Examples of mathematical modeling tales from the crypt

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters

On the proportion of cancer stem cells in a tumour

It is now generally accepted that cancers contain a sub-population, the cancer stem cells (CSCs), which initiate and drive a tumour’s growth. At least until recently it has been widely assumed that only a small proportion of the cells in a tumour are CSCs. Here we use a mathematical model, supported by experimental evidence, to show that such an assumption is unwarranted. We show that CSCs may comprise any possible proportion of the tumour, and that the higher the proportion the more aggressive the tumour is likely to be

Evolutionary history and identification of conservation units in the giant otter, Pteronura brasiliensis.

The giant otter, Pteronura brasiliensis, occupies a range including the major drainage basins of South America, yet the degree of structure that exists within and among populations inhabiting these drainages is unknown. We sequenced portions of the mitochondrial DNA (mtDNA) cytochrome b (612 bp) and control region (383 bp) genes in order to determine patterns of genetic variation within the species. We found high levels of mtDNA haplotype diversity (h = 0.93 overall) and support for subdivision into four distinct groups of populations, representing important centers of genetic diversity and useful units for prioritizing conservation within the giant otter. We tested these results against the predictions of three hypotheses of Amazonian diversification (Pleistocene Refugia, Paleogeography, and Hydrogeology). While the phylogeographic pattern conformed to the predictions of the Refugia Hypothesis, molecular dating using a relaxed clock revealed the phylogroups diverged from one another between 1.69 and 0.84 Ma, ruling out the influence of Late Pleistocene glacial refugia. However, the role of Plio-Pleistocene climate change could not be rejected. While the molecular dating also makes the influence of geological arches according to the Paleogeography Hypothesis extremely unlikely, the recent Pliocene formation of the Fitzcarrald Arch and its effect of subsequently altering drainage pattern could not be rejected. The data presented here support the interactions of both climatic and hydrological changes resulting from geological activity in the Plio-Pleistocene, in shaping the phylogeographic structure of the giant otter

Neurogene Stammzelltransplantation in die Kochlea

Zusammenfassung: Hintergrund: Die Stammzelltherapie ist insbesondere im Hinblick auf eine Applikation im Innenohr interessant, da die Haarzellen nicht regenerieren. Einmal abgestorbene Haarzellen werden nicht ersetzt, es kommt zu einem irreversiblen Hörverlust. In den vergangenen Jahren konnten Stammzellen mit wechselndem Erfolg ins Innenohr appliziert werden, zum Teil haben sie sich zu Innenohrzellen entwickelt. In der vorliegenden Studie wollten wir untersuchen, wie sich neuronale Vorläuferzellen verhalten, wenn sie in vitro und in vivo auf ein geschädigtes Innenohr aufgebracht werden. Methoden: Neuronale Vorläuferzellen wurden von E9,5Tage alten Mausembryonen isoliert und danach mit einem Virus, der das grün fluoreszierende Protein (GFP) exprimiert, infiziert. In der Folge wurden die GFP+-neuralen Vorläuferzellen sowohl auf ein geschädigtes Corti-Organ in vitro aufgebracht als auch Mäusen ins zuvor geschädigte Innenohr in vivo appliziert. Anschließend wurden die Vorläuferzellen bzw. ihr Bezug zum Corti-Organ analysiert. Ergebnisse: Sowohl auf ein geschädigtes Corti-Organ aufgebrachte GFP+-neurale Vorläuferzellen als auch in vivo in geschädigte Innenohren transplantierte GFP+-neurale Vorläuferzellen konnten nach Transplantation nachgewiesen werden. Interessanterweise haben sich die GFP+-neuralen Vorläuferzellen nicht zufällig auf dem Organ niedergelassen, sondern ein gewisses Muster gezeigt. Insbesondere konnte nach der In-vivo-Applikation gesehen werden, dass die GFP+-neuralen Vorläuferzellen sich im Bereich des Corti-Organs in der Region von abgestorbenen Haarzellen angesiedelt haben. Schlussfolgerung: Neuronale Vorläuferzellen haben ein großes Potenzial, einmal abgestorbene Haarzellen zu ersetzen. Allerdings braucht es noch intensive Forschung bis zur klinischen Anwendun

Relativistic Mean Field Approximation in a Density Dependent Parametrization Model at Finite Temperature

In this work we calculate the equation of state of nuclear matter for different proton fractions at zero and finite temperature within the Thomas Fermi approach considering three different parameter sets: the well-known NL3 and TM1 and a density dependent parametrization proposed by Typel and Wolter. The main differences are outlined and the consequences of imposing beta-stability in these models are discussed.Comment: 13 pages, 10 figure

Modelling multiscale aspects of colorectal cancer

Colorectal cancer (CRC) is responsible for nearly half a million deaths annually world-wide [11]. We present a series of mathematical models describing the dynamics of the intestinal epithelium and the kinetics of the molecular pathway most commonly mutated in CRC, the Wnt signalling network. We also discuss how we are coupling such models to build a multiscale model of normal and aberrant guts. This will enable us to combine disparate experimental and clinical data, to investigate interactions between phenomena taking place at different levels of organisation and, eventually, to test the efficacy of new drugs on the system as a whole

Lambda-proton correlations in relativistic heavy ion collisions

The prospect of using lambda-proton correlations to extract source sizes in relativistic heavy ion collisions is investigated. It is found that the strong interaction induces a large peak in the correlation function that provides more sensitive source size measurements than two-proton correlations under some circumstances. The prospect of using lambda-proton correlations to measure the time lag between lambda and proton emissions is also studied.Comment: 4 pages, 3 figure, revtex style. Two short paragraphs are added at referees' recommendations. Phys. Rev. Lett. in pres