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Table of contents
General Introduction
I Characterizing normality
Introduction
1 Predicting sea urchin’s normal development from a small cohort of digital embryos
1.1 Introduction
1.2 A small cohort of digital sea urchin throughout their cleavage period
1.3 Feature Extraction andMeasuring
1.4 Emergence of embryo-level dynamics from individual cell features
1.5 Spatial modeling
1.6 Discussion
2 Variability in the sea urchin development: A multi-level data driven probabilistic model
2.1 Introduction
2.2 Image acquisition and digital reconstruction
2.2.1 Image acquisition
2.2.2 Image processing
2.3 Multi-levelmeasures and rescaling
2.3.1 Individual cell features
2.3.2 Intermediate cell groups
2.4 Observation and approximation of multi-level statistics
2.4.1 Estimation of cell feature distributions in cell groups
2.4.2 Cell volume and surface area dynamics
2.4.3 Independence along the lineage
2.5 Multi-level probabilistic model
2.5.1 Prototype
2.6 Biomechanical model description
2.7 Comparison to experimental data
2.7.1 Metrics
2.7.2 Objective functions
2.7.3 Initial State
2.7.4 Validation – Parameter space
3 Perspectives and open problems raised by the probabilistic model of development
3.1 The probabilistic model implies a monoid structure
3.1.1 Monoid Structure
3.1.2 Formalization as a dynamical system
3.1.3 Fluctuation theory and robustness
3.2 Parameters evolution
3.2.1 Waddington’s epigenetic landscape
3.2.2 Kupiec’s ontophylogenesis
Conclusion
II Characterizing diversity
4 Sources of biological diversity and randomness
4.1 Sources of variability in biology
4.1.1 Gene mutations
4.1.2 Epigenetic and stochasticity
4.2 Randomness and its formalisms in mathematics and physics
4.2.1 Probability theory
4.2.2 Randomness in algorithmic theories
4.2.3 Randomness in dynamical systems and ergodic theory
4.2.4 Randomness in quantummechanics – Quantum mechanics as a generalized probability theory
4.3 Variability andmodels in biology
4.3.1 Models and simulation as tools for exploring some dynamics of the living
4.3.2 Living organisms are organized objects involving different levels of organization with heterogeneous dynamics
4.4 Conclusion
5 Variable phenotypic expressivity and incomplete penetrance of the zebrafishmutant line squintcz
5.1 Introduction
5.2 Materials and methods
5.3 Results
5.4 Discussion
6 Biological diversity and quantummechanics formalism
6.1 Introduction
6.2 Variability in biology, emergence of new phenotypes
6.2.1 Squint experiment – an incomplete list of phenotypes
6.3 Correlating several observables
6.3.1 Mendel’s model of inheritance: a formal analog of entanglement
6.4 Discussion
7 Evolution and development: toward an ontogenetic tree
7.1 Introduction
7.2 Reconstructing the ontogenetic tree of the Danio rerio embryogenesis
7.2.1 The concept of an ontogenetic tree
7.2.2 Formalization of the tree
7.2.3 Observing the phylotypic stage
7.3 Discussion and conclusion
Conclusion
III Quantifying biological shapes
8 Using persistent homology to quantify tissue shape and organization
8.1 Introduction
8.2 Global characterization of epithelial tissues
8.2.1 Network of cellular connectivity
8.2.2 Complex networks approach shows some limitations
8.2.3 Persistent homology
8.2.4 Quantitative comparison by computing features on top of barcodes
8.2.5 Classification of tissues
8.2.6 Summary
8.3 Random surfaces with arbitrary degree distribution to model tissue topology
8.3.1 Use of a null model
8.3.2 Topological hypotheses are necessary
8.3.3 Randomly gluing polygons
8.3.4 Topological characteristics of random surfaces
8.3.5 Comparison of the null model and the data for each of the features
8.4 Discussion and Conclusion
9 Tissue shape dynamics: cell proliferation and cell displacements
9.1 Introduction
9.2 Time evolving networks
9.2.1 Time evolution of static measurements
9.2.2 Looking at spatiotemporal networks
9.3 Using genealogy as a parameter – historical dependency of shape
9.4 Conclusion
Conclusion
General Conclusion
