Mathematical Models of Cell-Based Morphogenesis: Passive and Active Remodeling (Theoretical Biology)

Contents
Chapter 1: Introduction
	References
Chapter 2: Cell Center Model
	2.1 Cell Properties (Honda 1978, 1983)
	2.2 Mathematics of the Cell Center Model (Honda 1983)
	2.3 Dirichlet Approximation (Honda 1978)
	2.4 Deviation from Dirichlet Domains (Honda 1978)1
	2.5 Approximation of Actual Cell Patterns Using the Cell Center Model (Honda 1978)
	2.6 Cell Division
	2.7 Cell Disappearance1
	2.8 Summary
	References
Chapter 3: Applications of the Cell Center Model
	3.1 Neat Arrangement of Cells in the Mammalian Epidermis (Honda et al. 1996)
	3.2 Cell Patterns Consisting of Large and Small Cells (Honda et al. 2000)
	3.3 Formation of Pore Patterns Using the Dirichlet Geometry (Honda and Yoshizato 1994a, b, c)
	3.4 From Polygonal Patterns to Branching Patterns
		3.4.1 Formation of Blood Vessel Branching In Vivo
		3.4.2 Computer Simulation of the Branching Formation of Blood Vessels
	3.5 Other Applications of the Geometry of Dirichlet Domains and Voronoi Polyhedra
	3.6 Summary
	References
Chapter 4: Vertex Model
	4.1 Cell Boundaries and Tricellular Contact
	4.2 Geometry of a Trijunction of Three Lines (Honda 1983)
	4.3 Boundary Shortening (BS) Procedure (Honda and Eguchi 1980)3
	4.4 Discrimination of Normal Epithelia from Nonepithelial Tissues Using the BS Procedure (Honda 1983)
	4.5 Tissue Transformation from an Aggregate of Packed Cells to a Surface-Contracting Cell Sheet
	4.6 Reconnection of Paired Vertices of an Edge
	4.7 Vertex Dynamics (Nagai and Honda 2001)
	4.8 Summary
	References
Chapter 5: Applications of 2D Cell Models
	5.1 Wound Closure in Epithelial Tissues (Nagai and Honda 2009)
	5.2 Cell Death Leads to Ordered Cell Patterns
	5.3 Passively Elongated Epithelial Tubes (Honda et al. 2009)
	5.4 Cell Patterns Composed of Heterogeneous Cells
		5.4.1 Differential Cell Adhesion Theory
		5.4.2 Two Types of Cells in the Oviduct Epithelium
		5.4.3 The Kagome Pattern (Star Pattern)6
		5.4.4 A Balanced State between Boundary Contraction and Differential Adhesion6
		5.4.5 Quantitative Estimation of the Difference in Intercellular Adhesions6
		5.4.6 Computer Simulations of the Kagome-Checkerboard Pattern Transformation6
		5.4.7 Molecular Basis of Cell Adhesion between Heterogenic Cell Types
	5.5 Summary
	References
Chapter 6: 3D Vertex Model
	6.1 Expression of an Aggregation of Polyhedral Cells
	6.2 Equation of Motion in 3D Vertex Dynamics (Honda et al. 2004)7
	6.3 Reconnection of Neighboring Vertices7
	6.4 Structure of Packed Polyhedra in 3D Space7
	6.5 Formation of a Spherical Cell Aggregate
	6.6 Flattening of a Cell Aggregate by Centrifugal Force7
	6.7 Viscoelastic Properties of Cell Aggregates7
	6.8 Modification of 3D Vertex Dynamics
	6.9 Transition of a Cell Aggregate to a Vesicle (Honda et al. 2008)
	6.10 Fundamentals of Vertex Dynamics
	6.11 Summary
	References
Chapter 7: The World of Epithelial Sheets
	7.1 Morphogenesis of Multicellular Animals Is Deformation of a Closed Epithelial Envelope
	7.2 Classification of Epithelial Cells
	7.3 Crucial Roles of Vacuolar Apical Compartments (VACs) in Epithelization
	7.4 Evolutionary Merit of Enclosure of the Animal Body Within an Epithelial Cell Sheet
	7.5 Signaling Molecules for Formation of the Apicobasal Polarity of Epithelial Cells
	7.6 Summary
	References
Chapter 8: Cells Themselves Produce Force for Active Remodeling
	8.1 Cell Rearrangement Involving Cell Intercalation
	8.2 Convergent Extension (CE) Mediated by an Anisotropic Contractile Force in 3D Space
	8.3 CE Mediated by an Anisotropic Contractile Force on a Cylindrical Surface10
	8.4 Global Dynamics of a Cylindrical Surface10
	8.5 CE Mediated by Anisotropic Cell Stiffness on a Cylindrical Surface10
	8.6 Planar Cell Polarity Signaling Links CE Orientations of Tissues
	8.7 Mathematical Modeling of Supracellular Actomyosin Cable Formation11
	8.8 Observation of PCP Signaling Proteins in the Neural Plate11
	8.9 Invagination of Epithelial Sheets
	8.10 Summary
	References
Chapter 9: Expansion of Shape-Dimension
	9.1 Twisting of a Strip of Sheet: A Narrow Rectangular Sheet (Honda et al. 2019)
	9.2 Twisting of the Heart Tube
		9.2.1 Helical Looping in Computer Simulations
		9.2.2 Mechanism of Determination of Output of the Handedness of Helical Heart Tubes
			9.2.2.1 Anisotropic Convergent Extension (CE)
			9.2.2.2 Peculiar Remodeling of an Artificial Tube via CE of Constituent Cells
		9.2.3 Computer Simulations of the Initial Heart Tube13
		9.2.4 Position-Specific Deformation of Cell Colonies in the Process of Helix Loop Formation13
		9.2.5 Mechano-physical Mechanism That Determines the Handedness of the Helical Loop13
			9.2.5.1 Distinctive Feature of the Cell-Based Vertex Dynamics Model13
			9.2.5.2 Intrinsic and Extrinsic Factors Causing Left-Handed Helical Looping13
			9.2.5.3 Consideration of CE of Collective Cells Across Different Animal Species13
		9.2.6 Conclusion Regarding the Mechanism Underlying Left-Handed Helical Looping of the Heart Tube
	9.3 Summary
	References
Chapter 10: Mathematical Cell Models and Morphogenesis
	10.1 Mathematical Cell Models Are a Bridge to Link Shape Formation with Genes
	10.2 Self-Construction of Shapes Recapitulated via Mathematical Models
	10.3 Successive Self-Construction
	10.4 Summary
	Reference