Dynamic Modelling under Uncertainty

Kinetic models of metabolism require detailed knowledge of kinetic parameters. However, due to measurement errors or lack of data this knowledge is often uncertain. The model of glycolysis in the parasitic protozoan Trypanosoma brucei is a particularly well analysed example of a quantitative metabolic model, but so far it has been studied with a fixed set of parameters only. Here we evaluate the effect of parameter uncertainty. In order to define probability distributions for each parameter, information about the experimental sources and confidence intervals for all parameters were collected. We created a wiki-based website dedicated to the detailed documentation of this information: the SilicoTryp wiki (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). Using information collected in the wiki, we then assigned probability distributions to all parameters of the model. This allowed us to sample sets of alternative models, accurately representing our degree of uncertainty. Some properties of the model, such as the repartition of the glycolytic flux between the glycerol and pyruvate producing branches, are robust to these uncertainties. However, our analysis also allowed us to identify fragilities of the model leading to the accumulation of 3-phosphoglycerate and/or pyruvate. The analysis of the control coefficients revealed the importance of taking into account the uncertainties about the parameters, as the ranking of the reactions can be greatly affected. This work will now form the basis for a comprehensive Bayesian analysis and extension of the model considering alternative topologies.
Author Summary An increasing number of mathematical models are being built and analysed in order to obtain a better understanding of specific biological systems. These quantitative models contain parameters that need to be measured or estimated. Because of experimental errors or lack of data, our knowledge about these parameters is uncertain. Our work explores the effect of including these uncertainties in model analysis. Therefore, we studied a particularly well curated model of the energy metabolism of the parasite Trypanosoma brucei, responsible for African sleeping sickness. We first collected all the information we could find about how the model parameters were defined on a website, the SilicoTryp wiki (http:///silicotryp.ibls.gla.ac.uk/wiki/). From this information, we were able to quantify our uncertainty about each parameter, thus allowing us to analyse the model while explicitly taking these uncertainties into account. We found that, even though the model was well-defined and most of its parameters were experimentally measured, taking into account the remaining uncertainty allows us to gain more insight into model behavior. We were able to identify previously unrecognised fragilities of the model, leading to new hypotheses amenable to experimental testing.