Mathematical Modeling for Genes to Collective Cell Dynamics

✍ Scribed by Tetsuji Tokihiro

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 179
• Series: Theoretical Biology
• Category: Library

✦ Synopsis

This book describes the dynamics of biological cells and their mathematical modeling. The topics cover the dynamics of RNA polymerases in transcription, construction of vascular networks in angiogenesis, and synchronization of cardiomyocytes. Statistical analysis of single cell dynamics and classification of proteins by mathematical modeling are also presented.

The book provides the most up-to-date information on both experimental results and mathematical models that can be used to analyze cellular dynamics. Novel experimental results and approaches to understand them will be appealing to the readers. Each chapter contains 1) an introductory description of the phenomenon, 2) explanations about the mathematical technique to analyze it, 3) new experimental results, 4) mathematical modeling and its application to the phenomenon. Elementary introductions for the biological phenomenon and mathematical approach to them are especially useful for beginners.

The importance of collaboration between mathematics and biological sciences has been increasing and providing new outcomes. This book gives good examples of the fruitful collaboration between mathematics and biological sciences. 

✦ Table of Contents

Preface
Contents
1 Transcription Dynamics: Cellular Automaton Model of Polymerase Dynamics for Eukaryotes
1.1 Brief Review of Transcription
1.2 Experimental Result
1.3 Cellular Automaton and Traffic Flow Model
1.3.1 What Is Cellular Automaton?
1.3.2 Traffic Flow Cellular Automaton
1.4 Cellular Automaton Model of Transcription Dynamics
References
2 Angiogenesis: Dynamics of Endothelial Cells in Sprouting and Bifurcation
2.1 Angiogenesis: A Biological Overview
2.1.1 Introduction
2.1.2 Mechanisms Involved in Cell Migration
2.1.3 Endothelial Cell Behaviors During Angiogenesis
2.1.4 Cell-to-Cell Junction Proteins as a Modulator of Angiogenesis
2.1.5 Clinical Significance of Angiogenesis
2.2 Modeling by Differential and Difference Equations
2.2.1 Continuous Model and Discrete Model
2.2.2 Newtonian Equation of Motion
2.2.3 Diffusion Equation
2.3 Mathematical Model for the Dynamics of Endothelial Cells in Angiogenesis
2.3.1 Introduction
2.3.2 Discrete Model for EC Dynamics
2.3.3 Cell-Mixing and Scaling Behavior of EC Dynamics
2.3.4 Pattern Formation of the Model with Elongation and Bifurcation of Neogenetic Vessels
2.3.5 A Continuous Model for Angiogenesis
2.3.6 Exact Solutions of the Continuous Model in Case of Constant VEGF Concentration
2.3.7 Numerical Simulations in the Presence of VEGF Concentration Gradient
2.3.8 Concluding Remarks
2.4 Two-Dimensional Pattern Formation with Ellipses
2.4.1 Two-Dimensional Extension of the Model
2.4.2 Pattern Formation and Order Parameter
References
3 Synchronization and Fluctuation of Cardiac Muscle Cells
3.1 Introduction
3.2 The Stochastic Phase Models for the Cardiomyocyte Beating
3.2.1 Some Preliminaries for the Stochastic Phase Model
3.2.1.1 The Phase Model
3.2.1.2 The Brownian Motion and White Noise
3.2.1.3 Itô's Integral
3.2.1.4 Itô's Formula
3.2.2 The Phase Model for an Isolated Cardiomyocyte
3.2.3 The Phase Model for Two Coupled Cardiomyocytes
3.2.4 The CV of Synchronization
3.2.5 The Phase Model for N-cardiomyocytes Network
3.3 Experimental Approach
3.3.1 On-Chip Cellomics Technology: Reconstructive Understanding of the Community Effect in Cardiomyocytes
3.3.2 Photothermal Etching on Agarose Layer for Cell Network Formation Control
3.3.3 Community Effect of Cells for Their Synchronization (1): Two-Cell Model
3.3.4 Community Effect of Cells for Their Synchronization (2): Cell Number Dependence
3.3.5 Community Effect of Cells on Their Synchronization (3): Mixture of Different Types of Cells
3.3.6 Summary of Experimental Results
3.3.7 Ability and Limitation of Constructed Experimental Approach
3.4 Numerical Approach to Synchronization of Cardiomyocytes
3.4.1 Comparison of the Mathematical Modeling with Experimental Results and Numerical Simulations
3.4.1.1 Mathematical Modeling for Synchronization of Cardiomyocytes
3.4.1.2 Numerical Simulation Method
3.4.1.3 Comparison of the Model with Experimental Results of Two Cardiomyocytes
3.4.1.4 Comparison with the Kuramoto Model
3.4.2 Numerical Experiments
3.4.2.1 Size and Configuration Dependence on Fluctuation of the System
3.4.2.2 Dependence of Cell Properties and Numbers on Fluctuation of the System
3.4.3 Discussion
3.5 Summary
References
4 Statistical Analysis of Cellular Directional Movement: Application for Research of Single Cell Movement
4.1 Single Cell Movement
4.1.1 Persistent Random Walk
4.1.2 Mean Squared Displacement (MSD) and the Fürth Formula
4.2 Circular Statistics
4.2.1 Raw Data Plot
4.2.2 Histograms
4.2.3 Summary Statistics
4.2.4 Probability Models
4.3 Application for Single Cell Movement
References
5 Protein Structures
5.1 Introduction
5.2 Lattice Polymer Models
5.2.1 Self-avoiding Walk
5.2.2 HP Model
5.2.3 An Extension of HP Model: Including Coulomb Force
5.3 Fatgraph Model
References