Schulten K., Kosztin I. Lectures in Theoretical Biophysics

Urbana: University of Illinois at Urbana-Champaign, 2000. — 211 p.Dynamics under the Influence of Stochastic Forces
Newton's Equation and Langevin's Equation
Stochastic Differential Equations
How to Describe Noise
Ito calculus
Fokker-Planck Equations
Stratonovich Calculus
Appendix: Normal Distribution Approximation
Stirling's Formula
Binomial Distribution
Einstein Diffusion Equation
Derivation and Boundary Conditions
Free Diffusion in One-dimensional Half-Space
Fluorescence Microphotolysis
Free Diffusion around a Spherical Object
Free Diffusion in a Finite Domain
Rotational Diffusion
Smoluchowski Diffusion Equation
Derivation of the Smoluchoswld Diffusion Equation for Potential Fields
One-Dimensional Diffuson in a Linear Potential
Diffusion in an infinite space Q^ = ] — oo,oo[
Diffusion in a Half-Space fico = [, oof
Diffusion in a One-Dimensional Harmonic Potential
Random Numbers
Randomness
Random Number Generators
Homogeneous Distribution
Gaussian Distribution
Monte Carlo integration
Brownian Dynamics
Discretization ol Time
Monte Carlo Integration ol Stochastic Processes
Ito Calculus and Brownian Dynamics
Free Diffusion
Reflective Boundary Conditions
The Brownian Dynamics Method Applied
Diffusion in a Linear Potential
Diffusion in a Harmonic Potential
Harmonic Potential with a Reactive Center
Free Diffusion in a Finite Domain
Hysteresis in a Harmonic Potential
Hysteresis in a Bistable Potential
Noise-Induced Limit Cycles
The Bonhoeffer-van der Pol Equations
Analysis
Derivation ol Canonical Model
Linear Analysis ol Canonical Model
Hopl Bifurcation Analysis
Systems ol Coupled Bonhoeffer-van der Pol Neurons
Alternative Neuron Models
Standard Oscillators
Active Rotators
Integrate-and-Fire Neurons
Conclusions
Adjoint Smoluchowski Equation
The Adjoint Smoluchowski Equation
Correlation Functions
Rates of Diffusion-Controlled Reactions
Relative Diffusion ol two Free Particles
Diffusion-Controlled Reactions under Stationary Conditions
Examples
Ohmic Resistance and Irreversible Work
Smoluchowski Equation for Potentials: Extremum Principle and Spectral Expansion
Minimum Principle for the Smoluchowski Equation
Similarity to Sell-Adjoint Operator
Eigenlunctions and Eigenvalues ol the Smoluchowski Operator
Brownian Oscillator
The Brownian Oscillator
One-Dimensional Diffusion in a Harmonic Potential
Fokker-Planck Equation in x and v for Harmonic Oscillator
Velocity Replacement Echoes
Rate Equations for Discrete Processes
Generalized Moment Expansion
Curve Crossing in a Protein: Coupling of the Elementary Quantum Process to Motions of the ProteinThe Generic Model: Two-State Quantum System Coupled to an Oscillator
Two-State System Coupled to a Classical Medium
Two State System Coupled to a Stochastic Medium
Two State System Coupled to a Single Quantum Mechanical Oscillator
Two State System Coupled to a Multi-Modal Bath of Quantum Mechanical Oscillators
From the Energy Gap Correlation Function Ai£[R(£)] to the Spectral Density J{uj)
Evaluating the Transfer Rate
Appendix: Numerical Evaluation of the Line Shape Function