一个良性肿瘤细胞生长的计算机仿真模型

本文建立了一个良性肿瘤在正常细胞组织中生长的计算机仿真模型。初始细胞模型采用二维Voronoi结构,使用繁特卡罗法将其离散成x^*y个小细胞,对肿瘤与正常细胞分别施加蒙特卡罗工关过程使细胞生长。根据细胞组织内营养水平可以决定肿瘤细胞（分别为休眠细胞和有生长繁殖能力的细胞）的生长状态。     

Stochastic Gompertz model of tumour cell growth

In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

A nonlinear structured population model of tumor growth with quiescence

A nonlinear structured cell population model of tumor growth is considered. The model distinguishes between two types of cells within the tumor: proliferating and quiescent. Within each class the behavior of individual cells depends on cell size, whereas the probabilities of becoming quiescent and returning to the proliferative cycle are in addition controlled by total tumor size. The asymptotic behavior of solutions of the full nonlinear model, as well as some linear special cases, is investigated using spectral theory of positive simigroup of operators. Supported in part by the National Science Foundation under Grant No. DMS-8722947     

A model of tumor growth based on cell cycle kinetics

This work describes a mathematical model of growth based on the kinetics of the cell cycle. A traditional model of the cell cycle has been used, with the addition of a resting (G₀) state from which cells could reenter the reproductive cycle. The model assumes that a growth regulatory substance regulates the transition of cells to and from the resting state. Other transitions between the phases of the cycle were modeled as a first order process. Cell loss is an important feature of growth kinetics, and has been represented by a general but tractable mathematical form. The resulting model forms a system of ordinary nonlinear differential equations. Analytic methods are employed first in the study of this system. Simplifying assumptions regarding cell loss give rise to special cases for which equilibrium solutions can be found. One special case, which assumes first order loss from all cell cycle phases at equal rates, is presented here. For small time values, approximations corresponding to exponential growth were developed. The equations describing an intrinsic growth rate were derived. Simulation methods were used to further characterize the behavior of this model. Parameter values were chosen based on animal tumor cell cycle kinetic data, resulting in a set of 45 model simulations. Several tumor treatment protocols were simulated which illustrated the importance of the intrinsic growth rate and cell loss concepts. Although the qualitative behavior regarding absolute and relative growth is reasonable, this model awaits data for model fitting, parameter estimation, or revision of the equations.     

Seminal plasma enhances cervical adenocarcinoma cell proliferation and tumour growth in vivo

Cervical cancer is one of the leading causes of cancer-related death in women in sub-Saharan Africa. Extensive evidence has shown that cervical cancer and its precursor lesions are caused by Human papillomavirus (HPV) infection. Although the vast majority of HPV infections are naturally resolved, failure to eradicate infected cells has been shown to promote viral persistence and tumorigenesis. Furthermore, following neoplastic transformation, exposure of cervical epithelial cells to inflammatory mediators either directly or via the systemic circulation may enhance progression of the disease. It is well recognised that seminal plasma contains an abundance of inflammatory mediators, which are identified as regulators of tumour growth. Here we investigated the role of seminal plasma in regulating neoplastic cervical epithelial cell growth and tumorigenesis. Using HeLa cervical adenocarcinoma cells, we found that seminal plasma (SP) induced the expression of the inflammatory enzymes, prostaglandin endoperoxide synthase (PTGS1 and PTGS2), cytokines interleukin (IL) -6, and -11 and vascular endothelial growth factor-A (VEGF-A). To investigate the role of SP on tumour cell growth in vivo, we xenografted HeLa cells subcutaneously into the dorsal flank of nude mice. Intra-peritoneal administration of SP rapidly and significantly enhanced the tumour growth rate and size of HeLa cell xenografts in nude mice. As observed in vitro, we found that SP induced expression of inflammatory PTGS enzymes, cytokines and VEGF-A in vivo. Furthermore we found that SP enhances blood vessel size in HeLa cell xenografts. Finally we show that SP-induced cytokine production, VEGF-A expression and cell proliferation are mediated via the induction of the inflammatory PTGS pathway.     

Relationship between cytoplasmic pH and proliferation during exponential growth and cellular quiescence

Flow cytometry was used to measure intracellular pH (pHi) on an individual cell basis during exponential and plateau phases of growth. In all three cell lines examined a range of pHi values was associated with exponential growth. When cells from the extremes of the pHi distribution were sorted using a fluorescence-activated cell sorter and then restained for cellular DNA content, it was found that the higher pHi values were associated with enrichment of the S, G2, and M phases of the cell cycle, with a corresponding increase in the percentage of G1 cells at the lower pH1 range, suggesting cell-cycle dependence of pHi. It has been shown previously (I. W. Taylor and P. Hodson, 1984, J. Cell Physiol. 121, 517) that PMC-22 human melanoma cells are capable of entering a distinct pH-dependent quiescent state in response to the acidification of the growth medium which occurs naturally during growth to plateau phase. Simultaneous measurement of pHi and external pH showed that under these conditions pHi was maintained at control values down to an external pH of approximately 6.5, below which cytoplasmic acidification took place. This fall in pHi coincided with the onset of the transition to quiescence. Individual quiescent cells (defined by failure to incorporate bromodeoxyuridine during a 24-h exposure) could not be identified as such on the basis of a low pHi, suggesting that the probability of cell cycling is reduced by lowering pHi. Those cells which remained in cycle showed a markedly reduced rate of DNA synthesis, but a cell-cycle phase distribution similar to that in exponential growth, indicating that prolongation of all cell-cycle phases is an additional factor influencing overall population growth. The external pH at which both of these effects on cell proliferation kinetics took place in vitro is similar to that which occurs regionally within solid tumors, suggesting that pH effects could play a significant role in determining tumor cell growth in vivo.     

A multiphase model describing vascular tumour growth

In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found in vivo in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs.     

The influence of cell volume changes on tumour cell proliferation

Ion channels and cell volume control participate in a wide variety of cellular functions, including cell proliferation. According to the pump-leak model or the double Donnan system, the cell volume is constant in physiological medium so long as the cell metabolism and the Na-K pump are not inhibited and the passive Na⁺ permeability is not dramatically increased. At short term, this model has been supported by a large number of experiments made on different cell types. However, at long term, it may be insufficient to describe the volume control because it does not take into account the fact that cells possess a large number of membrane transporters and interconnected volume regulatory mechanisms. In this review, we present recent results indicating that, in physiological conditions, ion channels may have important roles in cell volume control. Furthermore, we emphasize that cell proliferation and volume are phenomenologically correlated. On the basis of the macromolecular crowding theory, the possibility that the cell osmolyte and water content mediates this correlation is discussed.Abbreviations 4-AP 4-aminopyridine - NPPB 5-nitro-2-(3-phenylpropylamino)benzoic acid - TEA tetraethylammonium - TOR target of rapamycin Presented at the Biophysical Society Meeting on Ion channels—from structure to desease held in May 2003, Rennes, France     

A unified stoichiometric model for oxidative and oxidoreductive growth of yeasts

Yeasts degrade glucose through different metabolic pathways, where the choice of the pathway is dependent on the nature of the limitation in the various substrates. When oxygen is limiting in addition to glucose, yeasts often grow according to a mixture of oxidative and reductive metabolism. Oxygen may be limiting either by supply or by inherent biological restrictions such as the respiratory bottleneck in Saccharomyces cerevisiae or by both. A unified model incorporating both supply and biological limitations is proposed for the quantitative prediction of growth rates, consumption and production rates, as well as key metabolite concentrations during mixed oxidoreductive metabolism occuring as a result of such oxygen limitations. This simple unstructured model can be applied to different yeast strains while at the same time requiring a minimum number of measured parameters. "Estimators" are utilized in order to predict the presence of supply-side or biological limitations. The values of these estimators also characterize the relative importance of oxidative to total metabolism. Results from the aerobic and oxygen-limited chemostat cultures were used to corroborate the model predictions. During these experiments, the heat released by the yeast cultures was also monitored on-line. The model correctly predicted the overall stoichiometry, steady-state concentrations, and rates including heat dissipation rates measured in the various situations of oxygen limitations. Direct continuous measurements such as heat can be used in conjunction with the unified model for on-line proces control. (c) 1992 John Wiley & Sons, Inc.     

Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis

OBJECTIVE: Cancer stem cells have been identified as the growth root for various malignant tumours and are thought to be responsible for cancer recurrence following treatment. MATERIALS AND METHODS: Here, a predictive mathematical model for the cancer stem cell hypothesis is used to understand tumour responses to chemotherapeutic drugs and judge the efficacy of treatments in arresting tumour growth. The impact of varying drug efficacies on different abnormal cell populations is investigated through the kinetics associated with their decline in response to therapy. RESULTS AND CONCLUSIONS: The model predicts the clinically established 'dandelion phenomenon' and suggests that the best response to chemotherapy occurs when a drug targets abnormal stem cells. We compare continuous and periodic drug infusion. For the latter, we examine the relative importance of the drug cell-kill rate and the mean time between successive therapies, to identify the key attributes for successful treatment.     

WI-38 cell long-term quiescence model system: A valuable tool to study molecular events that regulate growth

A number of cell culture model systems have been used to study the regulation of cell cycle progression at the molecular level. In this paper we describe the WI-38 cell long-term quiescence model system. By modulating the length of time that WI-38 cells are density arrested, it is possible to proportionately alter the length of the prereplicative or G-1 phase which the cell traverses after growth factor stimulation in preparation for entry into DNA synthesis. Through studies aimed at understanding the cause and molecular nature of the prolongation of the prereplicative phase, we have determined that gene expression plays an important role in establishing growth factor “competence” and that once the cell becomes “competent” there is a defined order to the molecular events that follow during the remainder of G-1. More specifically, we have determined that the prolongation represents a delay in the ability of long term quiescent cells to become fully “competent” to respond to growth factors which regulate progression through G-1 into S. This prolongation appears to occur as a result of changes during long term quiescence in the ability of immediate early G-1 specific genes (such as c-myc) to activate the expression of early G-1 specific genes (such as ornithine decarboxylase). While ODC is the first and thus far only growth associated gene identified as a target of c-myc (and the Myc/Max protein complex), it is likely that further studies in this model system will reveal other early G-1 growth regulatory genes. We anticipate that future follow-up studies in this model system will provide additional valuable information abuot the function of growth-regulatory genes in controlling growth factor responsiveness and cell cycle progression.     

A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K ⁺)-limited environment. Our both continuous and discrete models illustrate ‘cancer immunoediting’ as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202–206].     

Evolution of cell motility in an individual-based model of tumour growth

Tumour invasion is driven by proliferation and importantly migration into the surrounding tissue. Cancer cell motility is also critical in the formation of metastases and is therefore a fundamental issue in cancer research. In this paper we investigate the emergence of cancer cell motility in an evolving tumour population using an individual-based modelling approach. In this model of tumour growth each cell is equipped with a micro-environment response network that determines the behaviour or phenotype of the cell based on the local environment. The response network is modelled using a feed-forward neural network, which is subject to mutations when the cells divide. With this model we have investigated the impact of the micro-environment on the emergence of a motile invasive phenotype. The results show that when a motile phenotype emerges the dynamics of the model are radically changed and we observe faster growing tumours exhibiting diffuse morphologies. Further we observe that the emergence of a motile subclone can occur in a wide range of micro-environmental growth conditions. Iterated simulations showed that in identical growth conditions the evolutionary dynamics either converge to a proliferating or migratory phenotype, which suggests that the introduction of cell motility into the model changes the shape of fitness landscape on which the cancer cell population evolves and that it now contains several local maxima. This could have important implications for cancer treatments which focus on the gene level, as our results show that several distinct genotypes and critically distinct phenotypes can emerge and become dominant in the same micro-environment.     

A new mathematical model for avascular tumour growth

The early development of solid tumours has been extensively studied, both experimentally via the multicellular spheroid assay, and theoretically using mathematical modelling. The vast majority of previous models apply specifically to multicell spheroids, which have a characteristic structure of a proliferating rim and a necrotic core, separated by a band of quiescent cells. Many previous models represent these as discrete layers, separated by moving boundaries. Here, the authors develop a new model, formulated in terms of continuum densities of proliferating, quiescent and necrotic cells, together with a generic nutrient/growth factor. The model is oriented towards an in vivo rather than in vitro setting, and crucially allows for nutrient supply from underlying tissue, which will arise in the two-dimensional setting of a tumour growing within an epithelium. In addition, the model involves a new representation of cell movement, which reflects contact inhibition of migration. Model solutions are able to reproduce the classic three layer structure familiar from multicellular spheroids, but also show that new behaviour can occur as a result of the nutrient supply from underlying tissue. The authors analyse these different solution types by approximate solution of the travelling wave equations, enabling a detailed classification of wave front solutions.