A cellular automata model of tumor-immune system interactions

We present a hybrid cellular automata-partial differential equation model of moderate complexity to describe the interactions between a growing tumor next to a nutrient source and the immune system of the host organism. The model allows both temporal and two-dimensional spatial evolution of the system under investigation and is comprised of biological cell metabolism rules derived from both the experimental and mathematical modeling literature. We present numerical simulations that display behaviors which are qualitatively similar to those exhibited in tumor-immune system interaction experiments. These include spherical tumor growth, stable and unstable oscillatory tumor growth, satellitosis and tumor infiltration by immune cells. Finally, the relationship between these different growth regimes and key system parameters is discussed.     

A stochastic model in tumor growth

A stochastic model of solid tumor growth based on deterministic Gompertz law is presented. Tumor cells evolution is described by a one-dimensional diffusion process limited by two absorbing boundaries representing healing threshold and patient death (carrying capacity), respectively. Via a numerical approach the first exit time problem is analysed for the process inside the region restricted by the boundaries. The proposed model is also implemented to simulate the effects of a time-dependent therapy. Finally, some numerical results are obtained for the specific case of a parathyroid tumor.     

A mathematical model for drug administration by using the phagocytosis of red blood cells

 A mathematical model for the delivery of drug directly to the macrophages by using the phagocytosis of senescent red blood cells is proposed. The model is based on the following assumption: At time t=0 a preassigned red blood cell population n(0, a)=φ(a), a>0, loaded by the drug, is injected in the blood circulation. Among the cells of that population only those with an age a≧ā (ā=120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than ā. Within the red blood cells it cannot be metabolized, neither can it diffuse through their membranes. The emphasis of the paper is on the mathematical properties and on the formulation of the control problem. Received 15 December 1994; received in revised form 20 July 1995     

Interaction of PD-L1 on tumor cells with PD-1 on tumor-specific T cells as a mechanism of immune evasion: implications for tumor immunotherapy

Programmed death receptor ligand 1 (PD-L1, also called B7-H1) is a recently described B7 family member. In contrast to B7-1 and B7-2, PD-L1 does not interact with either CD28 or CTLA-4. To date, one specific receptor has been identified that can be ligated by PD-L1. This receptor, programmed death receptor 1 (PD-1), has been shown to negatively regulate T-cell receptor (TCR) signaling. Upon ligating its receptor, PD-L1 has been reported to decrease TCR-mediated proliferation and cytokine production. PD-1 gene–deficient mice developed autoimmune diseases, which early led to the hypothesis of PD-L1 regulating peripheral tolerance. In contrast to normal tissues, which show minimal surface expression of PD-L1 protein, PD-L1 expression was found to be abundant on many murine and human cancers and could be further up-regulated upon IFN- stimulation. Thus, PD-L1 might play an important role in tumor immune evasion. This review discusses the currently available data concerning negative T-cell regulation via PD-1, the blockade of PD-L1/PD-1 interactions, and the implications for adoptive T-cell therapies.     

A delay differential equation model for tumor growth

We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle. We analyze the stability of the system and prove a theorem based on the argument principle to determine the stability of a fixed point and show that the stability may depend on the delay. We show theoretically and through numerical simulations that periodic solutions may arise through Hopf Bifurcations.Send offprint requests to:Minaya Villasana     

具免疫应答和细胞内部时滞的HIV-1感染模型的稳定性分析

考虑了CTLs免疫应答和细胞内部时滞建立HIV-1感染的数学模型.对模型的无感染平衡点全局稳定性进行了分析,对CTLs未激活和CTLs已激活的感染平衡点给出了局部稳定的充分条件.数值模拟支持了得到的理论结果.     

The inhibition of TNF-alpha anti-tumoral properties by blocking antibodies promotes tumor growth in a rat model

Tumor necrosis factor (TNF) antagonists represent a milestone in the therapy of autoimmune conditions. Anti-TNF antibodies have been approved for clinical use and during the last eight years thousands of patients have been treated. However, the long-term sequelae of anti-TNF agents in promoting carcinogenesis remain unclear. This study sought to define the role of intra-tumor TNF-alpha production on cancer cell progression and to determine whether TNF-alpha antibodies can suppress anti-tumoral immunity. Using an experimental animal tumor model we demonstrate that anti-TNF-alpha antibodies hinder anti-tumor immune responses and promote growth of immunogenic rat colon tumors (REG) that are always rejected by immunocompetent untreated rats. The major role of TNF-alpha in the anti-tumoral immune response was confirmed by transfecting progressive and tolerogenic rat colon tumor cells (PRO) with the TNF-alpha gene. PRO tumor cells secreting TNF-alpha induce tumor-infiltrating dendritic cell (DC) activation. This triggers a potent immune response leading to tumor rejection and long-lasting immunity. Therefore, the prominent role of TNF-alpha in anti-tumoral immune responses underscores the need for caution and close surveillance following the administration of TNF inhibitors.     

Approximate solution of a model of biological immune responses incorporating delay

A model of the humoral immune response, proposed by Dibrov, Livshits and Volkenstein (1977b), in which the antibody production by a constant target cell population depends on the antigenic stimulation at earlier times, is considered from an analytic standpoint. A method of approximation based on a consideration of the asymptotic limit of large delay in the antibody response is shown to be applicable, and to give results similar to those obtained numerically by the above authors. The relevance of this type of approximation to other systems exhibiting outbreak phenomena is discussed.     

Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia

Cyclical neutropenia (CN) is a rare hematopoietic disorder in which the patient's neutrophil level drops to extremely low levels for a few days approximately every three weeks. CN is effectively treated with granulocyte colony stimulating factor (G-CSF), which is known to interfere with apoptosis in neutrophil precursors and to consequently increase the circulating neutrophil level. However, G-CSF treatment usually fails to eliminate the oscillation. In this study, we establish an age-structured model of hematopoiesis, which reduces to a set of four delay differential equations with specific forms of initial functions. We numerically investigate the possible stable solutions of the model equations with respect to changes in the parameters as well as the initial conditions. The results show that the hematopoietic system possesses multistability for parameters typical of the normal healthy state. From our numerical results, decreasing the proliferation rate of neutrophil precursors or increasing the stem cell death rate are two possible mechanisms to induce cyclical neutropenia, and the periods of the resulting oscillations are independent of the changing parameters. We also discuss the dependence of the model solution on the initial condition at normal parameter values corresponding to a healthy state. Using insight from our results we design a hybrid treatment method that is able to abolish the oscillations in CN.     

The selection of tumor variants with altered expression of classical and nonclassical MHC class I molecules: implications for tumor immune escape

Tumor immune escape variants can be identified in human and experimental tumors. A variety of different strategies are used by tumor cells to avoid recognition by different immune effector mechanisms. Among these escape routes, alteration of MHC class I cell surface expression is one of the mechanisms most widely used by tumor cells. In this review we focus our attention on the T-cell immune selection of MHC class I–deficient tumor variants. Different altered MHC class I phenotypes that originate from multiple molecular mechanisms can be identified in human tumors. MHC-deficient tumor clones can escape T-cell immune responses, but are in theory more susceptible to NK-cell–mediated lysis. In this context, we also review the controversial issue of the aberrant expression of nonclassical HLA class I molecules, particularly HLA-G, in tumors. This expression may be relevant in tumor cells that have lost the capacity to interact with NK inhibitory receptors—namely, those tumor cells with no HLA-B or HLA-C expression. Most published studies have not analyzed these possibilities and do not provide information about the complete HLA-A, HLA-B, or HLA-C molecule profiles of the tumors studied. In contrast, HLA-E has been reported to be expressed in some tumor cell lines with very low HLA-A, HLA-B, and HLA-C expression, suggesting that HLA-E may indeed, in some cases, play a role by inhibiting NK lysis of cells that otherwise would be destroyed by NK cells. Finally, we provide evidence that the status of the immune system in the tumor-bearing animal is capable of defining the MHC profile of the tumor cells. In other words, MHC class I–negative metastatic colonies are produced in immunocompetent animals, and MHC class I–positive colonies in T-cell immunodeficient individuals.This article forms part of the Symposium in Writing Tumor escape from the immune response, published in Vol. 53.     

Autologous control of a highly malignant syngeneic CRNK-16 leukemia in the rat: a role for NK cells

It is unclear whether autologous immunity could be recruited to restrict the progression of leukemia. Patients harboring leukemia commonly display suppressed cell mediated immunity, which may contribute to their inability to control the disease. Immune response against leukemia is evident in allogeneic HLA-mismatched bone marrow transplantation, implicating the involvement of NK cells. This graft-versus-leukemia (GVL) activity suggests that, if not suppressed, an autologous NK cell response could potentially control acute leukemia that had down-regulated HLA expression. In the current study we assessed the role of non-suppressed autologous NK cells in controlling a syngeneic highly malignant leukemia, the CRNK-16 line, that constitute a major cause of natural death in aged F344 rats. A minuscule dose of 60 CRNK-16 leukemia cells per rat was sufficient to induce 50% mortality rates, and animals that survived this challenge did not show improved survival upon a second challenge. The CRNK-16 line was found to exhibit low levels of MHC-I, and selective in vivo depletion of NK cells nullified in vitro NK activity against the CRNK-16 line and reduced survival rates from this leukemia. In vivo activation of NK cells, employing low doses of poly I-C or IL-12, increased in vitro NK activity against the leukemia and dramatically improved survival rates when treatment was initiated before, but not after leukemia inoculation. These results indicate the ability of competent autologous NK cells to restrict highly malignant non-immunogenic leukemia. Thereby, this model presents an opportunity to study specific in vivo NK-leukemia interactions.     

The ovarian follicle as a model for the cell-mediated control of tissue growth

Summary Thy-1⁺ cells, producing Thy-1⁺ material, have been demonstrated by the indirect immunoperoxidase technique in the theca of growing ovarian follicles of the rat. OX-2 antigen, known as the minor glycoprotein of rat thymocytes, was detected in granulosa cells of non-growing follicles. Ia⁺ cells of dendritic type and/or activated macrophages were identified in the granulosa of advanced degenerating follicles, and remnants of the zona pellucida exhibited immunoglobulins. In some ovaries immunoglobulins were also bound to the zona pellucida of oocytes of early degenerating antral follicles. Medium-sized antral follicles with degenerating granulosa were occasionally invaded by cells carrying antigens of cytotoxic T lymphocytes or other T lymphocyte subsets, while degenerating large antral follicles were sometimes invaded by cells exhibiting antigen of cells with natural killer function (but not antigens of T lymphocytes). Granulosa cells of some degenerating antral follicles exhibited class-I antigens derived from the major histocompatibility complex. We suggest that cell-mediated control mechanisms of antigen expression and metabolism of tissue cells during their differentiation and degeneration should be considered in addition to the well-documented hormonal dependence of some tissues.     

Uptake and presentation of malignant glioma tumor cell lysates by monocyte-derived dendritic cells

Malignant glioma of the CNS is a tumor with a very bad prognosis. Development of adjuvant immunotherapy is hampered by interindividual and intratumoral antigenic heterogeneity of gliomas. To evaluate feasibility of tumor vaccination with (autologous) tumor cells, we have studied uptake of tumor cell lysates by dendritic cells (DCs), and the T-cell stimulatory capacity of the loaded DCs. DCs are professional antigen-presenting cells, which have already been used as natural adjuvants to initiate immune responses in human cancer. An efficacious uptake of tumor cell proteins, followed by processing and presentation of tumor-associated antigens by the DCs, is indeed one of the prerequisites for a potent and specific stimulation of T lymphocytes. Human monocytes were differentiated in vitro to immature DCs, and these were loaded with FITC-labeled tumor cell proteins. Uptake of the tumor cell proteins and presentation of antigens in the context of both MHC class I and II could be demonstrated using FACS analysis and confocal microscopy. After further maturation, the loaded DCs had the capacity to induce specific T-cell cytotoxic activity against tumor cells. We conclude that DCs loaded with crude tumor lysate are efficacious antigen-presenting cells able to initiate a T-cell response against malignant glioma tumor cells.     

具免疫时滞的HIV感染模型动力学性质分析

讨论了一类具免疫时滞的HIV感染模型.分析了未感染平衡点的全局渐近稳定性,给出了感染无免疫平衡点及感染免疫平衡点局部渐近稳定的充分条件.数值模拟结果表明,当易感细胞生成率的取值使得基本再生数满足平衡存在的条件且低于某一临界值时,时滞对平衡点的稳定性没有影响;若大于该临界值,随着时滞增大,稳定性开关发生,平衡点不稳定,出现一系列Hopf分支,最终表现为周期波动模式.     

关于具时滞的捕食-被捕食系统的稳定性与Hopf分支

研究了一类具时滞的捕食—被捕食系统正平衡解的稳定性和Hopf分支的存在性,即以转化率l为参数,得到存在一列l_k(k=0,1,2…),使当l∈(0,l_0)时正平衡解是渐近稳定的;当l>l_0时,正平衡解是不稳定的,而每一个l_k都是该系统的Hopf分支值,改进了一些已知的工作。     

Functional mechanism of Ginsenosides on tumor growth and metastasis

Ginsengs, has long been used as one medicinal herb in China for more than two thousand years. Many studies have shown that ginsengs have preventive and therapeutic roles for cancer, and play a good complementary role in cancer treatment. Ginsenosides, as most important constituents of ginseng, have been extensively investigated and emphasized in cancer chemoprevention and therapeutics. However, the functional mechanism of Ginsenosides on cancer is not well known. This review will focus on introducing the functional mechanisms of ginsenosides and their metabolites, which regulate signaling pathways related with tumor growth and metastasis. Ginsenosides inhibit tumor growth via upregulating tumor apoptosis, inducing tumor cell differentiation and targeting cancer stem cells. In addition, Ginsenosides regulate tumor microenvironment via suppressing tumor angiogenesis-related proteins and pathways. Structural modification of ginsenosides and their administration alone or combinations with other Chinese medicines or chemical medicines have recently been developed to be a new therapeutic strategy for cancer.     

A mathematical model to study the effects of drugs administration on tumor growth dynamics

A mathematical model for describing the cancer growth dynamics in response to anticancer agents administration in xenograft models is discussed. The model consists of a system of ordinary differential equations involving five parameters (three for describing the untreated growth and two for describing the drug action). Tumor growth in untreated animals is modelled by an exponential growth followed by a linear growth. In treated animals, tumor growth rate is decreased by an additional factor proportional to both drug concentration and proliferating cells. The mathematical analysis conducted in this paper highlights several interesting properties of this tumor growth model. It suggests also effective strategies to design in vivo experiments in animals with potential saving of time and resources. For example, the drug concentration threshold for the tumor eradication, the delay between drug administration and tumor regression, and a time index that measures the efficacy of a treatment are derived and discussed. The model has already been employed in several drug discovery projects. Its application on a data set coming from one of these projects is discussed in this paper.