The Mathematical Biology of Diatoms

About this book

This book contains unique, advanced applications using mathematics, algorithmic techniques, geometric analysis, and other computational methods in diatom research.

Historically, diatom research has centred on taxonomy and systematics. While these topics are of the utmost importance, other aspects of this important group of unicells have been increasingly explored in the biological sciences. While mathematical applications are still rare, they are starting to take hold and provide an extensive avenue of new diatom research, including applications in multidisciplinary fields.

The work contained in this volume is an eclectic mix of analytical studies on diatoms. Mathematical treatment of the various biological disciplines covered in this book ranges from implicit, but succinct studies to more elaborate detailed computational studies. Topics include growth models, nanostructure, nanoengineering, cell growth, araphid diatoms, valve ontogeny, diatom metabolism, diatom motility, synchronization, diatom kinematics, photonics, biogenic sensors, photochemistry, diatom light response, colony growth, siliceous unicells, algal kinetics, diatom structure, diatom imaging, functional morphology, geometric structure, biomineralization, high-resolution imaging, non-destructive imaging, and 3D structure. This wide-ranging volume provides an introductory as well as an advanced treatment of recent interests in diatom research.

The mathematical research in this volume may be applicable to studies of other unicells, biomechanics, biological processes, physio-chemical analyses, or nanoscience.

Contents

List of Figures   xiii
List of Tables   xxxi
Preface   xxxv

Part I: Diatom Form and Size Dynamics   1
1. Modeling the Stiffness of Diploneis Species Based on Geometry of the Frustule Cut with Focused Ion Beam Technology / Andrzej Witkowski, Romuald Dobosz, Tomasz Plocinski, Przemyslaw Dabek, Izabela Zglobicka, Horst Lange-Bertalot, Thomas G. Bornman, Renata Dobrucka, Michal Gloc and Krzysztof J. Kurzydlowski   3
2. Size-Resolved Modeling of Diatom Populations: Old Findings and New Insights / Jonas Ziebarth, Werner M. Seiler and Thomas Fuhrmann-Lieker   19
3. On the Mathematical Description of Diatom Algae: From Siliceous Exoskeleton Structure and Properties to Colony Growth Kinetics, and Prospective Nanoengineering Applications / Alexey I. Salimon, Julijana Cvjetinovic, Yuliya Kan, Eugene S. Statnik, Patrick Aggrey, Pavel A. Somov, Igor A. Salimon, Joris Everaerts, Yekaterina D. Bedoshvili, Dmitry A. Gorin, Yelena V. Likhoshway, Philipp V. Sapozhnikov, Nikolai A. Davidovich, Olga Y. Kalinina, Kalin Dragnevski and Alexander M. Korsunsky   63

Part II: Diatom Development, Growth and Metabolism   103
4. Ring to the Linear: Valve Ontogeny Indicates Two Potential Evolutionary Pathways of Core Araphid Diatoms / Shigeki Mayama and Momoko Kushida   105
5. Mathematical Basis for Diatom Growth Modeling / Dariush Sardari   121
6. Diatom Growth: How to Improve the Analysis of Noisy Data / Olga Kourtchenko, Kai T. Lohbeck, Bjoern Andersson and Tuomas Rajala   141
7. Integrating Metabolic Modeling and High-Throughput Data to Characterize Diatoms Metabolism / Juan D. Tibocha-Bonilla, Manish Kumar, Karsten Zengler and Cristal Zuniga   165

Part III: Diatom Motility   193
8. Modeling the Synchronization of the Movement of Bacillaria paxillifer by a Kuramoto Model with Time Delay / Thomas Harbich   195
9. The Psychophysical World of the Motile Diatom Bacillaria paradoxa / Bradly Alicea, Richard Gordon and Jesse Parent   229
10. Pattern Formation in Diatoma vulgaris Colonies: Observations and Description by a Lindenmayer-System / Thomas Harbich   265
11. RAPHE: Simulation of the Dynamics of Diatom Motility at the Molecular Level - The Domino Effect Hydration Model with Concerted Diffusion / Shruti Raj Vansh Singh, Krishna Katyal and Richard Gordon   291

Part IV: Diatom Ecological and Environmental Analysis   343
12. Following the Photons Route: Mathematical Models Describing the Interaction of Diatoms with Light / Edoardo De Tommasi, Alessandra Rogato, Diego Caratelli, Luciano Mescia and Johan Gielis   345
13. A Generalized Model for the Light Response of the Nonphotochemical Quenching of Chlorophyll Fluorescence of Diatoms / Joao Serodio and Johann Lavaud   393
14. Coscinodiscus wailesii as Biogenic Charge-Based Sensors for Heavy Metal Ion Contamination Detection / Rajeshwari Taruvai Kalyana Kumar, Diem-Thuy Le, Antra Ganguly and Shalini Prasad   413

Acknowledgments  425
References   425
Index   427

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Biography

Janice L. Pappas has BA, BS and PhD degrees from the University of Michigan and an MA degree from Drake University. She is a mathematical biologist researching diatoms and invertebrates. She is a Great Lakes aquatic ecologist with studies on-board research vessels and in the lab, resulting in computational analyses of fish distributions in coastal wetlands and ecological informatics analysis of phytoplankton seasonal succession. Other studies include applications to diatom studies using Morse theory and morphospace dynamics, fuzzy measures in systematics, vector spaces in ecological analysis, information theory and Hamiltonian mechanics in morphogenesis, optimization, group and probability theory in macroevolutionary processes, and applied computer vision techniques in diatom imaging studies.