Stochastic modeling of nonlinear epidemiology

The objectives of this paper to analyse, model and simulate the spread of an infectious disease by resorting to modern stochastic algorithms. The approach renders it possible to circumvent the simplifying assumption of linearity imposed in the majority of the past works on stochastic analysis of epidemic processes. Infectious diseases are often transmitted through contacts of those infected with those susceptible; hence the processes are inherently nonlinear. According to the classical model of Kermack and McKendrick, or the SIR model, three classes of populations are involved in two types of processes: conversion of susceptibles (S) to infectives (I) and conversion of infectives to removed (R). The master equations of the SIR process have been formulated through the probabilistic population balance around a particular state by considering the mutually exclusive events. The efficacy of the present methodology is mainly attributable to its ability to derive the governing equations for the means, variances and covariance of the random variables by the method of system-size expansion of the nonlinear master equations. Solving these equations simultaneously along with rates associated influenza epidemic data yields information concerning not only the means of the three populations but also the minimal uncertainties of these populations inherent in the epidemic. The stochastic pathways of the three different classes of populations during an epidemic, i.e. their means and the fluctuations around these means, have also been numerically simulated independently by the algorithm derived from the master equations, as well as by an event-driven Monte Carlo algorithm. The master equation and Monte Carlo algorithms have given rise to the identical results.     

Stochastic modeling of controlled-drug release

A drug release process by the oral route is random in nature and thus is subject to constant fluctuations. Moreover, individuals have varied tolerances to such fluctuations. The objective of this work is to characterize these fluctuations by a stochastic formalism. The system under consideration, i.e., the gastrointestinal tract consists of four consecutive compartments, i.e., stomach, duodenum, jejunum, and ileum. The master equation of the system as well as the governing equations for the means, variances, and covariances of the random variables, each representing the number of microspheres in an individual compartment, have been derived through the probabilistic population balance. These equations have been numerically solved to predict the total release fraction of drug and its internal fluctuations, and the dynamic statistics (means, variances, and covariances) of the amount of drug in each compartment at any time after administration. The dissolution-intensity functions in the model have been recovered from the available in vitro dissolution data from controlled-release pellets of isosorbide-5-nitrate (IS-5-N) by assuming that the rate of release is of the first order. The residence times and transition-intensity functions of drug in the individual compartments have been estimated from the available data generated by the gamma scintigraphies of IS-5-N pellets labeled by ¹¹¹In. Based on these parameters, the total numbers of dissolved drug microspheres and their fluctuations at any instance have been calculated. The model is in accord with the existing in vivo dissolution data of the same drug independently obtained through plasma analysis. More important, the model predicts that fluctuations in terms of the standard deviations of the numbers of particles in the duodenum, jejunum, and ileum can be of the same orders of magnitude as the corresponding mean numbers when 100 microspheres are simultaneously administered orally; in practice, such fluctuations characterized by these deviations could result in an undesirable release profile. Discussion is given of the potential direct clinical application of the results obtained as well as the plausible indirect application of these results and the model derived to the analyses of chemical and biochemical reactors.     

A fully continuous individual-based model of tumor cell evolution

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these four elements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar.     

Stress chaperone GRP78/BiP confers chemoresistance to tumor-associated endothelial cells

The tumor vasculature is essential for tumor growth and survival and is a key target for anticancer therapy. Glioblastoma multiforme, the most malignant form of brain tumor, is highly vascular and contains abnormal vessels, unlike blood vessels in normal brain. Previously, we showed that primary cultures of human brain endothelial cells, derived from blood vessels of malignant glioma tissues (TuBEC), are physiologically and functionally different from endothelial cells derived from nonmalignant brain tissues (BEC) and are substantially more resistant to apoptosis. Resistance of TuBEC to a wide range of current anticancer drugs has significant clinical consequences as it represents a major obstacle toward eradication of residual brain tumor. We report here that the endoplasmic reticulum chaperone GRP78/BiP is generally highly elevated in the vasculature derived from human glioma specimens, both in situ in tissue and in vitro in primary cell cultures, compared with minimal GRP78 expression in normal brain tissues and blood vessels. Interestingly, TuBEC constitutively overexpress GRP78 without concomitant induction of other major unfolded protein response targets. Resistance of TuBEC to chemotherapeutic agents such as CPT-11, etoposide, and temozolomide can be overcome by knockdown of GRP78 using small interfering RNA or chemical inhibition of its catalytic site. Conversely, overexpression of GRP78 in BEC rendered these cells resistant to drug treatments. Our findings provide the proof of principle that targeting GRP78 will sensitize the tumor vasculature to chemotherapeutic drugs, thus enhancing the efficacy of these drugs in combination therapy for glioma treatment.     

Regulation of multidrug resistance in cancer cells by hyaluronan

Multidrug resistance in cancer cells is often due to ATP-dependent efflux pumps, but is also linked to alterations in cell survival and apoptotic signaling pathways. We have found previously that perturbation of hyaluronan-tumor cell interaction by treatment with hyaluronan oligosaccharides suppresses the phosphoinositide 3-kinase/Akt cell survival signaling pathway in cancer cells and reduces tumor growth in vivo. Here we find that these oligomers suppress both the MAP kinase and phosphoinositide 3-kinase pathways in multidrug resistant tumor cells and sensitize these cells to a variety of chemotherapeutic drugs. On the other hand, increased hyaluronan production induces resistance in drug-sensitive tumor cells. Likewise, increased expression of emmprin, which is a glycoprotein that is present on the surface of most malignant cancer cells and that stimulates hyaluronan production, also induces increased resistance. Thus, perturbation of hyaluronan signaling may provide a dual therapeutic role, since it has intrinsic suppressive effects on tumor growth as well as sensitizing cancer cells to chemotherapeutic agents.     

靶向Survivin基因与肿瘤

Survivin基因不仅表达于绝大多数的肿瘤细胞中,也存在于人体正常的细胞中,它具有抑制凋亡和调节有丝分裂的双重作用．临床研究表明：下调Survivin基因的表达或者抑制Survivin蛋白的功能,可以降低肿瘤细胞的生长潜力、增加凋亡的比例,而且可以增强肿瘤细胞对抗肿瘤药物和放射线的敏感性．许多抗肿瘤药物通过诱导细胞凋亡而发挥功能．但某些肿瘤表现出对它们的耐药性。导致肿瘤耐药性的一个最重要的因素就是Survivin的表达．有关细胞凋亡途径和Survivin基因表达等方面的研究可为发现和发展新型抗肿瘤药物提供新的途径．     

Phenotypic characterization of telomerase-immortalized primary non-malignant and malignant tumor-derived human prostate epithelial cell lines

In vitro human prostate cell culture models are critical for clarifying the mechanism of prostate cancer progression and for testing preventive and therapeutic agents. Cell lines ideal for the study of human primary prostate tumors would be those derived from spontaneously immortalized tumor cells; unfortunately, explanted primary prostate cells survive only short-term in culture, and rarely immortalize spontaneously. Therefore, we recently have generated five immortal human prostate epithelial cell cultures derived from both the benign and malignant tissues of prostate cancer patients with telomerase, a gene that prevents cellular senescence. Examination of these cell lines for their morphologies and proliferative capacities, their abilities to grow in low serum, to respond to androgen stimulation, to grow above the agar layer, to form tumors in SCID mice, suggests that they may serve as valid, useful tools for the elucidation of early events in prostate tumorigenesis. Furthermore, the chromosome alterations observed in these immortalized cell lines expressing aspects of the malignant phenotypes imply that these cell lines accurately recapitulate the genetic composition of primary tumors. These novel in vitro models may offer unique models for the study of prostate carcinogenesis and also provide the means for testing both chemopreventive and chemotherapeutic agents.     

Modeling the effects of vasculature evolution on early brain tumor growth

Mathematical modeling of both tumor growth and angiogenesis have been active areas of research for the past several decades. Such models can be classified into one of two categories: those that analyze the remodeling of the vasculature while ignoring changes in the tumor mass, and those that predict tumor expansion in the presence of a non-evolving vasculature. However, it is well accepted that vasculature remodeling and tumor growth strongly depend on one another. For this reason, we have developed a two-dimensional hybrid cellular automaton model of early brain tumor growth that couples the remodeling of the microvasculature with the evolution of the tumor mass. A system of reaction-diffusion equations has been developed to track the concentration of vascular endothelial growth factor (VEGF), Ang-1, Ang-2, their receptors and their complexes in space and time. The properties of the vasculature and hence of each cell are determined by the relative concentrations of these key angiogenic factors. The model exhibits an angiogenic switch consistent with experimental observations on the upregulation of angiogenesis. Particularly, we show that if the pathways that produce and respond to VEGF and the angiopoietins are properly functioning, angiogenesis is initiated and a tumor can grow to a macroscopic size. However, if the VEGF pathway is inhibited, angiogenesis does not occur and tumor growth is thwarted beyond 1-2mm in size. Furthermore, we show that tumor expansion can occur in well-vascularized environments even when angiogenesis is inhibited, suggesting that anti-angiogenic therapies may not be sufficient to eliminate a population of actively dividing malignant cells.     

Mathematical modeling of ovarian cancer treatments: sequencing of surgery and chemotherapy

Ovarian cancer has long been one of the most common forms of cancer in women. The main treatment for ovarian cancer comprises a combination of surgery and chemotherapy. In an effort to improve treatment strategies, a variety of mathematical models have been developed in the literature. In this paper, we consider a simple mathematical model that incorporates tumor growth as well as the effects of chemotherapeutic and surgical treatments in ovarian cancer. We consider several growth models and combine them with different cell-kill hypotheses. Surgery is assumed to eliminate a fixed fraction of tumor cells instantaneously. We discuss how different models predict the optimal sequencing of chemotherapeutic and surgical treatments. This work has been carried out in the context of ovarian cancer; however, the results may also be useful for other kind of cancers.     

The importance of individual developmental variation in stage‐structured population models

Population stage structure is fundamental to ecology, and models of this structure have proven useful in many different systems. Many ecological variables other than stage, such as habitat type, site occupancy and metapopulation status are also modelled using transitions among discrete states. Transitions among life stages can be characterised by the distribution of time spent in each stage, including the mean and variance of each stage duration and within‐individual correlations among multiple stage durations. Three modelling traditions represent stage durations differently. Matrix models can be derived as a long‐run approximation from any distribution of stage durations, but they are often interpreted directly as a Markov model for stage transitions. Statistical stage‐duration distribution models accommodate the variation typical of cohort development data, but such realism has rarely been incorporated in population theory or statistical population models. Delay‐differential equation models include lags but no variation, except in limited cases. We synthesise these models in one framework and illustrate how individual variation and correlations in development can impact population growth. Furthermore, different development models can yield the same long‐term matrix transition rates but different sensitivities and elasticities. Finally, we discuss future directions for estimating realistic stage duration models from data.     

Cancer stem cells--old concepts, new insights

Cancer has long been viewed as an exclusively genetic disorder. The model of carcinogenesis, postulated by Nowell and Vogelstein, describes the formation of a tumor by the sequential accumulation of mutations in oncogenes and tumor suppressor genes. In this model, tumors are thought to consist of a heterogeneous population of cells that continue to acquire new mutations, resulting in a highly dynamic process, with clones that out compete others due to increased proliferative or survival capacity. However, novel insights in cancer stem cell research suggest another layer of complexity in the process of malignant transformation and preservation. It has been reported that only a small fraction of the cancer cells in a malignancy have the capacity to propagate the tumor upon transplantation into immuno-compromised mice. Those cells are termed 'cancer stem cells' (CSC) and can be selected based on the expression of cell surface markers associated with immature cell types. In this review, we will critically discuss these novel insights in CSC-related research. Where possible we integrate these results within the genetic model of cancer and illustrate that the CSC model can be considered an extension of the classic genetic model rather than a contradictory theory. Finally, we discuss some of the most controversial issues in this field.     

Formulating variable carrying capacity by exploring a resource dynamics-based feedback mechanism underlying the population growth models

Most of the population growth models comprise the concept of carrying capacity presume that a stable population would have a saturation level characteristic. This indicates that the population growth models have a common implicit feature of resource-limited growth, which contributes at a later stage of population growth by forming a numerical upper bound on the population size. However, a general underlying resource dynamics of the models has not been previously explored, which is the focus of present study. In this paper, we found that there exists a conservation of energy relationship comprising the terms of available resource and population density, jointly interpreted here as total available vital energy in a confined environment. We showed that this relationship determines a density-dependent functional form of relative population growth rate and consequently the parametric equations are in the form depending upon the population density, resource concentration, and time. Thus, the derived form of relative population growth rate is essentially a feedback type, i.e., updating parametric values for the corresponding population density. This resource dynamics-based feedback approach has been implemented for formulating variable carrying capacity in a confined environment. Particularly, at a constant resource replenishment rate, a density-dependent population growth equation similar to the classic logistic equation is derived, while one of the regulating factors of the underlying resource dynamics is that the resource consumption rate is directly proportional to the resource concentration. Likewise two other population growth equations similar to two known popular growth equations are derived based on this resource dynamics-based feedback approach. Using microcosm-derived data of fungus T. virens, we fitted one derived population growth model against the datasets, and concluded that this approach is practically implementable for studying a single population growth regulation in a confined environment.     

Diffusion analysis and stationary distribution of the two-species lottery competition model

The lottery model is a stochastic population model in which juveniles compete for space. Examples include sedentary organisms such as trees in a forest and members of marine benthic communities. The behavior of this model appears to be characteristic of that found in other sorts of stochastic competition models. In a community with two species, it was previously demonstrated that coexistence of the species is possible if adult death rates are small and environmental variation is large. Environmental variation is incorporated by assuming that the birth rates and death rates are random variables. Complicated conditions for coexistence and competitive exclusion have been derived elsewhere. In this paper, simple and easily interpreted conditions are found by using the technique of diffusion approximation. Formulae are given for the stationary distribution and means and variances of population fluctuations. The shape of the stationary distribution allows the stability of the coexistence to be evaluated.     

Tumor microenvironment: the role of the tumor stroma in cancer

The tumor microenvironment, composed of non-cancer cells and their stroma, has become recognized as a major factor influencing the growth of cancer. The microenvironment has been implicated in the regulation of cell growth, determining metastatic potential and possibly determining location of metastatic disease, and impacting the outcome of therapy. While the stromal cells are not malignant per se, their role in supporting cancer growth is so vital to the survival of the tumor that they have become an attractive target for chemotherapeutic agents. In this review, we will discuss the various cellular and molecular components of the stromal environment, their effects on cancer cell dynamics, and the rationale and implications of targeting this environment for control of cancer. Additionally, we will emphasize the role of the bone marrow-derived cell in providing cells for the stroma.     

TSPO over-expression increases motility, transmigration and proliferation properties of C6 rat glioma cells

Gliomas are one of the most malignant cancers. The molecular bases regulating the onset of such tumors are still poorly understood. The translocator protein (TSPO), formerly known as the peripheral-type benzodiazepine receptor, is a mitochondrial permeability transition (MPT)-pore protein robustly expressed in gliomas and involved in the regulation of apoptosis and cell proliferation. TSPO expression levels have been correlated with tumor malignancy. Here we describe the production of C6 rat glioma cells engineered to over-express the TSPO protein with the aim of providing the first direct evidence of a correlation between TSPO expression level and glioma cell aggressiveness. We observed that TSPO potentiates proliferation, motility and transmigration capabilities as well as the ability to overcome contact-induced cell growth inhibition of glioma cells. On the whole, these data demonstrate that TSPO density influences metastatic potential of glioma cells. Since several data suggest that TSPO ligands may act as chemotherapeutic agents, in this paper we also demonstrate that TSPO ligand-induced cell death is dependent on TSPO density. These findings suggest that the use of TSPO ligands as chemotherapeutic agents could be effective on aggressive tumor cells with a high TSPO expression level.     

Effects of Low Confluency,Serum Starvation and Hypoxia on the Side Population of Cancer Cell Lines

The cancer stem cell theory describes a small subset of cancer cells that have the ability to initiate and drive the growth of a tumor. The niche refers to the environmental factors and the surrounding cells within which the tumor develops. The exact relationship between cancer stem cells and the tumor niche is not known. However, using side population analysis by flow cytometry, it is possible to analyze the relationship between environmental stresses and putative cancer stem cells. The side population is a subpopulation of cells that efflux Hoechst 33342 and has been previously shown to be enriched for cancer stem cells. Using this technique, we characterized the response of side population cells to low confluency, serum starvation and hypoxia using three different human cancer cell lines. We found that these stresses, characteristic of the tumor niche enrich the side population of DLD1, SW480 and MCF7 cancer cell lines, thus possibly predisposing the tumor to a more malignant phenotype.     

Disentangling the relative importance of changes in climate and land-use intensity in driving recent bird population trends

Threats to biodiversity resulting from habitat destruction and deterioration have been documented for many species, whilst climate change is regarded as increasingly impacting upon species' distribution and abundance. However, few studies have disentangled the relative importance of these two drivers in causing recent population declines. We quantify the relative importance of both processes by modelling annual variation in population growth of 18 farmland bird species in the UK as a function of measures of land-use intensity and weather. Modelled together, both had similar explanatory power in accounting for annual fluctuations in population growth. When these models were used to retrodict population trends for each species as a function of annual variation in land-use intensity and weather combined, and separately, retrodictions incorporating land-use intensity were more closely linked to observed population trends than retrodictions based only on weather, and closely matched the UK farmland bird index from 1970 onwards. Despite more stable land-use intensity in recent years, climate change (inferred from weather trends) has not overtaken land-use intensity as the dominant driver of bird populations.     

Animal models relevant to human prostate carcinogenesis underlining the critical implication of prostatic stem/progenitor cells

Recent development of animal models relevant to human prostate cancer (PC) etiopathogenesis has provided important information on the specific functions provided by key gene products altered during disease initiation and progression to locally invasive, metastatic and hormone-refractory stages. Especially, the characterization of transgenic mouse models has indicated that the inactivation of distinct tumor suppressor proteins such as phosphatase tensin homolog deleted on chromosome 10 (PTEN), Nkx3.1, p27(KIP1), p53 and retinoblastoma (pRb) may cooperate for the malignant transformation of prostatic stem/progenitor cells into PC stem/progenitor cells and tumor development and metastases. Moreover, the sustained activation of diverse oncogenic signaling elements, including epidermal growth factor receptor (EGFR), sonic hedgehog, Wnt/β-catenin, c-Myc, Akt and nuclear factor-kappaB (NF-κB) also may contribute to the acquisition of more aggressive and hormone-refractory phenotypes by PC stem/progenitor cells and their progenies during disease progression. Importantly, it has also been shown that an enrichment of PC stem/progenitor cells expressing stem cell-like markers may occur after androgen deprivation therapy and docetaxel treatment in the transgenic mouse models of PC suggesting the critical implication of these immature PC cells in treatment resistance, tumor re-growth and disease recurrence. Of clinical interest, the molecular targeting of distinct gene products altered in PC cells by using different dietary compounds has also been shown to counteract PC initiation and progression in animal models supporting their potential use as chemopreventive or chemotherapeutic agents for eradicating the total tumor cell mass, improving current anti-hormonal and chemotherapies and preventing disease relapse.