Multiscale Modeling of Developmental Systems
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Table of contents
- Contentsv
- Contributorsxiii
- Introductionxvii
- Chapter 1. Models of Biological Pattern Formation: From Elementary Steps to the Organization of Embr1
- I. Introduction2
- II. Primary Pattern Formation by Local Self-Enhancement and Long-Ranging Inhibition6
- III. The Two Main Body Axes21
- IV. Subpatterns33
- V. Conclusion53
- Acknowledgments54
- References54
- Chapter 2. Robustness of Embryonic Spatial Patterning in Drosophila melanogaster65
- I. Introduction65
- II. Robustness in the Developmental Context69
- III. Scaling of AP Patterning in Drosophila77
- IV. Models of the Segment Polarity Network80
- V. Dorsal-Ventral Patterning in Drosophila87
- VI. Conclusions105
- Note added in proof108
- Acknowledgments108
- References108
- Chapter 3. Integrating Morphogenesis with Underlying Mechanics and Cell Biology113
- I. Introduction113
- II. Xenopus laevis as a Model System114
- III. Distinct and Separable Tissue-Scale Processes115
- IV. Complex Trajectories through Dynamic Microenvironments121
- V. At the Cell-Scale: Act Locally Move Globally124
- VI. Molecular-Scale: Mechanics, Adhesion, and Traction127
- VII. Modeling Morphogenesis: A Grand Challenge128
- Acknowledgments129
- References129
- Chapter 4. The Mechanisms Underlying Primitive Streak Formation in the Chick Embryo135
- I. Introduction136
- II. Structure of the Early Embryo136
- III. Experimental Observations of Streak Formation137
- IV. Mesoderm Induction140
- V. Cellular Mechanisms of Streak Formation143
- VI. Mechanisms of Movement150
- VII. Challenges for Modeling and Computational Approaches151
- VIII. Outlook152
- References153
- Chapter 5. Grid-Free Models of Multicellular Systems, with an Application to Large-Scale Vortices Ac157
- I. Introduction158
- II. Grid-Free Models of Multicellular Systems158
- III. Recent Experimental Results Concerning Primitive Streak Formation164
- IV. Components of the Planar Cell Polarity Mechanism167
- V. Phenomenological Cell-Based Model of the Chick Epiblast170
- VI. Computer Simulations: Formation and Maintenance of Vortices during Streak Formation170
- VII. Discussion and Conclusions174
- Acknowledgments179
- Appendix A. Details of the Model179
- Appendix B. The XY Model of Ferromagnetism181
- References181
- Chapter 6. Mathematical Models for Somite Formation183
- I. Introduction183
- II. Models for Somite Formation186
- III. Discussion198
- IV. Perspective200
- Acknowledgments200
- References200
- Chapter 7. Coordinated Action of N-CAM, N-cadherin, EphA4, and ephrinB2 Translates Genetic Prepatter205
- I. Introduction206
- II. Patterns of Gene Expression and Protein Distribution during Somitogenesis208
- III. From Genetic Oscillators to Adhesion/Repulsion-Protein Patterns211
- IV. From Adhesion-Protein Patterns to Segmentation214
- V. Computer Simulation of Segmentation215
- VI. Results and Discussion222
- VII. Conclusion229
- Acknowledgments230
- Introduction to Appendices230
- Appendix A. Python Code to Execute Somitogenesis Simulations (somite.py)231
- Appendix B. CC3D ML Code to Execute Somitogenesis Simulations (somite.xml)233
- Appendix C. Python Steppables for Somitogenesis Simulations (somiteSteppables.py)236
- References244
- Chapter 8. Branched Organs: Mechanics of Morphogenesis by Multiple Mechanisms249
- I. Introduction249
- II. Background251
- III. Candidate Physical Mechanisms253
- IV. Models of Branching258
- V. Discussion263
- Acknowledgments265
- References265
- Chapter 9. Multicellular Sprouting during Vasculogenesis269
- I. Introduction270
- II. Empirical Data, in vivo272
- III. Elongated Structures, in vitro277
- IV. Mathematical Model of Sprout Formation281
- V. Conclusions287
- Acknowledgments287
- References287
- Chapter 10. Modeling Lung Branching Morphogenesis291
- I. Introduction291
- II. Modeling in vitro Lung Branching Morphogenesis296
- III. Functional Modeling-Structure and Air Flow300
- IV. Future Directions300
- V. Numerical Simulations of Branching Morphogenesis Models301
- References306
- Chapter 11. Multiscale Models for Vertebrate Limb Development311
- I. Introduction312
- II. Tissue Interactions and Gene Networks of Limb Development313
- III. Models for Chondrogenic Pattern Formation316
- IV. Simulations of Chondrogenic Pattern Formation323
- V. Discussion and Future Directions332
- Acknowledgments336
- References336
- Chapter 12. Tooth Morphogenesis in vivo, in vitro, and in silico341
- I. Introduction342
- II. The Use of Mammalian Tooth for Developmental and Evolutionary Biology343
- III. Morphological Changes During Tooth Development344
- IV. Gene Networks in Tooth Development347
- V. The Formation of the Cusps348
- VI. Spacing Between Cusps349
- VII. Morphodynamic Model 1350
- VIII. Model 1 and Tooth Dynamics353
- IX. Morphodynamic Model 2355
- X. What Do Model Dynamics Reveal About Developmental Dynamics358
- XI. Tooth Model in Comparison to Other Models of Organ Development366
- XII. Concluding Remarks367
- Acknowledgments368
- References368
- Chapter 13. Delaunay-Object-Dynamics: Cell Mechanics with a 3D Kinetic and Dynamic Weighted Delaunay373
- I. Overview of Methods in Theoretical Biology374
- II. Delaunay-Based Interaction378
- III. Voronoi-Cells Approximate Real Cells380
- IV. Delaunay-Dynamics382
- V. Equation of Motion for Vertices384
- VI. Mechanics Matters392
- VII. Conclusion396
- Acknowledgments396
- References397
- Chapter 14. Cellular Automata as Microscopic Models of Cell Migration in Heterogeneous Environments401
- I. Introduction402
- II. Idea of the LGCA Modeling Approach406
- III. LGCA Models of Cell Motion in a Static Environment408
- IV. Analysis of the LGCA Models414
- V. Results and Discussion420
- Acknowledgments424
- References432
- Chapter 15. Multiscale Modeling of Biological Pattern Formation435
- I. Introduction436
- II. Quantitative Modeling437
- III. Building Cellular and Tissue-Level Models for a Simple Biological System439
- IV. Mean-Field Theory and the Interrelationship of Models at Different Spatial Scales444
- V. Multiple Scale Analysis447
- VI. Discussion457
- References458
- Chapter 16. Relating Biophysical Properties Across Scales461
- I. Introduction462
- II. Theory and Computer Modeling463
- III. Results470
- IV. Conclusions480
- Acknowledgments482
- References482
- Chapter 17. Complex Multicellular Systems and Immune Competition: New Paradigms Looking for a Mathem485
- I. Introduction485
- II. Conceptual Lines Towards a Mathematical Biological Theory486
- III. From Hartwell's Theory of Modules to Mathematical Structures488
- IV. A Simple Application and Perspectives491
- V. What Is Still Missing for a Biological Mathematical Theory496
- References500
- Index503
Mathematical and computational biology is playing an increasingly important role in the biological sciences. This science brings forward unique challenges, many of which are, at the moment, beyond the theoretical techniques available. Developmental biology, due to its complexity, has lagged somewhat behind its sister disciplines (such as molecular biology and population biology) in making use of quantitative modeling to further biological understanding. This volume comprises work that is among the best developmental modeling available and we feel it will do much to remedy this situation.
This book is aimed at all those with an interest in the interdisciplinary field of computer and mathematical modeling of multi-cellular and developmental systems. It is also a goal of the Editors to attract more developmental biologists to consider integrating modeling components into their research. Most importantly, this book is intended to serve as a portal into this research area for younger scientists – especially graduate students and post-docs, from both biological and quantitative backgrounds.
* Articles written by leading exponents in the field
* Provides techniques to address multiscale modeling
* Coverage includes a wide spectrum of modeling approaches
* Includes descriptions of the most recent advances in the field
This book is aimed at all those with an interest in the interdisciplinary field of computer and mathematical modeling of multi-cellular and developmental systems. It is also a goal of the Editors to attract more developmental biologists to consider integrating modeling components into their research. Most importantly, this book is intended to serve as a portal into this research area for younger scientists – especially graduate students and post-docs, from both biological and quantitative backgrounds.
* Articles written by leading exponents in the field
* Provides techniques to address multiscale modeling
* Coverage includes a wide spectrum of modeling approaches
* Includes descriptions of the most recent advances in the field