direction through reinforcement learning strategies (Schulman et al., 2017). This method not only significantly improves computational efficiency but also discovers sequence-function relationships difficult to find through traditional methods (Müller et al., 2018), providing a new computational paradigm for rational design of functional macromolecules. Although the system currently has limitations in sequence length and multi-objective optimization, the framework has shown tremendous potential in LL-37 and other antimicrobial peptide optimization, providing new methods for subsequent innovative drug discovery, protein engineering, and synthetic biology fields.

Conclusion

CytoFlow demonstrates that the future of peptide engineering lies not in isolated computational tools, but in integrated systems that unify sequence design, activity prediction, and production optimization. Our framework has not only achieved significant improvements in LL-37 engineering but also established new standards for computational methods in synthetic biology.

Through the synergistic combination of reinforcement learning, hypergraph neural networks, and fermentation modeling, we created a system that learns, adapts, and improves with each experimental cycle. The enhanced variant activity we achieved is just the beginning—CytoFlow lays the foundation for a new era of rational peptide design.

As we open-source CytoFlow to the iGEM community and beyond, we envision a future where any team can rapidly engineer peptides for therapeutic, industrial, or research applications. The cell factory (Cytopia) is no longer a distant dream but an achievable reality, powered by the computational framework we have developed.

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The CytoFlow framework represents the culmination of intensive computational and experimental work by the Jiangnan-China iGEM team. We thank our advisors, collaborators, and the broader iGEM community for their support in realizing this vision.

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