The Mathematical Biology of Diatoms E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Diatoms: Biology and Applications
• Sprache: Englisch

Seitenzahl: 963

Veröffentlichungsjahr: 2023

Beschreibung

THE MATHEMATICAL BIOLOGY OF DIATOMS 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.

Leseprobe

Table of Contents

Cover

Series Page

Title Page

Copyright Page

List of Figures

List of Tables

Preface

Part I: Diatom Form and Size Dynamics

1 Modeling the Stiffness of

Diploneis

Species Based on Geometry of the Frustule Cut with Focused Ion Beam Technology

1.1 Introduction

1.2 Material and Methods

1.3 Results

1.4 Discussion

Acknowledgments

References

2 Size-Resolved Modeling of Diatom Populations: Old Findings and New Insights

2.1 Introduction

2.2 The MacDonald–Pfitzer Rule and the Need for Matrix Descriptions

2.3 Cardinal Points and Cycle Lengths

2.4 Asymmetry, Delay and Fibonacci Growth

2.5 Continuous vs. Discrete Modeling

2.6 Simulation Models

2.7 Oscillatory Behavior

2.8 Conclusion

Acknowledgment

References

3 On the Mathematical Description of Diatom Algae: From Siliceous Exoskeleton Structure and Properties to Colony Growth Kinetics, and Prospective Nanoengineering Applications

3.1 Introduction

3.2 Hierarchical Structuring of Matter: Diatom Algae and the Bio-Assisted Nanostructured Additive Manufacturing Paradigm

3.3 Structural Design of Diatom Frustules

3.4 Mechanical Performance of Diatom Frustules – Experimental Characterization

3.5 Engineering Applications of Diatomaceous Earth

3.6 NEMS/MEMS Perspective

3.7 On the Mathematical Description of Self-Organized Diatom Frustule Growth 87

3.8 On the Kinetics of Diatom Colony Growth

3.9 Advanced Pattern Analysis of the Hierarchical Structure of Diatom Frustules

3.10 Concluding Remarks

Acknowledgement

References

Part II: Diatom Development, Growth and Metabolism

4 Ring to the Linear: Valve Ontogeny Indicates Two Potential Evolutionary Pathways of Core Araphid Diatoms

4.1 Introduction

4.2 Material and Methods

4.3 Results

4.4 Discussion

4.5 Conclusion

References

5 Mathematical Basis for Diatom Growth Modeling

5.1 Introduction

5.2 General Physiology of Diatoms

5.3 Mathematical View of Diatom Growth

5.4 Physical Basis for Diatom Modeling

5.5 Review of Existing Mathematical Models

5.6 Results

5.7 Conclusion

5.8 Prospects

References

6 Diatom Growth: How to Improve the Analysis of Noisy Data

6.1 Introduction

6.2 Simulation Trials

6.3 Empirical Example

6.4 Conclusions and Recommendations

References

7 Integrating Metabolic Modeling and High-Throughput Data to Characterize Diatoms Metabolism

7.1 Introduction

7.2 Characterization of Diatom Genomes

7.3 Metabolic Modeling of Diatoms: Data and Outcomes

7.4 Modeling Applications to Study Bioproduction and Genome Changes in Diatoms

7.5 Conclusions

References

Part III: Diatom Motility

8 Modeling the Synchronization of the Movement of

Bacillaria paxillifer

by a Kuramoto Model with Time Delay

8.1 Introduction

8.2 Materials and Methods

8.3 Time Dependence of the Relative Motion of Adjacent Diatoms

8.4 Modeling Interacting Oscillators of a

Bacillaria

Colony

8.5 Kuramoto Model

8.6 Discussion

Acknowledgment

References

9 The Psychophysical World of the Motile Diatom

Bacillaria paradoxa

Abbreviations

9.1 Introduction

9.2 Measurement Techniques

9.3 CPGs vs. CoPGs

9.4 Aneural Regulation

9.5 Broader Picture of Intelligence and Emergence

9.6 Discussion

Acknowledgments

References

10 Pattern Formation in Diatoma vulgaris Colonies: Observations and Description by a Lindenmayer-System

10.1 Introduction

10.2 Materials and Methods

10.3 Results

10.4 Discussion

Acknowledgment

Appendix 10A: Calculation Scheme

Appendix 10B: Accordance with the D0L-System

References

11 RAPHE: Simulation of the Dynamics of Diatom Motility at the Molecular Level – The Domino Effect Hydration Model with Concerted Diffusion

11.1 Introduction

11.2 Parameters

11.3 Ising Lattice Modeling

11.4 Allowing Bias

11.5 Computer Representation

11.6 The Roles of the Cell Membrane, Canal Raphes, and the Diatotepum

11.7 Raphan and the Raphe

11.8 The Jerky Motion of Diatoms

11.9 Diffusion and Concerted Diffusion of Raphan

11.10 Shear and Janus-Faced Causation: Motility and Raphan Tilting

11.11 The Domino Effect Causes Size Independence of Diatom Speed

11.12 Quantitating the Swelling of Raphan in the Diatom Trail

11.13 A Schematic of Raphan Discharge

11.14 Transitions of Raphan

11.15 The Roles of the Diatom Trail

11.16 Outline of the Simulation

11.17 Results

11.18 Discussion

11.19 Conclusion

Dedication

Appendix 11.1

Appendix 11.2

References

Part IV: Diatom Ecological and Environmental Analysis

12 Following the Photons Route: Mathematical Models Describing the Interaction of Diatoms with Light

12.1 Introduction

12.2 The Underwater Light Field

12.3 Novel Geometrical Models for Diatoms

12.4 Going Through the Wall: Simulating Light Propagation in the Frustule

12.5 Fractional Calculus for Diatoms

12.6 Beyond the Glass Cage: The Fate of Light Inside the Cell

12.7 Conclusions

References

13 A Generalized Model for the Light Response of the Nonphotochemical Quenching of Chlorophyll Fluorescence of Diatoms

13.1 Introduction

13.2 Model Formulation

13.3 Results

13.4 Discussion

Acknowledgments

References

14

Coscinodiscus wailesii

as Biogenic Charge-Based Sensors for Heavy Metal Ion Contamination Detection

14.1 Introduction

14.2 Materials and Methods

14.3 Results and Discussion

14.4 Conclusion

Acknowledgments

References

Index

Also of Interest

End User License Agreement

List of Tables

Chapter 2

Table 2.1

Reported life cycles and cardinal points of selected species. Cycle lengths marked with a star are rough estimates based on the reported size diminution speeds and the size range. The size in brackets marks the size at which cells were observed to become sexually inducible.

Table 2.2

Size clusters for

P. delicatissima

according to Schwarz

et al

. [2.76]. Given is mean

μ

i

, standard deviation

σ

i

(from graph), lower boundary, cluster range and holding time

τ

for the Gaussian functions and their derived clusters, respectively.

Table 2.3

Parameters used in the model of D’Alelio

et al

. Given is the original denotation in the paper [2.19] as well as an abbreviated version used here in the mathematical expressions.

Table 2.4

Selected parameters used in the Hense–Beckmann PPND model. Parameters for the second, bulk phytoplankton species (index

P

instead of

B

) are omitted here.

Table 2.5

Selected variables and parameters used in the Hense–Beckmann DiaLCM model as far as mentioned in the text. For a complete list please refer to the appendix of the original article [2.36].

Table 2.6

Parameters used in the Fuhrmann-Lieker

et al

. model.

Table 2.7

Comparison of the models. C: class model treated with differential equations, D: class model treated with difference equations, I: individual-based branching model.

Chapter 3

Table 3.1

Summary of various experiments of diatom algae by nanoindentation and bending tests.

Chapter 6

Table 6.1

Study details for each of the diatom species shown in Figure 6.2. The species are given in alphabetic order; the study details include species-specific information (symmetry type, natural habitat type), the growth experiment-specific metadata (type of treatment, biomass proxy, the length of the experiment, total number of observations, approximate number of observations in the exponential phase, light cycle conditions), and a reference. *Indicates unpublished growth data from the authors presented in Subsection 6.1.3.

Table 6.2

Average ranking of estimators in terms of quality metrics, averaged over challenge sets with varying noise and sampling frequency. Mean of ranks over challenge sets. Lower values signify better performance.

Table 6.3

Average ranking of estimators in terms of quality metrics, averaged over challenge sets with a crash event on day 7 and varying noise and sampling frequency. Means of ranks over challenge sets. Lower values signify better performance.

Table 6.4

Average ranking of estimators in terms of quality metrics, averaged over challenge sets with experiment stopped at day 7 and varying noise and sampling frequency. Means of ranks over challenge sets. Lower values signify better performance.

Table 6.5

Estimated difference of mean growth rates in two temperatures. Growth rates are derived from different methods.

Chapter 7

Table 7.1

Comparison of annotation methods used on diatom genomes.

Table 7.2

Tools for predicting subcellular localization of the proteome of diatoms. This table contains information about the tools that have previously been applied to diatoms’ genomes.

Table 7.3

Omics datasets that will facilitate the metabolic modeling of diatoms.

Chapter 9

Table 9.1

A demonstration of how autonomy can be partitioned into generated and observed components.

Chapter 10

Table 10.1

Observed processes and their frequencies.

Table 10.2

Measured angles and standard deviations.

Chapter 11

Table 11.1

The set of parameters that require values for a run of the RAPHE computer program. Except for the number of events simulated, we have 9 independent input variables that could vary between individual diatoms and species. A variable that changes with each event is labeled “none” under Default value.

Table 11.2

States and rates. All rates in columns 4 through 7 (variable: total_columns-1) are set to zero at the beginning of each computational loop for an event. For those events that can happen, the rates are then calculated and become positive real numbers, indicated here by a + in those columns for this example of a raphe configuration. These are recalculated for each event after concatenation. The actual numbers depend on the values for the parameters in Table 11.1. If groups contain oppositely directed raphans, they are first concatenated, as described in the text. Only already concatenated groups are shown here. States of lattice sites are shown both numerically and via symbols. -1 / means hydrates to the left, 0 means empty, +1 \ means hydrates to the right. The diatom is presumed to move in the opposite direction (variable: directionForDiatom) of the hydration when hydration occurs, by a fixed amount (variable: distanceIncrementContributedBySwelling). For readability of the code, the column names correspond to variable names, which are assigned the column number.

Table 11.3

Published data on pennate diatom speeds and their lengths. Speeds in threedimensional substrates are not compiled here. As in our simulation, data for the typical smooth, clean microscope slide is assembled here and all other properties related to the substrate are ignored, such as adhesion, roughness, gaps, or obstacles.

Chapter 12

Table 12.1

Symbols, units and definitions of the quantities in Eq. 12.8.

Table 12.2

Low-order Padé approximants expressed in terms of the operator

P

defined in Eq. (12.40).

Chapter 13

Table 13.1

Notations.

Table 13.2

Results of fitting of Eq. (13.5) to NPQ vs.

E

and Y(NPQ) vs.

E

curves measured in diatoms or diatom-dominated communities. Growth conditions/Treatment: sampling dates, conditions applied during growth or before the measurement of the light curves, when more than one LC available for the same taxon (HL: high growth light; LL: low growth light). LC: light curve protocol (LCx: steady state LC; RLCx: rapid light curve, x seconds of light step; UP, Down: sequential increase or decrease light levels, respectively).

Chapter 14

Table 14.1

Toxicity limits, common sources, sensing modality, and limit of detection.

Table 14.2

FTIR spectra and band assignment for their corresponding functional groups.

Guide

Cover

Table of Contents

Series Page

Title Page

Copyright

List of Figures

List of Tables

Preface

Begin Reading

Index

Also of Interest

End User License Agreement

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