© 2015

Mathematical Analysis of Complex Cellular Activity


Part of the Frontiers in Applied Dynamical Systems: Reviews and Tutorials book series (FIADS, volume 1)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Richard Bertram, Joël Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger
    Pages 1-52
  3. Vivien Kirk, James Sneyd
    Pages 53-107

About this book


This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently.

The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes.

Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells

Review 2: Vivien Kirk, James Sneyd: The Nonlinear Dynamics of Calcium


Cell Biology Dynamical Systems Theory Geometric Singular Perturbation Nonlinear Dynamics Oscillatory Processes

Authors and affiliations

  1. 1.Department of MathematicsFlorida State UniversityTallahasseUSA
  2. 2.Department of Mathematics and BiologicalFlorida State UniversityTallahasseeUSA
  3. 3.Department of Mathematical SciencesIndiana University-Purdue University IndIndianapolisUSA
  4. 4.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  5. 5.Department of MathematicsUniversity of SydneySydneyAustralia
  6. 6.Deparment of MathematicsThe University of AucklandPrivate BagNew Zealand
  7. 7.Department of MathematicsUniversity of AucklandAucklandNew Zealand

About the authors

Professor Richard Bertram is a Mathematics Professor at Florida State University. His current academic interests include the intersection between biology and mathematics.

Professor James Sneyd is a Professor in Applied Mathematics at The University of Auckland and his current research interests include mathematical physiology and nonlinear dynamical systems.

Bibliographic information

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