© 2012

Introduction to Modeling Biological Cellular Control Systems


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

  1. 1.Department of MathematicsUniversity of Central ArkansasConwayUSA

Bibliographic information


From the reviews:

“This book addresses the modeling, simulation, analysis and control of biochemical processes of systems arising in cellular biology. … The book is very well written in an-easy way to grasp the essential elements of the various topics. Further, the book provides the necessary introductory material on control systems and MATLAB useful for those with background in cellular biology only. This book is a welcome addition to this growing interdisciplinary field … .” (D. Subbaram Naidu,, November, 2013)

“The book under review compiles and presents essential knowledge in modeling, analysis, simulation and parameter estimation of biological cellular control systems. … Although interested mathematicians and biologists are the targeted audience, the best background that one needs to be able to follow the book easily is probably (bio)chemical or process engineering. … the book is quite self-contained and highly recommended as course material in the field of modeling and control of cellular mechanisms.” (Gábor Szederkényi, Mathematical Reviews, May, 2013)