Study On Nonlinear Stochastic Dynamics Of Tumor Cell Phenotypic Switch

The tumor,especially the malignant tumor,is one of the serious diseases which destroy the human's health.The colorectal cancer and breast cancer which have the high rate of incidence and death are the main reason for the death of male and female cancer patients respectively.The heterogeneity of tumors is the essential problem which is difficult to be solved in the clinical therapy.Many experiments show that the reason of the heterogeneity of tumors is that there are different cancer cell phenotypes which can stochastically switch from one phenotype to another.Thus,understanding the mechanisms and dynamics of cancer cell phenotype stochastic switch has become a challenging task in biophysics.In this thesis,the unidirectional phenotype switching system which is concerned with the three cancer cell phenotypes of the colonic crypt in colorectal cancer and the bidirectional phenotype switching system which is concerned with three cancer cell phenotypes of breast tumor are investigated by virtue of the stochastic nonlinear theory and the numerical simulation technique.The study on nonlinear stochastic dynamics of cancer cell phenotype switching is launched and the main results are presented as following:First,based on the continuous deterministic model of the colonic crypt,the relative fluctuations of the different cell populations induced by the noise around equilibrium states with four feedback mechanisms(LL,LS,SL,SS)are studied.The theoretical formulae of Fano factors,covariances,and susceptibilities around the steady states are derived by virtue of the Langevin theory.Under the reasonable range of physiologically parameter values,the three cell populations(stem cells(SCs),transit cells(TCs)and differentiated cells(DCs))dynamic equilibrium in the normal colonic crypt,the steady state values w:ith the net growth rates increasing and the relative fluctuations around the steady states are numerically illustrated under the four different feedback mechanisms.We found that the cell populations dynamic equilibrium in the normal colonic crypt can be illustrated by all the four feedback mechanisms,but the behaviors of relative fluctuations around steady states are obvious different with different feedback mechanisms.With the increasing of net growth rate of TCs,we firstly found that a van der Waals-like liquid-gas phase transition loop,which can demonstrate that there exists a transient phase(colonic adenoma)between the normal(healthy tissue)and cancerous(colorectal cancer)phases and qualitatively explain the transition process from the healthy colonic crypt to cancerous crypt,appears on the Fano factors of TCs around the steady state in the cases of LS and SS feedbacks.Our novel findings suggest that the mathematical model with LS or SS feedback might be better to elucidate the dynamics between the normal and abnormal(cancerous)phases in a colonic crypt.Second,based on the epithelial-mesenchymal transition(EMT)process induced by the external signal(TGF-?)in the breast tumor,we found a core gene negative regulatory circuit model,proposed a series of dynamical equations which can illustrate the cancer cell phenotypic switch in breast cancer,and built a Waddington-like epigenetic landscape(potential landscape).We approximately derived the formula of mean first passage time(MFPT)of two kinds of cancer cell(the stem cell and the basal cell)phenotypic switch,which is used to judge the main direction of phenotypic switch and qualitatively consistent with numerical results.Besides,we studied how the different systemic parameters,such as the noise intensity,the external signal intensity,the self-activation strength of regulators or the repression strength,to influence the direction of phenotypic switch of this two cell phenotypes.Most importantly,the dynamical equations we proposed can be used to illustrate a series of macroscopic physiological phenomena in breast cancers,such as the three breast cancer cell phenotypes(stem cells,basal cells,and luminal cells)coexistence,the "TGF-? paradox" in tumor therapy,the five clinical subtypes of breast cancer cells,the phenotypic equilibrium in populations of breast cancer cell line under certain microenviroment,and the effects of transient TGF-? on cancer metastasis.Our results could provide new insights into how the microenvironmental fluctuations,gene mutations and external signals to influence the heterogeneity of breast tumors(the proportion of different phenotypes in the tumor)and we hope that these results can give some help for the new designs of biologists'experiments and some potential tumor clinical therapy strategies.