Modelling the consequences of interactions between tumour cells.

Classical models of tumorigenesis assume that the mutations which cause tumours to grow act in a cell-autonomous fashion. This is not necessarily true. Sometimes tumour cells may adopt genetic strategies that boost their own replication and which also influence other cells in the tumour, whether directly or as a side-effect. Tumour growth as a whole might be enhanced or retarded. We have used mathematical models to study two non-autonomous strategies that tumour cells may use. First, we have considered the production by tumour cells of an angiogenesis growth factor that benefits both the cell from which it originates and neighbouring cells. Second, we have analysed a situation in which tumour cells produce autocrine-only or paracrine-only growth factors to prevent programmed cell death. In the angiogenesis model, stable genetic polymorphisms are likely to occur between cells producing and not producing the growth factor. In the programmed cell death model, cells with autocrine growth factor production can spread throughout the tumour. Production of paracrine-only growth factor is never selected because it is 'altruistic' (that is of no benefit to the cell that makes the growth factor), despite being potentially beneficial to tumour growth as a whole. No polymorphisms can occur in the programmed cell death model. Production of angiogenesis and other growth factors in tumours may be under stable genetic, rather than epigenetic, control, with implications for therapies aimed at such targets. Many of the mutations observed in tumours may have non-autonomous effects

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

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

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

Monoclonal antibody assay of serum placental alkaline phosphatase in the monitoring of testicular tumours.

A monoclonal antibody (H17E2) recognising both placental alkaline phosphatase (PLAP) and testicular PLAP-like alkaline phosphatase was incorporated in a solid phase immunoassay. This was used to measure levels of PLAP in 257 sera from 148 patients with germ cell neoplasms of the testis. High levels of PLAP were found in all patients with active seminomas (mean 0.85 O.D.) compared to those in clinical remission (mean 0.20 O.D.) (P less than 0.0001). More importantly, changing levels of PLAP correlated with the course of disease in 79 samples from 33 patients with seminoma (P less than 0.0001). Elevated PLAP levels were also noted in patients in remission who were smokers (mean 0.32 O.D.) compared to non-smokers (mean 0.15 O.D.) (P less than 0.001). These data demonstrate that determination of PLAP levels using this sensitive immunoassay is an important new adjunct in the monitoring of the response to treatment in patients with seminoma

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