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enzyme kinetics, use plausible approximations, others, like Hill equations for dose-response curves, are outdated.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.

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