The aim of this paper is (i)to study breast cancer growth by mean of a mathematical model describing cell population dynamics during cancer growth, and (ii)to use this model to reproduce and explain experimental data. We started from a linear model describing cancer subpopulations evolution based on the Cancer Stem Cell (CSC) theory, and we added feedback mechanisms from the cell populations to mimic micro-environment effects in cancer growth. In details, we hypothesized two feedback mechanisms and we studied their effects both separately and combined together. In this way we obtained three new models that we tuned using data derived by TUBO Cancer cell line and describing the evolution of the total cell population and the subpopulations over time. Finally, we exploited these three models to understand which combination of feedback mechanisms better describe the experimental data.

MOTIVATION: Many drug combinations are routinely assessed to identify synergistic interactions in the attempt to develop novel treatment strategies. Appropriate software is required to analyze the results of these studies. RESULTS: We present Combenefit, new free software tool that enables the visualization, analysis and quantification of drug combination effects in terms of synergy and/or antagonism. Data from combinations assays can be processed using classical Synergy models (Loewe, Bliss, HSA), as single experiments or in batch for High Throughput Screens. This user-friendly tool provides laboratory scientists with an easy and systematic way to analyze their data. The companion package provides bioinformaticians with critical implementations of routines enabling the processing of combination data. AVAILABILITY AND IMPLEMENTATION: Combenefit is provided as a Matlab package but also as standalone software for Windows (http://sourceforge.net/projects/combenefit/). CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Stochastic Symmetric Nets (SSNs) are a High-Level Stochastic Petri Net formalism which provides a parametric system description and an efficient analysis technique that exploit system symmetries to automatically aggregate its states. Even if significant reductions can be achieved in highly symmetric models, the reduced state space can still be too large to derive and/or solve the underlying stochastic process, so that Monte Carlo simulation and fluid approximation remain the only viable ways that need to be explored. In this paper, we contribute to this line of research by proposing a new approach based on fluid approximation to automatically derive from an SSN model a set of ordinary differential equations (ODEs) which mimic the system behavior, and by showing how the SSN formalism allows us to define an efficient translation method which reduces the size of the corresponding ODE system with an automatic exploitation of system symmetries. Additionally, some case studies are presented to show the effectiveness of the method and the relevance of its application in practical cases.

BACKGROUND: Cancer stem cell theory suggests that cancers are derived by a population of cells named Cancer Stem Cells (CSCs) that are involved in the growth and in the progression of tumors, and lead to a hierarchical structure characterized by differentiated cell population. This cell heterogeneity affects the choice of cancer therapies, since many current cancer treatments have limited or no impact at all on CSC population, while they reveal a positive effect on the differentiated cell populations. RESULTS: In this paper we investigated the effect of vaccination on a cancer hierarchical structure through a multi-level model representing both population and molecular aspects. The population level is modeled by a system of Ordinary Differential Equations (ODEs) describing the cancer population's dynamics. The molecular level is modeled using the Petri Net (PN) formalism to detail part of the proliferation pathway. Moreover, we propose a new methodology which exploits the temporal behavior derived from the molecular level to parameterize the ODE system modeling populations. Using this multi-level model we studied the ErbB2-driven vaccination effect in breast cancer. CONCLUSIONS: We propose a multi-level model that describes the inter-dependencies between population and genetic levels, and that can be efficiently used to estimate the efficacy of drug and vaccine therapies in cancer models, given the availability of molecular data on the cancer driving force.