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

Topological analysis of the vasculature of angiopoietin-expressing tumours through scale-space tracing

This work describes the topological analysis of the vasculature of tumours. The analysis is performed with a scale-space technique, which traces the centrelines of vessels as topological ridges of the image intensities and then obtains a series of measurements, which are used to compare the vasculatures. Besides the measurements directly associated with the centrelines, the scales obtained allow the estimation of width andthusareacoveredwithvessels. Tumours of SW1222 human colorectal carcinoma xenografts were observed when growing in dorsal skin-fold window chambers in mice. Three variants of the tumours expressing either endogenous levels of angiopoietins (WT) or over-expressing either angiopoietin-1 (Ang-1) or angiopoietin-2 (Ang-2) were assessed with/without vascular targeted therapy. The scale-space technique was able to discriminate between the vasculatures of the three different tumour types prior to treatment. Results also suggested that over-expression of Ang-2 was associated with susceptibility of the tumour vasculature to the vascular disrupting agent, combretastatin A4 phosphate (CA4P). Substantiation of this finding would point to the potential of tumour Ang-2 expression as a predictive bio-marker for response to CA4P

Cancer and systemic inflammation: treat the tumour and treat the host

Determinants of cancer progression and survival are multifactorial and host responses are increasingly appreciated to have a major role. Indeed, the development and maintenance of a systemic inflammatory response has been consistently observed to confer poorer outcome, in both early and advanced stage disease. For patients, cancer-associated symptoms are of particular importance resulting in a marked impact on day-to-day quality of life and are also associated with poorer outcome. These symptoms are now recognised to cluster with one another with anorexia, weight loss and physical function forming a recognised cluster whereas fatigue, pain and depression forming another. Importantly, it has become apparent that these symptom clusters are associated with presence of a systemic inflammatory response in the patient with cancer. Given the understanding of the above, there is now a need to intervene to moderate systemic inflammatory responses, where present. In this context the rationale for therapeutic intervention using nonselective anti-inflammatory agents is clear and compelling and likely to become a part of routine clinical practice in the near future. The published literature on therapeutic intervention using anti-inflammatory agents for cancer-associated symptoms was reviewed. There are important parallels with the development of useful treatments for the systemic inflammatory response in patients with rheumatological disease and cardiovascular disease

One-carbon metabolism in cancer

Cells require one-carbon units for nucleotide synthesis, methylation and reductive metabolism, and these pathways support the high proliferative rate of cancer cells. As such, anti-folates, drugs that target one-carbon metabolism, have long been used in the treatment of cancer. Amino acids, such as serine are a major one-carbon source, and cancer cells are particularly susceptible to deprivation of one-carbon units by serine restriction or inhibition of de novo serine synthesis. Recent work has also begun to decipher the specific pathways and sub-cellular compartments that are important for one-carbon metabolism in cancer cells. In this review we summarise the historical understanding of one-carbon metabolism in cancer, describe the recent findings regarding the generation and usage of one-carbon units and explore possible future therapeutics that could exploit the dependency of cancer cells on one-carbon metabolism

Homeostatic competition drives tumor growth and metastasis nucleation

We propose a mechanism for tumor growth emphasizing the role of homeostatic regulation and tissue stability. We show that competition between surface and bulk effects leads to the existence of a critical size that must be overcome by metastases to reach macroscopic sizes. This property can qualitatively explain the observed size distributions of metastases, while size-independent growth rates cannot account for clinical and experimental data. In addition, it potentially explains the observed preferential growth of metastases on tissue surfaces and membranes such as the pleural and peritoneal layers, suggests a mechanism underlying the seed and soil hypothesis introduced by Stephen Paget in 1889 and yields realistic values for metastatic inefficiency. We propose a number of key experiments to test these concepts. The homeostatic pressure as introduced in this work could constitute a quantitative, experimentally accessible measure for the metastatic potential of early malignant growths.Comment: 13 pages, 11 figures, to be published in the HFSP Journa

Stochastic Physics, Complex Systems and Biology

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibrium, spontaneous random "mutations" and "adaptations". On an evlutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.Comment: 10 page

Mosaic DNA imports with interspersions of recipient sequence after natural transformation of Helicobacter pylori

Helicobacter pylori colonizes the gastric mucosa of half of the human population, causing gastritis, ulcers, and cancer. H. pylori is naturally competent for transformation by exogenous DNA, and recombination during mixed infections of one stomach with multiple H. pylori strains generates extensive allelic diversity. We developed an in vitro transformation protocol to study genomic imports after natural transformation of H. pylori. The mean length of imported fragments was dependent on the combination of donor and recipient strain and varied between 1294 bp and 3853 bp. In about 10% of recombinant clones, the imported fragments of donor DNA were interrupted by short interspersed sequences of the recipient (ISR) with a mean length of 82 bp. 18 candidate genes were inactivated in order to identify genes involved in the control of import length and generation of ISR. Inactivation of the antimutator glycosylase MutY increased the length of imports, but did not have a significant effect on ISR frequency. Overexpression of mutY strongly increased the frequency of ISR, indicating that MutY, while not indispensable for ISR formation, is part of at least one ISR-generating pathway. The formation of ISR in H. pylori increases allelic diversity, and contributes to the uniquely low linkage disequilibrium characteristic of this pathogen