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Title

Computational Biophysics
Author

Paul Abbott
Organization: University of Western Australia
Department: Physics
URL: http://www.uwa.edu.au/people/paul.c.abbott
Education level

College
Objectives

The objectives of this course are:

  • to use computers as an aid to understanding real physical systems;
  • learn efficient methods for the analysis of these systems
Materials

Recommended reading:
  • Mathematica: A Practical Approach by Nancy Blachman (Prentice Hall, 1992)
  • Mathematica for the Sciences by Richard E. Crandall (Addison-Wesley, 1991).
    		•
    Description

    The broad categories of computational biophysics are Simulation, Visualisation and Modelling. At a finer scale, it embraces a wide range of areas including numerical methods, algorithms and data analysis. Simulation and modelling are usually taught by stressing numerical techniques -- this course focuses on using symbolic or computer algebra.

    This course is problematic in that the students are not math majors. However, one measure of its success is that many of students completing this course then make use of Mathematica in their other courses.

    Topics:
    Assignments: Introduction to Mathematica-- provides some of the background necessary for the following sessions:

    • Notebooks
    • Instructions
    • Basic Navigation
    • Numerical Calculations
    • Algebraic Calculations
    • Plots


    Stochastic Processes -- presents applications of random number generators(rngs)in computer simulation of stochastic processes:

    • Random number generation in Mathematica
    • One dimensional random walk
    • Fitting data in the presence of noise
    • Modelling fern growth
    • Two dimensional random walk


    Molecular Conformation -- introduces numerical methods for conformational modelling, and for solving minimisation problems:

    • Preliminaries
    • Coulomb potential
    • Lennard-Jones potential
    • Ethane rotational conformation


    Population Dynamics -- applies numerical methods for discrete (iterative) models and for solving ordinary differential equations (ODEs) to models from population dynamics:

    • Discrete logistic equation for a single species
    • Continuous logistic equation for a single species
    • Kermack-MacKendrick disease model


    Fourier Transform -- introduces Fourier methods which have application in convolution or deconvolution of data, correlation and autocorrelation, filtering, and power spectrum estimation:

    • Definition of DFT
    • One-dimensional DFT
    • Two-dimensional DFT
    • Applications


    Action Potential -- models voltage-dependent membrane currents in the squid giant axon using the Hodgkin-Huxley formalism:

    • RC Circuit
    • Passive Transmission Line
    • Hodgkin-Huxley Model
    Subject

    *Science > Physics > Biophysics