{"title":"IL-27和抗pd -1联合治疗癌症:一个简化的数学模型","authors":"Kenton D. Watt, Kang-Ling Liao","doi":"10.5206/mase/15100","DOIUrl":null,"url":null,"abstract":"Many experiential and clinical trials in cancer treatment show that a combination of immune checkpoint inhibitor with another agent can improve the tumor reduction. Anti Programmed death 1 (Anti-PD-1) is one of these immune checkpoint inhibitors that re-activate immune cells to inhibit tumor growth. In this work, we consider a combination treatment of anti-PD-1 and Interleukin-27 (IL-27). IL-27 has anti-cancer functions to promote the development of Th1 and CD8$^+$ T cells, but it also upregulates the expression of PD-1 and Programmed death ligand 1 (PD-L1) to inactivate these T cells. Thus, the functions of IL-27 in tumor growth is controversial. Hence, we create a simplified mathematical model to investigate whether IL-27 is pro-cancer or anti-cancer in the combination with anti-PD-1 and to what degree anti-PD-1 improves the efficacy of IL-27. Our synergy analysis for the combination treatment of IL-27 and anti-PD-1 shows that (i) ant-PD-1 can efficiently improve the treatment efficacy of IL-27; and (ii) there exists a monotone increasing function $F_c(G)$ depending on the treatment efficacy of anti-PD-1 $G$ such that IL-27 is an efficient anti-cancer agent when its dose is smaller than $F_c(G)$, whereas IL-27 is a pro-cancer agent when its dose is higher than $F_c(G)$. Our analysis also provides the existence and the local stability of the trivial, non-negative, and positive equilibria of the model. Combining with simulation, we discuss the effect of the IL-27 dosage on the equilibria and find that the T cells and IFN-$\\gamma$ could vanish and tumor cells preserve, when the production rate of T cells by IL-27 is low or the dosage of IL-27 is low.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Combination therapy for cancer with IL-27 and anti-PD-1: A simplified mathematical model\",\"authors\":\"Kenton D. Watt, Kang-Ling Liao\",\"doi\":\"10.5206/mase/15100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many experiential and clinical trials in cancer treatment show that a combination of immune checkpoint inhibitor with another agent can improve the tumor reduction. Anti Programmed death 1 (Anti-PD-1) is one of these immune checkpoint inhibitors that re-activate immune cells to inhibit tumor growth. In this work, we consider a combination treatment of anti-PD-1 and Interleukin-27 (IL-27). IL-27 has anti-cancer functions to promote the development of Th1 and CD8$^+$ T cells, but it also upregulates the expression of PD-1 and Programmed death ligand 1 (PD-L1) to inactivate these T cells. Thus, the functions of IL-27 in tumor growth is controversial. Hence, we create a simplified mathematical model to investigate whether IL-27 is pro-cancer or anti-cancer in the combination with anti-PD-1 and to what degree anti-PD-1 improves the efficacy of IL-27. Our synergy analysis for the combination treatment of IL-27 and anti-PD-1 shows that (i) ant-PD-1 can efficiently improve the treatment efficacy of IL-27; and (ii) there exists a monotone increasing function $F_c(G)$ depending on the treatment efficacy of anti-PD-1 $G$ such that IL-27 is an efficient anti-cancer agent when its dose is smaller than $F_c(G)$, whereas IL-27 is a pro-cancer agent when its dose is higher than $F_c(G)$. Our analysis also provides the existence and the local stability of the trivial, non-negative, and positive equilibria of the model. Combining with simulation, we discuss the effect of the IL-27 dosage on the equilibria and find that the T cells and IFN-$\\\\gamma$ could vanish and tumor cells preserve, when the production rate of T cells by IL-27 is low or the dosage of IL-27 is low.\",\"PeriodicalId\":93797,\"journal\":{\"name\":\"Mathematics in applied sciences and engineering\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics in applied sciences and engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5206/mase/15100\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/15100","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Combination therapy for cancer with IL-27 and anti-PD-1: A simplified mathematical model
Many experiential and clinical trials in cancer treatment show that a combination of immune checkpoint inhibitor with another agent can improve the tumor reduction. Anti Programmed death 1 (Anti-PD-1) is one of these immune checkpoint inhibitors that re-activate immune cells to inhibit tumor growth. In this work, we consider a combination treatment of anti-PD-1 and Interleukin-27 (IL-27). IL-27 has anti-cancer functions to promote the development of Th1 and CD8$^+$ T cells, but it also upregulates the expression of PD-1 and Programmed death ligand 1 (PD-L1) to inactivate these T cells. Thus, the functions of IL-27 in tumor growth is controversial. Hence, we create a simplified mathematical model to investigate whether IL-27 is pro-cancer or anti-cancer in the combination with anti-PD-1 and to what degree anti-PD-1 improves the efficacy of IL-27. Our synergy analysis for the combination treatment of IL-27 and anti-PD-1 shows that (i) ant-PD-1 can efficiently improve the treatment efficacy of IL-27; and (ii) there exists a monotone increasing function $F_c(G)$ depending on the treatment efficacy of anti-PD-1 $G$ such that IL-27 is an efficient anti-cancer agent when its dose is smaller than $F_c(G)$, whereas IL-27 is a pro-cancer agent when its dose is higher than $F_c(G)$. Our analysis also provides the existence and the local stability of the trivial, non-negative, and positive equilibria of the model. Combining with simulation, we discuss the effect of the IL-27 dosage on the equilibria and find that the T cells and IFN-$\gamma$ could vanish and tumor cells preserve, when the production rate of T cells by IL-27 is low or the dosage of IL-27 is low.