Overview of DeepTX framework. (A) Cells stimulated by DNA damaging drugs cause damage to the DNA double strands, which will slow down or even stop the movement of RNA Pol II on the DNA double strands. Changes in the state of RNA Pol II movement will lead to changes in the kinetics of gene expression bursts (including burst frequency and burst size), which will affect cell fate decisions such as apoptosis, differentiation, and survival. (B) The input to the DeepTX framework is scRNA-seq data, and the output is the burst kinetics corresponding to each gene. The core of the DeepTX inference framework is a hierarchical model, which is a mixture of the stationary distribution of the mechanism model solved by the neural network (Step 1) and the binomial distribution followed by the sequencing process. This hierarchical model is used to infer the out dynamics parameters corresponding to the data distribution (Step 2).

Solving TXmodel using deep learning. (A) With the TXmodel and corresponding model parameters θ, we obtain a steady distribution using the SSA simulation and the moment statistics employing binomial moment theory. These results are compared with the distribution and moment statistics of the neural network’s output to calculate the neural network’s loss value. The parameters of the neural network are optimized using gradient descent until convergence is achieved, indicating attainment of optimal parameters. (B) Comparison between SSA results and DeepTX prediction results for four sets of test parameters. The gray histograms represent the distribution simulated by SSA, while the red curve indicates the distribution predicted by DeepTX. (C) Verification results of the moment statistics predicted by DeepTX and the true moments on a test set containing 1000 elements. (D) The loss curve during DeepTX training. The blue curve represents that the loss function is composed of KL divergence of distributions, and the red curve represents that the loss function is composed of KL divergence of distributions and statistics. (E) Box plots of the Hellinger distance between the true distribution and the predicted distribution by DeepTX of different loss types on the test set.

Inferring TXmodel from scRNA-seq data. (A) The dynamic parameters are sampled from a given prior distribution, and as input to the neural network, the solution of the corresponding dynamic model can be obtained by using this parameter. The solution of the dynamic model is mixed with the binomial distribution to obtain the model observed distribution. Loss values were obtained using the observed distribution of the data obtained from the scRNA-seq data compared to the observed distribution of the model. The loss values are optimized until convergence using gradient descent to obtain the parameters of the mechanism model and the posterior distribution of its parameters. (B) The scatters represent the real BS and BF values of the SSA synthetic set parameters, and the depth of the color represents the error between the inferred BS (BF) and the true BS (BF). (C, D) The blue solid line represents the edge density of the burst kinetics of the model, and the red dashed line represents the true value. (E) The marginal density for the five parameters of the model, where the red dashed line represents the true value.

Burst size enhancer delays cell cycle. (A) Density map of BS of genes treated with IdU drugs compared to BS of genes not treated with drugs. Green dots represent up-regulated BS differential genes. (B) Schematic representation of the simultaneous enhancement of both BS and noise of a gene accompanied by the mean value of the gene remaining unchanged after IdU drug treatment. The blue plane represents the relationship between burst kinetics (BS and BF) and the mean. The orange plane represents the relationship between mean and noise. (C) Schematic diagram of the mechanism by which IdU drug treatment affects the mitotic cell cycle transition of cells via DNA damage. (D) Gene GO enrichment analysis is performed on the green dots of BS in (A) to obtain enrichment pathway diagram. (E, F) Pathways obtained by GSEA enrichment analysis of BS of genes.

Low dose 5FU treatment induces cell apoptosis by enhancing burst frequency. (A) Comparison of gene bursting kinetics and statistics between control and 10-dose 5FU treated cells. (B) Density map of inferred burst size. (C) Volcano map of the fold changes (FC) of inferred burst size between control and 10-dose 5FU treated cells. (D) Mechanism diagram of apoptosis induced by low-dose 5FU drug treatment. (E) Gene GO enrichment analysis is performed on the green dots of BS in (A) to obtain enrichment pathway diagram.

High dose 5FU treatment may promotes cell drug resistance by altering burst frequency. (A) Density map of inferred burst size. (B) Volcano map of the fold changes (FC) of inferred burst size between control and 50-dose 5FU treated cells. (C) Schematic diagram of the mechanism by which 5FU drug treatment induces cells to produce antioxidant properties and then continue to survive. (D) Gene GO enrichment analysis is performed on the green dots of BS in (A) to obtain enrichment pathway diagram. (E) UMAP of G0 arrest quality score (QS) of control and 50-dose 5FU treated cells. (F) Proportion of G0 arrested (drug-resistant) and cycling (non-resistant) cells. (G) Comparison of gene bursting kinetics and statistics of G0 arrested genes between control and 50-dose 5FU treated cells.