Möller, Mark: A hybrid algorithm for the simulation of biochemical reactions and diffusion. 2006
Inhalt
- Summary
- Preamble
- Table of Contents
- List of Tables
- List of Figures
- List of Abbreviations
- List of Notations
- 1 Introduction
- 2 State of the Art
- 2.1 Meaning of Chemical Reactions & Diffusion for Biological Systems
- 2.2 From Systems Biology to Mathematical Modeling
- 2.3 Modeling
- 2.4 Existing Methods
- 2.5 Existing Implementations
- 3 COAST for Reaction and Diffusion
- 3.1 Concept of COAST
- 3.2 Derivation of the Fundamentals
- 3.3 The Reaction Algorithm
- 3.4 Extending COAST to Diffusion
- 3.5 The Discrete Diffusion Model
- 3.6 The Values of the Discretization Parameters
- 3.6.1 First Condition: Approximation of Continuous Distributions
- 3.6.2 Second Condition: Approximation of Moments
- 3.6.3 Third Condition: Positive Probabilities
- 3.6.4 Fourth Condition: Small Changes of Particle Numbers
- 3.7 Summary of Formulas for
- 3.8 Calculation of Transitions
- 3.9 The Algorithm
- 3.10 The Error Parameter alpha
- 4 Test Simulations
- 4.1 Test Simulations Using COAST
- 4.2 Test Simulations Regarding COAST's Extension to Diffusion
- 4.3 General Technical Considerations
- 5 Discussion and Conclusion
- 5.1 Reflecting on COAST
- 5.2 The Adoption of COAST to Diffusion
- 5.3 Combining Reaction and Diffusion Algorithms
- 5.4 Final Conclusions
- Bibliography
- A Numerical solution of chemical differential equations
- A.1 Bimolecular Reaction; One Specie
- A.2 Unimolecular Reaction
- A.3 Bimolecular Reaction; Two Species (Part 1)
- A.4 Bimolecular Reaction; Two Species (Part 2)
- A.5 Bimolecular Reaction; Two Species (Part 3)
- B Belousov-Zhabotinsky Reaction
- C Additional Information