Introduction to Modeling Biological Cellular Control Systems

  • Weijiu Liu

Part of the MS&A book series (MS&A)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Weijiu Liu
    Pages 1-9
  3. Weijiu Liu
    Pages 11-36
  4. Weijiu Liu
    Pages 37-68
  5. Weijiu Liu
    Pages 69-93
  6. Weijiu Liu
    Pages 95-122
  7. Weijiu Liu
    Pages 123-171
  8. Weijiu Liu
    Pages 189-205
  9. Weijiu Liu
    Pages 207-221
  10. Weijiu Liu
    Pages 223-228
  11. Back Matter
    Pages 229-268

About this book


This textbook contains the essential knowledge in modeling, simulation, analysis, and applications in dealing with biological cellular control systems. In particular, the book shows how to use the law of mass balance and the law of mass action to derive an enzyme kinetic model - the Michaelis-Menten function or the Hill function, how to use a current-voltage relation, Nernst potential equilibrium equation, and Hodgkin and Huxley's models to model an ionic channel or pump, and how to use the law of mass balance to integrate these enzyme or channel models into a complete feedback control system. The book also illustrates how to use data to estimate parameters in a model, how to use MATLAB to solve a model numerically, how to do computer simulations, and how to provide model predictions. Furthermore, the book demonstrates how to conduct a stability and sensitivity analysis on a model.


Biochemical processes Calcium dynamics Enzyme kinetics Feedback control Mathematical modeling

Authors and affiliations

  • Weijiu Liu
    • 1
  1. 1.Department of MathematicsUniversity of Central ArkansasConwayUSA

Bibliographic information