|Title||Structural identifiability of large systems biology models|
|Source||Wageningen University. Promotor(en): J. Molenaar, co-promotor(en): J.D. Stigter. - Wageningen : Wageningen University - ISBN 9789463952262 - 173|
Mathematical and Statistical Methods - Biometris
|Publication type||Dissertation, internally prepared|
A fundamental principle of systems biology is its perpetual need for new technologies that can solve challenging biological questions. This precept will continue to drive the development of novel analytical tools. The virtuous cycle of biological progress can therefore only exist when experts from different disciplines including biology, chemistry, computer science, engineering, mathematics, and medicine collaborate.
General opinion is however that one of the challenges facing the systems biology community is the lag in the development of such technologies. The topic of structural identifiability in particular has been of interest to the systems biology community. This is because researchers in this field often face experimental limitations. These limitations, combined with the fact that systems biology models can contain vast numbers of unknown parameters, necessitate an identifiability analysis. In reality, analysing the structural identifiability of systems biology models, even when they contain only a few states and system parameters, may be challenging. As these models increase in size and complexity, this difficulty is exasperated, and one becomes limited to only a few methods capable of analysing large ordinary differential equation models.
In this thesis I study the use of a computationally efficient algorithm, well suited to the analysis of large models, in the model development process. The three related objectives of this thesis are: 1) develop an accurate method to asses the structural identifiability of large possibly nonlinear ordinary differential models, 2) implement thismethod in the preliminary design of experiments, and 3) use the method to address the topic of structural unidentifiability.
To improve the method’s accuracy, I systematically study the role of individual factors, such as the number of experimentally measured sensors, on the sharpness of results. Based on the findings, I propose measures that can improve numerical accuracy.
To address the second objective, I introduce an iterative identifiability algorithm that can determine minimal sets of outputs that need to be measured to ensure a model’s local structural identifiability. I also illustrate how one could potentially reduce the computational demand of the algorithm, enabling a user to detect minimal output sets of large ordinary differential equation models within minutes.
For the last objective, I investigate the role of initial conditions in a model’s structural unidentifiability. I show that the method can detect problematic values for large ordinary differential equation models. I illustrate its role in reinstating the local structural identifiability of a model by identifying problematic initial conditions.
I also show that the method can provide theoretical suggestions for the reparameterization of structurally unidentifiable models. The novelty of this work is that the algorithm allows for unknown initial conditions to be parameterised and accordingly, repameterisations requiring the transformation of states, associated with unidentifiable initial conditions, can easily be obtained. The computational efficiency of the method allows for the reparameterisation of large ordinary differential equation models in particular.
To conclude, in this thesis I introduce an method that can be used during the model development process in an array of useful applications. These include: 1) determining minimal output sets, 2) reparameterising structurally unidentifiable models and 3) detecting problematic initial conditions. Each of these application can be implemented before any experiments are conducted and can play a potential role in the optimisation of the modelling process.