Mathematical Biology of Diatoms

Mathematical Biology of Diatoms

Pappas, Janice L.

John Wiley & Sons Inc

01/2024

480

Dura

Inglês

9781119750437

15 a 20 dias

666

Descrição não disponível.
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 Plocinski, Przemyslaw Dabek, Izabela Zglobicka, Horst Lange-Bertalot, Thomas G. Bornman, Renata Dobrucka, Michal Gloc and Krzysztof J. Kurzydlowski

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 Mueller 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, Bjoern 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
Joao Serodio 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
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