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

Failure of Ceftriaxone in an Intravenous Drug User with Invasive Infection Due to Ralstonia pickettii

Abstract. : We report a case of septic arthritis due to Ralstonia pickettii in an intravenous drug user with unfavorable clinical course under antibiotic therapy with ceftriaxone despite in vitro susceptibility to the drug. The treatment failure may have been due to a discrepancy between in vitro and in vivo susceptibility of R. pickettii, or to resistance development mediated by a recently described inducible ß-lactamas

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

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

Allele loss occurs frequently at hMLH1, but rarely at hMSH2, in sporadic colorectal cancers with microsatellite instability.

Mutations at the hMSH2 and hMLH1 mismatch repair loci have been implicated in the pathogenesis of colorectal cancer. Tumours with two allelic mutations at a mismatch repair locus develop replication errors (RERs). In the hereditary non-polyposis colorectal cancer (HNPCC) syndrome, one mutation is inherited and the other acquired somatically: in RER+ sporadic colorectal cancers, both mutations are somatic. RER+ tumours tend to have a low frequency of allele loss, presumably because they acquire most mutations through RERs. However, before a second mismatch repair mutation has occurred somatically, there is no reason to suppose that allele loss occurs less frequently in tumours that are to become RER+. Indeed, this second mutation might itself occur by allele loss. We have searched for allele loss at the hMSH2 and hMLH1 loci in RER+ and RER- sporadic colorectal cancers. Loss occurred at the hMLH1 locus in 7/17 (41%) RER+ tumours, compared with 6/40 (15%) RER- cancers (chi2=3.82, P approximately 0.05). At hMSH2, 2/22 RER+ sporadic cancers (9%) had lost an allele, compared with 2/40 (5%) RER- cancers (chi2=0.03, P>0.5). Taken together with previous studies which focused on colorectal cancers from HNPCC families, the data suggest that allele loss at hMLH1, but not at hMSH2, contributes to defective mismatch repair in inherited and sporadic colorectal cancer

Hepatitis with Fibrin-Ring Granulomas

Abstract : We describe a 66-year-old woman hospitalized with fever, fatigue and hepatopathy. In her medical history arterial hypertension (treated with propranolol and lisinopril), diabetes mellitus type 2 (no treatment before admission) and a gout arthropathy were noted wherefore a therapy with allopurinol 300 mg per day has been started 4 months before. Liver biopsy revealed fibrin-ring granulomas, compatible with allopurinolinduced hepatitis. Because of persistence of high fever after stopping allopurinol, steroids (1 mg/kg) were started. Under this treatment, she developed pancytopenia and fever. The bone marrow aspiration revealed Leishmania infantum. A second liver biopsy showed amastigotes and a disappearance of the granulomas. The history revealed a travel to Malta 2 years earlier. Despite adequate treatment with liposomal amphotericin B the patient deteriorated and finally died in septic shoc

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