Inhaltsangabe1 Mathematical Methods in Biophysics Rajiv R.P. Singh 1.1. Functions of One Variable and Ordinary Differential Equations 1.2. Functions of Several Variables: Diffusion Equation in One Dimension 1.3. Random Walks and Diffusion 1.4. Random Variables, Probability Distribution, Mean, and Variance 1.5. Diffusion Equation in Three Dimensions 1.6. Complex Numbers, Complex Variables, and Schrödinger's Equation 1.7. Solving Linear Homogeneous Differential Equations 1.8. Fourier Transforms 1.9. Nonlinear Equations: Patterns, Switches and Oscillators 2 Quantum Mechanics Basic to Biophysical Methods William Fink 2.1. Quantum Mechanics Postulates 2.2. OneDimensional Problems 2.3. The Harmonic Oscillator 2.4. The Hydrogen Atom 2.5. Approximate Methods 2.6. Many Electron Atoms and Molecules 2.7. The Interaction of Matter and Light 3 Computational Modeling of Receptor-Ligand Binding and Cellular Signaling Processes Subhadip Raychaudhuri, Philippos Tsourkas, and Eric Willgohs 3.1. Introduction 3.2. Differential Equation-Based Mean-Field Modeling 3.3. Application: Clustering of Receptor-Ligand Complexes 3.4. Modeling Membrane Deformation as a Result of Receptor-Ligand Binding 3.5. Limitations of Mean-Field Differential Equation-Based Modeling 3.6. Master Equation: Calculating the Time Evolution of a Chemically Reacting System 3.7. Stochastic Simulation Algorithm (SSA) of Gillespie 3.8. Application of the Stochastic Simulation Algorithm (SSA) 3.9. Free Energy-Based Metropolis Monte Carlo Simulation 3.10. Application of Metropolis Monte Carlo Algorithm 3.11. Stochastic Simulation Algorithm with Reaction and Diffusion:Probabilistic Rate Constant-Based Method 3.12. Mapping Probabilistic and Physical Parameters 3.13. Modeling Binding between Multivalent Receptors and Ligands 3.14. Multivalent Receptor-Ligand Binding and Multimolecule Signaling Complex Formation 3.15. Application of Stochastic Simulation Algorithm with Reaction and Diffusion 3.16. Choosing the Most Efficient Simulation Method 3.17. Summary 4 Fluorescence Spectroscopy Yin Yeh, Samantha Fore, and Huawen Wu 4.1. Introduction 4.2. Fundamental Process of Fluorescence 4.3. Fluorescence Microscopy 4.4. Types of Biological Fluorophores 4.5. Application of Fluorescence in Biophysical Research 4.6. Dynamic Processes Probed by Fluorescence 5 Electrophysiological Measurements of Membrane Proteins TsungYu Chen, YuFung Lin, and Jie Zheng 5.1. Membrane Bioelectricity 5.2. Electrochemical Driving Force 5.3. Voltage Clamp versus Current Clamp 5.4. Principles of Silver Chloride Electrodes 5.5. Capacitive Current and Ionic Current 5.6. Gating and Permeation Functions of Ion Channels 5.7. TwoElectrode Voltage Clamp for Xenopus Oocyte Recordings 5.8. PatchClamp Recordings 5.9. PatchClamp Fluorometry 6 SingleParticle Tracking Michael J. Saxton 6.1. Introduction 6.2. The Broader Field 6.3. Labeling the Dots 6.4. Locating the Dots 6.5. Connecting the Dots 6.6. Interpreting the Dots: Types of Motion 6.7. Is It Really a Single Particle? 6.8. Enhancing z-Resolution 6.9. Can a Single Fluorophore Be Seen in a Cell? 6.10. Colocalization 6.11. Example: Motion in the Plasma Membrane Is More Complicated