Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

Cancer recurrence times from a branching process model

As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. This is the main cause of cancer related mortality. Here we investigate a conceptually simple model of metastasis formation where metastatic lesions are initiated at a rate which depends on the size of the primary tumor. The evolution of each metastasis is described as an independent branching process. We assume that the primary tumor is resected at a given size and study the earliest time at which any metastasis reaches a minimal detectable size. The parameters of our model are estimated independently for breast, colorectal, headneck, lung and prostate cancers. We use these estimates to compare predictions from our model with values reported in clinical literature. For some cancer types, we find a remarkably wide range of resection sizes such that metastases are very likely to be present, but none of them are detectable. Our model predicts that only very early resections can prevent recurrence, and that small delays in the time of surgery can significantly increase the recurrence probability.Comment: 26 pages, 9 figures, 4 table

An integrative analysis of post-translational histone modifications in the marine diatom Phaeodactylum tricornutum

BACKGROUND: Nucleosomes are the building blocks of chromatin where gene regulation takes place. Chromatin landscapes have been profiled for several species, providing insights into the fundamental mechanisms of chromatin-mediated transcriptional regulation of gene expression. However, knowledge is missing for several major and deep-branching eukaryotic groups, such as the Stramenopiles, which include the diatoms. Diatoms are highly diverse and ubiquitous species of phytoplankton that play a key role in global biogeochemical cycles. Dissecting chromatin-mediated regulation of genes in diatoms will help understand the ecological success of these organisms in contemporary oceans. RESULTS: Here, we use high resolution mass spectrometry to identify a full repertoire of post-translational modifications on histones of the marine diatom Phaeodactylum tricornutum, including eight novel modifications. We map five histone marks coupled with expression data and show that P. tricornutum displays both unique and broadly conserved chromatin features, reflecting the chimeric nature of its genome. Combinatorial analysis of histone marks and DNA methylation demonstrates the presence of an epigenetic code defining activating or repressive chromatin states. We further profile three specific histone marks under conditions of nitrate depletion and show that the histone code is dynamic and targets specific sets of genes. CONCLUSIONS: This study is the first genome-wide characterization of the histone code from a stramenopile and a marine phytoplankton. The work represents an important initial step for understanding the evolutionary history of chromatin and how epigenetic modifications affect gene expression in response to environmental cues in marine environments

Survival and prognosis among 1545 patients with contemporary polycythemia vera: an international study.

Under the auspices of an International Working Group, seven centers submitted diagnostic and follow-up information on 1545 patients with World Health Organization-defined polycythemia vera (PV). At diagnosis, median age was 61 years (51% females); thrombocytosis and venous thrombosis were more frequent in women and arterial thrombosis and abnormal karyotype in men. Considering patients from the center with the most mature follow-up information (n=337 with 44% of patients followed to death), median survival (14.1 years) was significantly worse than that of the age- and sex-matched US population (P<0.001). In multivariable analysis, survival for the entire study cohort (n=1545) was adversely affected by older age, leukocytosis, venous thrombosis and abnormal karyotype; a prognostic model that included the first three parameters delineated risk groups with median survivals of 10.9-27.8 years (hazard ratio (HR), 10.7; 95% confidence interval (CI): 7.7-15.0). Pruritus was identified as a favorable risk factor for survival. Cumulative hazard of leukemic transformation, with death as a competing risk, was 2.3% at 10 years and 5.5% at 15 years; risk factors included older age, abnormal karyotype and leukocytes 15 × 10(9)/l. Leukemic transformation was associated with treatment exposure to pipobroman or P32/chlorambucil. We found no association between leukemic transformation and hydroxyurea or busulfan use