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

Successful Treatment of Disseminated Nocardiosis Complicated by Cerebral Abscess with Ceftriaxone and Amikacin: Case Report

We report the case of an 85-year-old female patient who suffered from disseminated Nocardia asteroides infection complicated by a cerebral abscess. Treatment with amikacin for 2 weeks and ceftriaxone for 6 weeks led to complete recovery, and there was no recurrence of disease over a follow-up period of 12 months after therapy. The use of ceftriaxone in combination with amikacin might significantly shorten the duration of treatment for patients with disseminated nocardiosis. This combination of antibiotics merits further investigation with use of a larger sample of patient

An immunohistological study of testicular germ cell tumours using two different monoclonal antibodies against placental alkaline phosphatase.

Using two monoclonal antibodies directed against placental alkaline phosphatase (H17E2 and D20L) the immunohistological staining of testicular germ cell tumours was compared with that of a wide range of normal and malignant tissues. All seminomas and malignant teratomas tested gave strong positive labelling with H17E2 but were either negative or only patchily positive with D20L. Neither antibody gave any positive reaction on the normal tissues tested. All other malignancies were negative with both antibodies apart from two cases of ovarian and one case of endometrical cancer (strongly stained by H17E2) and three cases of colonic carcinoma (weakly and patchily stained by both H17E2 and D20L). This indicates that germ cell neoplasms generally express a form of placental alkaline phosphatase recognised by antibody H17E2

Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer

Colorectal cancer is initiated in colonic crypts. A succession of genetic mutations or epigenetic changes can lead to homeostasis in the crypt being overcome, and subsequent unbounded growth. We consider the dynamics of a single colorectal crypt by using a compartmental approach [Tomlinson IPM, Bodmer WF (1995) Proc Natl Acad Sci USA 92: 11130-11134], which accounts for populations of stem cells, differential cells, and transit cells. That original model made the simplifying assumptions that each cell popuation divides synchronously, but we relax these assumptions by adopting an age-structured approach that models asynchronous cell division, and by using a continuum model. We discuss two mechanims that could regulate the growth of cell numbers and maintain the equilibrium that is normally observed in the crypt. The first will always maintain an equilibrium for all parameter values, whereas the second can allow unbounded proliferation if the net per capita growth rates are large enough. Results show that an increase in cell renewal, which is equivalent to a failure of programmed cell death or of differentiation, can lead to the growth of cancers. The second model can be used to explain the long lag phases in tumor growth, during which news, higher equilibria are reached, before unlimited growth in cell number ensues

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

Increased glycation and oxidative damage to apolipoprotein B100 of LDL cholesterol in patients with type 2 diabetes and effect of metformin

OBJECTIVE The aim of this study was to investigate whether apolipoprotein B100 of LDL suffers increased damage by glycation, oxidation, and nitration in patients with type 2 diabetes, including patients receiving metformin therapy. RESEARCH DESIGN AND METHODS For this study, 32 type 2 diabetic patients and 21 healthy control subjects were recruited; 13 diabetic patients were receiving metformin therapy (median dose: 1.50 g/day). LDL was isolated from venous plasma by ultracentrifugation, delipidated, digested, and analyzed for protein glycation, oxidation, and nitration adducts by stable isotopic dilution analysis tandem mass spectrometry. RESULTS Advanced glycation end product (AGE) content of apolipoprotein B100 of LDL from type 2 diabetic patients was higher than from healthy subjects: arginine-derived AGE, 15.8 vs. 5.3 mol% (P < 0.001); and lysine-derived AGE, 2.5 vs. 1.5 mol% (P < 0.05). Oxidative damage, mainly methionine sulfoxide residues, was also increased: 2.5 vs. 1.1 molar equivalents (P < 0.001). 3-Nitrotyrosine content was decreased: 0.04 vs. 0.12 mol% (P < 0.05). In diabetic patients receiving metformin therapy, arginine-derived AGE and methionine sulfoxide were lower than in patients not receiving metformin: 19.3 vs. 8.9 mol% (P < 0.01) and 2.9 vs. 1.9 mol% (P < 0.05), respectively; 3-nitrotyrosine content was higher: 0.10 vs. 0.03 mol% (P < 0.05). Fructosyl-lysine residue content correlated positively with fasting plasma glucose. Arginine-derived AGE residue contents were intercorrelated and also correlated positively with methionine sulfoxide. CONCLUSIONS Patients with type 2 diabetes had increased arginine-derived AGEs and oxidative damage in apolipoprotein B100 of LDL. This was lower in patients receiving metformin therapy, which may contribute to decreased oxidative damage, atherogenicity, and cardiovascular disease

Signatures of QCD Phase Transition in a Newborn Compact Star

We study the scenario that a new born strange quark star cools to the Quantum ChromoDynamics (QCD) phase transition temperature and converts to a neutron star, and we calculate the evolution of temperature and luminosity of the compact star. We argue that the conversion energy released can be of the order $10^{53}$ erg. We also propose that a second neutrino burst will be emitted at the completion of this phase transition.Comment: 6 pages, 1 figure, minor modified and subtitles added, typos corrected. Accepted for publication in Monthly Notice Lette

People of the British Isles: preliminary analysis of genotypes and surnames in a UK control population

There is a great deal of interest in fine scale population structure in the UK, both as a signature of historical immigration events and because of the effect population structure may have on disease association studies. Although population structure appears to have a minor impact on the current generation of genome-wide association studies, it is likely to play a significant part in the next generation of studies designed to search for rare variants. A powerful way of detecting such structure is to control and document carefully the provenance of the samples involved. Here we describe the collection of a cohort of rural UK samples (The People of the British Isles), aimed at providing a well-characterised UK control population that can be used as a resource by the research community as well as providing fine scale genetic information on the British population. So far, some 4,000 samples have been collected, the majority of which fit the criteria of coming from a rural area and having all four grandparents from approximately the same area. Analysis of the first 3,865 samples that have been geocoded indicates that 75% have a mean distance between grandparental places of birth of 37.3km, and that about 70% of grandparental places of birth can be classed as rural. Preliminary genotyping of 1,057 samples demonstrates the value of these samples for investigating fine scale population structure within the UK, and shows how this can be enhanced by the use of surnames