This book contains unique, advanced applications using mathematics, algorithmic techniques, geometric analysis, and other computational methods in diatom research.
Historically, diatom research has centered 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 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 range 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.
Table of 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 3
Andrzej Witkowski, Romuald Dobosz, Tomasz Płociński, Przemysław Dąbek, Izabela Zgłobicka, Horst Lange-Bertalot, Thomas G. Bornman, Renata Dobrucka, Michał Gloc and Krzysztof J. Kurzydłowski
1.1 Introduction 4
1.2 Material and Methods 6
1.2.1 Focused Ion Beam (FIB) Milling 6
1.2.2 Modeling 6
1.3 Results 8
1.3.1 FIB Processing 8
1.3.2 Modeling 11
1.4 Discussion 14
1.4.1 Practical Meaning of the Frustule Geometric Characters 14
1.4.2 Documenting the Mechanical Strength of the Diatom Frustule 14
Acknowledgments 16
References 16
2 Size-Resolved Modeling of Diatom Populations: Old Findings and New Insights 19
Jonas Ziebarth, Werner M. Seiler and Thomas Fuhrmann-Lieker
2.1 Introduction 19
2.2 The MacDonald-Pfitzer Rule and the Need for Matrix Descriptions 20
2.3 Cardinal Points and Cycle Lengths 21
2.3.1 Considered Cardinal Parameters 21
2.3.2 Factors Determining Cardinal Points 22
2.3.3 Experimental Data 24
2.4 Asymmetry, Delay and Fibonacci Growth 26
2.4.1 The Müller Model 26
2.4.2 The Laney Model 28
2.5 Continuous vs. Discrete Modeling 28
2.5.1 Discrete Dynamical Systems 29
2.5.2 The Perron-Frobenius Theorem 33
2.5.3 Continuous Dynamical Systems 35
2.5.4 Extensions and Generalizations 37
2.5.5 Individual-Based Models 39
2.6 Simulation Models 41
2.6.1 The Schwarz et al. Model 41
2.6.2 The D’Alelio et al. Model 43
2.6.3 The Hense-Beckmann Model 45
2.6.4 The Terzieva-Terziev Model 48
2.6.5 The Fuhrmann-Lieker et al. Model 49
2.7 Oscillatory Behavior 52
2.7.1 Reproduction of Experimental Data 52
2.7.2 Coupling to External Rhythms 53
2.8 Conclusion 55
Acknowledgment 56
References 56
3 On the Mathematical Description of Diatom Algae: From Siliceous Exoskeleton Structure and Properties to Colony Growth Kinetics, and Prospective Nanoengineering Applications 63
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
3.1 Introduction 64
3.2 Hierarchical Structuring of Matter: Diatom Algae and the Bio-Assisted Nanostructured Additive Manufacturing Paradigm 64
3.3 Structural Design of Diatom Frustules 65
3.4 Mechanical Performance of Diatom Frustules - Experimental Characterization 73
3.4.1 Nanoindentation Testing of Diatom Frustules 75
3.4.2 AFM Studies of Diatom Frustules 77
3.5 Engineering Applications of Diatomaceous Earth 80
3.6 NEMS/MEMS Perspective 85
3.7 On the Mathematical Description of Self-Organized Diatom Frustule Growth 87
3.8 On the Kinetics of Diatom Colony Growth 90
3.9 Advanced Pattern Analysis of the Hierarchical Structure of Diatom Frustules 92
3.10 Concluding Remarks 95
Acknowledgement 96
References 96
Part II: Diatom Development, Growth and Metabolism 103
4 Ring to the Linear: Valve Ontogeny Indicates Two Potential Evolutionary Pathways of Core Araphid Diatoms 105
Shigeki Mayama and Momoko Kushida
4.1 Introduction 106
4.2 Material and Methods 107
4.2.1 Fragilaria mesolepta 107
4.2.2 Staurosira binodis 108
4.2.3 Induction of Synchronous Division 109
4.2.4 Electron Microscopy 110
4.3 Results 110
4.3.1 Fragilaria mesolepta 110
4.3.2 Staurosira binodis 112
4.4 Discussion 114
4.5 Conclusion 116
References 117
5 Mathematical Basis for Diatom Growth Modeling 121
Dariush Sardari
5.1 Introduction 121
5.2 General Physiology of Diatoms 122
5.3 Mathematical View of Diatom Growth 123
5.4 Physical Basis for Diatom Modeling 127
5.4.1 Diatom Dimensions 127
5.4.2 Ambient Temperature 129
5.4.3 Light Intensity and Duration 129
5.5 Review of Existing Mathematical Models 130
5.5.1 Gompertz Model 130
5.5.2 Monod Model 131
5.5.3 Michaelis-Menten Model 132
5.5.4 Droop Model 133
5.5.5 Aquaphy Model 134
5.5.6 Mechanistic Model 134
5.6 Results 135
5.7 Conclusion 135
5.8 Prospects 136
References 136
6 Diatom Growth: How to Improve the Analysis of Noisy Data 141
Olga Kourtchenko, Kai T. Lohbeck, Björn Andersson and Tuomas Rajala
6.1 Introduction 142
6.1.1 What is a Growth Curve? 142
6.1.2 Why Measure Growth? 142
6.1.3 Diatoms and Their Growth 143
6.1.4 Growth Data Analysis and Growth Parameter Estimation 147
6.2 Simulation Trials 150
6.2.1 Methodology for the Simulation Trials 150
6.2.2 Candidate Methods for Estimating the Specific Growth Rate 152
6.2.3 Simulation Trials Results 153
6.2.3.1 Results with Only the Noise Challenge 153
6.2.3.2 Results when Crashing Occurs 155
6.2.3.3 Results when Censoring Occurs 156
6.2.3.4 Overall Results and Ranking of the Methods 157
6.3 Empirical Example 158
6.4 Conclusions and Recommendations 159
References 161
7 Integrating Metabolic Modeling and High-Throughput Data to Characterize Diatoms Metabolism 165
Juan D. Tibocha-Bonilla, Manish Kumar, Karsten Zengler and Cristal Zuniga
7.1 Introduction 166
7.2 Characterization of Diatom Genomes 166
7.2.1 Available Genomics Data 166
7.2.2 Computational Tools to Allocate Gene Functions by Subcellular Localization 169
7.3 Metabolic Modeling of Diatoms: Data and Outcomes 172
7.3.1 Using Genomic Information to Build Genome-Scale Metabolic Models 172
7.3.2 Comprehensive Diatom Omic Datasets Are Useful to Constrain Metabolic Models 173
7.3.3 Unraveling New Knowledge About Central Carbon Metabolism of Diatoms 178
7.3.4 Light-Driven Metabolism that Enables Acclimation to High Light Intensities 178
7.4 Modeling Applications to Study Bioproduction and Genome Changes in Diatoms 180
7.4.1 Predicting Diatom-Heterotroph Interactions and Horizontal Gene Transfer Using Community Metabolic Models 180
7.4.2 Optimization and Scale-Up of the Production of Valuable Metabolites 181
7.4.3 Potential for the Study of Proteome Allocation in Diatoms 182
7.5 Conclusions 183
References 183
Part III: Diatom Motility 193
8 Modeling the Synchronization of the Movement of Bacillaria paxillifer by a Kuramoto Model with Time Delay 195
Thomas Harbich
8.1 Introduction 195
8.2 Materials and Methods 198
8.3 Time Dependence of the Relative Motion of Adjacent Diatoms 198
8.4 Modeling Interacting Oscillators of a Bacillaria Colony 203
8.4.1 Observation of the Movement Activity at Uncovered Rhaphes 203
8.4.2 Interaction of Neighboring Diatoms 204
8.4.3 Coupled Oscillators 205
8.5 Kuramoto Model 207
8.5.1 Adaptation of the Kuramoto Model for a Bacillaria Colony 207
8.5.2 Analyses and Approximations 208
8.5.3 Critical Coupling 212
8.5.3.1 Uncoupled Oscillators 212
8.5.3.2 Two Oscillators 213
8.5.3.3 Chains without Retardation 214
8.5.3.4 Identical Oscillator Frequencies and Sufficiently Small Delay 214
8.5.3.5 Remarks on the General Case 214
8.5.4 Statistical Considerations and Monte Carlo Simulations 215
8.5.4.1 Expected Value and Standard Deviation 215
8.5.4.2 Distribution of Critical Coupling 216
8.5.5 Simulation of Non-Synchronous States 218
8.5.5.1 Numerical Integration 218
8.5.5.2 Visualization of the Transient 218
8.5.5.3 Discrete Fourier Transform 219
8.5.6 Coupling to a Periodic Light Source 221
8.6 Discussion 223
Acknowledgment 225
References 226
9 The Psychophysical World of the Motile Diatom Bacillaria paradoxa 229
Bradly Alicea, Richard Gordon and Jesse Parent
Abbreviations 230
9.1 Introduction 230
9.1.1 Aneural Architecture of Bacillaria 232
9.1.2 Aneural Cognition in a Broader Context 233
9.1.3 Psychophysics as Diatom Information Processing 235
9.1.4 Information Processing and Aneural Cognition 236
9.1.5 Hebbian Intelligence and Predictive Processing 237
9.2 Measurement Techniques 238
9.2.1 Weber-Fechner Law 238
9.2.2 Connectionist Network 240
9.2.3 Algorithmic Information 240
9.2.4 Collective Pattern Generator 241
9.2.5 Dynamical States of the CoPG 242
9.3 CPGs vs. CoPGs 242
9.3.1 Potential of Predictive Processing 247
9.3.2 Phase Transitions in Bacillaria Movement 247
9.4 Aneural Regulation 248
9.5 Broader Picture of Intelligence and Emergence 249
9.5.1 Pseudo-Intelligence 249
9.6 Discussion 250
Acknowledgments 252
References 252
10 Pattern Formation in Diatoma vulgaris Colonies: Observations and Description by a Lindenmayer-System 265
Thomas Harbich
10.1 Introduction 265
10.2 Materials and Methods 268
10.2.1 Cultivation and Recording of Images 268
10.2.2 Formal Notation of Types of Concatenation and Splitting Processes 269
10.2.3 Methods to Observe the Processes 272
10.2.3.1 Basic Options 272
10.2.3.2 Long-Term Observations 272
10.2.3.3 Analysis of Single Images 273
10.3 Results 273
10.3.1 Observation of Elementary Splitting Processes 273
10.3.2 Observation of Synchronism 274
10.3.3 Observation of the Processes and Appearance of Colonies 275
10.3.3.1 Splitting of Elements of Types c and d 275
10.3.3.2 Splitting of Elements of Types a and b - Dynamic Analysis 276
10.3.3.3 Separation of Elements of Types a and b - Static Analysis 277
10.3.3.4 Dependence on Environmental Parameters 278
10.3.4 Theory Formation 278
10.3.4.1 Description of the Asymmetry 278
10.3.4.2 Lindenmayer System 281
10.3.5 Outer Shape of the Colonies 284
10.4 Discussion 285
Acknowledgment 287
Appendix 10A: Calculation Scheme 287
Appendix 10B: Accordance with the D0L-System 288
References 289
11 RAPHE: Simulation of the Dynamics of Diatom Motility at the Molecular Level - The Domino Effect Hydration Model with Concerted Diffusion 291
Shruti Raj Vansh Singh, Krishna Katyal and Richard Gordon
11.1 Introduction 292
11.2 Parameters 293
11.3 Ising Lattice Modeling 295
11.4 Allowing Bias 298
11.5 Computer Representation 299
11.6 The Roles of the Cell Membrane, Canal Raphes, and the Diatotepum 300
11.7 Raphan and the Raphe 301
11.8 The Jerky Motion of Diatoms 301
11.9 Diffusion and Concerted Diffusion of Raphan 302
11.10 Shear and Janus-Faced Causation: Motility and Raphan Tilting 303
11.11 The Domino Effect Causes Size Independence of Diatom Speed 304
11.12 Quantitating the Swelling of Raphan in the Diatom Trail 306
11.13 A Schematic of Raphan Discharge 307
11.14 Transitions of Raphan 308
11.15 The Roles of the Diatom Trail 310
11.16 Outline of the Simulation 311
11.17 Results 312
11.18 Discussion 315
11.19 Conclusion 316
Dedication 318
Appendix 11.1 318
Appendix 11.2 318
References 328
Part IV: Diatom Ecological and Environmental Analysis 343
12 Following the Photons Route: Mathematical Models Describing the Interaction of Diatoms with Light 345
Edoardo De Tommasi, Alessandra Rogato, Diego Caratelli, Luciano Mescia and Johan Gielis
12.1 Introduction 346
12.2 The Underwater Light Field 347
12.2.1 The Travel of Light from the Sun into Water Bodies 347
12.2.2 Numerical Computation of the Underwater Optical Field 349
12.3 Novel Geometrical Models for Diatoms 352
12.3.1 Gielis Transformations 352
12.3.2 Laplace and Fourier Revisited 355
12.4 Going Through the Wall: Simulating Light Propagation in the Frustule 356
12.4.1 Plane Wave Expansion (PWE) Method 359
12.4.2 Finite Difference Time Domain (FDTD) Method 362
12.4.3 Wide-Angle Beam Propagation Method (WA-BPM) 364
12.4.4 Fast Fourier Transform (FFT) Approach 368
12.5 Fractional Calculus for Diatoms 368
12.5.1 Fractional Calculus Based Dielectric Dispersion Model 370
12.5.2 Basic Time-Marching Scheme 370
12.5.3 Uniaxial Perfectly Matched Layer Boundary Conditions 374
12.6 Beyond the Glass Cage: The Fate of Light Inside the Cell 376
12.6.1 The Diatom Chloroplast and its Evolution 377
12.6.2 The Photosynthetic and Electron Transport Chain 378
12.6.3 The Photoprotection Mechanism 379
12.6.4 The Diatom Photoreceptors 380
12.6.5 Chlorophyll Optical Signals for Satellite Population Monitoring 380
12.7 Conclusions 383
References 384
13 A Generalized Model for the Light Response of the Nonphotochemical Quenching of Chlorophyll Fluorescence of Diatoms 393
João Serôdio and Johann Lavaud
13.1 Introduction 394
13.2 Model Formulation 395
13.2.1 Nonphotochemical Quenching Indices NPQ and Y(NPQ) 395
13.2.2 Standard Model for NPQ LCs 397
13.2.3 Generalized Model for NPQ LCs 397
13.2.4 Model Fitting and Parameter Estimation 398
13.3 Results 403
13.4 Discussion 406
13.4.1 Model Assumptions 406
13.4.2 Fitting to Experimental Data 407
13.4.3 Application 407
Acknowledgments 409
References 409
14 Coscinodiscus wailesii as Biogenic Charge-Based Sensors for Heavy Metal Ion Contamination Detection 413
Rajeshwari Taruvai Kalyana Kumar, Diem-Thuy Le, Antra Ganguly and Shalini Prasad
14.1 Introduction 413
14.2 Materials and Methods 416
14.2.1 Chemicals and Reagents 416
14.2.2 Cell Culture 416
14.2.3 Heavy Metal Doping and Characterization 416
14.2.4 Electrophoretic Measurements 417
14.3 Results and Discussion 417
14.3.1 Effect of Heavy Metal Doping on Cell Culture 417
14.3.2 Effect of Heavy Metal Doping on Zeta Potential 418
14.3.3 Dependency of pH on Surface Charge Potential 419
14.3.4 FTIR Characterization 421
14.4 Conclusion 424
Acknowledgments 425
References 425
Index 427
