Growth models with stochastic differential equations. an example from tumor immunology

The effects of demographic and environmental stochasticity on the qualitative behavior of a mathematical model from tumor immunology are studied. The model is defined in terms of a stochastic differential equation whose solution is a limiting diffusion process to a branching process with random environments.     

Stochastic epidemic models: A survey

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.     

Current advances and expectations in tumor immunology]

Natural killer (NK) cells and Interferon (IFN)-gamma have been implicated in immune surveillance against tumor. We demonstrated the critical role of perforin in NK cell-mediated cytotoxic activity and anti-tumor effect in IFN-gamma inducible IL-12. And, we recently reported that TRAIL is constitutively expressed on a substantial proportion of murine NK cells in the liver, and which is responsible for spontaneous cytotoxicity and the anti-metastatic activity against TRAIL-sensitive tumor cells along with perforin and Fas ligand. Interestingly, the TRAIL expression on liver NK cells appeared to be regulated by endogenously produced IFN-gamma. Consisting with this finding, IL-12 and NKT cell specific ligand, alpha-Galactosylceramide (alpha-GalCer), induced TRAIL-mediated cytotoxcity and anti-tumor effect, and which was mediated by TRAIL expressed on IFN-gamma-activated NK cells. Tumor necrosis factor(TNF)-related apoptosis-inducing ligand (TRAIL) is a type II transmembrane protein belonging to the TNF family, which preferentially induces apoptotic cell death in various tumor cells in vitro. Preclinical studies in mice and nonhuman primates have shown that administration of recombinant soluble forms of TRAIL could suppress the growth of TRAIL-sensitive tumor xenografts with no apparent systemic toxicity. These studies suggested a potential utility of TRAIL as a cancer therapeutic, although TRAIL expression at protein levels and its physiological roles in tumor surveillance has remained unknown. Presented findings provide the first evidence for the physiological function of TRAIL as a tumor suppressor.     

The complex role of B7 molecules in tumor immunology

T-cell activation requires the interaction of the T-cell receptor with a cognate major histocompatibility complex (MHC)-peptide complex. Initiated by antigen engagement, the adaptive immune response is orchestrated by a complex balance between stimulatory and inhibitory signals that are predominantly controlled by members of the B7 family. Here, we review the current knowledge on B7 family members concerning their constitutive and regulated expression, modulation of the immune response and their role in the evasion of host immune surveillance. We also discuss recent therapeutic strategies that aim to improve immune-cell recognition of tumors and induce tolerance to autoreactive immune responses in normal tissues by manipulating B7 functions.     

A Volterra representation for some neuron models

A Volterra-like polynomial representation is derived and its convergence discussed for two neuronal models in which subthreshold inputs are integrated either without loss (integrate and fire) or with a decay which follows an exponential time course (leaky integrator). This polynomial representation provides a kind of nonlinear transfer function for the nonlinear encoding process. Standard formulae are used to derive explicitely the output for various inputs as in linear system theory. Moreover, the nonlinear transfer function associated with cascades or networks of neurons can be also obtained. Finally, extensions and implications of these results are discussed.     

Translational models of tumor angiogenesis: A nexus of in silico and in vitro models

Emerging evidence shows that endothelial cells are not only the building blocks of vascular networks that enable oxygen and nutrient delivery throughout a tissue but also serve as a rich resource of angiocrine factors. Endothelial cells play key roles in determining cancer progression and response to anti-cancer drugs. Furthermore, the endothelium-specific deposition of extracellular matrix is a key modulator of the availability of angiocrine factors to both stromal and cancer cells. Considering tumor vascular network as a decisive factor in cancer pathogenesis and treatment response, these networks need to be an inseparable component of cancer models. Both computational and in vitro experimental models have been extensively developed to model tumor-endothelium interactions. While informative, they have been developed in different communities and do not yet represent a comprehensive platform. In this review, we overview the necessity of incorporating vascular networks for both in vitro and in silico cancer models and discuss recent progresses and challenges of in vitro experimental microfluidic cancer vasculature-on-chip systems and their in silico counterparts. We further highlight how these two approaches can merge together with the aim of presenting a predictive combinatorial platform for studying cancer pathogenesis and testing the efficacy of single or multi-drug therapeutics for cancer treatment.     

A survey of anthocyanins in fruits of some angiosperms,I

The anthocyanin pigments in the fruits of fifty-two species belonging to seventeen families of angiosperms were investigated paper-chromatographicallly. They were identified as cyanidin 3-monoglucoside, pelargonidin 3-monoglucoside, cyanidin 3-rutinoside, pelargonidin 3-rutinoside, cyanidin 3-xylosylglucoside, cyanidin 3-xylosylgalactoside, delphinidin 3-xylosylglucoside and delphinidin 3-sophorosido-5-monoglucoside. Of those anthocyanins detected, the most common was cyanidin 3-monoglucoside. In general, the plants belonging to a certain genus contained the same anthocyanin.     

Animal models for gastric Helicobacter immunology and vaccine studies

Over the last decade animal models have been used extensively to investigate disease processes and therapy for Helicobacter pylori infections. The H. pylori animal models which have been used in pathogenesis and vaccine studies include the gnotobiotic pig, non-human primates, cats, dogs, and several species of rodents including mice, rats, gerbils and guinea pigs. H. felis infection of mice and H. mustelae infection of ferrets have also been used. Recently, investigators have begun using transgenic mice and gene-targeted 'knock-out' mice to investigate Helicobacter infections. Each of these animal models has distinct advantages and disadvantages which are discussed in this minireview. The choice of an animal model is dictated by factors such as cost and an understanding of how each model will or will not allow fulfillment of experimental objectives.     

A study of some diffusion models of population growth

The stochastic differential equations of many diffusion processes which arise in studies of population growth in random environments can be transformed, if the Stratonovich stochastic calculus is employed, to the equation of the Wiener process. If the transformation function has certain properties then the transition probability density function and quantities relating to the time to first attain a given population size can be obtained from the known results for the Wiener process. Some other random growth processes can be derived from the Ornstein-Uhlenbeck process. These transformation methods are applied to the random processes of Malthusian growth, Pearl-Verhulst logistic growth and a recent model of density independent growth due to Levins.     

Analytical models for FMS design optimization: A survey

This paper surveys the analytical methods that have been developed for optimizing the design of flexible manufacturing systems. A classification of the design issues into six groups is proposed first. The two main mathematical tools used for performance analysis are presented briefly. Then, the literature is analyzed critically according to the problem classification given. Suggestions for further work within each area are given throughout the paper and some general remarks concerning the whole field are finally made.     

A survey of mathematical models of competition with an inhibitor

Mathematical models of the effect of inhibitors on microbial competition are surveyed. The term inhibitor is used in a broad sense and includes toxins, contaminants, allelopathic agents, etc. This includes both detoxification where the inhibitor is viewed as a pollutant and control where the inhibitor is viewed as an aid to controlling a bioreactor. The inhibitor may be supplied externally or may be created as an anti-competitor toxin. This includes plasmid-bearing, plasmid-free competition. The literature is spread across journals in different disciplines and with different notation. The survey attempts to present the mathematical models and the results of the corresponding analysis within a common framework and notation. Detailed mathematical proofs are not given but the methods of proof are indicated, references cited, and the results presented in tables. Open problems are indicated where there is a gap in the theory.