A large body of data suggests that mitochondrial abnormalities may link gene defects and/or environmental challenges to many pathologies including several neurodegenerative processes (for reviews, see [1
]). Mitochondria are essential organelles serving as the main site of oxygen use within cells. The divalent reduction of oxygen by the respiratory chain is tightly coupled to ATP synthesis by the oxidative phosphorylation machinery. However, a small proportion of the electrons passing through the electron transport chain reacts with molecular oxygen in a monovalent reduction reaction [5
]. This process yields the superoxide anion, which can be converted into other reactive oxygen species (ROS), such as hydrogen peroxide and the highly reactive hydroxyl radical, through enzymatic and non-enzymatic reactions [6
]. Cells possess an impressive arsenal of weapons for counteracting excess ROS production, including superoxide dismutases, catalases, peroxidases and low molecular mass redox compounds, such as ascorbic acid and glutathione. However, overproduction of the superoxide anion due to the abnormal reduction of key components of the respiratory chain (e.g. ubiquinone and cytochrome bc1) or to the impairment of antioxidant defences adversely affects various cellular processes and constituents (for recent reviews see [7
]). Disruptions of the respiratory chain or cellular defences are thus increasingly being implicated in acquired and inherited diseases and appear to play a key role in the aetiology of many neurodegenerative disorders, including Alzheimer's and Parkinson's diseases [10
Due to its unique redox properties and chemical reactivity, iron appears to be a key player in abnormal ROS generation, principally as a catalyst of the Fenton and Haber-Weiss reactions [12
]. This essential micronutrient is the redox component of the haem and iron-sulphur cluster [FeS] cofactors of many important proteins or enzymes. Iron homeostasis is thus tightly regulated, at all levels. The deregulation of iron homeostasis due to gene defects or environmental stresses leads to a wide range of diseases, from anaemia (iron deficiency) to haemochromatosis (iron overload) [13
] with consequences for cellular metabolism that remain poorly understood. The modelling of iron homeostasis in relation to the main features of metabolism, energy production and oxidative stress may provide new clues to the ways in which changes in biological processes in a normal cell lead to disease.
In the growing field of systems biology, several attempts have been made to model cellular processes. For complex systems, these models can be classified into static [16
] and dynamic models [18
]. Dynamic models are generally analyzed and/or simulated with specific methods as a function of the availability (or lack) of numerical data. The approaches used include ordinary differential equations, stochastic simulation algorithms [21
], agent or rule-based approaches [24
], Boolean approaches (probabilistic or otherwise) [26
], or Petri nets (with hybrid extensions) [30
]. Most of these models are based on well known pathways (cell cycle control, glycolysis, signal transduction, etc.), or well studied processes relevant to cell physiology (e.g. action potential propagation in neurons).
Our understanding of the relations between oxidative metabolism and iron homeostasis is based on a large body of qualitative knowledge from heterogeneous sources, often lacking numerical data. It is therefore not possible to derive mathematical relationships based on biological knowledge for the entire system, and the model has to include uncertain knowledge. As a consequence, despite several attempts to construct models accurately describing certain aspects of iron homeostasis (at the level of the cell [33
] or organism [30
]), no formal model linking iron homeostasis to metabolism control and oxidative stress has yet been developed.
We describe here an approach based on probabilistic Boolean modelling that can deal effectively with vast amounts of heterogeneous knowledge not always associated with quantitative data. Using this approach, we were able to construct a realistic model of cell fate including oxygen, carbon, nitrogen, sulphur, phosphate and iron homeostasis. This methodology dealt well with the mixture of precise and uncertain knowledge. Despite its large size (642 elements and 1007 reactions), we were able to simulate the model and analyse its dynamics. We focused on a simple unicellular eukaryotic system, the yeast Saccharomyces cerevisiae
, which has many features (genes, proteins, pathways, cell compartmentalisation) similar to those of mammalian cells. We first validated the model by simulating 198 in silico
mutations resulting from the deletion of individual genes from the model (with a small number of elements kept constant in the model). An independent validation was provided by analysing the key transition from anaerobic to aerobic metabolism, by comparing in silico
reactions frequencies with experimental fluxomic data [36
]. The results of individual deletions were compared with experimental data for real mutants, for which detailed phenotypic analyses were available. We were able to classify the in silico
mutants into groups of similar "phenotype" profiles, making it possible to identify original properties of the model. The model was used to explore several alternative hypothesis in order to better understand some unexpected phenotypes in mutants.
In this study, we focused on iron homeostasis and oxidative stress. However, we believe that the proposed modelling strategy could be useful for other systems. Typically, it should allow the building of large models with a high level of biological relevance that can cope with both a lack of numerical data and precise knowledge.