KINDLE: Knowledge-Guided Distillation for Prior-Free Gene Regulatory Network Inference

We sincerely appreciate your thoughtful and valuable feedback. We will address the concerns and questions point by point in the following responses.

Question 1

"W" is an important variable to evaluate the causality aspect of prediction, but was not explicitly specified in experiments. An ablation on W would really help to compare causal prediction ability to baselines.

Our response

We apologize for the oversight of not explicitly specifying the variable $W$ in the experiments. During the KINDLE training process, we conducted experiments with five distinct values of $W$ (1, 2, 4, 8, and 16). Among these, $W = 16$ yielded the optimal results, which are the results reported in the paper. We will add a clarification regarding the setting of $W$ in Lines 291-296 to enhance reader comprehension.

Question 2

Gaussian RBF distillation outperforms other losses but requires careful tuning of λ (kernel width). No analysis shows robustness to λ variation.

Our response

We wish to emphasize that prior to applying the Gaussian RBF kernel, the input features underwent standardization ($\mu = 0$, $\sigma = 1$). This preprocessing step substantially mitigates the model's sensitivity to $\lambda$ by ensuring distances in the feature space are on comparable scales. We will add clarification regarding the $\lambda$ setting in Lines 291-296 to enhance reader comprehension.

Question 3

What happens if we set $T=1$ and $W=1$ in the equations and some of the experiments? How does this affect the output and efficiency of the model?

Our response

Setting both $T$ and $W$ to 1 enables the inference of a GRN for each individual cell, thereby capturing single-cell resolution dynamic GRNs. Specifically, since each cell is assigned a pseudotime, each time step corresponds to a single cell. Under the configuration where $T = 1$ and $W = 1$, KINDLE takes the gene expression profile of the cell at the preceding pseudotime step as input and predicts the expression profile of the subsequent cell. Consequently, the model effectively learns the GRN associated with the preceding cell. This approach allows us to infer the GRN for every cell along the developmental trajectory. By temporally aligning the GRNs inferred for each cell, we can observe the dynamic evolution of GRNs throughout development. For instance, focusing on the regulatory interaction between Gene A and Gene B, their inferred regulation strength within each cell-specific GRN varies. This enables the reconstruction of the temporal trajectory of the regulatory strength for this gene pair, allowing observation of up- or down-regulation at specific developmental phases, thereby yielding deeper mechanistic insights into underlying molecular processes.

As noted in our response to Question 1, we evaluated five distinct values for $W$ (1, 2, 4, 8, and 16). However, we observed that the performance achieved with $T = 1$ and $W = 1$ was inferior to that obtained when both parameters were set to 16. We attribute this primarily to technical limitations inherent in single-cell RNA sequencing, which introduce significant noise and bias into the gene expression data. A key challenge is data sparsity, often manifested as dropout events (genes with actual expression that are erroneously recorded as zero counts due to insufficient sequencing depth). When $T$ and $W$ are both set to 1, this noise and sparsity disproportionately impair model performance. In contrast, increasing the number of input cells processed by the model (e.g., setting $T$ and $W$ to 16) mitigates these effects by effectively averaging out stochastic noise. This leads to enhanced model robustness and optimal performance. We will provide a more detailed explanation regarding the impact of $T$ and $W$ settings on model behavior in Lines 297-315 to improve reader comprehension.

Question 4

In what manner does KINDLE manage to detect gene interactions that are not included in the prior knowledge dataset?

Our response

We precisely employ privileged-feature distillation to ensure KINDLE detects gene interactions beyond those included in the prior knowledge. Specifically, prior-based methods constrain the model to learn only within the $K$ edges provided by the prior knowledge, precluding the inference of gene interactions out of prior. To leverage the prior knowledge while overcoming this fundamental limitation, we adopt a distillation strategy. The teacher model incorporates the prior network as input, which acts as a mask within the Transformer's self-attention mechanism. This mask restricts attention computation exclusively to the $K$ edges specified by the prior knowledge. The knowledge learned by the teacher model from the prior is then distilled into the student model. Critically, the student model does not receive the prior knowledge as input. Instead, it learns features transferred from the teacher model. Furthermore, the self-attention computation within the student model operates without any masking mechanism (refer to the difference in the spatial layers between the teacher and student models in Figure 2). This enables the student model to compute interactions between all possible gene pairs rather than be restricted in the $K$ edges from prior. Thus, while learning the features distilled from the teacher, the student model simultaneously retains the capacity to detect gene interactions absent from the prior knowledge, thereby achieving high inference accuracy and resolving the inherent limitation of prior-based methods.

Question 5

Could you elaborate on the process of chunking the T time steps? What criteria or methodology are used for this chunking?

Our response

We apologize for the omission of a detailed description regarding the process of chunking the $T$ time steps. We will now provide a comprehensive explanation of this procedure. let $G \in \mathbb{R}^{N \times M}$ denotes the temporal single-cell expression matrix, where $N$ represents temporally ordered cellular states and $M$ is the number of genes. our time series data $G = [\mathbf{e}_1,\ldots,\mathbf{e}_N]^T$ possesses the temporal relationships of genes during the differentiation process as we map each cell to a pseudotime (each cell corresponds to a single time step), $\mathbf{e}_i \in \mathbb{R}^{M}$ represents the gene expression at the $i$-th time step. After that, we split $G$ into dataset $\mathcal{D} = ((\mathbf{X}_i,\mathbf{Y}_i)|i = 1,\ldots,L)$, where $\mathbf{X}_i$ are input samples, $\mathbf{Y}_i$ are the ground truth associated to each sample and $L$ is the number of samples. This yields the assignments that $\mathbf{X}_i \coloneqq G[i:i+T,:]$ and $\mathbf{Y}_i \coloneqq G[i+T:i+T+W,:]$, where $G[a:b,:]$ denotes the row submatrix from index $a$ to $b-1$, capturing $T$ and $W$ consecutive cells respectively. In conclusion, we construct input $\mathbf{X}$ and ground truth $\mathbf{Y}$ through sliding-window sampling on the temporally ordered cell matrix $G$, utilizing adjacent windows of length $T$ and $W$ respectively.

Question 6

How many GPU hours were required for training KINDLE? How does the computational cost of KINDLE compare to other baseline methods in terms of efficiency and resource consumption?

Our response

When $T$ and $W$ are set to 16, KINDLE requires an average of 20 minutes to complete 30 training epochs across all four datasets on an 80GB NVIDIA A100 GPU, with total GPU memory consumption of 30GB. KINDLE is more efficient compared to prior-based baselines CEFCON and Celloracle, while maintaining comparable runtime to NetREX. Specifically, CEFCON employs a graph neural network architecture that incurs higher computational complexity than KINDLE's Transformer framework and the requirement to compute both a real network and a false network for contrastive learning substantially increases its training time (approximately 1 hour). Celloracle's execution time is often prolonged due to the computationally intensive process of constructing prior networks from scATAC-seq data, which can take several hours to days. Additionally, its GRN inference relies on iterating through each gene to perform ridge regression, resulting in low efficiency.

Regarding memory usage, KINDLE exhibits comparable but marginally higher GPU memory consumption than the other methods. This is attributable to the simultaneous loading and computation of both teacher and student models during training. We acknowledge this limitation entails a risk of memory overflow when processing large-scale datasets. To mitigate this, we plan to explore memory-optimized attention implementations (e.g., Flash Attention) in future optimization of KINDLE.

Question 7

A visualization of which regulatory insights the teacher transfers to the student would be helpful.

Our response

We agree that visualizing the features transferred from the teacher to the student model would enhance reader comprehension. However, under the current official regulations, we are not permitted to upload experimental results such as images or videos. We commit to making these visualizations available once permission is granted.

We hope the responses provided above adequately address the reviewer's concerns. If there are any aspects that remain unclear, please do not hesitate to contact us further, we remain fully available to provide additional details.

We appreciate the reviewer's insightful questions. We will address them below by clarifying the nature of the feature and describing the visualization approach.

1. What is the feature transferred from the teacher to the student?

As formalized in Equation (4), the distillation loss constrains the relationship between the teacher's output $f\_{\theta\_{T}}(\mathbf{G}\_{1:T})$ and the student's output $f\_{\theta\_{S}}(\mathbf{G}\_{1:T})$. Teacher model incorporates a spatial layer that computes an $M×M$ attention matrix ($M$ is the number of genes). This matrix quantifies attention scores between gene pairs, representing regulatory strength within the GRN context. During self-attention computation, this matrix is multiplied by the value tensor $V$ to generate the final outputs $f\_{\theta\_{T}}(\mathbf{G}\_{1:T})$ (see pseudocode, page 21, lines 13-15 for detailed information). This attention matrix is referred to the transferred feature. Crucially, within the teacher model, this matrix integrates prior knowledge via a masking mechanism, enabling the learning of comprehensive gene-gene regulatory relationships guided by this prior. It thereby encodes inter-gene dependencies and directs the model’s predictions of future gene expression values. Calculation of the distillation loss between $f\_{\theta\_{T}}(\mathbf{G}\_{1:T})$ and $f\_{\theta\_{S}}(\mathbf{G}\_{1:T})$ indirectly transfers this feature (specifically, the prior-informed attention patterns) from teacher to student.

2. How to visualize the feature transfer?

To investigate how the feature transferred from the teacher influences the student, we extract the attention matrix $A\_{T}$ and $A\_{S}$ from the spatial layer of teacher and student model, and employ the following visualization methods:

• Heatmap: We generate separate heatmaps for $A\_{T}$, $A\_{S}$, and their difference matrix $A\_{S} - A\_{T}$. Visual inspection reveals that $A\_{T}$ and $A\_{S}$ exhibit broadly similar patterns. The difference heatmap shows extensive regions of minimal deviation (visualized as white), indicating successful transfer of the teacher's prior-informed attention patterns to the student model. Conversely, localized areas of higher deviation (visualized as red) reflect regulatory relationships learned independently by the student, which lie outside the scope of the prior knowledge.
• Scatter Plot: We extract the corresponding attention scores from both matrices and generate a scatter plot with $A\_{T}$ on the x-axis and $A\_{S}$ on the y-axis. Each point represents the attention score for a specific gene pair $(i, j)$. This visualization reveals that a large majority of points cluster tightly around $y = x$. This demonstrates that the student has effectively learned the regulatory pattern for these gene pairs directly from the teacher. Points deviating significantly from $y = x$ represent regulatory relationships learned independently by the student, not covered by the prior knowledge.

We sincerely appreciate your insightful feedback, which has significantly strengthened our work. We hope the responses provided comprehensively address the reviewer's concerns. Should any aspects require further clarification, we remain available to provide additional details upon request. If you find we have successfully addressed your concerns, we would be grateful for your reconsideration of our manuscript. Thanks a lot!

We are deeply grateful to the reviewer for your recognition of our manuscript. We have carefully read your thoughtful and valuable feedback and will provide point-by-point responses to address your concerns and questions.

Regarding the references for quadratic scaling in lines 31-33, we primarily drew upon BEELINE [1] and a comprehensive review on GRN inference [2]. BEELINE establishes a benchmark framework for GRN evaluation and proposes various metrics to assess the accuracy, robustness, and computational efficiency of GRN inference methods. The review article provides a systematic examination of the field, encompassing single-modal and multi-modal inference approaches, downstream GRN analyses, as well as current limitations and future research directions.

Both references offer authoritative summaries of the GRN inference landscape, delivering valuable insights into methodological approaches, persistent challenges, and evaluation strategies within the field. To strengthen reader comprehension, we will explicitly add citations for these two articles in lines 31-33.

[1] Aditya Pratapa, Amogh P Jalihal, Jeffrey N Law, Aditya Bharadwaj, and TM Murali. Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data. Nature methods, 17(2):147–154, 2020.

[2] Pau Badia-i Mompel, Lorna Wessels, Sophia Müller-Dott, Rémi Trimbour, Ricardo O Ramirez Flores, Ricard Argelaguet, and Julio Saez-Rodriguez. Gene regulatory network inference in the era of single-cell multi-omics. Nature Reviews Genetics, 24(11):739–754, 2023.

We hope the responses provided above adequately address the reviewer's concerns. If there are any aspects that remain unclear, please do not hesitate to contact us further, we remain fully available to provide additional details.

We are deeply grateful to the reviewer for your recognition of our manuscript. We have carefully read your thoughtful and valuable feedback, and will provide point-by-point responses below to address your concerns and questions.

Question 1

How does prior information help in the framework? Or what process is to be adapted to minimize the potential bias distillation process?

Our response

1. The prior information utilized in our framework is compiled from over 50 public data sources, consolidating regulatory pairs extracted from extensive experimental studies and literature. Within the transformer architecture, this prior functions as an attention mask during self-attention computation. It explicitly constrains the attention mechanism to focus solely on edges documented in the prior knowledge, while suppressing computation for irrelevant gene pairs. Through this guided attention mechanism, the teacher model develops a global understanding of gene regulatory relationships. The features learned under this prior guidance are subsequently distilled into the student model, enabling the latter to maintain high predictive performance without explicit prior constraints during inference.
2. During experimentation, we observed that gene expression data exhibits inherent sparsity primarily attributable to technical limitations of sequencing protocols (e.g., dropout events where expressed genes yield zero counts). This sparsity introduces systematic biases in raw expression values. As both teacher and student models take these expression profiles as input during distillation, the technical biases become progressively amplified throughout the knowledge transfer process, ultimately compromising model performance. To mitigate this potential bias propagation, we propose applying imputation algorithms as a preprocessing step. These methods estimate biologically plausible expression values for technical zeros, thereby recovering expression levels obscured by sequencing artifacts, reducing systematic bias in input data, and ultimately enhancing the overall accuracy of the distillation process.

Question 2

In common biological experiments, there are some conditions with a few replicates for each condition. Please discuss the potential adoption of the current framework to this type of data.

Our response

Thank you for raising this important point regarding the applicability of KINDLE to datasets with limited replicates, which is indeed a common scenario in biological experiments. We propose that KINDLE can adapt to such data through three potential solutions:

1. Take advantage of consolidated prior knowledge

The teacher model is trained on a consolidated prior network integrating experimentally validated regulatory relationships sourced from over 50 public databases and literature resources. Critically, these foundational datasets originate from large-scale experimental studies inherently possessing substantial replicate samples. When inferring GRNs for a target condition with sparse replicates, the scale and biological relevance of this integrated prior knowledge become paramount. By distilling patterns learned from these evidence-rich, high-replicate sources, the teacher model provides the student model with a robust foundation of general regulatory principles. This significantly reduces the student model's reliance on extensive replicates, effectively serving as a powerful biologically grounded regularizer to compensate for data sparsity in the target condition.

2. Leverage appropriate data augmentation strategies

1. Standard augmentation: Applying standard data augmentation techniques to the limited expression profiles, such as adding biologically plausible noise.
2. Generative model-based augmentation: Utilizing generative models (e.g., VAE, GAN and diffusion models) trained on relevant expression data to synthesize plausible additional expression profiles.

It should be noted that employing data augmentation requires careful validation to ensure biological fidelity and avoid introducing artifacts. Nevertheless, these strategies represent potential avenues within the KINDLE framework to further mitigate limitations imposed by scarce replicates.

3. Transfer knowledge from biologically similar cell types

During teacher model training, data from biologically similar cell types exhibiting abundant replicate samples can be utilized. Knowledge distilled from these related, replicate-rich datasets is encoded within the teacher model and subsequently transferred to the student model. The student model then undergoes lightweight finetuning using the limited target-condition replicates. This process mirrors the "pretraining & finetuning" paradigm, enabling effective adaptation of the downstream model to specific data-scarce scenarios.

Question 3

There are more improvement in terms of AUPRC, compared with AUROC. Can the authors explain what could be the reason?

Our response

We thank the reviewer for raising this point. We wish to emphasize that in Lines 592-602, we discuss why AUPRC is a more robust metric compared to AUROC. Specifically, let $\mathcal{E}\_{potential}$ represents the set of all explorable gene pairs and $\mathcal{E}\_{true}$ denotes the edges present in the ground truth network. As detailed in Table 2, which presents the distribution of positive and negative labels across the four datasets, we observe severe label imbalance in all datasets, with negative labels exceeding 99% of the total. In such scenarios characterized by extreme class imbalance, AUROC disproportionately emphasizes the majority class (negative edges). This occurs because AUROC relies heavily on the false positive rate ($FPR = \frac{FP}{(FP + TN)}$). When $\mathcal{E}\_{true} \leq \mathcal{E}\_{potential}$, the sum $FP + TN \approx |\mathcal{E}\_{potential}|$, rendering AUROC overly optimistic in evaluating model performance. Conversely, as analyzed in the literature (i.e., The Relationship Between Precision-Recall and ROC Curves), AUPRC is better equipped to handle such imbalanced scenarios. Therefore, AUPRC serves as a more robust metric for assessing model performance under severe label imbalance than AUROC.

Consequently, the significant improvements demonstrated by KINDLE in AUPRC (compared to the more modest gains in AUROC) provide stronger evidence for its superior performance over the baseline models.

We hope the responses provided above adequately address the reviewer's concerns. If there are any aspects that remain unclear, please do not hesitate to contact us further, we remain fully available to provide additional details.

We sincerely appreciate your thoughtful and valuable feedback. We will address the concerns and questions point by point in the following responses.

Question 1

Though leveraging the idea of privileged distillation information is interesting, why do we have to distill that? In terms of the recommendation system, privileged features are not seen during the inference, since we have to recommend items before knowing the click rate. However, I didn’t observe the necessity of using it in regulatory network inference. In my understanding, we can still observe the prior network during inference. Is there any offline/online setting? Or any other reasons?

Our response

1. Clarification on prior knowledge usage during inference

We emphasize that our inference phase does not incorporate prior knowledge, consistent with the reviewer's observation that "privileged features are not seen during inference" in recommendation systems. As detailed in Lines 54–56 of our manuscript, the student model is trained without prior knowledge. Further, Lines 56–58 explicitly state that during inference, the student model exclusively accepts gene expression data as input to infer a prior-free GRN. Additionally, Figure 2 visually demonstrates that prior knowledge is solely provided to the teacher model, not the student model, and only gene expression matrices are input during inference.

2. Rationale for knowledge distillation

The motivation for distillation is elaborated in Lines 30–43 and Figure 1. Specifically, Inferring GRNs without priors involves an exponentially large search space (with $M$ genes, there are $M*(M−1)$ gene pairs to evaluate). While prior-based methods reduce this space to the $K$ edges provided in the prior knowledge to improve model performance, they introduce two critical issues:

• The accuracy of the prior knowledge network will severely affect the model's performance, which depends on the overlap between the prior knowledge and the ground truth.
• The inferred GRN is strictly limited to a subset of the $K$ prior edges, preventing discovery of real regulatory relationships outside this set. Given that priors are empirical and often contain high false-positive rates, this approach inherently caps model performance.

Therefore, we propose utilizing a distillation approach to address the limitations inherent in prior-based methods. Our teacher model incorporates a prior knowledge network to learn comprehensive gene regulatory relationships. Subsequently, these learned features are input into the student model. Crucially, the student model operates without requiring prior knowledge input. Instead, it learns the gene regulatory relationships by distilling knowledge from the features provided by the teacher model, thereby enabling prior-free GRN inference. The self-attention computation within the student model operates without any masking mechanism (refer to the difference in the spatial layers between the teacher and student models in Figure 2). This enables the student model to compute interactions between all possible gene pairs rather than be restricted in the $K$ edges from prior. Since the student model does not receive prior knowledge input, it inherently avoids the two problems associated with prior networks. Furthermore, by employing the distillation strategy, we ensure the student model maintains robust inference accuracy.

Question 2

Following the above, if we look at Equation (4), it consists of both prediction loss and distillation loss. If the prior network is available during the inference, could the distillation loss be simply replaced by a regularization term that directly minimizes the distance between student learned A and prior M? It would be helpful if the authors could clarify whether they have any justification—either intuitive, theoretical, or empirical—for preferring distillation over direct regularization. Is there any additional information beyond the prior network M that is transferred from the teacher model during distillation?

Our response

1. Clarification on prior knowledge usage during inference

As elaborated in our response to Question 1, the prior knowledge network is unavailable during the inference phase. The rationale for employing the distillation loss is also detailed therein.

2. Justification for preferring distillation over direct regularization

The regularization term suggested by the reviewers, which directly minimizes the distance between the adjacency matrix $A$ learned by the student model and the prior matrix $M$, represents a valid approach for model optimization. However, we contend that the regularization term is unable to address the fundamental limitations inherent in prior-based methods (Lines 38-43). Specifically, the teacher model incorporates the prior knowledge network as an input during training, it utilizes this prior as a mask within the Transformer's self-attention mechanism. This mask constrains the attention calculation exclusively to gene pairs specified within the prior network. Consequently, if the student model's learned $A$ is forced to approximate the prior $M$, the resulting regulatory relationships would remain confined to the $K$ edges defined by the prior. This confinement does not resolve the core limitations of prior-based methods. Precisely for this reason, we adopted the distillation strategy. The student model does not receive the prior as input, instead, it learns from the features distilled by the teacher model. This approach enables the beneficial propagation of prior knowledge to the student while simultaneously circumventing the constraints imposed by the prior's limitations.

3. Temporal causality will be transferred to student model

Beyond the prior knowledge network $M$, the temporal causal relationships between genes learned by the teacher model are also distilled to the student model. The mechanism by which the teacher model learns these temporal causal associations through the temporal layer is detailed in Lines 50-53 and 113-116. Specifically, for time point $t$, a temporal mask is enforced to constrain each gene to attend only to information from preceding time steps ($< t$). Within the self-attention mechanism, attention weights between genes across these historical time steps are computed. Based on these weights, information from all time steps prior to $t$ undergoes weighted aggregation. This enables the representation of a gene at the current time step $t$ to integrate relevant historical context, thereby learning temporal dependencies among genes and ultimately leading to more accurate predictions of future gene expression.

Question 3

In line 189-190, the author mentions that they select top-k from the adjacent matrix, and k is exactly the same as the ground truth. Is there any risk of information leakage, since the users have to first know the number of correct connections? Do other baselines rely on this setting? If setting a threshold (e.g., 0.5), does that still work well?

Our response

We emphasize that selecting the top $K$ edges constitutes the standard procedure for obtaining the final inferred GRN within the GRN inference field and all baseline methods rely on this setting. Crucially, this procedure does not introduce information leakage. The selection occurs solely during the final inference stage, the value of $K$ itself is not incorporated into the model's training process. Its function is analogous to setting the number of clusters in clustering algorithms, which determines the final output structure without influencing the core learning algorithm.

Question 4

In terms of the writing, Equation (4) should be more clear. Inside the regulatory distillation loss, both $\theta_{S}$ and $\theta_{T}$ use same input, but teacher model should include an additional term representing prior network. In line 97, “hypnosis” should be “hypothesis”?

Our response

We sincerely thank the reviewer for identifying these two points. Specifically, we acknowledge that Equation (4) should explicitly reflect the teacher model's requirement for the prior knowledge network as an additional input, and we confirm that the term in Line 97 should correctly be "hypothesis". We apologize for these errors and confirm both will be rectified in the final manuscript.

We hope the responses provided above adequately address the reviewer's concerns. If there are any aspects that remain unclear, please do not hesitate to contact us further, we remain fully available to provide additional details.

We thank the reviewer for raising this point. We wish to emphasize that restricting the student model from using a prior network because its introduction will hurt model performance.

As highlighted, utilizing a prior network confines the model's exploration to the $K$ edges provided by the prior. Here, "model performance" specifically refers to its capability to discover novel regulatory relationships, a core competency critically valued within the GRN field for assessing a model's practical utility. Prior knowledge networks represent regulatory relationships already extensively validated through repeated experiments and literature reports. In real-world biological applications, however, scientists are fundamentally more interested in identifying novel regulatory relationships. This enables the discovery of new key transcription factors or target genes influencing diseases or developmental processes, thereby revealing unprecedented biological mechanisms, explaining the origins of complex phenotypes, or providing novel targets and intervention strategies for disease diagnosis and therapy.

For example, analyzing gene expression data from cancer cells might reveal, through GRN inference, a previously unknown transcription factor regulating a novel pro-oncogenic gene network. This discovery could subsequently be validated through knockdown experiments targeting the new transcription factor to assess its therapeutic potential, ultimately leading to the development of precision therapies targeting this pathway.

Relying solely on inference within validated prior knowledge inherently constrains a model's ability to discover novel regulatory interactions. Our distillation strategy is designed precisely to enable the student model to learn from prior knowledge while simultaneously retaining and enhancing its capacity to uncover new regulatory relationships.

We sincerely appreciate your insightful feedback, which has significantly strengthened our work. We hope the responses provided comprehensively address the reviewer's concerns. Should any aspects require further clarification, we remain available to provide additional details upon request. If we have addressed your concerns, we would be grateful for your reconsideration of our manuscript. Thanks!

We hope the responses provided adequately address the reviewer's concerns. We wonder if there are any aspects that remain unclear, if so, we remain fully available to provide additional details to enhance the manuscript. Thanks for your time and valuable feedback!