The coronavirus disease 2019 (COVID-19) pandemic caused by the coronavirus strain has had massive global impact, and has interrupted economic and social activity. The daily confirmed COVID-19 cases in Saudi Arabia are shown to be affected by some explanatory variables that are recorded daily: recovered COVID-19 cases, critical cases, daily active cases, tests per million, curfew hours, maximal temperatures, maximal relative humidity, maximal wind speed, and maximal pressure. Restrictions applied by the Saudi Arabia government due to the COVID-19 outbreak, from the suspension of Umrah and flights, and the lockdown of some cities with a curfew are based on information about COVID-15. The aim of the paper is to propose some predictive regression models similar to generalized linear models (GLMs) for fitting COVID-19 data in Saudi Arabia to analyze, forecast, and extract meaningful information that helps decision makers. In this direction, we propose some regression models on the basis of inverted exponential distribution (IE-Reg), Bayesian (BReg) and empirical Bayesian regression (EBReg) models for use in conjunction with inverted exponential distribution (IE-BReg and IE-EBReg). In all approaches, we use the logarithm (log) link function, gamma prior and two loss functions in the Bayesian approach, namely, the zero-one and LINEX loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey's bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IE-Reg, IE-BReg, and IE-EBReg using some criteria, such as Akaike's information criterion (AIC), Bayesian information criterion (BIC), deviance (D), and mean squared error (MSE). Finally, we apply the collected data of the daily confirmed from March 23 - June 21, 2020 with the corresponding explanatory variables to the theoretical findings. IE-EBReg shows good model for the COVID-19 cases in Saudi Arabia compared with the other models
Citation: Sarah R. Al-Dawsari, Khalaf S. Sultan. Modeling of daily confirmed Saudi COVID-19 cases using inverted exponential regression[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2303-2330. doi: 10.3934/mbe.2021117
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The coronavirus disease 2019 (COVID-19) pandemic caused by the coronavirus strain has had massive global impact, and has interrupted economic and social activity. The daily confirmed COVID-19 cases in Saudi Arabia are shown to be affected by some explanatory variables that are recorded daily: recovered COVID-19 cases, critical cases, daily active cases, tests per million, curfew hours, maximal temperatures, maximal relative humidity, maximal wind speed, and maximal pressure. Restrictions applied by the Saudi Arabia government due to the COVID-19 outbreak, from the suspension of Umrah and flights, and the lockdown of some cities with a curfew are based on information about COVID-15. The aim of the paper is to propose some predictive regression models similar to generalized linear models (GLMs) for fitting COVID-19 data in Saudi Arabia to analyze, forecast, and extract meaningful information that helps decision makers. In this direction, we propose some regression models on the basis of inverted exponential distribution (IE-Reg), Bayesian (BReg) and empirical Bayesian regression (EBReg) models for use in conjunction with inverted exponential distribution (IE-BReg and IE-EBReg). In all approaches, we use the logarithm (log) link function, gamma prior and two loss functions in the Bayesian approach, namely, the zero-one and LINEX loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey's bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IE-Reg, IE-BReg, and IE-EBReg using some criteria, such as Akaike's information criterion (AIC), Bayesian information criterion (BIC), deviance (D), and mean squared error (MSE). Finally, we apply the collected data of the daily confirmed from March 23 - June 21, 2020 with the corresponding explanatory variables to the theoretical findings. IE-EBReg shows good model for the COVID-19 cases in Saudi Arabia compared with the other models
Abdominal aortic aneurysm (AAA) has a high prevalence in western countries and leads to a large number of cardiovascular deaths [1]. Aneurysm is defined as an increase in artery diameter by no less than 1.5 times. Aneurysm can appear in any part of arteries in the human body, with AAA being the most common subtype [2]. AAA will cause artery rupture and continuous bleeding, eventually leading to deaths. The mortality rate of AAA after artery rupture is 85~90% [3]. If the diameter of artery is more than 5.5 cm in AAA, surgery is usually performed to prevent artery rupture. AAA is a disease with complex pathological mechanisms, therefore, it is challenging to develop efficient therapeutic strategies to prevent or treat AAA [4]. Although several lines of evidence have suggested that AAA is a multi-gene and multi-factor disease, its pathogenesis is not completely clear [5].
The very association of arteriosclerosis (AS) and AAA may be up for debate. Previous studies have also indicated that arteriosclerosis (AS) is likely negatively associated with the growth of AAA but positively correlated with its presence [6–8]. It is widely believed that AAA is merely a consequence/manifestation of AS, but this notion is yet to be fully substantiated. Although revascularization and risk factor control methods are extensively utilized for the treatment of AS-related AAA clinically, the disease is still the most common cause of death. Therefore, in the era of precision medicine, novel strategies are urgently needed to prevent and treat AS-related AAA. However, the biomarkers and therapeutic targets for AS and AAA are yet to be sufficiently explored. Besides, a comprehensive analysis of the associations between AS and AAA at the transcriptomic level is still lacking.
Herein, we utilized gene expression profiles retrieved from the Gene Expression Omnibus (GEO) database to identify differentially-expressed genes (DEGs) in both AS and AAA patients. The physiopathological functions of these DEGs were then characterized bioinformatically to discover novel diagnostic biomarkers and treatment targets for AS-related AAA.
This research was supervised and supported by the research ethics committee of the Tianjin Medical University General Hospital. Moreover, this study was conducted in accordance with the declaration of Helsinki. The participants were granted informed consent prior to their enrollments in our study. Artery samples were collected from popliteal arteries of 4 AS and abdominal aortas of 4 AAA patients treated with lower limb amputation and artificial vessel replacement, respectively. Normal artery specimens from visceral arteries of 4 healthy donors were also collected as controls. After arterial resection, total RNA was extracted from tissues rapidly frozen in liquid nitrogen.
Two GEO (https://www.ncbi.nlm.nih.gov/geo/) datasets, namely GSE100927 (deposited by Marja) and GSE7084 (deposited by Gerard) were employed in this research. The GSE100927 dataset contains 104 samples, including 69 atherosclerotic peripheral artery samples and 35 control samples; while the GSE7084 dataset includes gene expression profiles of 15 abdominal aortas samples obtained from 7 AAA patients and 8 healthy controls.
We utilized the "affy", "affyPLM", and "limma" packages in R (http://www.bioconductor.org/packages/release/bioc/html/affy.html) [9] to analyze the GSE100927 and GSE7084 datasets. The data were background-adjusted, quantile-normalized, subjected to probe summarization, and log2 transformed, to generate a robust multi-array average (RMA) and log-transformed perfect match (PM) and mismatch (MM) probes. The initial p-values were adjusted by employing the Benjamini-Hochberg method, and fold changes (FCs) were computed on the basis of the false discovery rate (FDR). A gene was considered as a DEG if it had a |log2 FC| > 1 and an adjusted p value < 0.05. Subsequently, DEGs shared by the GSE100927 and GSE7084 datasets were isolated, based on which a Venn diagram was established using Venny 2.1 (http://bioinfogp.cnb.csic.es/tools/venny/index.html).
To annotate the functions of DEGs shared by the GSE100927 and GSE7084 datasets, we performed gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses on them using R. We also used the "clusterProfiler" software in R for gene set enrichment analysis (GSEA) [10]. All visualizations were processed by the "ggplot2" package in R.
The comprehensive information of the hub proteins retrieved from STRING (https://string-db.org/), an online database for the retrieval of inter-gene and inter-protein interactions, was utilized to establish a PPI network, which was visualized using the Cytoscape software (Version 3.7.2) [11]. Subsequently, most important modules within the PPI network were identified by the "Molecular Complex Detection (MCODE)" function of Cytoscape with the following identification criteria: an MCODE score of more than 5, degree and node score cutoff values of 2 and 0.2, respectively, and a maximum depth of 100.
Based on the cutoff criteria of degree computed by the "cytoHubba" function of Cytoscape, genes that played important roles in the PPI network were the hub genes. The DEGs were scored by the 12 scoring methods of the "cytoHubba" function, and the top ten genes with the highest scores in each scoring method were registered. Based on the 12 ranking lists obtained, upset charts were constructed and the number of times that a gene was registered was counted.
We extracted total RNA from the above-mentioned artery samples using the TRIzol reagent (TransGen Biotech, China). The total RNA was then reversely transcribed into cDNA using a real-time PCR mRNA detection kit (TIANGEN Biotech, China) before PCR amplification on a Roche Photorecycler 480 Real-time PCR system. The reaction consisted of the following steps: one step of 95˚C for 30 sec and 40 rounds of 95˚C for 5 sec and 60˚C for 20 sec. GAPDH was included as the internal reference. Relative transcript levels of target genes were determined by the 2-ΔΔCt method. The PCR primers were designed and synthesized by AoKe Dingsheng (Beijing, China) and their sequences are shown in Table 1.
| Gene | Primer sequence (5′→3′) | |
| SPI1 | F: GTGCCCTATGACACGGATCTA | R: AGTCCCAGTAATGGTCGCTAT |
| TYROBP | F: ACTGAGACCGAGTCGCCTTAT | R: ATACGGCCTCTGTGTGTTGAG |
| TLR2 | F: ATCCTCCAATCAGGCTTCTCT | R: GGACAGGTCAAGGCTTTTTACA |
| FCER1G | F: AGCAGTGGTCTTGCTCTTACT | R: TGCCTTTCGCACTTGGATCTT |
| MMP9 | F: TGTACCGCTATGGTTACACTCG | R: GGCAGGGACAGTTGCTTCT |
| GAPDH | F: ATGGCTACAGCAACAGGGT | R: TTATGGGGTCTGGGATGG |
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GraphPad Prism 8 was used to compare data from test and control samples. To analyze the clinical characteristics of AS patients, AAA patients and healthy controls, the quantitative data are expressed as means ± standard deviations (SDs). The Student's t-test and Wilcoxon rank sum test were implemented for analysis of data as appropriate. P values less than 0.05 were indicative of statistical significance. All statistical analyses in this study were conducted with the SPSS 26.0 software (IBM, USA).
Microarray data from both GEO datasets were normalized and subjected to principal component analysis (PCA) for evaluating differences in biological characteristics between samples (Figure 1A, B), thereby ensuring data accuracy. Genes with a |log2 FC| > 1 and an adjusted p value < 0.05 were identified using the "Limma" package in R. Compared with controls, 324 and 477 overexpressed and 113 and 370 underexpressed genes were identified in the peripheral artery samples of AS and AAA patients in the GSE100927 and GSE7084 datasets, respectively (Figure 2). The DEGs are also presented by volcano plots and heat maps shown in Figure 1C–F. The DEGs shared by the GSE100927 and GSE7084 datasets were exhibited by a Venn diagram (Figure 3A), including 169 upregulated and 37 downregulated DEGs.
The functions of the identified DEGs were explored via GO and KEGG enrichment analyses in R. The results suggested that the DEGs shared by the GSE100927 and GSE7084 datasets were significantly enriched with biological processes (BP) terms of "neutrophil activation", "immune response", and "neutrophil degranulation", a molecular function (MF) term of "actin binding", as well as a cellular components (CC) term of "secretory granule membrane" in the GO analysis (Figure 3B). Our KEGG analysis suggested that these shared DEGs were associated with 10 pathways, such as "lipid and atherosclerosis", "phagosome", and "osteoclast differentiation" (Figure 3C).
To characterize the interactions between proteins encoded by these shared DEGs, a PPI network was built by STRING (Version 11.0) and visualized by Cytoscape (Figure 4A). The network consisted of 190 nodes (representing 190 proteins) and 1715 edges (representing 1715 interactions between the proteins). In addition, 3 essential modules were identified from the network by MCODE in Cytoscape (Table 2). According to the upset chart, five genes (namely SPI1, TYROBP, TLR2, FCER1G and MMP9) were registered more than 5 times and were regarded as hub genes (Figure 4B). Interestingly, these genes were also included in the modules with the highest MCODE scores (Figure 4C).
| Cluster | Score | Nodes | Edges | Node IDs |
| 1 | 19.6 | 21 | 196 | LAPTM5, FCER1G, LY86, CCR1, CD53, FCGR2A, FCGR3A, CSF1R, TYROBP, C1QA, SPI1, IL10RA, LILRB2, CYBB, CTSS, LCP2, MNDA, CD74, MPEG1, AIF1, ITGAM |
| 2 | 8.5 | 21 | 85 | CCL5, ITGAL, CCL3, PARVG, CCR5, CCR7, IGSF6, BTK, CD83, TLR2, IL1B, CSF3R, HLA-DRA, VAV1, CD68, HK3, FGR, CD14, MYO1F, CCL4, NCF2 |
| 3 | 6.207 | 30 | 90 | EVI2B, MS4A6A, CCRL2, IL7R, VAMP8, SYK, APOE, LILRB3, STK10, ADAM8, HCST, LYN, HMOX1, INPP5D, SLA, ALOX5, CXCR4, CORO1A, MMP9, CXCL16, NCF4, PTPN6, TREM1, IL1RN, HCLS1, SLC2A5, AQP9, PLAU, RAC2, VAV3 |
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Differential expression of the DEGs, as revealed by bioinformatic methods, was further confirmed by qRT-PCR using cDNA obtained from artery samples from AS patients (n = 4), AAA patients (n = 4), and healthy controls (n = 4). As shown in Figure 5, SPI1, TYROBP, TLR2, FCER1G and MMP9 were significantly upregulated both in AS and AAA samples compared with normal controls.
A large number of clinical investigations h.ave comprehensively exhibited an enhanced risk of AAA in patients with AS. However, the mechanism underlying the association between AS and AAA remains elusive, although it has been speculated to be associated with chronic inflammation, degradation of extracellular matrix, apoptosis of vascular smooth muscle cells, and thrombosis [12], physiological characteristics that also contribute to the formation of atherosclerotic plaques, suggesting that AS, which frequently affects the aneurysm wall, is a crucial risk factor for AAA. We herein discovered 5 key genes implicated in AS-related AAA, namely SPI1, TYROBP, TLR2, FCER1G and MMP9. These genes have the potential to become novel biomarkers and treatment targets for AS-related AAA. Our findings not only provide further insights into the pathogenic mechanisms of AS-related AAA, but also have clinical significance—they suggest several potential early diagnostic markers to prevent the progression of AAA.
Among the identified hub genes, SPI1 encodes PU.1, an ETS-domain transcription factor that is required for the development of myeloid cells and can regulate intercellular communications to facilitate immune responses [13]. The role of the SPI1 in AAA progression is unclear. According to previous findings, the expression of SPI1 gene is upregulated during the differentiation of myeloid cells and remains persistently high in B cells, monocytes, mast cells, circulating neutrophils, and other granulocytes in human [14]. Pan et al. found that SPI1 expression was significantly increased in Tibetan minipigs subjected to a high-fat/cholesterol diet [15], further implying that the activation of myeloid cells is critical for AS development. TYROBP, which has a synonym of DNAX-activating protein of 12 kDa (DAP12), encodes a transmembrane receptor ubiquitously expressed in neutrophils, natural killer cells, and monocytes/macrophages that transduces immune signals via a tyrosine-based activation motif [16]. DAP12 has been extensively implicated in the survival, reproduction, polarization, and differentiation of multiple types of immune cells, particularly the monocytes/macrophages [16]. Wang et al. observed that DAP12 was expressed at a high level in APOE mice, which facilitated the development of AS plaques via the TREM-1/DAP12 pathway [17]. Hinterseher et al. observed that TYROBP was highly expressed in human AAA and was involved in the pathogenesis of AAA through the NK cell-mediated cytotoxicity pathway [18]. TLR2 encodes a cell membrane protein that identifies microorganism invasions and regulates innate immune reactions [19]. Jabłońska et al. found significantly higher levels of TNF-α, IL-4 and TLR2 in AAA patients compared with healthy controls, and suggested that TLR2 may be involved in the aortic and systemic inflammatory responses in AAA patients [20]. Lee et al. showed that TLR2 could activate p38 and ERK1/2 signaling pathways, selectively regulate IL-6–mediated RANKL upregulation and OPG downregulation, and induce the differentiation of VSMCs into chondrocytes, thereby resulting in vascular calcification during AS development [21]. FCER1G (CD23) encodes a high-affinity cell membrane receptor for IgE, which is upregulated during aging [22]. FCER1G was demonstrated to be able to regulate hypertension and platelet hyperaggregability during thrombus formation [23–25]. Given that AAA is tightly associated with these diseases, it is reasonable that FCER1G may be implicated in the development of AAA. MMP9 encodes a matrix metalloproteinase that reorganizes and degrades extracellular matrix during collagen catabolic processes, leading to the instability and rupture of atherosclerotic plaques [26,27]. This molecule activates the immune responses that lead to atherosclerotic plaque destabilization by facilitating the degranulation, transendothelial migration, and differentiation of leukocytes, as well as activating interleukin signaling pathways. However, its role in AAA progression remains controversial. Hurks et al. found that the MMP9 levels remained stable in a study of inflammation in AAA artery wall [28]. Another study found that MMP9 level in AAA was correlated with intraluminal thrombus amount, implying that thrombus activated MMP9 [29].
In this study, we identified DEGs shared by the AS and AAA cohorts and discovered 5 hub genes (namely SPI1, TYROBP, TLR2, FCER1G and MMP9) by PPI network construction and identification of key modules. The relationship between these genes, AS and AAA needs to be further investigated in future studies.
By analyzing GEO datasets using bioinformatic methods and verifying the results by in vitro experiments, we not only identified 206 DEGs shared by both AS and AAA cohorts, but also detected 5 hub genes (SPI1, TYROBP, TLR2, FCER1G and MMP9) linking AS and AAA, which may be used as potential biomarkers for the diseases. More importantly, these hub genes may become potential treatment targets for AS-related AAA, which will facilitate the establishment of new therapeutic strategies, including early prevention and precision treatment.
Our study has some limitations. Firstly, our research was based on microarray data retrieved from a public database. Secondly, since transcript abundances of genes may not be able to accurately reflect the corresponding protein levels, for example, we do not know which type of cells are mainly involved in the expression of these hub genes, and whether the complex in vivo environment will mask some of more meaningful genes, additional in vitro and in vivo studies are required to characterize the functions of the key genes. Therefore, large-scale prospective clinical investigations can, to some extent, better support our findings.
We thank Yudi Liu for technical assistance.
This study was supported by the National Natural Science Foundation of China [Grant Numbers 82070489].
This study was approved on June, 2021 by the Institutional Review Board of the Tianjin Medical University General Hospital with an approval number of IRB2021-WZ-080.
The authors declare that they have no competing interests.
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Figures(6) / Tables(8)
Sarah R. Al-Dawsari, Khalaf S. Sultan. Modeling of daily confirmed Saudi COVID-19 cases using inverted exponential regression[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2303-2330. doi: 10.3934/mbe.2021117
| Gene | Primer sequence (5′→3′) | |
| SPI1 | F: GTGCCCTATGACACGGATCTA | R: AGTCCCAGTAATGGTCGCTAT |
| TYROBP | F: ACTGAGACCGAGTCGCCTTAT | R: ATACGGCCTCTGTGTGTTGAG |
| TLR2 | F: ATCCTCCAATCAGGCTTCTCT | R: GGACAGGTCAAGGCTTTTTACA |
| FCER1G | F: AGCAGTGGTCTTGCTCTTACT | R: TGCCTTTCGCACTTGGATCTT |
| MMP9 | F: TGTACCGCTATGGTTACACTCG | R: GGCAGGGACAGTTGCTTCT |
| GAPDH | F: ATGGCTACAGCAACAGGGT | R: TTATGGGGTCTGGGATGG |
DownLoad:
CSV
| Cluster | Score | Nodes | Edges | Node IDs |
| 1 | 19.6 | 21 | 196 | LAPTM5, FCER1G, LY86, CCR1, CD53, FCGR2A, FCGR3A, CSF1R, TYROBP, C1QA, SPI1, IL10RA, LILRB2, CYBB, CTSS, LCP2, MNDA, CD74, MPEG1, AIF1, ITGAM |
| 2 | 8.5 | 21 | 85 | CCL5, ITGAL, CCL3, PARVG, CCR5, CCR7, IGSF6, BTK, CD83, TLR2, IL1B, CSF3R, HLA-DRA, VAV1, CD68, HK3, FGR, CD14, MYO1F, CCL4, NCF2 |
| 3 | 6.207 | 30 | 90 | EVI2B, MS4A6A, CCRL2, IL7R, VAMP8, SYK, APOE, LILRB3, STK10, ADAM8, HCST, LYN, HMOX1, INPP5D, SLA, ALOX5, CXCR4, CORO1A, MMP9, CXCL16, NCF4, PTPN6, TREM1, IL1RN, HCLS1, SLC2A5, AQP9, PLAU, RAC2, VAV3 |
DownLoad:
CSV
| Gene | Primer sequence (5′→3′) | |
| SPI1 | F: GTGCCCTATGACACGGATCTA | R: AGTCCCAGTAATGGTCGCTAT |
| TYROBP | F: ACTGAGACCGAGTCGCCTTAT | R: ATACGGCCTCTGTGTGTTGAG |
| TLR2 | F: ATCCTCCAATCAGGCTTCTCT | R: GGACAGGTCAAGGCTTTTTACA |
| FCER1G | F: AGCAGTGGTCTTGCTCTTACT | R: TGCCTTTCGCACTTGGATCTT |
| MMP9 | F: TGTACCGCTATGGTTACACTCG | R: GGCAGGGACAGTTGCTTCT |
| GAPDH | F: ATGGCTACAGCAACAGGGT | R: TTATGGGGTCTGGGATGG |
| Cluster | Score | Nodes | Edges | Node IDs |
| 1 | 19.6 | 21 | 196 | LAPTM5, FCER1G, LY86, CCR1, CD53, FCGR2A, FCGR3A, CSF1R, TYROBP, C1QA, SPI1, IL10RA, LILRB2, CYBB, CTSS, LCP2, MNDA, CD74, MPEG1, AIF1, ITGAM |
| 2 | 8.5 | 21 | 85 | CCL5, ITGAL, CCL3, PARVG, CCR5, CCR7, IGSF6, BTK, CD83, TLR2, IL1B, CSF3R, HLA-DRA, VAV1, CD68, HK3, FGR, CD14, MYO1F, CCL4, NCF2 |
| 3 | 6.207 | 30 | 90 | EVI2B, MS4A6A, CCRL2, IL7R, VAMP8, SYK, APOE, LILRB3, STK10, ADAM8, HCST, LYN, HMOX1, INPP5D, SLA, ALOX5, CXCR4, CORO1A, MMP9, CXCL16, NCF4, PTPN6, TREM1, IL1RN, HCLS1, SLC2A5, AQP9, PLAU, RAC2, VAV3 |
