Simple mathematical models of gene regulatory dynamics.

*(English)*Zbl 1360.92002
Lecture Notes on Mathematical Modelling in the Life Sciences. Cham: Springer (ISBN 978-3-319-45317-0/pbk; 978-3-319-45318-7/ebook). xiv, 124 p. (2016).

This book reviews the state of the art and the work conducted since the 1960s for the understanding of the dynamic behaviour of bacterial operons; it covers a broad range of models from simple examples such as repressible and inducible systems to more complicated, real-life ones, presented in the third part.

The book is structured in three parts. It commences with a general introduction of deterministic modelling techniques such as inducible and repressible models for the prokaryotic gene regulation (in the first chapter) and other general dynamic considerations (in the second chapter). Here, the authors present the four main operon dynamics: no-control, inducible regulation, repressible regulation and bistable switches. The appearance of cell growth effects and the consequences of transcriptional or translational delays are also discussed; this part concludes with an overview on fast and slow variables.

In the second part, the authors focus on the inclusion of noise in the regulatory models. First, the master equation approach is described (third chapter), with an emphasis on its relation to deterministic models and an evaluation of its stability. In the fourth chapter, intrinsic versus extrinsic noise effects are discussed with focus on the dynamics with bursting and the role of the Gaussian distributed noise on the molecular degradation rate.

In the third part of the book, the authors present three examples, for which the mathematical model and the quantitative studies are included: the lactose operon pathway (Chapter 5), the tryptophan operon in E. coli (Chapter 6) and the lysis-lysogeny switch in the \(\lambda\) phage. The book represents a systematic overview of the field, however, its style makes it accessible mainly to post graduates and established researchers. Nevertheless, the thorough approach based on both definitions, theorems and practical examples makes the book a reliable, self-contained, and comprehensive study.

The book is structured in three parts. It commences with a general introduction of deterministic modelling techniques such as inducible and repressible models for the prokaryotic gene regulation (in the first chapter) and other general dynamic considerations (in the second chapter). Here, the authors present the four main operon dynamics: no-control, inducible regulation, repressible regulation and bistable switches. The appearance of cell growth effects and the consequences of transcriptional or translational delays are also discussed; this part concludes with an overview on fast and slow variables.

In the second part, the authors focus on the inclusion of noise in the regulatory models. First, the master equation approach is described (third chapter), with an emphasis on its relation to deterministic models and an evaluation of its stability. In the fourth chapter, intrinsic versus extrinsic noise effects are discussed with focus on the dynamics with bursting and the role of the Gaussian distributed noise on the molecular degradation rate.

In the third part of the book, the authors present three examples, for which the mathematical model and the quantitative studies are included: the lactose operon pathway (Chapter 5), the tryptophan operon in E. coli (Chapter 6) and the lysis-lysogeny switch in the \(\lambda\) phage. The book represents a systematic overview of the field, however, its style makes it accessible mainly to post graduates and established researchers. Nevertheless, the thorough approach based on both definitions, theorems and practical examples makes the book a reliable, self-contained, and comprehensive study.

Reviewer: Irina Ioana Mohorianu (Norwich)

##### MSC:

92-02 | Research exposition (monographs, survey articles) pertaining to biology |

92C40 | Biochemistry, molecular biology |

92C42 | Systems biology, networks |

92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |