Heterogeneity in multistage carcinogenesis and mixture modeling

Carcinogenesis is commonly described as a multistage process, in which stem cells are transformed into cancer cells via a series of mutations. In this article, we consider extensions of the multistage carcinogenesis model by mixture modeling. This approach allows us to describe population heterogeneity in a biologically meaningful way. We focus on finite mixture models, for which we prove identifiability. These models are applied to human lung cancer data from several birth cohorts. Maximum likelihood estimation does not perform well in this application due to the heavy censoring in our data. We thus use analytic graduation instead. Very good fits are achieved for models that combine a small high risk group with a large group that is quasi immune

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

Stochastic Process Pharmacodynamics: Dose Timing in Neonatal Gentamicin Therapy as an Example

We consider dosing regimens designed to cure patients by eradicating colony forming units (CFU) such as bacteria. In the field of “population” pharmaco-kinetics/dynamics (PK/PD), inter-individual variability (IIV) of patients is estimated using model parameter statistical distributions. We consider a more probabilistic approach to IIV called stochastic process theory, motivated by the fact that tumor treatment planning uses both approaches. Stochastic process PD can supply additional insights and suggest different dosing regimens due to its emphasis on the probability of complete CFU eradication and its predictions on “pure chance” fluctuations of CFU number per patient when treatment has reduced this integer to less than ~100. To exemplify the contrast between stochastic process PD models and standard deterministic PD models, which track only average CFU number, we analyze, neglecting immune responses, neonatal intravenous gentamicin dosing regimens directed against Escherichia coli. Our stochastic calculations predict that the first dose is crucial for CFU eradication. For example, a single 6 mg/kg dose is predicted to have a higher eradication probability than four daily 4 mg/kg doses. We conclude: (1) neonatal gentamicin dosing regimens with larger first doses but smaller total doses deserve investigation; (2) in general, if standard PK/PD models predict average CFU number drops substantially below 100, the models should be modified to incorporate stochastic effects more accurately, and will then usually make more favorable, or less unfavorable, predictions for front boosting (“hit hard early”). Various caveats against over-interpreting the calculations are given. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1208/s12248-014-9715-3) contains supplementary material, which is available to authorized users

Molecular Methods for Research on Actinorhiza

Actinorhizal root nodules result from the interaction between a nitrogen-fixing actinomycete from the genus Frankia and roots of dicotyledonous trees and shrubs belonging to 25 genera within 8 plant families. Most actinorhizal plants can reach high rates of nitrogen fixation comparable to those found in root nodule symbiosis of the legumes. As a consequence, these trees are able to grow in poor and disturbed soils and are important elements in plant communities worldwide. While the basic knowledge of these symbiotic associations is still poorly understood, actinorhizal symbioses emerged recently as original systems to explore developmental strategies to form nitrogen-fixing nodules. Many tools have been developed in recent years to explore the interaction between Frankia and actinorhizal plants including molecular biology, biochemistry, and genomics. However, technical difficulties are often encountered to explore these symbiotic interactions, mainly linked to the woody nature of the plant species and to the lack of genetic tools for their bacterial symbionts. In this chapter, we report an inventory of the main recent molecular tools and techniques developed for studying actinorhizae