记忆诱导下肿瘤细胞发展的动力学演化  

Dynamic evolution of memory-induced tumor cell development

作　　者：张盼盼[1,2] 白晓君 张昕 王浩华[1,2] ZHANG Panpan;BAI Xiaojun;ZHANG Xin;WANG Haohua(School of Mathematics and Statistics,Hainan University,Haikou 570228,China;Hainan Key Laboratory for engineering modeling and statistical calculation,Haikou 570228,China)

机构地区：[1]海南大学数学与统计学院,海南海口570228 [2]海南省工程建模与统计计算重点实验室,海南海口570228

出　　处：《海南大学学报(自然科学版中英文)》2025年第1期91-102,共12页Natural Science of Hainan University

基　　金：国家自然科学基金项目(12261028,11961018);海南省重点研发项目(ZDYF2021SHFZ231);海南省自然科学基金项目(120RC451,2019RC168);海南省研究生创新创业项目(Qhys2023-117)。

摘　　要：研究具有非马尔可夫性的肿瘤细胞生长模型,通过定义记忆尺度,刻画肿瘤细胞演化进程的非马氏依赖性。首先,证明了肿瘤细胞演化进程中有效转移速率的存在性,进而论证带记忆网络与马氏网络的等价性。此等价性依赖于记忆尺度的可控性,诱导肿瘤细胞生长进程的涨落,规范了不同进程下肿瘤细胞生长的噪声理论表达。数值模拟结果表明,细胞突变中的记忆尺度放大肿瘤细胞表达的噪声水平;反之,吞噬过程中的记忆尺度压制肿瘤进程的噪声,即肿瘤细胞的演化受记忆水平的双重影响。In the report,the tumor cell growth model with non-Markovian characteristics was studied,and the memory scales were defined to characterize the non-Markovian dependence of tumor cell evolution.Firstly,the existence of an effective metastasis rate in the evolutionary process of tumor cells was demonstrated;secondly,the equivalence between memory networks and Markov networks was demonstrated.The equivalence depended on the controllability of memory scale,which induced the fluctuations of the growth process of tumor cells and normalized the theoretical expression of the noise in the tumor cell growth during the different processes.The numerical simulation results indicated that the memory scale in the cell mutations amplifies the noise level expressed by tumor cells;on the contrary,the memory scale during the phagocytosis process suppresses the noise of tumor progression,which suggested that the evolution of tumor cells is influenced by the dual effects of the memory levels.

关 键 词：肿瘤细胞生长模型 分子记忆 噪声 非马氏过程 网络等价性 

分 类 号：R181[医药卫生—流行病学] O232[医药卫生—公共卫生与预防医学]