This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and stem cell regeneration. The diffusion of morphogens is addressed by introducing various reaction-diffusion equations based on different hypotheses concerning the process of morphogen gradient formation. The robustness of steady-state gradients is also covered through boundary value problems.

The introduction gives an overview of the relevant biological concepts (cells, DNA, organism development) and provides the requisite mathematical preliminaries on continuous dynamics and stochastic modeling. A basic understanding of calculus is assumed.

The techniques described in this book encompass a wide range of mechanisms, from molecular behavior to population dynamics, and the inclusion of recent developments in the literature together with first-hand results make it an ideal reference for both new students and experienced researchers in the field of systems biology and applied mathematics.

Auteur
Jinzhi Lei (Ph.D. 2001, Beihang University) is Professor at the School of Mathematical Sciences, Tiangong University, China. He was a postdoc at UC, Irvine (20042005) and Associate Researcher at the Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, China (20062019). His research focuses on modeling dynamical blood diseases, cancer development and stem cell regeneration.

Contenu

Biological BackgroundInformation, Energy, and Matter.- 2. Mathematical PreliminaryContinuous Dynamics.- 3. Mathematical PreliminaryStochastic Modeling.- 4. Stochastic Modeling of Gene Expression.- 5. Mathematical Models for Gene Regulatory Network Dynamics.- 6. Dynamical Modeling of Stem Cell Regeneration.- 7. Mathematical Models of Morphogen Gradients and Growth Control.