
Alzheimer's disease stands as one of the most widespread neurodegenerative conditions associated with aging, giving rise to dementia and posing significant public health challenges. Mathematical models are considered as valuable tools to gain insights into the mechanisms underlying the onset, progression, and potential therapeutic approaches for AD. In this paper, we introduce a mathematical model for AD that employs the fractal fractional operator in the Caputo sense to characterize the temporal dynamics of key cell populations. This model encompasses essential elements, including amyloid-β (Aβ), neurons, astroglia and microglia. Using the fractal fractional operator, we have established the existence and uniqueness of solutions for the model under consideration, employing Leray-Schaefer's theorem and the Banach fixed-point methods. Utilizing functional techniques, we have analyzed the proposed model stability under the Ulam-Hyers condition. The suggested model has been numerically simulated by using a fractional Adams-Bashforth approach, which involves a two-step Lagrange polynomial. For numerical simulations, different ranges of fractional order values and fractal dimensions are considered. This new fractal fractional operator in the form of the Caputo derivative was determined to yield better results than an ordinary integer order. Various outcomes are shown graphically by for different fractal dimensions and arbitrary orders.
Citation: Pooja Yadav, Shah Jahan, Kottakkaran Sooppy Nisar. Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative[J]. AIMS Public Health, 2024, 11(2): 399-419. doi: 10.3934/publichealth.2024020
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Alzheimer's disease stands as one of the most widespread neurodegenerative conditions associated with aging, giving rise to dementia and posing significant public health challenges. Mathematical models are considered as valuable tools to gain insights into the mechanisms underlying the onset, progression, and potential therapeutic approaches for AD. In this paper, we introduce a mathematical model for AD that employs the fractal fractional operator in the Caputo sense to characterize the temporal dynamics of key cell populations. This model encompasses essential elements, including amyloid-β (Aβ), neurons, astroglia and microglia. Using the fractal fractional operator, we have established the existence and uniqueness of solutions for the model under consideration, employing Leray-Schaefer's theorem and the Banach fixed-point methods. Utilizing functional techniques, we have analyzed the proposed model stability under the Ulam-Hyers condition. The suggested model has been numerically simulated by using a fractional Adams-Bashforth approach, which involves a two-step Lagrange polynomial. For numerical simulations, different ranges of fractional order values and fractal dimensions are considered. This new fractal fractional operator in the form of the Caputo derivative was determined to yield better results than an ordinary integer order. Various outcomes are shown graphically by for different fractal dimensions and arbitrary orders.
Gastric cancer (GC) ranks as the fifth most prevalent tumor worldwide [1]. With 768,793 patients dying globally in 2020, GC ranks fourth in terms of death among cancers [2]. The prognostic outcomes of early GC patients have considerably improved with advancements in detection, surgery and radiotherapy. However, the effect of these strategies is limited, with a median survival duration of less than one year and a poor survival rate of five years, for advanced GC patients [3]. Compared with chemotherapy, molecular and immunological therapies have distinct impacts on the treatment of a small number of advanced GC patients [4,5,6]. However, the deficiency of indicators to predict the early diagnosis of GC necessitates the construction of a novel prognostic and diagnostic risk model.
Pyroptosis, also known as inflammasome-induced programmed cell death, is a new type of cell death (PCD) [7]. Excessive inflammasome activation in pyroptosis is strongly associated with various human diseases and disorders [8]. For example, gasdermin superfamily proteins are the most common pyroptosis inducers; the N-terminal regions of proteins from this family form pores across the cell membrane, thereby leading to the secretion of IL-1β and IL-18 [9]. In addition, the caspase-1-mediated inflammation-associated cell death pathway in pyroptosis involves the AIM2-, NLRP1-, NLRP3-, NLRC4- and pyrin-inflammasomes, and it is known as the most traditional inflammasome pathway [10]. Compared to standard therapies, induction of pyroptosis represents a potential strategy for cancer treatment [11]. Thus, new pyroptosis-associated markers that expand current knowledge of pyroptosis in GC and forecast the prognosis of GC patients are urgently needed.
lncRNAs with over 200 nucleotides [12] are important regulators of gene expression, growth, differentiation, progression and chromatin dynamics [13]. In a growing number of scientific studies, aberrant expression of lncRNAs has been identified as a prognostic marker in a variety of malignancies. For example, AK023391, a lncRNA that promotes gastric cancer, plays a critical role in stimulating the PI3K/Akt signal transduction pathway and has been used as a predictive and therapeutic biomarker in patients with GC [14]. Furthermore, MT1JP, a downregulated lncRNA in GC linked to GC survival, functions as a type of ncRNA to compete with miR-92a-3p and mediates FBXW7 expression to regulate GC progression [15]. Furthermore, EGR1-induced HNF1A-AS1 modulates a variety of pro- and anti-growth regulators to promote the development of GC, thereby serving as a potential therapeutic target and prognostic biomarker in this disorder [16]. However, only a limited number of investigations on pyroptosis-associated lncRNAs and their involvement in the prognosis of GC patients have been published to date, representing a gap that needs to be filled. Recently, applications of information and computer technology in health care have expanded rapidly [17], such as bioinformatics analysis, deep learning [18], machine learning [19] and Mendelian stochastic studies [20]. Unlike traditional diagnostic and analytical methods, algorithmic analysis has many advantages, including speed, low cost and high accuracy. This study aimed to construct a predictive model through bioinformatics analysis to solve many problems in the diagnosis and treatment of gastric cancer that are currently being encountered in clinical practice.
TCGA (The Cancer Genome Atlas) was used to obtain the expression profiles of 52 pyroptosis-associated genes and 14056 lncRNAs for our investigation. We built a predictive signature to analyze the survival values of GC patients based on 10 pyroptosis-associated lncRNAs. Then, depending on the median cutoff, the predictive model classified GC individuals into two different risk groups. Survival results, risk states and lncRNA expression levels were analyzed using patient data from the training, testing and entire groups. Furthermore, we examined the prognostic capacity of this constructed model, demonstrating that the predictive signature could recognize the differences between the two risk groups. The model was also utilized to examine the tumor immune microenvironment as well as the tumor immunotherapeutic reaction, and significant changes in the expression of immunological biomarkers were noted between the two risk groups. Then, we analyzed and summarized the mutation data, demonstrating that this model exhibited better predictive ability using tumor mutational burden data. Finally, to identify a more efficacious chemotherapy regimen for GC patients, we used a drug susceptibility analysis to compare the IC50 values using the GDSC database [21], demonstrating that the appropriate chemotherapy had better effects in the high-risk group. The validation results from the lnCAR database indicated that AC005332.1, AC009812.4 and AP000695.1 levels were significantly increased in gastric tumor tissue compared with normal tissue, and the overall survival of the patients with GC had statistically significant in high and low AP000695.1 group. These results were consistent with the results based on TCGA GC cohort, which showed that AC005332.1, AC009812.4 and AP000695.1 were crucial biomarkers involved in the regulation of GC progression.
In conclusion, we developed a predictive model for GC patients using hub pyroptosis-associated lncRNAs. The effect of pyroptosis-associated lncRNAs on predicting survival and immunological responses was revealed, providing a new method to identify effective diagnostic biomarkers and paving the way for the treatment of GC patients.
RNA transcriptome sequencing information of 32 normal samples and 375 GC samples, the corresponding clinical information (age, sex, cancer differentiation grade and TNM stage) and the mutation information were abstracted from TCGA (https://portal.gdc.cancer.gov/) [22]. Normalized RNA-seq data were obtained in the fragment per kilobase million (FPKM) format. GC patients without survival data were omitted to reduce statistical bias. TNM (T: tumor; N: node; M: metastasis).
Fifty-two pyroptosis-associated genes were retrieved from prior publications [23,24,25,26,27,28,29,30,31,32,33]. The specific gene names are shown in Supplementary Table 1. The STRING database (https://string-db.org/) was used to explore possible potential interactions between pyroptosis-associated genes, and a protein interaction network was constructed. We hid disconnected nodes and set a minimum required interaction score (high confidence: 0.007) in the network. We also used the TCGA database to obtain the profiles of lncRNAs and pyroptosis-associated genes. A total of 739 pyroptosis-associated lncRNAs were identified based on Pearson's correlation analysis [34]. |Pearson R| > 0.4 and p < 0.001 were employed as criteria. The above results were visualized with a Sankey plot using the R packages limma, dplyr, ggalluvial and ggplot2 [35].
The entire TCGA cohort was classified into training and validation cohorts based on a ratio of 1:1. The training cohort was used to establish a pyroptosis-associated lncRNA model, and the entire and testing cohorts were used to verify this risk model. The clinical baseline information of the above two cohorts is presented in Supplementary Table 2. No statistically significant differences in clinical features were noted between the two datasets (p > 0.05). We used univariate Cox regression analysis and survival statistics of GC individuals to assess the prognosis of 739 pyroptosis-associated lncRNAs (p < 0.05), and forest plots were drawn. Prognosis-associated lncRNAs were identified using LASSO to narrow the number of lncRNAs (using the penalty parameter estimated by 10-fold cross-validation) [36]. We discovered that 20 pyroptosis-associated lncRNAs were strongly associated with the overall survival (OS) of GC patients. Twenty pyroptosis-associated lncRNAs were analyzed using multivariate Cox regression analysis, and a risk model based on 10 pyroptosis-associated lncRNAs was created [37]. The above process was performed using the R packages survival, caret, glmnet, survminer and timeROC. The risk score was computed using the following formula: Risk score = coe (lncRNA1) × exp (lncRNA1) + coe (lncRNA2) × exp (lncRNA2) + … + coe (lncRNAn) × exp (lncRNAn), where coe (lncRNAn) indicates the coefficient of lncRNAs and exp (lncRNAn) indicates the expression of lncRNAs [38]. The median score was calculated to classify the individuals into two groups: a low-risk group and a high-risk group.
Principal component analysis was used to reduce dimensionality, identify models and visualize different-dimensional data from the whole set of genes [39], 52 pyroptosis genes, 10 pyroptosis-associated lncRNAs and the prognostic signature, depending on the expression data of 10 pyroptosis-associated lncRNAs. Principal component analysis was also used to cluster GC patients, and a 3D scatterplot was used to display the distribution of GC patients with the R package scatterplot3D [37]. All samples containing GC patients were divided into low- and high-risk subsets based on the training set's median, which served as a cutoff criterion. To explain the differences in survival outcomes between the two groups, we employed Kaplan‒Meier analysis [40]. This approach was performed with the survminer and survival packages in R.
In GC individuals, multivariate and univariate Cox regression analyses were used to determine whether the risk score was an independent factor compared to other clinical features (age, sex, TNM stage and grade) [41]. To analyze the independent prognosis of the pyroptosis-associated lncRNA model, we used the dplyr, survival, rms and pec packages of R to construct the C-index [42]. The survival, survminer and time ROC packages of R were used to construct the ROC curve [43], which examined the independent predictors associated with various clinical features, such as age, sex, clinical phase, TNM stage and risk score. We assessed the relationship between the model and the clinical features using the chi-square test. The sensitivity and specificity of the predictive signature on the one-, three- and five-year OS of GC patients were also assessed.
Various clinical features (age, sex, TNM stage and grade) and risk scores were established to forecast the one-, three- and five-year OS using a predictive nomogram [44]. To demonstrate the consistency between the practical result and the forecast outcome of this risk model, we also constructed calibration curves using the survival, regplot and rms packages of R. The predictive ability of the proposed nomogram models was demonstrated based on the Hosmer-Lemeshow test.
Using the R package limma, the differentially expressed genes (DEGs) between the high- and low-risk groups were discovered. The restricted condition was set to log2 |fold change| > 1 and false discovery rate < 0.05. To determine the biological activities of the DEGs, we used Gene Ontology analysis [45]. Three parts of the GO analysis, biological process (BP), cellular component (CC) and molecular function (MF), were examined. The R packages clusterProfiler, org.Hs.eg.db, enrichplot, ggplot2, ggpubr and dplyr were used in this approach. The p value was calculated to identify the threshold of outcome, and p < 0.05 indicated that the functional statement was considerably enriched.
To assist the determination of the quantities of immune pathways and tumor-infiltrating immune cells (TIICs) for each sample in various risk groups, a single sample gene-set enrichment analysis (ssGSEA) score was computed. To study and summarize the mutation information from TCGA, we used the R package maftools. The tumor mutational burden (TMB) was calculated depending on tumor mutant genes [37]. To compare the survival outcomes of patients in different TMB groups, we used the survival package in R. The TMB could be utilized to predict the possibility of an immunotherapeutic response in the future. The waterfall diagram demonstrated the relationship between TMB and risk ratings in GC patients.
We performed drug analysis to evaluate the response based on the IC50 available in the GDSC database for every sample using the R packages limma, ggpubr, pRRophetic and ggplot2 [46] to identify potential drugs targeting the pyroptosis-associated lncRNA signature for treating GC patients. To compare the IC50 differences between popular antineoplastic drugs in the high- and low-risk categories, the Wilcoxon signed rank test was employed. We discovered that 12 compounds had substantial differences in predicted IC50 in the two groups, and the high-risk group was more susceptible to the above compounds.
The lnCAR database (https://lncar.renlab.org/) collected and collated differential expression analysis of 52,306 samples and survival analysis of 12,883 samples from 10 tumors (bladder, breast, cervical, colon, esophageal, gastric, liver, lung, ovarian and prostate cancers) from the GEO database [47]. Low-throughput data, such as real-time PCR and northern blot data, were integrated into the lnCAR database as validation datasets. We analyzed the expression levels of hub pyroptosis-associated lncRNAs in GC from the lnCAR database. We also performed survival analysis of hub pyroptosis-associated lncRNAs in GC from the Sento Academic website (https://www.xiantao.love/).
Statistical analyses were performed with R software (version 4.2.0). Clinicopathological characteristics, TMB and drug sensitivity differences between the high- and low-risk groups were analyzed with the Wilcoxon test. The prognostic values were tested by utilizing principal component analysis, a predictive nomogram, functional analysis and Kaplan‒Meier analysis. To compare categorical data among various groups, the chi-square test was employed. Here, p < 0.05 was considered statistically significant (*p < 0.05; **p < 0.01; ***p < 0.001).
The flow chart for constructing the risk model and the subsequent analysis is displayed in Figure 1. TCGA was used to extract the matrix information of 52 pyroptosis-associated genes and 14056 lncRNAs. Pyroptosis-associated lncRNAs were defined as lncRNAs that had a sufficient correlation with 52 pyroptosis genes (|Pearson R| > 0.4 and p < 0.001). Finally, using the Sankey plot, the co-expression network of pyroptosis-associated lncRNAs was displayed, and 739 pyroptosis-associated lncRNAs were identified as pyroptosis-associated lncRNAs (Figure 2A). In the entire TCGA cohort, links between 52 pyroptosis genes and 10 prognostic pyroptosis-associated lncRNAs were identified (Figure 2B). A protein interaction network of pyroptosis-associated genes was constructed (Figure S1). These prognostic pyroptosis-associated lncRNAs were used for subsequent model construction.
In total, 52 pyroptosis-associated lncRNAs associated with OS were screened with univariate Cox regression (Figure 3A). LASSO analysis is a common multiple regression analysis technique. Thus, we used LASSO to narrow the number of lncRNAs to 20 (Figure 3B, C). Furthermore, using multivariate Cox analysis, 10 pyroptosis-associated lncRNAs were identified as prognostic factors that were independently connected with OS and utilized to build a predictive signature to estimate the predictive outcomes in GC patients. The risk model classified GC patients into two different risk categories depending on their median risk score. The scattering of survival outcomes between the two different categories was demonstrated using the entire TCGA cohort (Figure 4A), and survival times were clearly evident when using the entire TCGA cohort (Figure 4B). Distinct expression standards of 10 pyroptosis-associated lncRNAs were represented in the entire TCGA cohort (Figure 4C). Survival analysis revealed that the high-risk group had a lower OS than the low-risk group (p < 0.001) in the entire TCGA cohort (Figure 4D).
To test the predictive capacity of the constructed signature, we calculated the risk score for each individual in the training cohort and testing cohort utilizing the consistent method. The survival results, risk status and lncRNA expression standards of each individual from the training cohort and testing cohort are shown (Figure 5A–C, E–G). The individuals in the high-risk category had a greater risk of dying than those in the low-risk category. Kaplan‒Meier analysis revealed that the OS of the high-risk category was obviously lower (Figure 5D, H).
Subgroups of patients from the entire TCGA cohort were created based on sex, grade, stage or tumor phase, and the overall survivals of the low-risk subgroups were also better (Figure 6A–D). In this step, we first constructed a predictive signature and explored the predictive expression of the 10 pyroptosis-associated lncRNA signatures in the training, testing and entire cohorts, and the predictive value of this model was better evaluated.
According to the whole gene set, 52 pyroptosis genes, 10 pyroptosis-associated lncRNAs and a predictive signature constructed by 10 pyroptosis-associated lncRNAs, principal component analysis was performed to test the differences between the two risk groups (Figure 7A–D). The locations of the two risk groups were considerably split (Figure 7A–C). In addition, the model results revealed that the two risk categories had clearly different distributions (Figure 7D). The findings showed that the predictive model could differentiate between the two risk groups, which confirmed the grouping efficiency of the signature.
To determine whether the risk model based on pyroptosis-associated lncRNAs had independent predictive ability for GC, we used univariate and multivariate Cox regression. Using univariate Cox regression, the HR of the risk score was 1.132 with a 95% confidence interval (CI) of 1.090–1.175 (p < 0.001) (Figure 8A). The HR for pyroptosis-associated lncRNAs was 1.150 with a 95% confidence interval of 1.105–1.196 (p < 0.001) (Figure 8B). These results suggested that clinical and pathological factors, including sex, age, TNM stage and grade, were not connected to the risk model. The concordance index of the predictive signature increased over time, outperforming other clinical features, such as sex, age, TNM stage and grade, implying that the predictive signature could accurately predict the survival outcomes of GC patients (Figure 8C). To examine the specificity and responsiveness of the predictive signature in forecasting the results of GC patients, the AUC was calculated. The AUC of the risk grade was greater than that of other clinical variables, indicating that the predictive ability of the risk signature was quite reliable (Figure 8D). The AUC was 0.743 at one year, 0.685 at three years and 0.715 at five years, as shown in Figure 8E. All of the above indicators demonstrated that the risk score of this predictive model was superior to other clinical characteristics.
This nomogram incorporating the risk score and clinical characteristics was constructed to forecast the one-, three- and five-year OS occurrences in patients with GC. Compared with clinical criteria, the risk score of the predictive signature suggested that the nomogram had better forecast power (Figure 9A). The predicting rates of the one-, three- and five-year OS exhibited perfect conformance on the correlation plot (Figure 9B). The above results indicated that the nomogram exhibited good forecasting ability.
Depending on the predictive signature, the enrichment degree and engagement of various immune infiltrating cells and pathways in GC were sufficiently investigated. The scores of tumor-infiltrating immune cell types in the two risk groups were determined (Figure 10A). High scores of tumors infiltrating immune cells, including DCs, iDCs, macrophages, mast cells, neutrophils, pDCs, T helper cells, TILs and Tregs, were noted in the high-risk group. We also performed ssGSEA of immune functions by comparing the two risk groups (Figure 10B). The above results showed that the high-risk group had a higher score of infiltration functions compared with the low-risk group. We performed Gene Ontology enrichment to determine the potential molecular function of the pyroptosis-associated risk model, revealing the participation of several immune-associated biological activities (Figure S2). We found that the pyroptosis-associated genes in the risk model were mainly enriched in positive regulation of enzyme inhibitor action, peptidase mediator activity, peptidase inhibitor action, collagen-containing extracellular matrix, negative mediation of hydrolase action, regulation of peptidase action, adverse mediation of proteolysis and adverse mediation of peptidase action.
The relationship between the pyroptosis-associated lncRNA model and immunotherapeutic indicators was also explored. Gene mutations were analyzed to gain novel insight into the molecular mechanism in subgroups of the pyroptosis-associated lncRNA model. The mutation data of the pyroptosis-associated genes were evaluated using the R package maftools. Different predictors were used to classify the mutations. The top 20 driver genes (TTN, TP53, MUC16, ARID1A, LRP1B, SYNE1, FLG, FAT4, CSMD3, PCLO, DNAH5, KMT2D, FAT3, HMCN1, OBSCN, ZFHX4, RYR2, SPTA1, PIK3CA and CSMD1) with the highest mutation incidences between the two different risk subgroups are shown in Figure 10C, D. The low-risk group exhibited a greater incidence of gene mutation compared with the high-risk group (88.36 vs. 87.86%). Genes with a mutation rate of greater than 20% in the high-risk group included TTN, TP53, MUC16, ARID1A and SYNE1. TTN, TP53, MUC16, ARID1A, LRP1B, SYNE1, FLG, FAT4, CSMD3 and PCLO were identified as genes with mutation rates of greater than 20% in the low-risk subgroups. The most common mutation in both groups was Missense_mutation followed by Multi_Hit, Frame_Shift_Del and Nonsense_ mutation.
In many malignancies, including gastric cancer, a connection is noted between treatment intervention and TMB. The higher the TMB score is, the more cancer genetic mutations. In addition, a higher TMB score was noted in tumors with more abnormal cells. Thus, it was possible for immune cells to find the tumor. This type of tumor was a good candidate for tumor immunological treatment. We then calculated tumor mutational burden scores using the mutation data. The TMB in the high-risk category was lower, demonstrating that pyroptosis-associated factors exhibited a stronger relationship with the TMB (Figure 10E). Gastric cancer patients with a high TMB score had a considerably greater survival rate (Figure 10F). The above results indicated that TMB could act as an independent predictive factor in gastric cancer. Then, we tested whether the risk model could predict the OS of GC patients together with tumor mutational burden. Patients with two different TMB scores in the high-risk category (called H-TMB/high and L-TMB/high) had a lower survival rate than individuals with the two different TMB groups in the low-risk category (H-TMB/low and L-TMB/low) (Figure 10G). Based on our findings, the pyroptosis-associated lncRNA model could have increased predictive value with tumor mutational burden. The above results implied that immune infiltrating levels, mutation incidence and TMB significantly differed in the two risk groups, and this information can be used to guide individual treatment.
We used a drug sensitivity analysis to assess the IC50 differences between risk categories from the GDSC database to identify a better chemotherapy regimen for GC patients. With the exception of ABT.888 and AKT inhibitor VIII, the low-risk group was more responsive to A.443654, A.770041, AICAR, AMG.706, AS601245, ATRA, AUY922, axitinib, AZ628 and AZD.0530 (Figure 11A–L). We hypothesized that the effect of adequate treatment was superior in high-risk populations and that the information derived from these studies would be useful to guide individual chemotherapy.
We further explored the expression of hub pyroptosis-associated lncRNAs in the lnCAR database. The results indicated that AC005332.1, AC009812.4 and AP000695.1 levels were significantly increased in gastric tumor tissue compared with normal tissue (Figure 12A–C). And the overall survival of the patients with GC had statistically significant in high and low AP000695.1 group (p < 0.05) (Figure 12D). These results were consistent with the results based on TCGA GC cohort, demonstrating that AC005332.1, AC009812.4 and AP000695.1 were crucial biomarkers in regulating GC progression. The above results provide novel ideas to explore the specific mechanisms of the initiation and development of gastric cancer.
GC is well known as a common gastrointestinal system tumor with a high morbidity and mortality rate, and it receives an increasing amount of attention each year [48]. A reliable method to correctly predict the outcomes of GC patients is currently not available. In addition, pyroptosis has a dual effect on the appearance and growth of cancers. Pyroptotic cell death in the oxygen-deficit area of the tumor center could impair antitumor immunity and facilitate tumor formation [26]. On the other hand, pyroptosis can trigger an immune reaction and slow tumor development by causing acute inflammation in the tumor microenvironment [49]. For example, the AIM2 inflammasome has been shown to regulate mTOR to diminish S6K1 activation, thereby suppressing tumor progression [50]. However, the interaction of pyroptosis-associated genes in GC and their underlying potential to forecast GC patient prognosis remain unknown.
Furthermore, the critical role of lncRNAs in the induction of pyroptosis in tumor cells has been verified. For instance, previous work focused on GSDME to investigate the crucial function of lncRNAs involved in ionizing radiation (IR)-regulated pyroptosis in colon cancer cells [51]. The findings shed light on the biochemical processes driving IR-induced damage in cancer radiation treatment and could provide a solid theoretical framework for the development of colon cancer treatments. Furthermore, microRNA-4306 and Sirtuin1 (SIRT1) regulate the expression of LINC00958, which is involved in the induction of oral squamous cell carcinoma cell death by missing in melanoma 2 [52]. Nevertheless, research on lncRNAs connected to pyroptosis in tumors, particularly GC, is severely poor. As a result, we aimed to develop a predictive model based on pyroptosis-associated lncRNAs in patients with gastric cancer with the goal of generating a model that could accurately predict the outcomes of GC patients and provide a promising treatment option in the future.
The purpose of our study was to identify the association between pyroptosis-associated lncRNAs and GC patient outcome based on the expression data and biological activity of pyroptosis-associated lncRNAs in GC. Pyroptosis-associated lncRNAs were identified through co-expression analyses. To create a pyroptosis-associated lncRNA risk model, we used LASSO for univariate and multivariate Cox regression. The predictive signature comprising 10 pyroptosis-associated lncRNAs (AC005332.1, AC009812.4, AC015802.5, AC040904.1, AC053503.4, ADNP−AS1, AP000695.1, LIMS1−AS1, SACS−AS1 and SOX9−AS1) was confirmed to be an independent factor of prognosis. Among the 10 lncRNAs of the predictive model, several pyroptosis-associated lncRNAs have been reported to facilitate tumor incidence and progression. For example, a SOX9-AS1/miR-5590-3p/SOX9 positive feedback loop that signals through the Wnt/β-catenin pathway causes the progression and metastasis of HCC, suggesting that SOX9-AS1 represents a promising new predictive and therapeutic target for HCC [53]. Therefore, more researchers would like to study the role of pyroptosis-associated lncRNAs in GC and assess their value as predictive indicators.
Our study also discovered that this risk model was closely connected with immunotherapeutic markers and the prediction of sensitivity to medication. Various immunological biomarkers differed between the two risk groups. The above outcomes further showed that the pyroptosis-associated lncRNA model had a significant effect on the immune cell-infiltrating environment. We can focus more on the high-risk group because in the high-risk group, immune cells as well as immune function have higher scores. Relationships between treatment efficacy and TMB are noted in many malignancies, including gastric cancer. The TMB was higher in the low-risk group, demonstrating that the pyroptosis-associated signature was closely related to TMB. The survival probability of GC patients in the high TMB group was increased. TMB was identified as a risk-independent predictive marker in gastric cancer based on the findings of this study. The IC50 in the GDSC database was compared between risk categories using a drug susceptibility assessment. We found that the effect of adequate treatment is superior in high-risk populations. Finally, we further explored the expression of hub pyroptosis-associated lncRNAs in the lnCAR database.
The pathogenic stage is an important factor in the decision regarding GC treatment. However, GC patients in the same pathological stage also exhibit diverse clinical results, demonstrating that earlier categorization approaches are ineffective in providing reliable predictions and distinguishing the heterogeneity of GC. As a result, the established pyroptosis-associated lncRNA model provides a novel and accurate method to predict the survival outcomes and immunological responses of GC patients. We also validated the above results using the lnCAR database. The novelty of our work lies in the combination of two factors (pyroptosis and lncRNA) that play an important role in gastric cancer to establish a new prediction model. The main contribution is that, currently, earlier staging methods are ineffective in providing reliable predictions and facilitating the differentiation of gastric cancer heterogeneity based on a multitude of bioinformatics and computer algorithms. Here, we constructed and validated a prediction model to provide an accurate and simple method to predict patient survival and provide a theoretical basis for patient treatment. The model can be reproduced, making it attractive for clinical translation and implementation. Despite the significant findings of our study, we note that our research had several flaws and limitations. Research on the correlation between pyroptosis-linked lncRNAs and the tumor immune microenvironment remains in its initial phases and requires a more thorough analysis. Moreover, an in vivo test was used to confirm the expression activity of pyroptosis-associated lncRNAs. Based on the above results, we constructed a prognostic model consisting of 10 pyroptosis-linked lncRNAs. Recently, ncRNAs, including lncRNAs, miRNAs and circRNAs, have attracted considerable attention from scientists [54]. Prediction studies focused on interacting factors will provide valuable insights into the genetic markers and ncRNAs associated with GC, such as the lncRNA-miRNA-mRNA ceRNA network [55,56,57] and circRNA-miRNA-mRNA network [58]. Ideally, the simultaneous use of several correlated molecular targets increases the sensitivity and reliability of candidate genes as biomarkers [59], which also represents the direction of our future research.
In conclusion, we developed an excellent risk model to forecast the outcomes of GC patients based on 10 pyroptosis-associated lncRNAs, including AC005332.1, AC009812.4, AC015802.5, AC040904.1, AC053503.4, ADNPAS1, AP000695.1, LIMS1AS1, SACSAS1 and SOX9AS1. Validation results showed that AC005332.1, AC009812.4 and AP000695.1 were crucial biomarkers in regulating GC progression. And the overall survival of the patients with GC had statistically significant in high and low AP000695.1 group. More importantly, the above findings could elucidate the function of pyroptosis-associated lncRNAs and provide adequate evidence for prognostic prediction in GC patients. Furthermore, the predictive risk model demonstrated efficacy in identifying GC patients who would benefit from immunotherapy.
Jinsong Liu and Wenbin Lu designed this work. Yuyang Dai and Qian Liu integrated and analyzed the data. Jinsong Liu wrote this manuscript. Yueyao Lu, Jianzhong Deng and Xiuling Liu edited and modified the manuscript. This manuscript was approved by all of the authors.
This research project was funded by the National Natural Science Foundation of China [grant number 81872275], Medical Research Project of Jiangsu Health Commission [M2020002], the Changzhou High-Level Medical Talents Training Project [No: 2016CZBJ054] and the funds of Changzhou Sci & Tech Program [grant numbers CJ20220007, CJ20220006, CJ20210015].
The data from the public database are open access, and this study does not need the approval of the clinical ethics committee. The study complied with the corresponding rules of the public database.
The authors have no conflicts of interest to disclose.
[1] | Patterson C (2018) The state of the art of dementia research: New frontiers. World Alzheimer Report . |
[2] |
Fotuhi M, Hachinski V, Whitehouse PJ (2009) Changing perspectives regarding late-life dementia. Nat Rev Neurol 5: 649-658. https://doi.org/10.1038/nrneurol.2009.175 ![]() |
[3] |
Nebel RA, Aggarwal NT, Barnes LL, et al. (2018) Understanding the impact of sex and gender in Alzheimer's disease: a call to action. Alzheimers Dement 14: 1171-1183. https://doi.org/10.1016/j.jalz.2018.04.008 ![]() |
[4] |
Zárate S, Stevnsner T, Gredilla R (2017) Role of estrogen and other sex hormones in brain aging. Neuroprotection and DNA repair. Front Aging Neurosci 9: 430. https://doi.org/10.3389/fnagi.2017.00430 ![]() |
[5] | What Are the Symptoms of High Estrogen? (2022). Available from: https://www.medicalnewstoday.com/articles/323280#treatment |
[6] |
Navakkode S, Gaunt JR, Pavon MV, et al. (2021) Sex-specific accelerated decay in time/activity-dependent plasticity and associative memory in an animal model of Alzheimer's disease. Aging Cell 20: e13502. https://doi.org/10.1111/acel.13502 ![]() |
[7] |
Jung YJ, Chung WS (2018) Phagocytic roles of glial cells in healthy and diseased brains. Biomol Ther 26: 350. https://doi.org/10.4062/biomolther.2017.133 ![]() |
[8] |
Selkoe DJ (1997) Alzheimer's Disease–Genotypes, Phenotype, and Treatments. Sci 275: 630-631. https://doi.org/10.1126/science.275.5300.630 ![]() |
[9] |
Holtzman DM, Bales KR, Tenkova T, et al. (2000) Apolipoprotein E isoform-dependent amyloid deposition and neuritic degeneration in a mouse model of Alzheimer's disease. Pro Natl Acad Sci 97: 2892-2897. https://doi.org/10.1073/pnas.050004797 ![]() |
[10] |
Perry VH, Nicoll JA, Holmes C (2010) Microglia in neurodegenerative disease. Nat Rev Neurol 6: 193-201. https://doi.org/10.1038/nrneurol.2010.17 ![]() |
[11] |
Lue LF, Kuo YM, Beach T, et al. (2010) Microglia activation and anti-inflammatory regulation in Alzheimer's disease. Mol Neurobiol 41: 115-128. https://doi.org/10.1007/s12035-010-8106-8 ![]() |
[12] |
Neumann J, Sauerzweig S, Rönicke R, et al. (2008) Microglia cells protect neurons by direct engulfment of invading neutrophil granulocytes: a new mechanism of CNS immune privilege. J Neurosci 28: 5965-5975. https://doi.org/10.1523/JNEUROSCI.0060-08.2008 ![]() |
[13] |
Pang Y, Campbell L, Zheng B, et al. (2010) Lipopolysaccharide-activated microglia induce death of oligodendrocyte progenitor cells and impede their development. Neurosci 166: 464-475. https://doi.org/10.1016/j.neuroscience.2009.12.040 ![]() |
[14] | Granas A, Dugundji J (2003) Fixed point theory. New York: Springer 14. https://doi.org/10.1007/978-0-387-21593-8 |
[15] |
Varnum MM, Ikezu T (2012) The classification of microglial activation phenotypes on neurodegeneration and regeneration in Alzheimer's disease brain. Arch Immunol Ther Exp 60: 251-266. https://doi.org/10.1007/s00005-012-0181-2 ![]() |
[16] |
Proctor CJ, Boche D, Gray DA, et al. (2013) Investigating interventions in alzheimer's disease with computer simulation models. PLoS One 8: e73631. https://doi.org/10.1371/journal.pone.0073631 ![]() |
[17] |
Hadjichrysanthou C, Ower AK, de Wolf F, et al. (2018) Alzheimer's Disease Neuroimaging Initiative. The development of a stochastic mathematical model of Alzheimer's disease to help improve the design of clinical trials of potential treatments. PLoS One 13: e0190615. https://doi.org/10.1371/journal.pone.0190615 ![]() |
[18] |
Perez C, Ziburkus J, Ullah G (2016) Analyzing and modeling the dysfunction of inhibitory neurons in Alzheimer's disease. PLoS One 11: e0168800. https://doi.org/10.1371/journal.pone.0168800 ![]() |
[19] |
Macdonald A, Pritchard D (2000) A mathematical model of Alzheimer's disease and the ApoE gene. ASTIN Bull 30: 69-110. https://doi.org/10.2143/AST.30.1.504627 ![]() |
[20] |
Hane F, Augusta C, Bai O (2018) A hierarchical Bayesian model to predict APOE4 genotype and the age of Alzheimer's disease onset. PLoS One 13: e0200263. https://doi.org/10.1371/journal.pone.0200263 ![]() |
[21] |
Jack CR, Holtzman DM (2013) Biomarker modeling of Alzheimer's disease. Neuron 80: 1347-1358. http://dx.doi.org/10.1016/j.neuron.2013.12.003 ![]() |
[22] |
Young AL, Oxtoby NP, Daga P, et al. (2014) A data-driven model of biomarker changes in sporadic Alzheimer's disease. Brain 137: 2564-2577. https://doi.org/10.1093/brain/awu176 ![]() |
[23] |
Puri IK, Li L (2010) Mathematical modeling for the pathogenesis of Alzheimer's disease. PLoS One 5: e15176. https://doi.org/10.1371/journal.pone.0015176 ![]() |
[24] |
Hao W, Friedman A (2016) Mathematical model on Alzheimer's disease. BMC Syst Biol 10: 1-8. https://doi.org/10.1186/s12918-016-0348-2 ![]() |
[25] | Bertsch M, Franchi B, Marcello N, et al. (2017) Alzheimer's disease: a mathematical model for onset and progression. Math Med Biol 34: 193-214. https://doi.org/10.1093/imammb/dqw003 |
[26] |
Vosoughi A, Sadigh-Eteghad S, Ghorbani M, et al. (2020) Mathematical models to shed light on amyloid-beta and tau protein dependent pathologies in Alzheimer's disease. Neurosci 424: 45-57. https://doi.org/10.1016/j.neuroscience.2019.09.017 ![]() |
[27] |
Helal M, Hingant E, Pujo-Menjouet L, et al. (2014) Alzheimer's disease: analysis of a mathematical model incorporating the role of prions. J Math Biol 69: 1207-1235. https://doi.org/10.1007/s00285-013-0732-0 ![]() |
[28] | Caputo M, Fabrizio M (2015) A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl 1: 73-85. http://dx.doi.org/10.12785/pfda/010201 |
[29] | Losada J, Nieto JJ (2015) Properties of a new fractional derivative without singular kernel. Progr Fract Differ Appl 1: 87-92. http://dx.doi.org/10.12785/pfda/010202 |
[30] |
Yadav P, Jahan S, Shah K, et al. (2023) Fractional-order modelling and analysis of diabetes mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator. Alex Eng J 81: 200-209. https://doi.org/10.1016/j.aej.2023.09.006 ![]() |
[31] |
Atangana A, Khan MA (2019) Validity of fractal derivative to capturing chaotic attractors. Chaos Solit 126: 50-59. https://doi.org/10.1016/j.chaos.2019.06.002 ![]() |
[32] |
He JH (2018) Fractal calculus and its geometrical explanation. Results Phys 10: 272-276. https://doi.org/10.1016/j.rinp.2018.06.011 ![]() |
[33] |
Gomez-Aguilar JF, Cordova-Fraga T, Abdeljawad T, et al. (2020) Analysis of fractal–fractional malaria transmission model. Fractals 28: 2040041. https://doi.org/10.1142/S0218348X20400411 ![]() |
[34] |
Ali Z, Rabiei F, Shah K, et al. (2021) Qualitative analysis of fractal-fractional order COVID-19 mathematical model with case study of Wuhan. Alex Eng J 60: 477-489. https://doi.org/10.1016/j.aej.2020.09.020 ![]() |
[35] |
Qu H, Ur Rahman M, Arfan M, et al. (2022) Investigating fractal-fractional mathematical model of Tuberculosis (TB) under fractal-fractional Caputo operator. Fractals 30: 2240126. https://doi.org/10.1142/S0218348X22401260 ![]() |
[36] |
Rivers-Auty J, Mather AE, Peters R, et al. (2020) Anti-inflammatories in Alzheimer's disease-potential therapy or spurious correlate?. Brain Commun 2: fcaa109. https://doi.org/10.1093/braincomms/fcaa109 ![]() |
[37] | Lynch AM, Murphy KJ, Deighan BF, et al. (2010) The impact of glial activation in the aging brain. Aging Dis 1: 262. |
[38] |
Babu NR, Balasubramaniam P (2023) Master-slave synchronization for glucose–insulin metabolism of type-1 diabetic Mellitus model based on new fractal–fractional order derivative. Math Comput Simul 204: 282-301. https://doi.org/10.1016/j.matcom.2022.08.014 ![]() |
[39] | Babu NR, Balasubramaniam P, Ratnavelu K (2023) Existence and uniqueness for a new perturbed chaotic jerk circuit model based on fractal-fractional derivative. AIP Conf 2756. |
[40] | Shah K, Abdalla B, Abdeljawad T, et al. (2024) A Fractal-Fractional Order Model to Study Multiple Sclerosis: A Chronic Disease. Fractals 2440010. https://doi.org/10.1142/S0218348X24400103 |
[41] | Shah K, Abdeljawad T (2024) Study of radioactive decay process of uranium atoms via fractals-fractional analysis. S Afr J Chem Eng 48: 63-70. https://doi.org/10.1016/j.sajce.2024.01.003 |
[42] |
Khan ZA, Shah K, Abdalla B, et al. (2023) A numerical study of complex dynamics of a chemostat model under fractal-fractional derivative. Fractals 31: 2340181. https://doi.org/10.1142/S0218348X23401813 ![]() |
[43] |
Shah K, Abdeljawad T (2023) On complex fractal-fractional order mathematical modeling of CO 2 emanations from energy sector. Phys Scr 99: 015226. https://doi.org/10.1088/1402-4896/ad1286 ![]() |
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