Mathematical Biology of Diatoms

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.

• List of Figures xiiiList of Tables xxxiPreface xxxvPart I: Diatom Form and Size Dynamics 11 Modeling the Stiffness of Diploneis Species Based on Geometry of the Frustule Cut with Focused Ion Beam Technology 3Andrzej Witkowski, Romuald Dobosz, Tomasz Płociński, Przemysław Dąbek, Izabela Zgłobicka, Horst Lange-Bertalot, Thomas G. Bornman, Renata Dobrucka, Michał Gloc and Krzysztof J. Kurzydłowski1.1 Introduction 41.2 Material and Methods 61.2.1 Focused Ion Beam (FIB) Milling 61.2.2 Modeling 61.3 Results 81.3.1 FIB Processing 81.3.2 Modeling 111.4 Discussion 141.4.1 Practical Meaning of the Frustule Geometric Characters 141.4.2 Documenting the Mechanical Strength of the Diatom Frustule 14Acknowledgments 16References 162 Size-Resolved Modeling of Diatom Populations: Old Findings and New Insights 19Jonas Ziebarth, Werner M. Seiler and Thomas Fuhrmann-Lieker2.1 Introduction 192.2 The MacDonald–Pfitzer Rule and the Need for Matrix Descriptions 202.3 Cardinal Points and Cycle Lengths 212.3.1 Considered Cardinal Parameters 212.3.2 Factors Determining Cardinal Points 222.3.3 Experimental Data 242.4 Asymmetry, Delay and Fibonacci Growth 262.4.1 The Müller Model 262.4.2 The Laney Model 282.5 Continuous vs. Discrete Modeling 282.5.1 Discrete Dynamical Systems 292.5.2 The Perron-Frobenius Theorem 332.5.3 Continuous Dynamical Systems 352.5.4 Extensions and Generalizations 372.5.5 Individual-Based Models 392.6 Simulation Models 412.6.1 The Schwarz et al. Model 412.6.2 The D’Alelio et al. Model 432.6.3 The Hense–Beckmann Model 452.6.4 The Terzieva–Terziev Model 482.6.5 The Fuhrmann-Lieker et al. Model 492.7 Oscillatory Behavior 522.7.1 Reproduction of Experimental Data 522.7.2 Coupling to External Rhythms 532.8 Conclusion 55Acknowledgment 56References 563 On the Mathematical Description of Diatom Algae: From Siliceous Exoskeleton Structure and Properties to Colony Growth Kinetics, and Prospective Nanoengineering Applications 63Alexey 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. Korsunsky3.1 Introduction 643.2 Hierarchical Structuring of Matter: Diatom Algae and the Bio-Assisted Nanostructured Additive Manufacturing Paradigm 643.3 Structural Design of Diatom Frustules 653.4 Mechanical Performance of Diatom Frustules – Experimental Characterization 733.4.1 Nanoindentation Testing of Diatom Frustules 753.4.2 AFM Studies of Diatom Frustules 773.5 Engineering Applications of Diatomaceous Earth 803.6 NEMS/MEMS Perspective 853.7 On the Mathematical Description of Self-Organized Diatom Frustule Growth 873.8 On the Kinetics of Diatom Colony Growth 903.9 Advanced Pattern Analysis of the Hierarchical Structure of Diatom Frustules 923.10 Concluding Remarks 95Acknowledgement 96References 96Part II: Diatom Development, Growth and Metabolism 1034 Ring to the Linear: Valve Ontogeny Indicates Two Potential Evolutionary Pathways of Core Araphid Diatoms 105Shigeki Mayama and Momoko Kushida4.1 Introduction 1064.2 Material and Methods 1074.2.1 Fragilaria mesolepta 1074.2.2 Staurosira binodis 1084.2.3 Induction of Synchronous Division 1094.2.4 Electron Microscopy 1104.3 Results 1104.3.1 Fragilaria mesolepta 1104.3.2 Staurosira binodis 1124.4 Discussion 1144.5 Conclusion 116References 1175 Mathematical Basis for Diatom Growth Modeling 121Dariush Sardari5.1 Introduction 1215.2 General Physiology of Diatoms 1225.3 Mathematical View of Diatom Growth 1235.4 Physical Basis for Diatom Modeling 1275.4.1 Diatom Dimensions 1275.4.2 Ambient Temperature 1295.4.3 Light Intensity and Duration 1295.5 Review of Existing Mathematical Models 1305.5.1 Gompertz Model 1305.5.2 Monod Model 1315.5.3 Michaelis-Menten Model 1325.5.4 Droop Model 1335.5.5 Aquaphy Model 1345.5.6 Mechanistic Model 1345.6 Results 1355.7 Conclusion 1355.8 Prospects 136References 1366 Diatom Growth: How to Improve the Analysis of Noisy Data 141Olga Kourtchenko, Kai T. Lohbeck, Björn Andersson and Tuomas Rajala6.1 Introduction 1426.1.1 What is a Growth Curve? 1426.1.2 Why Measure Growth? 1426.1.3 Diatoms and Their Growth 1436.1.4 Growth Data Analysis and Growth Parameter Estimation 1476.2 Simulation Trials 1506.2.1 Methodology for the Simulation Trials 1506.2.2 Candidate Methods for Estimating the Specific Growth Rate 1526.2.3 Simulation Trials Results 1536.2.3.1 Results with Only the Noise Challenge 1536.2.3.2 Results when Crashing Occurs 1556.2.3.3 Results when Censoring Occurs 1566.2.3.4 Overall Results and Ranking of the Methods 1576.3 Empirical Example 1586.4 Conclusions and Recommendations 159References 1617 Integrating Metabolic Modeling and High-Throughput Data to Characterize Diatoms Metabolism 165Juan D. Tibocha-Bonilla, Manish Kumar, Karsten Zengler and Cristal Zuniga7.1 Introduction 1667.2 Characterization of Diatom Genomes 1667.2.1 Available Genomics Data 1667.2.2 Computational Tools to Allocate Gene Functions by Subcellular Localization 1697.3 Metabolic Modeling of Diatoms: Data and Outcomes 1727.3.1 Using Genomic Information to Build Genome-Scale Metabolic Models 1727.3.2 Comprehensive Diatom Omic Datasets Are Useful to Constrain Metabolic Models 1737.3.3 Unraveling New Knowledge About Central Carbon Metabolism of Diatoms 1787.3.4 Light-Driven Metabolism that Enables Acclimation to High Light Intensities 1787.4 Modeling Applications to Study Bioproduction and Genome Changes in Diatoms 1807.4.1 Predicting Diatom-Heterotroph Interactions and Horizontal Gene Transfer Using Community Metabolic Models 1807.4.2 Optimization and Scale-Up of the Production of Valuable Metabolites 1817.4.3 Potential for the Study of Proteome Allocation in Diatoms 1827.5 Conclusions 183References 183Part III: Diatom Motility 1938 Modeling the Synchronization of the Movement of Bacillaria paxillifer by a Kuramoto Model with Time Delay 195Thomas Harbich8.1 Introduction 1958.2 Materials and Methods 1988.3 Time Dependence of the Relative Motion of Adjacent Diatoms 1988.4 Modeling Interacting Oscillators of a Bacillaria Colony 2038.4.1 Observation of the Movement Activity at Uncovered Rhaphes 2038.4.2 Interaction of Neighboring Diatoms 2048.4.3 Coupled Oscillators 2058.5 Kuramoto Model 2078.5.1 Adaptation of the Kuramoto Model for a Bacillaria Colony 2078.5.2 Analyses and Approximations 2088.5.3 Critical Coupling 2128.5.3.1 Uncoupled Oscillators 2128.5.3.2 Two Oscillators 2138.5.3.3 Chains without Retardation 2148.5.3.4 Identical Oscillator Frequencies and Sufficiently Small Delay 2148.5.3.5 Remarks on the General Case 2148.5.4 Statistical Considerations and Monte Carlo Simulations 2158.5.4.1 Expected Value and Standard Deviation 2158.5.4.2 Distribution of Critical Coupling 2168.5.5 Simulation of Non-Synchronous States 2188.5.5.1 Numerical Integration 2188.5.5.2 Visualization of the Transient 2188.5.5.3 Discrete Fourier Transform 2198.5.6 Coupling to a Periodic Light Source 2218.6 Discussion 223Acknowledgment 225References 2269 The Psychophysical World of the Motile Diatom Bacillaria paradoxa 229Bradly Alicea, Richard Gordon and Jesse ParentAbbreviations 2309.1 Introduction 2309.1.1 Aneural Architecture of Bacillaria 2329.1.2 Aneural Cognition in a Broader Context 2339.1.3 Psychophysics as Diatom Information Processing 2359.1.4 Information Processing and Aneural Cognition 2369.1.5 Hebbian Intelligence and Predictive Processing 2379.2 Measurement Techniques 2389.2.1 Weber-Fechner Law 2389.2.2 Connectionist Network 2409.2.3 Algorithmic Information 2409.2.4 Collective Pattern Generator 2419.2.5 Dynamical States of the CoPG 2429.3 CPGs vs. CoPGs 2429.3.1 Potential of Predictive Processing 2479.3.2 Phase Transitions in Bacillaria Movement 2479.4 Aneural Regulation 2489.5 Broader Picture of Intelligence and Emergence 2499.5.1 Pseudo-Intelligence 2499.6 Discussion 250Acknowledgments 252References 25210 Pattern Formation in Diatoma vulgaris Colonies: Observations and Description by a Lindenmayer-System 265Thomas Harbich10.1 Introduction 26510.2 Materials and Methods 26810.2.1 Cultivation and Recording of Images 26810.2.2 Formal Notation of Types of Concatenation and Splitting Processes 26910.2.3 Methods to Observe the Processes 27210.2.3.1 Basic Options 27210.2.3.2 Long-Term Observations 27210.2.3.3 Analysis of Single Images 27310.3 Results 27310.3.1 Observation of Elementary Splitting Processes 27310.3.2 Observation of Synchronism 27410.3.3 Observation of the Processes and Appearance of Colonies 27510.3.3.1 Splitting of Elements of Types c and d 27510.3.3.2 Splitting of Elements of Types a and b – Dynamic Analysis 27610.3.3.3 Separation of Elements of Types a and b – Static Analysis 27710.3.3.4 Dependence on Environmental Parameters 27810.3.4 Theory Formation 27810.3.4.1 Description of the Asymmetry 27810.3.4.2 Lindenmayer System 28110.3.5 Outer Shape of the Colonies 28410.4 Discussion 285Acknowledgment 287Appendix 10A: Calculation Scheme 287Appendix 10B: Accordance with the D0L-System 288References 28911 RAPHE: Simulation of the Dynamics of Diatom Motility at the Molecular Level – The Domino Effect Hydration Model with Concerted Diffusion 291Shruti Raj Vansh Singh, Krishna Katyal and Richard Gordon11.1 Introduction 29211.2 Parameters 29311.3 Ising Lattice Modeling 29511.4 Allowing Bias 29811.5 Computer Representation 29911.6 The Roles of the Cell Membrane, Canal Raphes, and the Diatotepum 30011.7 Raphan and the Raphe 30111.8 The Jerky Motion of Diatoms 30111.9 Diffusion and Concerted Diffusion of Raphan 30211.10 Shear and Janus-Faced Causation: Motility and Raphan Tilting 30311.11 The Domino Effect Causes Size Independence of Diatom Speed 30411.12 Quantitating the Swelling of Raphan in the Diatom Trail 30611.13 A Schematic of Raphan Discharge 30711.14 Transitions of Raphan 30811.15 The Roles of the Diatom Trail 31011.16 Outline of the Simulation 31111.17 Results 31211.18 Discussion 31511.19 Conclusion 316Dedication 318Appendix 11.1 318Appendix 11.2 318References 328Part IV: Diatom Ecological and Environmental Analysis 34312 Following the Photons Route: Mathematical Models Describing the Interaction of Diatoms with Light 345Edoardo De Tommasi, Alessandra Rogato, Diego Caratelli, Luciano Mescia and Johan Gielis12.1 Introduction 34612.2 The Underwater Light Field 34712.2.1 The Travel of Light from the Sun into Water Bodies 34712.2.2 Numerical Computation of the Underwater Optical Field 34912.3 Novel Geometrical Models for Diatoms 35212.3.1 Gielis Transformations 35212.3.2 Laplace and Fourier Revisited 35512.4 Going Through the Wall: Simulating Light Propagation in the Frustule 35612.4.1 Plane Wave Expansion (PWE) Method 35912.4.2 Finite Difference Time Domain (FDTD) Method 36212.4.3 Wide-Angle Beam Propagation Method (WA-BPM) 36412.4.4 Fast Fourier Transform (FFT) Approach 36812.5 Fractional Calculus for Diatoms 36812.5.1 Fractional Calculus Based Dielectric Dispersion Model 37012.5.2 Basic Time–Marching Scheme 37012.5.3 Uniaxial Perfectly Matched Layer Boundary Conditions 37412.6 Beyond the Glass Cage: The Fate of Light Inside the Cell 37612.6.1 The Diatom Chloroplast and its Evolution 37712.6.2 The Photosynthetic and Electron Transport Chain 37812.6.3 The Photoprotection Mechanism 37912.6.4 The Diatom Photoreceptors 38012.6.5 Chlorophyll Optical Signals for Satellite Population Monitoring 38012.7 Conclusions 383References 38413 A Generalized Model for the Light Response of the Nonphotochemical Quenching of Chlorophyll Fluorescence of Diatoms 393João Serôdio and Johann Lavaud13.1 Introduction 39413.2 Model Formulation 39513.2.1 Nonphotochemical Quenching Indices NPQ and Y(NPQ) 39513.2.2 Standard Model for NPQ LCs 39713.2.3 Generalized Model for NPQ LCs 39713.2.4 Model Fitting and Parameter Estimation 39813.3 Results 40313.4 Discussion 40613.4.1 Model Assumptions 40613.4.2 Fitting to Experimental Data 40713.4.3 Application 407Acknowledgments 409References 40914 Coscinodiscus wailesii as Biogenic Charge-Based Sensors for Heavy Metal Ion Contamination Detection 413Rajeshwari Taruvai Kalyana Kumar, Diem-Thuy Le, Antra Ganguly and Shalini Prasad14.1 Introduction 41314.2 Materials and Methods 41614.2.1 Chemicals and Reagents 41614.2.2 Cell Culture 41614.2.3 Heavy Metal Doping and Characterization 41614.2.4 Electrophoretic Measurements 41714.3 Results and Discussion 41714.3.1 Effect of Heavy Metal Doping on Cell Culture 41714.3.2 Effect of Heavy Metal Doping on Zeta Potential 41814.3.3 Dependency of pH on Surface Charge Potential 41914.3.4 FTIR Characterization 42114.4 Conclusion 424Acknowledgments 425References 425Index 427