Genomic expression patterns distinguish long-term from short-term glioblastoma survivors: a preliminary feasibility study

We used microarray analysis to investigate associations between genotypic expression profiles and survival phenotypes in patients with primary glioblastoma (GBM). Tumor samples from 7 long-term glioblastoma survivors (>24 months) and 13 short-term survivors (<9 months) were analyzed to detect differential patterns of gene expression between these groups and to identify genotypic subclasses of glioblastomas that correlate with survival phenotypes. Five unsupervised and three supervised clustering algorithms consistently and accurately grouped the tumors into genotypic subgroups corresponding to the two clinical survival phenotypes. Three unique prospective mathematical classification algorithms were subsequently trained to use expression data to stratify unknown glioblastomas between survival groups and performed this task with 100% accuracy in validation studies. A set of 1478 genes with significant differential expression (p<0.01) between long-term and short-term survivors was identified, and additional mathematical filtering was used to isolate a 43-gene "fingerprint" that distinguished survival phenotypes. Differential regulation of a subset of these genes was confirmed using RT-PCR. Gene ontology analysis of the fingerprint demonstrated pathophysiologic functions for the gene products that are consistent with current models of tumor biology, suggesting that differential expression of these genes may contribute etiologically to the observed differences in survival. These results demonstrate that unique expression profiles characterize genotypic subsets of primary GBMs associated with differential survival phenotypes, and these profiles can be used in a prospective fashion to assign unknown tumors to survival groups. Future efforts will focus on building more robust classifiers and identifying additional subclasses of gliomas with phenotypic significance.     

The mathematical biophysics of Nicolas Rashevsky

N. Rashevsky (1899-1972) was one of the pioneers in the application of mathematics to biology. With the slogan: mathematical biophysics : biology :: mathematical physics ; physics, he proposed the creation of a quantitative theoretical biology. Here, we will give a brief biography, and consider Rashevsky's contributions to mathematical biology including neural nets and relational biology. We conclude that Rashevsky was an important figure in the introduction of quantitative models and methods into biology.     

Immune-deficient mouse models for analysis of human stem cells

The field of murine models of xenotransplantation has grown immensely over the past two decades. The explosive growth in this field is in part due to the fact that good in vitro methods do not exist yet to allow examination of human stem cell homing into the bone marrow compartment versus other tissues, long-term survival of human stem cells, or differentiation into tissues outside of the hematopoietic system. Since these important aspects of human stem cell biology can be examined in vivo using immune-deficient mice, the number of different strains and models is constantly increasing. The current review discusses the merits and drawbacks of each immune-deficient mouse xenograft system as it stands to date and reviews how each immune-deficient mouse model has been used to further our knowledge of human hematopoietic stem cell biology.     

A rumor transmission model with various contact interactions

We consider a rumor transmission model with various contact interactions and explore what effect such interactions have on the spread of a rumor, in particular whether they can explain the rumor recursion. Through mathematical analysis and computer simulations, we conjecture that rumor recursion remains a major challenge to mathematical models of rumors beyond our model proposed here.     

On mathematical modeling of circadian rhythms, performance, and alertness

Mathematical models of neurobehavioral performance and alertness have both basic science and practical applications. These models can be especially useful in predicting the effect of different sleep-wake schedules on human neurobehavioral objective performance and subjective alertness under many conditions. Several relevant models currently exist in the literature. In principle, the development and refinement of any mathematical model should be based on an explicit modeling methodology, such as the Box modeling paradigm, that formally defines the model structure and calculates the set of parameters. While most mathematical models of neurobehavioral performance and alertness include homeostatic, circadian, and sleep inertia components and their interactions, there may be fundamental differences in the equations included in these models. In part, these may be due to differences in the assumptions of the underlying physiology. Because the choice of model equations can have a dramatic influence on the results, it is necessary to consider these differences in assumptions when examining the results from a model and when comparing results across models. This article presents principles of mathematical modeling and examples of how such procedures can be applied to the development and refinement of mathematical models of neurobehavioral performance and alertness. This article also presents several methods of testing and comparing these models, suggests different uses of the models, and discusses problems with current models.     

From exposure to effect: a comparison of modeling approaches to chemical carcinogenesis.

Standardized long-term carcinogenicity tests aim to reveal the relationship between exposure to a chemical and occurrence of a carcinogenic response. The analysis of such tests may be facilitated by the use of mathematical models. To what extent current models actually achieve this purpose is difficult to evaluate. Various aspects of chemically induced carcinogenesis are treated by different modeling approaches, which proceed very much in isolation of each other. With this paper we aim to provide for the non-mathematician a comprehensive and critical overview of models dealing with processes involved in chemical carcinogenesis. We cover the entire process of carcinogenesis, from exposure to effect. We succinctly summarize the biology underlying the models and emphasize the relationship between model assumptions and model formulations. The use of mathematics is restricted as far as possible with some additional information relegated to boxes.     

BIOCOMPUTATION: Some history and prospects

At first glance, biology and computer science are diametrically opposed sciences. Biology deals with carbon based life forms shaped by evolution and natural selection. Computer Science deals with electronic machines designed by engineers and guided by mathematical algorithms. In this brief paper, we review biologically inspired computing. We discuss several models of computation which have arisen from various biological studies. We show what these have in common, and conjecture how biology can still suggest answers and models for the next generation of computing problems. We discuss computation and argue that these biologically inspired models do not extend the theoretical limits on computation. We suggest that, in practice, biological models may give more succinct representations of various problems, and we mention a few cases in which biological models have proved useful. We also discuss the reciprocal impact of computer science on biology and cite a few significant contributions to biological science.     

Non-local concepts and models in biology

In this paper, we consider local and non-local spatially explicit mathematical models for biological phenomena. We show that, when rate differences between fast and slow local dynamics are great enough, non-local models are adequate simplifications of local models. Non-local models thus avoid describing fast processes in mechanistic detail, instead describing the effects of fast processes on slower ones. As a consequence, non-local models are helpful to biologists because they describe biological systems on scales that are convenient to observation, data collection, and insight. We illustrate these arguments by comparing local and non-local models for the aggregation of hypothetical organisms, and we support theoretical ideas with concrete examples from cell biology and animal behavior.     

Interactome networks and human disease

Complex biological systems and cellular networks may underlie most genotype to phenotype relationships. Here, we review basic concepts in network biology, discussing different types of interactome networks and the insights that can come from analyzing them. We elaborate on why interactome networks are important to consider in biology, how they can be mapped and integrated with each other, what global properties are starting to emerge from interactome network models, and how these properties may relate to human disease.     

From network models to network responses: integration of thermodynamic and kinetic properties of yeast genome-scale metabolic networks

Many important problems in cell biology arise from the dense nonlinear interactions between functional modules. The importance of mathematical modelling and computer simulation in understanding cellular processes is now indisputable and widely appreciated. Genome-scale metabolic models have gained much popularity and utility in helping us to understand and test hypotheses about these complex networks. However, there are some caveats that come with the use and interpretation of different types of metabolic models, which we aim to highlight here. We discuss and illustrate how the integration of thermodynamic and kinetic properties of the yeast metabolic networks in network analyses can help in understanding and utilizing this organism more successfully in the areas of metabolic engineering, synthetic biology and disease treatment.     

Calculation of Disease Dynamics in a Population of Households

Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptible-infectious-recovered-susceptible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks.     

Using cross-validation to evaluate predictive accuracy of survival risk classifiers based on high-dimensional data

Developments in whole genome biotechnology have stimulated statistical focus on prediction methods. We review here methodology for classifying patients into survival risk groups and for using cross-validation to evaluate such classifications. Measures of discrimination for survival risk models include separation of survival curves, time-dependent ROC curves and Harrell's concordance index. For high-dimensional data applications, however, computing these measures as re-substitution statistics on the same data used for model development results in highly biased estimates. Most developments in methodology for survival risk modeling with high-dimensional data have utilized separate test data sets for model evaluation. Cross-validation has sometimes been used for optimization of tuning parameters. In many applications, however, the data available are too limited for effective division into training and test sets and consequently authors have often either reported re-substitution statistics or analyzed their data using binary classification methods in order to utilize familiar cross-validation. In this article we have tried to indicate how to utilize cross-validation for the evaluation of survival risk models; specifically how to compute cross-validated estimates of survival distributions for predicted risk groups and how to compute cross-validated time-dependent ROC curves. We have also discussed evaluation of the statistical significance of a survival risk model and evaluation of whether high-dimensional genomic data adds predictive accuracy to a model based on standard covariates alone.     

Population dynamics of migratory trout, Salmo trutta, in a Lake District stream, 1966–83, and their implications for fisheries management

A short review summarises the chief conclusions of an 18-year investigation of the population dynamics of migratory trout, Salmo trutta L., in a Lake District stream. The chief factors affecting growth, survival and production have been identified and their effects summarized in a series of mathematical models. The implications of this work are discussed in relation to long-term investigations, data analysis and modelling, and the scientific management of trout populations. It is shown that mathematical models, based on long-term investigations, can be used to assess the effects on a fish population of changes due to natural causes (e.g., droughts and spates) or human activities. One of the main objectives of future work should be the development and improvement of models that can be used as tools for the conservation and management of fish stocks.     

Population Growth and Demography of Common Loons in the Northern United States

ABSTRACT We used recent developments in theoretical population ecology to construct basic models of common loon (Gavia immer) demography and population dynamics. We parameterized these models using existing survival estimates and data from long-term monitoring of loon productivity and abundance. Our models include deterministic, 2-stage, density-independent matrix models, yielding population growth-rate estimates (λ) of 0.99 and 1.01 for intensively studied populations in our Wisconsin, USA, and New Hampshire, USA, study areas, respectively. Perturbation analysis of these models indicated that estimated growth rate is extremely sensitive to adult survival, as expected for this long-lived species. Also, we examined 20 years of count data for the 2 areas and evaluated support for a set of count-based models of population growth. We detected no temporal trend in Wisconsin, which would be consistent with fluctuation around an average equilibrium state but could also result from data limitations. For New Hampshire, the model set included varying formulations of density dependence and partitioning of stochasticity that were enabled by the annual sampling resolution. The best model for New Hampshire included density regulation of population growth and, along with the demographic analyses for both areas, provided insight into the possible importance of breeding habitat availability and the abundance of nonbreeding adults. Based on these results, we recommend that conservation organizations include nonbreeder abundance in common loon monitoring efforts and that additional emphasis be placed on identifying and managing human influences on adult loon survival.     

Perspective on gravitational biology of amphibians]

We review here the scientific significance of the use of amphibians for research in gravitational biology. Since amphibian eggs are quite large, yet develop rapidly and externally, it is easy to observe their development. Consequently amphibians were the first vertebrates to have their early developmental processes investigated in space. Though several deviations from normal embryonic development occur when amphibians are raised in microgravity, their developmental program is robust enough to return the organisms to an ostensibly normal morphology by the time they hatch. Evolutionally, amphibians were the first vertebrate animal to come out of the water and onto land. Subsequently they diversified and have adaptively radiated to various habitats. They now inhabit aquatic, terrestrial, arboreal and fossorial niches. This diversity can be used to help study the biological effects of gravity at the organismal level, where macroscopic phenomena are associated with gravitational loading. By choosing different amphibian models and using a comparative approach one can effectively identify the action of gravity on biological systems, and the adaptation that vertebrates have made to this loading. Advances in cellular and molecular biology provide powerful tools for the study in many fields, including gravitational biology, and amphibians have proven to be good models for studies at those levels as well. The low metabolic rates of amphibians make them convenient organisms to work with (compared to birds and mammals) in the difficult and confined spaces on orbiting research platforms. We include here a review of what is known about and the potential for further behavioral and physiological researches in space using amphibians.     

Buyer beware: robustness analyses in economics and biology

Theoretical biology and economics are remarkably similar in their reliance on mathematical models, which attempt to represent real world systems using many idealized assumptions. They are also similar in placing a great emphasis on derivational robustness of modeling results. Recently philosophers of biology and economics have argued that robustness analysis can be a method for confirmation of claims about causal mechanisms, despite the significant reliance of these models on patently false assumptions. We argue that the power of robustness analysis has been greatly exaggerated. It is best regarded as a method of discovery rather than confirmation.