Uncovering the dynamic effects of DEX treatment on lung cancer by integrating bioinformatic inference and multiscale modeling of scRNA-seq and proteomics data

Abstract

Lung cancer is one of the leading causes of cancer-related death, with a five-year survival rate of 18%. It is a priority for us to understand the underlying mechanisms affecting lung cancer therapeutics’ implementation and effectiveness. In this study, we combine the power of Bioinformatics and Systems Biology to comprehensively uncover functional and signaling pathways of drug treatment using bioinformatics inference and multiscale modeling of both scRNA-seq data and proteomics data. Based on a time series of lung adenocarcinoma derived A549 cells after DEX treatment, we first identified the differentially expressed genes (DEGs) in those lung cancer cells. Through the interrogation of regulatory network of those DEGs, we identified key hub genes including TGFβ, MYC, and SMAD3 varied underlie DEX treatment. Further gene set enrichment analysis revealed the TGFβ signaling pathway as the top enriched term. Those genes involved in the TGFβ pathway and their crosstalk with the ERBB pathway presented a strong survival prognosis in clinical lung cancer samples. With the basis of biological validation and literature-based curation, a multiscale model of tumor regulation centered on both TGFβ-induced and ERBB-amplified signaling pathways was developed to characterize the dynamic effects of DEX therapy on lung cancer cells. Our simulation results were well matched to available data of SMAD2, FOXO3, TGFβ1, and TGFβR1 over the time course. Moreover, we provided predictions of different doses to illustrate the trend and therapeutic potential of DEX treatment. The innovative and cross-disciplinary approach can be further applied to other computational studies in tumorigenesis and oncotherapy. We released the approach as a user-friendly tool named BIMM (Bioinformatic Inference and Multiscale Modeling), with all the key features available at https://github.com/chenm19/BIMM.

1. Introduction

Lung cancer remains the most common cause of cancer-related death, which occupies 18% of mortality worldwide for all 36 cancers and with over 1.8 million deaths expected globally in 2021. The high lung cancer fatality rate is primarily attributed to the large proportion of patients (57%) diagnosed with metastatic disease, for which the five-year relative survival rate is 18% [1]. Therefore, effective therapeutic strategies are in urgent need. Glucocorticoids (GCs), which are commonly used to treat autoimmune disorders, are continually investigated as a potential strategy since they can be employed to treat inflammation and enhance the anti-tumor effect of drugs in chemotherapy [2,3]. As one of the most widely used synthetic glucocorticoids, Dexamethasone (DEX) has shown anti-cancer efficacy and anti-estrogenic activity in human non-small cell lung cancer (NSCLC) [4], but former computational studies have merely been done regarding coronavirus disease-19 rather than NSCLC [5]. Besides, DEX possesses extraordinary cost-effectiveness and far fewer side effects than virtually all other clinically widely used NSCLC therapy strategies, such as Tagrisso and Avastin, whereby further study can be made to testify its efficacy. Tumor-relevant subsystems and drug targets have been explored both in vivo [6,7] and in silico [8,9], however, the detailed DEX-dependent signaling pathways are yet understood.

Single-cell RNA sequencing (scRNA-seq) technology provides unprecedented opportunities for understanding cellular complexity [10-14]. Transcriptomic profiling in individual cells has revealed a variety of cell types and subpopulations. scRNA-seq technology not only provides profound insights into cellular composition but also allows for the interrogation of cellular hierarchies and the identification of cells transitioning between states [15-17], such as development and differentiation. Single-cell RNA sequencing is at the forefront of phenotyping cells with high resolution and has been widely applied in research and revealed the molecular determinants of human diseases [11]. For example, Welch J. et al. revealed the putative mechanisms of cell-type-specific regulation within their defined mouse cortical cell types [18]. Nativio R. et al. [19] identified molecular pathways underlying late-onset Alzheimer’s disease. Bian S. et al. [20] reconstructed genetic lineages and traced the transcriptomic dynamics through single-cell profiling. These studies highlight the significance of single-cell technology in accelerating the investigations of gene regulation and illuminating the causes and underlying mechanisms of human diseases, especially cancers [21].

Recently, physical tumor-microenvironment interaction [22], cell-cell communication [23,24], and tumorigenesis signaling cascades [25] have been explored by scRNA-seq data-based approaches. However, bioinformatics approaches rely on scRNA-seq data to infer gene regulatory networks, which only address “mechanisms” by proxy (i.e., correlations) without providing the underlying information (i.e., how genes interact with one another via activation, inhibition, or binding pathways). Mathematical modeling based on experiments is a central approach of systems biology, which has been applied to investigate complex signaling transduction pathways of tumorigenesis [26-28]. Indeed, modeling signaling transduction and crosstalk gives insights into the regulatory networks of oncogenes and the effects of anti-tumor treatments. The transforming growth factor β (TGFβ) –induced SMAD signaling is a quintessential pathway to regulate cancer progression [29], which is one core study object of modeling [30]. Systems biologists have also investigated crosstalk and feedback loops among tumor signaling transduction pathways to understand tumorigenesis and treatments, such as the negative feedback within the ERBB-amplified tumor proliferation pathway [26]. Although some detailed local mechanisms of the TGFβ-induced pathway, ERBB-amplified proliferation pathway, and downstream targets have been investigated by previous mathematical models for some cancers, the global connections of these two tumor regulatory pathways are rarely elucidated. Additionally, the effect of DEX has been explored for pancreatic cancer [31]; however, the molecular mechanisms of DEX treatment in lung cancer are yet clear.

In this study, we will integrate the knowledge and approaches from both Bioinformatics and Systems Biology domains to uncover the underlying molecular mechanisms of DEX therapy on lung cancer cells. With the collected lung adenocarcinoma derived A549 cells after DEX treatment, we will explore essential differentially expressed genes and their involved regulation pathways after DEX. Furthermore, we develop a multiscale model to investigate the underlying mechanisms of antitumor drugs and examine the regulatory networks obtained by the above bioinformatical analysis. The systematic approach using Bioinformatic Inference and Multiscale Modeling (BIMM) based on single-cell transcriptomics and proteomics data can better delineate the dynamic and longitudinal signaling pathways mediated by DEX in lung cancer cells.

2. Materials and methods

A schematic illustration of our work is shown in Fig. 1, including the identification of signaling pathways, kinetic modeling, and drug prediction. We first analyzed the scRNA-seq data to identify the variable genes and the involved interaction network. The network involved genes were used to infer intracellular signaling pathways associated with clinical significance. We further built the mathematical model based on the signaling pathways to mechanistically understand the dynamic regulations of drug response involved in lung cancer cells.

Fig. 1.

Schematic illustration of integrated Bioinformatics (anatomizing, reconstruction) and Systems Biology (integration, modeling) analysis on drug effect. (A) Analyze the scRNA-seq data of lung adenocarcinoma derived A549 cells with dexamethasone (DEX) treatment, then categorize genes into two types based on the pharmacokinetic properties of either drug sensitive or drug resistant. (B) Ground on the cell type-specific gene expression, then construct the gene regulatory multilayer network with crosstalk and feedback loops. (C) The important genes from network topology, biological knowledge, and clinical significance are identified and integrated for further modeling. (D) Develop a multiscale model of interactive genes, ligands, receptors, and drugs to characterize drug response.

Bioinformatics methods.

Uniform manifold approximation and projection (UMAP) was used to visualize cell clusters. Differentially expressed genes (DEGs) were identified using the “FindMarkers” function in R package of “Seurat” [32] R package. DEGs were evaluated with the Bonferroni-adjusted p-value (adj. P < 0.05) and the absolute log2-fold-change (∣log2 FC∣ ≥0.5). To identify putative transcriptional regulators of the DEGs, we utilized the GENIE3 [33] method. Significant regulatory networks associated with the differentially expressed genes after DEX treatment were identified.

Survival analysis.

Kaplan-Meier (KM) analysis was performed using the “survival” R package (http://cran.r-project.org/web/packages/survival/index.html). Log-rank test was used to test the differences in survival curves. To determine the accuracy of specific genes in predicting patients’ overall survival, the “survivalROC” function was used to generate time-dependent ROC curves from censored survival data using the KM method, which returns the true positive, false positive, and AUC at the time point of interest. The area under the curve (AUC) of the receiver operating characteristic (ROC) was used to evaluate the prognosis of these genes.

Pathway database.

Reactome (http://www.reactome.org) was a manually curated open-data resource of human pathways and reactions, which was an archive of biological processes and a tool for discovering potential functions. Gene sets derived from the Reactome [34] pathway database was downloaded from the MSigDB Collections.

Gene set enrichment analysis.

Functional enrichment based on the Reactome pathway database was assessed by hypergeometric test, which was used to identify a priori-defined gene set that showed statistically significant differences between two given clusters. The gene set enrichment analysis was performed by the clusterProfiler package [35]. Test P values were further adjusted by Benjamini-Hochberg correction, and adjusted P values less than 0.05 were considered statistically significant.

Mathematical modeling.

To understand molecular mechanisms of DEX treatments, we constructed an overall wiring diagram (Fig. 1D) by integrating the association between the hub genes and tumor cell development (Fig. 1B) with experimental evidence as well as hypotheses (Fig. 1C). In this study, the diagram (Fig. 1D) was translated into a system of ordinary differential equations (ODEs) based on biochemical rationales to describe reactions of synthesis, degradation, phosphorylation, and dephosphorylation.

Parameter optimization.

We optimized the model parameters of the ODE system by minimizing the residual error between empirical data and simulated results. Different optimization algorithms are used and compared to find the optimal parameter set, including Genetic Algorithms, Bayesian Algorithms, and Direct search. The simulated dynamics of variables were visualized after parameterization and evaluation using available data.

Data availability.

The time-series scRNA-seq data of lung adenocarcinoma derived A549 cells with dexamethasone (DEX) treatment is profiled using the sci-CAR protocol [36], which consists of cells after 0, 1, or 3 h of 100 nM DEX treatment. The raw scRNA-seq data [36] consists of 4277 cells profiled by sciCAR and can be downloaded from GEO database [37] with the accession number GSM3271040 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSM3271040). However, these 4277 cells are mixed without clear separation regarding different treatment times (Supplementary Fig. 1). To ensure that the profiled single cells are well separated with clearly phenotype differences (i.e., the cell embedding of 0 h, 1 h, and 3 h are clearly separated), we refer to the study [38] and use their processed co-assayed A549 data and processing steps, which uses ‘‘preprocessing” function with “min.Cells = 1” and “min.Features = 200” to include cells with at least 200 gene features and include features detected in at least 1 cell. The resulting data consists of 2641 cells, with the number of cells as 583, 983, and 1075 at 0, 1, and 3 h of 100 nM DEX treatment respectively. The protein data of SMAD2 and TGFβ1 were derived from literature [39], where the protein expression images of TGFβ1 and Smad2 in A549 cells were abstracted and processed with ImageJ.

3. Results

3.1. Bioinformatic inference of key signaling pathways

The scRNA-seq data was shown with the UMAP projection (Fig. 2A), with clearly discerned cell populations (0, 1, and 3 h cells after 100 nM dexamethasone (DEX) treatment. With the scRNA-seq data, we identified the differentially expressed genes (DEGs) for each of the cell populations, which were shown in the heatmap (Fig. 2B). Specifically, we identified the DEGs at each condition (0 h, 1 h, 3 h) by comparing them to all the other cells. For example, the DEGs of cells at 0 h cells were obtained by comparing cells at 0 h with the other cells at 1 h and 3 h, using the Seurat “FindMarkers” function. DEGs were evaluated with the Bonferroni-adjusted p-value (adj. P < 0.05) and the absolute log2-foldchange (∣log2 FC∣ ≥ 0.5). The DEGs identified for 0 h and 3 h consisted of 195 and 88 genes respectively. Fig. 2B showed the Heatmap of the top 35 DEGs under three conditions for clear visualization. A full list of the DEGs was shown in Supplementary Table 1. To identify the signaling pathways and key regulators based on the DEGs, we utilized the GENIE3 method to construct a regulatory network (Fig. 2C). Notably, genes including TGFβR1, SMAD3, ERBB2, ERK, EGF, and MYC were observed as the transcriptional hub, suggesting their key roles underlie drug response. The gene set enrichment analysis of the DEGs within the transcriptional network was performed using the REACTOME pathway database (Fig. 2D). These DEGs were significantly enriched in the TGF-beta receptor complex and ERBB2 signaling pathway, highlighting the underlying functional mechanisms. These enriched biological functions suggest that the crosstalk of the TGFβ signaling pathway and ERBB signaling pathway underlie cancer cells after drug treatment. The evidence inside the TTD database [40,41] bolsters the result of our gene set enrichment analysis since the SMAD2/3 pathway identified therein makes up part of the TGFβ signaling pathway we determined.

Fig. 2.

Inference of signaling network in lung cancer cells after drug treatment. (A) UMAP visualization of A549 cells, colored by DEX treatment time (0 h, 1 h, and 3 h). (B) Heatmap visualization of differentially expressed genes (DEGs) identified under different treatment time. (C) Transcriptional regulatory network inferred based on the DEGs after DEX treatment. (D) Enriched pathways identified based on the transcriptional regulatory network.

From the scRNA-seq data, the network hub genes showed substantial variations in lung cancer cells during different time points after DEX treatment (Fig. 3A). To further characterize these genes, we collected the TCGA lung adenocarcinoma (LUAD) data and performed differential expression analysis between tumor and normal samples using DEseq2 [42]. Interestingly, the network hub genes, such as EGF and ERBB2, showed higher expression levels in tumor samples (Fig. 3B). There were no significant differences in MYC and SMAD3 between tumor and normal samples. In contrast, genes FOXO3, a transcription factor, were observed with lower expression levels in tumors than in normal samples.

Fig. 3.

Clinical prognosis and significance of network hub genes. (A) Varied expression of genes involved in both transcriptional regulatory network and enriched pathways. (B) Boxplots illustrated the differential expressions of selected genes between tumor and normal tissues. (C) Kaplan-Meier survival curves for patients with LUAD, which were stratified (binary: high versus low) for the average expression of selected genes. Log-rank test P-values were shown. The y-axis was the probability of overall survival, and the x axis was time in days. (D) Prognostic accuracy of the selected genes was evaluated by AUC of the time-dependent ROC with respect to half year and 1 year survival of LUAD patients in the TCGA dataset.

Additionally, we evaluated whether those network hub genes would impact patient survival. Remarkably, significant associations were observed between their increased expression and decreased overall survival of LUAD patients from TCGA (Fig. 3C). The statistical significance of the difference between the K-M survival curves for patients in the high-risk group (blue) and low-risk group (red) was assessed using the log-rank test, with P-values of 0.001. The high-risk group of patients had a shorter overall survival time than the low-risk group. This result suggested the prognostic roles of those network hub genes in lung cancer patients. Moreover, we also evaluated the prognostic accuracy of the network hub genes by calculating the AUC of time-dependent ROC with respect to half-year and one-year survival of lung cancer patients. The hub genes showed good prognostic accuracy based on the TCGA LUAD dataset (Fig. 3D), demonstrating that these genes possessed convincingly strong prognostic power in predicting overall the survival rates of lung cancer patients.

3.2. Multiscale modeling of tumorigenesis regulatory network

Based on the tumor-relevant genes identified by bioinformatics inference (Figs. 2C and 3C), we construct a tumorigenesis regulatory network summarized in Fig. 4, comprising the TGFβ-induced tumor suppression pathway and ERBB-amplified proliferation pathway.

Fig. 4.

Multiscale modeling of the ERBB-amplified and TGFβ-induced feedback-crosstalk module that depicts the dynamic interplay between multilayer signals in signature genes. The ligand EGF (epidermal growth factor) binds to the cell-surface receptors ERBB2, which activates the expression of MAPK1, thereby promoting tumor growth. The ligand TGFβ (transforming growth factor) binds to the cell-surface receptors TGFβ-R1, and their complex activates the phosphorylation of SMAD2/3. MAPK1 represses transcription factors MYC and FOXO3. Concurrently, SMAD2/3 inhibits MYC, which represses the circuit of MAPK1 mutually. Solid lines denote activation/inhibition of the shown genes with arrow/bar, respectively. The dashed lines denote the potential binding between DEX and ERBB2, activation on TGFβ and TGFβ-R1.

The ERBB family is one of the quintessence of tumor development regulation, which controls multiple downstream signaling pathways and transcriptions [26]. The epidermal growth factor (EGF) binds to the cell-surface receptor ErbB2 and hence stimulates the phosphorylation of ErbB2. The phosphorylated receptor pERBB2 then stimulates the RAS/MEK/ERK mitogen-activated protein kinase (MAPK) cascade, activating many transcription factors correlated with tumorigenesis [26,27,43] (Fig. 4). Therefore, the ERBB-MAPK pathway is regarded as one potential target for treating cancer. MAPK, in turn, inhibits the transcription factors FOXO and activates MYC, while MYC functions to suppress the expressions of MAPK. The negative feedback reinforces the robustness of the regulatory network (Fig. 4).

In addition, several genes involved in the TGFβ-induced pathway are differentially expressed in tumor and normal cells. The TGFβ family plays pivotal roles in regulating multiple cellular activities to regulate growth inhibition and apoptosis [28,44]. According to the TTD database [40,41], the TGFβ ligand binds to the receptor TGFβR to phosphorylate and activate the transcription factors SMAD2/3. The phosphorylated SMAD complexes are denoted as pSMAD2/3, and they can control myriad downstream transcriptions, including inhibiting the activity of MYC involved in the aforementioned ERBB-regulated pathways [28,45] (Fig. 4). The crosstalk between different pathways combined with feedback loops contributes to the robustness of tumor growth and the resistance of anti-tumor treatments.

We proposed a mathematical model to investigate the therapeutic potential of DEX. DEX has been implicated in suppressing the ERBB-amplified proliferation pathway by disturbing the activation of MAPK [46-48]. The activation of the MAPK pathway has been verified to rescue the DEX-induced cell death [47]. Therefore, MAPK functions downstream in the DEX-induced apoptosis. Here, we assumed DEX inhibits the binding between ERBB and its receptor to disturb the downstream kinase cascade (Fig. 4, left dashed line). Additionally, DEX activates the TGFβ-induced pathway to inhibit the expression of oncogene MYC [44,49]. DEX causes increased protein levels of TGFβ1 and phosphorylated SMAD2 in A549 cells [39]. We found that the gene expression level of TGFβR1 elevates with DEX treated (Fig. 3A). Taken together, DEX likely functions upstream in the TGFβ-induced pathway though the underlying mechanism is unclear. On the ground of the co-target relationship between TGFβ and TGFβR1 [40,41], we assumed that DEX amplifies the expressions of both TGFβ and its receptor (Fig. 4, right dashed lines). In this study, we integrated the ERBB-amplified tumor pathway with the TGFβ-induced signaling pathway to investigate the dynamic effect of DEX in cancer.

By converting the regulatory network (Fig. 4) into a system of ODEs (Table 1), we proposed depicting the gene regulatory relationship among A549 cells and gleaning insights into the effectiveness of different doses of DEX treatment for anti-tumor. We use hyperparameter Θ to denote the model parameters which are necessary to characterize the rate constants of synthesis, degradation, activation, inhibition, binding, and unbind, as summarized in Table 2. Both Genetic Algorithms [50] and Direct Search [51] were used to optimize the model parameters. We define the objective function as the residue error between the empirical data and simulation results over time, as follows

$$f(\Theta )=\frac{1}{nm}\sum _{i=1}^n\sum _{j=1}^m\mid y_{i,j}-{\widehat{y}}_{i,j}\mid$$

where y_i,j and ${\widehat{y}}_{i,j}$ represent the expression level of species i at time j of empirical and simulated data, respectively. The optimization problem can be then solved as

$$\text{min}f(\Theta ).$$

Table 1.

Equations of ERBB-amplified, TGFβ-induced, and DEX-related pathways.

Equations of ERBB-amplified proliferation pathway

(1) dy[EGF]/dt = ksef − kdef[EGF] − kbefeb*[EGF]*[ERBB2] + kuefeb* [EGF_ERBB2] (2) dy[ERBB2]/dt = kseb − kdeb*[ERBB2] − kbefeb*[EGF]*[ERBB2] + kuefeb*[EGF_ERBB2] − kbdgeb *[DRUG] * [ERBB2] + kudgeb * [ERBB2_DRUG] (3) dy[EGF_ERBB2]/dt = − kdefeb*[EGF_ERBB2] + kbefeb*[EGF]*[ERBB2] − kuefeb*[EGF_ERBB2] (4) dy[MAPK1]/dt = ksmk*(1 + αefeb *[EGF_ERBB2] + βmcmk /(kmmcmk + [MYC])) − kdmk*[MAPK1] (5) dy[FOXO3]/dt = ksfo*( 1 + βmkfo /(kmmkfo + [MAPK1])) − kdfo* [FOXO3] Equations of TGF-β-induced pathway (6) dy[TGFβ2]/dt = kstb*(1 + αtbdg *[DRUG]) − kdtb *[TGFβ2] − kbtbtr* [TGFβ2]*[TGFβR1] + kutbtr *[TGFβ2_TGFβR1] (7) dy[TGFβR1]/dt = kstr*(1 + αtrdg *[DRUG]) − kdtr *[TGFβR1] − kbtbtr* [TGFβ2]*[TGFβR1] + kutbtr*[TGFβ2_TGFβR1] (8) dy[TGFβ2_TGFβR1]/dt = − kdtbtr*[TGFβ2_TGFβR1] + kbtbtr *[TGFβ2]*[TGFβR1] − kutbtr*[TGFβ2_TGFβR1] (9) dy[SMAD2 /3]/dt = kssd − kdsd*[SMAD2 /3] − kphosd*(1 + αtbtr *[TGFβ2_TGFβR1])*[SMAD2 /3] + kdephosd*[pSMAD2 /3] (10) dy[pSMAD2 /3]/dt = − kdsd*[pSMAD2 /3] + kphosd*(1 + αtbtr *[TGFβ2_TGFβR1])*[SMAD2 /3] − kdephosd*[pSMAD2 /3] (11) dy[MYC]/dt = ksmc*(1 + αmkmc *[MAPK1] + βsdmc / (kmpsdmc + [pSMAD2 /3])) − kdmc*[MYC] Equations of drug-related pathway (12) dy[ERBB2_DRUG] = − kddg*[ERBB2_DRUG] + kbdgeb*[DRUG]*[ERBB2] − kudgeb*[ERBB2_DRUG] (13) dy[DRUG] = − kddg*[DRUG] − kbdgtr *[DRUG]*[TGFβR1] + kudgtr*[TGFβR1_DRUG] − kbdgeb*[DRUG]*[ERBB2] + kudgeb *[ERBB2_DRUG]

Table 2.

Parameters values.

Parameter	Value (hour−1)	Description
ksef	7.3434	Synthesis rate of EGF
kbefeb	5.8913	Rate of binding between EGF and ERBB2
kuefeb	9.5653	Rate of unbinding of EGF-ERBB2 complex
kseb	3.9093	Synthesis rate of ERBB2
ksmk	1.6673	Synthesis rate of MAPK1
ksfo	0.6638	Synthesis rate of FOXO3
kstb	8.4325	Synthesis rate of TGFβ2
kbtbtr	8.8745	Rate of binding between TGFβ2 and TGFβR1
kutbtr	8.6590	Rate of unbinding of TGFβ2-TGFβR1 complex
kbdgeb	7.5729	Rate of binding between DEX and ERBB2
kudgeb	2.4692	Rate of unbinding of DEX-ERBB2 complex
kstr	3.4431	Synthesis rate of TGFβR1
kssd	3.1049	Synthesis rate of SMAD2/3
ksmc	0.9192	Synthesis rate of MYC
kphosd	0.3535	Phosphorylation rate of SMAD2/3
kdephosd	9.6013	Dephosphorylation rate of SMAD2/3
kddg	log(2)/24	Degradation rate of DEX
kdef, kdeb, kdefeb, kdmk, kdfo, kdtb, kdtr, kdtbtr, kdsd, kdmc	1	Rate of degradation
Parameter	Dimensionless	Description
αtbtr	1.6681	Activation coefficient of TGFβ2-TGFβR1 on the phosphorylation of SMAD2/3
αtbdg	0.2660	Activation coefficient of DEX on TGFβ2
αmkmc	4.9890	Activation coefficient of MAPK1 on MYC
αtrdg	0.2824	Activation coefficient of DEX on TGFBR1
αefeb	2.8630	Activation coefficient of EGF-ERBB2 on MAPK1
βmkfo	9.3507	Inhibition coefficient of MAPK1 on FOXO3
βmcmk	4.6547	Inhibition coefficient of EGF-ERBB2 on MAPK1
βsdmc	8.3417	Inhibition coefficient of PSMAD2/3 on MYC
kmmcmk	1.8342	Inhibition rate of EGF-ERBB2 on MAPK1
kmmkfo	3.4700	Inhibition rate of MAPK1 on FOXO3
kmpsdmc	6.6297	Inhibition rate of pSMAD2/3 on MYC

Genetic Algorithm returns a better optimization result compared to Direct Search. Table 2 lists the final optimized parameters that were used for model prediction. The simulation and optimization were implemented in MATLAB.

3.3. Biological interpretation and prediction

Our model accurately simulated gene regulatory patterns and drug response after applying DEX treatment to fully developed carcinomatous A549 cells. Based on the signature genes regulatory process, we formulated a set of ODEs to model the ERBB-amplified tumor pathway (Equations 1-5 ) with TGFβ-induced signaling (Equations 6-11), as shown in Table 1. We provided 1000 h for signature genes to level off before applying the drug in our simulation to simulate DEX treatment under a constant gene state. Following the two simulated pathways, drug and drug-associated complexes can be then determined by Equations 12-13. Due to the absence of valid empirical data on EGF, ERBB2, MAPK1, and MYC, we evaluated our simulations by assessing differences between simulated drug response values of pSMAD2/3, TGFβ, FOXO3, and TGFβR1 and their empirical data – protein levels of SMAD2 and TGFβ1 [39] as well as gene expression levels of FOXO3 and TGFβR1. The numerical values of experimental observations are extracted from the dataset of A549 and shown as the red circles in Fig. 5.

Fig. 5.

(A–B) Simulated protein profiles of signature genes SMAD2 and TGFβ1 after employing one dose of DEX treatment with corresponding empirical data (red circles) obtained from A549 cells after 0 and 48 h of 100 nM DEX treatment for protein profiles (1.18 and 1.12 respectively at 48 h) (Feng et al., 2018). (C–D) Simulated expression level of signature genes FOXO3 and TGFβR1 after 0, 1, and 3 h of 100 nM DEX treatment for gene expression levels (one dose). (E) DEX level over time after one dose of DEX treatment applied to the A549 cells. Note that all expression and protein levels are scaled to one at t = 0.

The simulated drug response of pSMAD2/3, TGFβ, FOXO3, and TGFβR1 precisely matches the empirical data concerning one dose of DEX treatment well in our model. Hence, our simulation correctly captured the drug response of these signature genes with respect to DEX treatment. To be more specific:

pSMAD2/3:

SMAD2/3 are downstream genes of TGFβ signaling pathways, which can translocate into the nucleus to regulate transcriptions [28]. When DEX treatment is applied, the phosphorylation process of SMAD2/3 is activated to reduce the protein level of the oncogene. The simulated drug response of pSMAD2/3 corresponds to the trend of subsidence after surging as we expected and fits the empirical data well, for which merely has a 0.05 shortage from the empirical protein level 1.18 at 48 h after applying DEX, as shown in Fig. 5A.

TGFβ:

The treatment of DEX directly acts on TGFβ in our model, which leads to a spike right after DEX exposure. The proliferated TGFβ binds with TGFβR1 and then activates the downstream reactions (e.g., phosphorylation of SMAD2/3) in the TGFβ-induced pathway as time passes. Our simulated result of TGFβ exhibits a proper augmentation right after applying the drug (Fig. 5B), then falls back after the initial surge and remains a slightly higher level than the starting point, which is in accordance with the empirical protein level 48 h after applying DEX.

FOXO3:

The simulated expression levels of FOXO3 are consistent with the three empirical values after 0, 1, and 3 h of DEX treatment (Fig. 5C), and it conforms to the trend of falling after an initial spike. The simulated values at 1 and 3 h immaculately match the empirical results. Nevertheless, the empirical expression level (1.117) after 2 h relative to that after 1 h is slightly greater than the simulated value (1.114). The minute deficit (0.003) of our simulated expression level may ascribe to the delayed reduction of MAPK1.

TGFβR1:

The simulated expression level of TGFβR1 scarcely has a diversion from the empirical data, and as a DEX activating gene, it shows an escalating trend right after the application of DEX treatment and remains a higher expression level than the starting point (Fig. 5D).

The half-life of DEX is set as 24 h, and the metabolic rate of our simulated DEX complies with the drug level over time (Fig. 5E). Moreover, the modeling we built is convincing when predicting the drug response of the signature genes we mentioned under different doses of DEX treatment. As shown in Fig. 6, all six genes or complexes have demonstrated an increase in protein or expression level in proportion to the increment of DEX dose. The signature genes in the ERBB-amplified pathway with negative feedback show a proper spring back therein; those in the TGFβ-induced pathway with positive feedback demonstrate matching subsidence after the surge. Besides, the drug takes effect and exhausts simultaneously for different doses of DEX. As we can observe in Fig. 6, all three lines in different colors diverge and converge at nearly the same time.

Fig. 6.

(A–F) Model prediction of the response of EGF-ERBB2, MAPK1, MYC, TGFβ-TGFβR1 complex, pSMAD2/3, and FOXO3 after doubling (2x) and tripling (3x) the dose of DEX treatment.

4. Discussion

Though current cancer treatment had shown unprecedented success [52,53], the underlying mechanisms remained incompletely understood. In this study, we utilized scRNA-seq data with bioinformatics analysis to precisely characterize the temporal dynamics of variable genes in lung cancer cells following DEX treatment. With the key molecular markers associated with drug response and clinical prognosis, we then depicted the dynamic signaling pathways through mathematical modeling using both scRNA-seq data and proteomics data.

Our BIMM approach was essential for predicting cancer treatment response and better understanding the fundamental mechanisms of treatment. More importantly, our study provided an innovative and cross-disciplinary approach that could be further applied to immunotherapies and other cancer treatment, providing insights into the underlying mechanisms for improving cancer therapeutics, as well as implicating potential molecular targets for driving cancer resistance. Our BIMM approach also holds the promise to include metabolite data. For specific metabolites and related functionalities, we will use the online tool MMEASE [54] for metabolite annotation and enrichment analysis, which contributes to the multi-scale modeling and downstream interpretation.

With the scRNA-seq data at different time points after treatment, we identified the variable genes with clinical significance, accompanied by knowledge support to construct the modeling components [55]. Compared with previous scRNA-seq data-based approaches [25,56], our work identified new tumor-associated hub genes, integrated multiple components of tumorigenesis signaling pathways, and analyzed underlying molecular mechanisms in a mathematical model. We did acknowledge that our identified underlying mechanisms were not the only ones underlie treatment. Myriad crosstalk, feedback regulations, and downstream response regulators collaborate to constitute the complex regulatory network of tumorigenesis and apoptosis. However, due to the limited number of genes in this scRNA-seq data, our identified pathways were shown with the most important clues in this context. For example, we filtered the most variable genes along with the time-series data and identified the top enriched pathway compatible with our model. Additionally, though the involved genes showed significant prognostic values in discerning patient subgroups with different survival, they did not present strong AUCs in predicting patients’ survival. It is acceptable since the TCGA data is based on bulk gene expression but not single-cell level.

The comparison between experimental observation and mathematical modeling using both scRNA-seq data and proteomics data further convinces the significance of scRNA-seq data identified genes. Additionally, model prediction provides insights into the potential effects of different DEX doses in cancer cells, which can be applied to investigate the dynamics and effects of downstream regulators for tumorigenesis in future studies. For future studies, based on the proteomics data of lung cancer cells, we will identify the optimal signature and its phenotype association using the ANPELA [57] and POSREG [58] tool, which is designed to acquire such proteomic biomarkers with good reproducibility. The selected optimal signature can be evaluated using the Met- aFS method [59].

Biographies

Minghan Chen is an assistant professor in the Department of Computer Science, Wake Forest University, NC, USA. Her research focuses on computational biology and optimization.

Chunrui Xu is a PhD student in Genetics, Bioinformatics, and Computational Biology (GBCB) program, Virginia Tech. Her research focuses on systems biology.

Ziang Xu is an undergraduate student in the Department of Computer Science, Wake Forest University, NC, USA. His research focuses on multiscale modeling.

Wei He is a postdoctoral fellow at Georgetown University. His research focuses on cancer systems biology.

Haorui Zhang is an undergraduate student in the Department of Mathematics and Statistics, Wake Forest University, NC, USA. His research focuses on statistical analysis.

Jing Su is an assistant professor in the Department of Biostatistics and Health Data Science, Indiana University School of Medicine, IN, USA. His research focuses on graph artificial intelligence and machine learning in biomedical informatics and precision health.

Qianqian Song is an assistant professor in the Department of Cancer Biology, Wake Forest School of Medicine, NC, USA. Her research focuses on machine learning and deep learning in bioinformatics and precision oncology.