Sensitivity of signaling pathway dynamics to plasmid transfection and its consequences.

This paper deals with development of signaling pathways models and using plasmid-based experiments to support parameter estimation. We show that if cells transfected with plasmids are used in experiments, the models should include additional components that describe explicitly effects induced by plasmids. Otherwise, when the model is used to analyze responses of wild type, i.e. non-transfected cells, it may not capture their dynamics properly or even lead to false conclusions. In order to illustrate this, an original mathematical model of miRNA-mediated control of gene expression in the NFκB pathway is presented. The paper shows what artifacts might appear due to experimental procedures and how to develop the models in order to avoid pursuing these artifacts instead of real kinetics.

Modeling epigenetic regulation of PRC1 protein accumulation in the cell cycle.

BACKGROUND: Epigenetic regulation contributes to many important processes in biological cells. Examples include developmental processes, differentiation and maturation of stem cells, evolution of malignancy and other. Cell cycle regulation has been subject of mathematical modeling by a number of authors that resulted in many interesting models and application of analytic techniques ranging from stochastic processes to partial differential equations and to integral, functional and operator equations. In this paper we address the question of how the regulation of protein contents influences the long-term dynamics of the population. To accomplish this, we follow the philosophy of a 1984 model by Kimmel et al., but adjust the details to fit the experimental data on protein PRC1 from a more recent paper. RESULTS: We built a model of cell cycle dynamics of the PRC1 and fitted it to the data made available by Cohen and his co-authors. We have run the model for a large number of cell generations, recording the PRC1 contents in all cells of the resulting pedigree, at constant time intervals. During cell division the PRC1 is unequally divided between daughter cells. The picture emerging from simulations of Data set 1 is that of a very well-tuned regulatory circuit that provides a stable distribution of PRC1 contents and interdivision times. Data set 2 seems qualitatively different, with more variation in cell cycle duration. CONCLUSIONS: The main question we address is whether the regulatory feedbacks deduced from single cell cycle data provide epigenetic regulation of cell characteristics in long run. PRC1 is a good candidate because of its role in setting timing of division. Findings of the current paper include tight regulation of the cell cycle (particularly the timing of the cell cycle) even that PRC1 is only one of the players in cell dynamics. Understanding that association, even close, does not necessarily imply causation, we consider this an interesting and important result.

Comparison of simple models of periodic protocols for combined anticancer therapy.

Several simple ordinary differential equation (ODE) models of tumor growth taking into account the development of its vascular network are discussed. Different biological aspects are considered from the simplest model of Hahnfeldt et al. proposed in 1999 to a model which includes drug resistance of cancer cells to chemotherapy. Some of these models can be used in clinical oncology to optimize antiangiogenic and cytostatic drugs delivery so as to ensure maximum efficacy. Simple models of continuous and periodic protocols of combined therapy are implemented. Discussion on the dynamics of the models and their complexity is presented.