Numerical Methods for the Life Scientist: Binding and Enzyme Kinetics Calculated with Gnu Octave and MATLAB

ISBN-13: 9783662505878 / Angielski / Miękka / 2016 / 149 str.

Heino Prinz

Opis

This textbook provides a step-by-step introduction to numerical solutions of non-linear and differential equations. The text includes a set of programs to calculate any reaction scheme on any personal computer, as well as typical examples from various related fields.

Spis treści

Introduction

Classical enzyme kinetics

Classical dose-response curves and the Hill coefficient

Classical association and dissociation kinetics and exponential fits

Numerical methods

Preparing the computer

Installation of Octave for different platforms

Installation of Linux

Running the provided programs

Data input and output

Binding equilibria

Analytical and numerical solution for equilibrium binding to one site

Equilibrium binding to two or more sites.

Equilibrium binding to two or more conformational states

Equilibrium binding for oxygen to hemoglobin (MWC model)

Equilibrium binding of more than one ligand (e.g. agonist and inhibitor)

Enzyme kinetics as coupled equilibria

Enzyme kinetics with competitive or noncompetitive inhibitors

Dose-response curves for receptor agonists and enzyme inhibitors

Binding kinetics

Ligand binding kinetics of first and second order

Numerical solutions of differential equations

Calculation of true enzyme kinetics

Dissociation by dilution and dissociation by competition (“chase”)

States and sites

Least squares fit to experimental data

The function lsqcurvefit

Comparing correct binding curves with Hill equations

Comparing real binding kinetics with current multi-exponential fits

Fitting experimental data

Causes for errors

Multi-parameter fits

Correlation of parameters

Selecting a model and minimizing the number of parameters

Degrees of freedom

Global Fits

Significance of parameters in multi-parameter fits

Comparing the two different approaches

Model independent versus model calculations

Global fit versus single fits

Make ends meet: Try to analyze reported data with new methods

Designing experiments for complete analysis

Appendix

Description of program files

Sample data

Comparing MATLAB and Octave code

Blurb

Enzyme kinetics, binding kinetics and pharmacological dose-response curves are currently analyzed by a few standard methods. Some of these, like Michaelis-Menten enzyme kinetics, use plausible approximations, others, like Hill equations for dose-response curves, are outdated. Calculating realistic reaction schemes requires numerical mathematical routines which usually are not covered in the curricula of life science. This textbook will give a step-by-step introduction to numerical solutions of non-linear and differential equations. It will be accompanied with a set of programs to calculate any reaction scheme on any personal computer. Typical examples from analytical biochemistry and pharmacology can be used as versatile templates. When a reaction scheme is applied for data fitting, the resulting parameters may not be unique. Correlation of parameters will be discussed and simplification strategies will be offered.