On Different Uses of Abstraction in Models of Developmental Systems
Abstraction is centrally important to the success of models, mathematical and otherwise, in biology. The move beyond traditional reductionist approaches towards a more holistic, system level, understanding of development, has produced a concurrent growth in the types of abstractions used in quantitative modelling. This is accompanied with new challenges and opportunities in evaluating and integrating the evidence provided by different modelling approaches and in constructing coherent and general models of complex biological processes. In this thesis, I address some of these challenges by critically assessing current models and proposing a new conceptual framework to address system level understanding of developmental systems. The integration of results from different modelling approaches is demonstrated with a novel approach to parameter inference for differential equation modelling of gene regulatory networks in a developmental patterning system. After a brief introduction motivating the work and highlighting some of the central themes. This is followed by the five principal results chapters which are each summarized below. Chapter 1 presents a critique of some recent work modelling the dynamics of stem cell differentiation. Some problems with the parameterization of one of the models are demonstrated and provide context for a more general discussion of the challenges in accounting for model complexity during model selection. The chapter concludes with a more general discussion of model selection and the appropriate integration of the resulting statistical evidence into a broader corpus of knowledge about the system. Chapter 2 considers the use of hierarchical systems of levels of abstraction in the analysis of complex developmental systems, with a particular focus on the tripartite system of levels proposed by the neuroscientist David Marr. Marr’s levels have been highly influential in computational neuroscience since their inception in the 1970’s and this chapter argues that such a framework has the potential to play an instrumental role in our attempts to understand complex developmental systems. To this end, a novel analysis of Marr’s levels is presented laying the groundwork for their application in the following chapter. Chapter 3 presents two detailed case studies in order to demonstrate how such a conceptual framework might be applied to different types of developmental systems. The first of these case studies analyses an information-based approach to studying gap gene patterning in the Drosophila embryo. This work highlights that some of the core ideas in Marr’s approach are, often implicitly, present in the literature regarding patterning systems however without the appropriate intellectual infrastructure to support them they have either been forgotten or not used to their full potential. In order to demonstrate how the type of functional analysis presented in the previous chapter might be extended beyond information processing systems, the second case study considers work modelling branching morphogenesis in the developing mouse mammary gland. A brief reprieve from the theoretical concerns of the preceding chapters comes with Chapter 4. A stand-alone analysis of gene expression data from the Drosophila embryo, this chapter establishes the presence of artefacts which can arise in such datasets during data acquisition. The final chapter (Chapter 5) builds on some of the insights in Chapter 3 to propose a specific method for combining top-down constraints on a lower-level model a gene regulatory network controlling cell-cell communication in a two cell system. This method presents a novel approach to parameter inference for differential equation models of the gene regulatory networks involved in developmental patterning systems.
Developmental Biology, Levels of Analysis, Model Selection, Bayesian Modelling, Developmental Axis Patterning
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