Tumor heterogeneity is a large obstacle for cancer study and treatment. Different cancer patients may involve different combinations of gene mutations or the distinct regulatory pathways for inducing the progression of tumor. Investigating the pathways of gene mutations which can cause the formation of tumor can provide a basis for the personalized treatment of cancer. Studies suggested that KRAS, APC and TP53 are the most significant driver genes for colorectal cancer. However, it is still an open issue regarding the detailed mutation order of these genes in the development of colorectal cancer. For this purpose, we analyze the mathematical model considering all orders of mutations in oncogene, KRAS and tumor suppressor genes, APC and TP53, and fit it on data describing the incidence rates of colorectal cancer at different age from the Surveillance Epidemiology and End Results registry in the United States for the year 1973–2013. The specific orders that can induce the development of colorectal cancer are identified by the model fitting. The fitting results indicate that the mutation order with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53 explain the age–specific risk of colorectal cancer with very well. Furthermore, eleven pathways of gene mutations can be accepted for the mutation order of genes with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53, and the alternation of APC acts as the initiating or promoting event in the colorectal cancer. The estimated mutation rates of cells in the different pathways demonstrate that genetic instability must exist in colorectal cancer with alterations of genes, KRAS, APC and TP53.
Background: Cancer is a leading cause of human death worldwide. Drug resistance, mainly caused by gene mutation, is a key obstacle to tumour treatment. Therefore, studying the mechanisms of drug resistance in cancer is extremely valuable for clinical applications. Objective: This paper aims to review bioinformatics approaches and mathematical models for determining the evolutionary mechanisms of drug resistance and investigating their functions in designing therapy schemes for cancer diseases. We focus on the models with drug resistance based on genetic mutations for cancer therapy and bioinformatics approaches to study drug resistance involving gene co-expression networks and machine learning algorithms. Results: We first review mathematical models with single-drug resistance and multidrug resistance. The resistance probability of a drug is different from the order of drug administration in a multidrug resistance model. Then, we discuss bioinformatics methods and machine learning algorithms that are designed to develop gene co-expression networks and explore the functions of gene mutations in drug resistance using multi-omics datasets of cancer cells, which can be used to predict individual drug response and prognostic biomarkers. Conclusion: It was found that the resistance probability and expected number of drug-resistant tumour cells increase with the increase in the net reproductive rate of resistant tumour cells. Constrained models, such as logistical growth resistance models, can be used to identify more clinically realistic treatment strategies for cancer therapy. In addition, bioinformatics methods and machine learning algorithms can also lead to the development of effective therapy schemes.
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