HiCBridge: Resolution Enhancement of Hi-C Data Using Direct Diffusion Bridge

We thank the reviewer for your time and efforts in reviewing our paper, and your constructive comments. Please see the detailed response below.

Weaknesses 1. The authors seem to have only used existing DDPM model to generate new low-resolution Hi-C data corresponding to the high-resolution ones. The authors have primarily relied on existing methods to generate the data, which, in itself, does not constitute a significant contribution. It is crucial for the authors to clearly explain the problem they aim to address and the challenges associated with it.

Please see General Comments, 1. Difference from original methods. We explored the best approach to leverage both the regression and generation capabilities of DDB and diffusion model. Various metrics show that our framework outperforms other models at Hi-C enhancement task. Additionally, our model has advantages not only in performance but also in the efficiency of Hi-C enhancement.

Weaknesses 2. The authors claim that the conventional regression models, which are based on the Mean Squared Error (MSE) loss, cause the model to regress to the mean in the target domain. This regression leads to blurring and loss of details. However, the author do not provide visual results to demonstrate this issue. The authors should elaborate on the challenges posed by the problem. Describing the difficulties and complexities associated with addressing the problem will highlight its importance and demonstrate the need for the proposed solutions.

Please see General Comments, 4. Biological Significance. We highlight the limitations of models trained with traditional MSE and GAN approaches. Our model showcases conservative reconstruction, preserving structural information without introducing artifacts that could potentially lead to misinterpretation of the reconstructed Hi-C data.

An MSE-based model tends to yield blurry output as it represents the average of all plausible reconstructions. In contrast, our approach breaks down the mapping into multiple timesteps, preventing regression to the mean. While GAN-based models excel at generating photo-realistic images by training generator and discriminator, a high level of similarity in the image domain does not necessarily ensure excellent biological reconstruction. Previous methods have incorporated various additional losses to involve biological meaning, but these approaches reduce the interpretability of the model and lead inadvertent results. Our method avoids using additional losses like perception loss or insulation loss.

Thanks for the valuable and constructive comment. For point-to-point response, see below.

Weaknesses 1. Although the application of diffusion-based methods to Hi-C is meaningful, the method seems lack of novelty. The authors should explain carefully the difference between the core method and previous Direct Diffusion Bridge.

Please see General Comments, 1. Difference from original methods. We propose the best framework for the Hi-C enhancement task through a combination of DDB and diffusion. Considering the regression performance of the DDB and the generative performance of the diffusion model at the same time, our model showed superior results on various metrics.

Weaknesses 2. I suggest the authors add comparison about memory and time consumption to help readers get a full picture of their method.

Please see General Comments, 2. Computation efficiency. Our model takes 0.16 seconds to process a single 256 $\times$ 256 Hi-C contact map and has a competitive memory requirement.

Question 1. Can you provide visualization of generated training data?

We visualized generated Hi-C data of GM12878 chromosome 13 using diffusion augmentation model in Fig. 8 in Appendix F of the revised paper. We used the generated data in order to train HiCBridge$^+$.

Question 2. During the process of enhancing resolution, new content will sprout. I am concerned whether the method will generate inrelevant or even harmful content, which may incur severe results.

Please see General Comments, 4. Biological significance. We verified HiCBridge recovers structural information without misleading contents.

We thank the reviewer for the constructive and valuable comments. Please see the detailed response below.

Weaknesses 1. Show its robustness to data biases and hyperparameter variations.

Please see General Comments 3. Robustness to data biases. We compared the ratio of data augmentation, as a hyperparameter, to verified the robustness of HiCBridge$^+$. While augmented data is beneficial for the generalization of HiCBridge, a high proportion of augmented data can pose challenges, contingent on data biases.

Weaknesses 2. A thorough comparative analysis against a wider array of both deep learning and traditional approaches. And by testing across diverse Hi-C datasets to ensure its generalizability.

We obtained enhanced Hi-C contact matices by Gaussian smoothing as a traditional method. We employed 2D Gaussian distribution with kernel size $n = 17$ and $\sigma_x = \sigma_y = 3$. The table below reveals that, although the traditional method demonstrates competitive results, our approach consistently outperforms all matrices. These findings underscore the superiority of our method.

Weaknesses 3. Elucidating the biological significance of the resolution enhancement through detailed case studies.

Please see General Comments, 4. Biological Significance. We compared our model with traditional MSE and GAN methods, and found that our model preserves structural information without introducing artifacts that can be misleading.

Weaknesses 4. Computational efficiency, an essential consideration for large-scale genomic data analysis.

Please see General Comments, 2. Computational Efficiency. About 250 million lengths of chromosome 1 can be represented by about 430 $\times$ 256 $\times$ 256 Hi-C contact maps, which our model takes about 70 seconds to process.

Weaknesses 5. An in-depth consideration of the method's limitations, such as the effects of sequencing depth and data noise.

It is important to note that our model is exclusively trained on inter-chromosomal connections, so a different method is needed to handle contact maps between chromosomes. Additionally, our models are limited to resolution enhancement for a bin size of 10kb. Lastly, biased data augmentation can potentially degrade the generalization of the model, as discussed in Weakness 1, where the results of our model are shown to be influenced by data bias. We have added these as our limitation in Appendix C of the revised paper.

Finally, the reviewer is kindly reminded that the data noise is mostly originated from shallow sequence depth and one of the main goals of our study is to enhancement data quality from relatively shallow sequencing depth using direct diffusion bridge. The low-resolution Hi-C data we trained corresponds to a sequence depth of about 1/16 of the high-resolution data. In this paper, our model has shown robust performance for different resolutions (1/16, 1/50 and 1/100) and different cell types; K562 (about 1/14), IMR90 (about 1/10).

We would like to thank the reviewer for the constructive comments and the thorough feedback. For point-to-point response, see below.

Weaknesses 1. The contribution of this paper is limited. The proposed HiCBridge directly borrows idea from the Direct Diffusion Bridge without any improvement. While the proposed diffusion-based data augmentation (Algorithm 1 and 2) is also trivial. It seems like the paper tends to apply the existing method to the new task, but lack of novelty.

Please see General Comments, 1. Difference from original methods along with the revised paper. We highlight that we found the optimal combination of DDB and diffusion for Hi-C enhancement task, which cannot be regarded as trivial given the importance of the Hi-C data processing.

Weaknesses 2. It is not clear how the Algorithm 1 can be used to generate the low-resolution data as your target distribution is based on x0 (high-resolution Hi-C data). Please check whether the x0 in Algorithm 1 should be x1.

Thanks for pointing out the typo. We have fixed our Algorithm 1 accordingly.

Weaknesses 3. It seems like the diffusion augmentation is unusable in higher resolution cases for inferior performance, according to the Table 4.

If our interpretation of the reviewer's comment is accurate, the aim is to clarify the subpar performance of HiCBridge$^+$ at extremely low resolutions (1/50 and 1/100). As highlighted in the General Comments, 3. Robustness to data biases, our analysis suggests that biased data augmentation holds the potential to compromise the model's generalization. While the incorporation of generated low-resolution data contributes to the overall generalization of HiCBridge, an excessive bias with such data may lead to a deterioration in HiCBridge$^+$'s performance across diverse Hi-C datasets. It is crucial to note that the data compared in Table 4 of our paper consists of downsampled data rather than real low-resolution data, presenting a distribution distinct from the one the model was trained on [1]. This finding offers a plausible explanation for the observed reduction in the generalizability of HiCBridge$^+$ compared to HiCBridge, especially at extremely low-resolution settings.

[1] A comprehensive evaluation of generalizability of deep-learning based Hi-C resolution improvement methods, Murtaza et al., Biorxiv, 2022

As the deadline for the Reviewer-Author discussion phase is fast approaching (there is only a day left), we respectfully ask whether we have addressed your questions and concerns adequately.

Dear reviewer LnZX,

This is a kind reminder as the deadline is imminent. We believe that we have addressed the concerns that you have raised. Specifically,

1. We have distinguished our work from previous papers by finding a proper combination of diffusion model and direct diffusion bridge for Hi-C enhancement to establish an effective and efficient framework.

2. We have corrected Algorithm 1, which was incorrectly stated.

3. We have explained that HiCBridge$^+$ underperforms at extremely low resolutions. An experiment in Table 11 in Appendix B showed that diffusion augmentation can suffer performance degradation due to shifts in the data distribution.

We would like to gently remind you that the end of the discussion period is imminent. We would appreciate it if you could let us know whether our comments addressed your concerns.

Best regards, Authors

Thank you for your detailed feedback and the encouraging comments. Please see the detailed response below.

Weaknesses 1. The robustness of the model against various datasets and its performance under different conditions (such as varying levels of input resolution) would need thorough examination.

We conducted a series of experiments to elucidate the generalization abilities of our models. We evaluated standard visual metrics, HiCRep and TAD Insulation score on different resolution (GM12878 from GSM1551551), different cell type (HMEC from GSE63525 and GSM1551610) and another species (CH12-LX from GSE63525 and GSM1551640). In the Table 12 in Appendix E of the revised paper, our models also reconstructed visual information and TAD boundaries on all Hi-C datasets. HMEC, with a resolution of about 1/20, poses a noisier dataset than our training data, and CH12-LX, being a mouse lymphoma cell, introduces a cross-species challenge. We supposed that these data shifts might contribute to the variation in SSIM or HiCRep performance in our models.

Weaknesses 2. The paper would benefi from a more detailed comparison with state-of-the-art models. This includes not only performance metrics but also computational efficiency, scalability, and the amount of training data required.

Please see General Comments, 2. Computation efficiency.

Weaknesses 3. The model's generalizability to different types of Hi-C data, such as those from various species or cells in different states, should be assessed. If the model has only been tested on a narrow range of data, its practical applicability could be limited.

As explained in the response to In Weakness 1, we verified our model’s generalizability at different cell type (HMEC; Human Mammary Epithelial Cells) and different species (CH12-LX; Mouse Lymphoma Cells).

Weaknesses 4. The paper should address the interpretability of the HiCBridge model. Understanding how the model makes its predictions is crucial, particularly in genomic studies where the biological implications of the findings are as important as the findings themselves.

To understand how the model handles a given input, we analyzed the attention map of the self-attention module in the first layer of HiCBridge$^+$. As depicted in Fig.7 in Appendix D of the revised paper, we observed that each head emphasized a distinct region: head 0 allocates more attention to diagonal bins, head 1 highlights regions slightly off the diagonals, head 2 is dedicated to a 0.5Mb range of bins, and head 3 focuses on bins in more distant regions. Accordingly, our network can understand semantic structure of the contact map, a desired property for Hi-C data processing.