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The mathematical biology of diatoms

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 th...

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Bibliographic Details
Other Authors:	Pappas, Janice L. (Editor)
Format:	eBook
Language:	English
Published:	Hoboken, NJ John Wiley & Sons, Inc. 2023
Series:	Diatoms : biology and applications
Subjects:	Diatoms / Fast Diatoms / Http://id.loc.gov/authorities/subjects/sh85037628 Diatomées
Online Access:	https://learning.oreilly.com/library/view/~/978111...
Collection:	O'Reilly - Collection details see MPG.ReNa

Table of Contents:

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
3.4.1 Nanoindentation Testing of Diatom Frustules
3.4.2 AFM Studies of Diatom Frustules
3.5 Engineering Applications of Diatomaceous Earth
3.6 NEMS/MEMS Perspective
3.7 On the Mathematical Description of Self-Organized Diatom Frustule Growth
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
Chapter 4 Ring to the Linear: Valve Ontogeny Indicates Two Potential Evolutionary Pathways of Core Araphid Diatoms
4.1 Introduction
4.2 Material and Methods
4.2.1 Fragilaria mesolepta
4.2.2 Staurosira binodis
4.2.3 Induction of Synchronous Division
4.2.4 Electron Microscopy
4.3 Results
4.3.1 Fragilaria mesolepta
4.3.2 Staurosira binodis
4.4 Discussion
4.5 Conclusion
References
Chapter 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
5.4.1 Diatom Dimensions
5.4.2 Ambient Temperature
5.4.3 Light Intensity and Duration
5.5 Review of Existing Mathematical Models
5.5.1 Gompertz Model
5.5.2 Monod Model
5.5.3 Michaelis-Menten Model
5.5.4 Droop Model
5.5.5 Aquaphy Model
5.5.6 Mechanistic Model
5.6 Results
5.7 Conclusion
5.8 Prospects
References
Chapter 6 Diatom Growth: How to Improve the Analysis of Noisy Data
6.1 Introduction
6.1.1 What is a Growth Curve?
6.1.2 Why Measure Growth?
Chapter 10 Pattern Formation in Diatoma vulgaris Colonies: Observations and Description by a Lindenmayer-System
10.1 Introduction
10.2 Materials and Methods
10.2.1 Cultivation and Recording of Images
10.2.2 Formal Notation of Types of Concatenation and Splitting Processes
10.2.3 Methods to Observe the Processes
10.2.3.1 Basic Options
10.2.3.2 Long-Term Observations
10.2.3.3 Analysis of Single Images
10.3 Results
10.3.1 Observation of Elementary Splitting Processes
10.3.2 Observation of Synchronism
10.3.3 Observation of the Processes and Appearance of Colonies
10.3.3.1 Splitting of Elements of Types c and d
10.3.3.2 Splitting of Elements of Types a and b
Dynamic Analysis
10.3.3.3 Separation of Elements of Types a and b
Static Analysis
10.3.3.4 Dependence on Environmental Parameters
10.3.4 Theory Formation
10.3.4.1 Description of the Asymmetry
10.3.4.2 Lindenmayer System
10.3.5 Outer Shape of the Colonies
10.4 Discussion
Acknowledgment
Appendix 10A: Calculation Scheme
Appendix 10B: Accordance with the D0L-System
References
Chapter 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
6.1.3 Diatoms and Their Growth
6.1.4 Growth Data Analysis and Growth Parameter Estimation
6.2 Simulation Trials
6.2.1 Methodology for the Simulation Trials
6.2.2 Candidate Methods for Estimating the Specific Growth Rate
6.2.3 Simulation Trials Results
6.2.3.1 Results with Only the Noise Challenge
6.2.3.2 Results when Crashing Occurs
6.2.3.3 Results when Censoring Occurs
6.2.3.4 Overall Results and Ranking of the Methods
6.3 Empirical Example
6.4 Conclusions and Recommendations
References
Chapter 7 Integrating Metabolic Modeling and High-Throughput Data to Characterize Diatoms Metabolism
7.1 Introduction
7.2 Characterization of Diatom Genomes
7.2.1 Available Genomics Data
7.2.2 Computational Tools to Allocate Gene Functions by Subcellular Localization
7.3 Metabolic Modeling of Diatoms: Data and Outcomes
7.3.1 Using Genomic Information to Build Genome-Scale Metabolic Models
7.3.2 Comprehensive Diatom Omic Datasets Are Useful to Constrain Metabolic Models
7.3.3 Unraveling New Knowledge About Central Carbon Metabolism of Diatoms
7.3.4 Light-Driven Metabolism that Enables Acclimation to High Light Intensities
7.4 Modeling Applications to Study Bioproduction and Genome Changes in Diatoms
7.4.1 Predicting Diatom-Heterotroph Interactions and Horizontal Gene Transfer Using Community Metabolic Models
7.4.2 Optimization and Scale-Up of the Production of Valuable Metabolites
7.4.3 Potential for the Study of Proteome Allocation in Diatoms
7.5 Conclusions
References
Part III: Diatom Motility
Chapter 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
Cover
Title Page
Copyright Page
Contents
List of Figures
List of Tables
Preface
Part I: Diatom Form and Size Dynamics
Chapter 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
1.2.1 Focused Ion Beam (FIB) Milling
1.2.2 Modeling
1.3 Results
1.3.1 FIB Processing
1.3.2 Modeling
1.4 Discussion
1.4.1 Practical Meaning of the Frustule Geometric Characters
1.4.2 Documenting the Mechanical Strength of the Diatom Frustule
Acknowledgments
References
Chapter 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
2.3.1 Considered Cardinal Parameters
2.3.2 Factors Determining Cardinal Points
2.3.3 Experimental Data
2.4 Asymmetry, Delay and Fibonacci Growth
2.4.1 The Müller Model
2.4.2 The Laney Model
2.5 Continuous vs. Discrete Modeling
2.5.1 Discrete Dynamical Systems
2.5.2 The Perron-Frobenius Theorem
2.5.3 Continuous Dynamical Systems
2.5.4 Extensions and Generalizations
2.5.5 Individual-Based Models
2.6 Simulation Models
2.6.1 The Schwarz et al. Model
2.6.2 The D'Alelio et al. Model
2.6.3 The Hense-Beckmann Model
2.6.4 The Terzieva-Terziev Model
2.6.5 The Fuhrmann-Lieker et al. Model
2.7 Oscillatory Behavior
2.7.1 Reproduction of Experimental Data
2.7.2 Coupling to External Rhythms
2.8 Conclusion
Acknowledgment
References
Chapter 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
8.4 Modeling Interacting Oscillators of a Bacillaria Colony
8.4.1 Observation of the Movement Activity at Uncovered Rhaphes
8.4.2 Interaction of Neighboring Diatoms
8.4.3 Coupled Oscillators
8.5 Kuramoto Model
8.5.1 Adaptation of the Kuramoto Model for a Bacillaria Colony
8.5.2 Analyses and Approximations
8.5.3 Critical Coupling
8.5.3.1 Uncoupled Oscillators
8.5.3.2 Two Oscillators
8.5.3.3 Chains without Retardation
8.5.3.4 Identical Oscillator Frequencies and Sufficiently Small Delay
8.5.3.5 Remarks on the General Case
8.5.4 Statistical Considerations and Monte Carlo Simulations
8.5.4.1 Expected Value and Standard Deviation
8.5.4.2 Distribution of Critical Coupling
8.5.5 Simulation of Non-Synchronous States
8.5.5.1 Numerical Integration
8.5.5.2 Visualization of the Transient
8.5.5.3 Discrete Fourier Transform
8.5.6 Coupling to a Periodic Light Source
8.6 Discussion
Acknowledgment
References
Chapter 9 The Psychophysical World of the Motile Diatom Bacillaria paradoxa
Abbreviations
9.1 Introduction
9.1.1 Aneural Architecture of Bacillaria
9.1.2 Aneural Cognition in a Broader Context
9.1.3 Psychophysics as Diatom Information Processing
9.1.4 Information Processing and Aneural Cognition
9.1.5 Hebbian Intelligence and Predictive Processing
9.2 Measurement Techniques
9.2.1 Weber-Fechner Law
9.2.2 Connectionist Network
9.2.3 Algorithmic Information
9.2.4 Collective Pattern Generator
9.2.5 Dynamical States of the CoPG
9.3 CPGs vs. CoPGs
9.3.1 Potential of Predictive Processing
9.3.2 Phase Transitions in Bacillaria Movement
9.4 Aneural Regulation
9.5 Broader Picture of Intelligence and Emergence
9.5.1 Pseudo-Intelligence
9.6 Discussion
Acknowledgments
References

The mathematical biology of diatoms

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