12 Introducing gene networks
A quick guide to cells and genetic networks
In the next few chapters, we will look at models for the regulation of gene expression in cells, and how simple feedback loops underlie some of the basic dynamics that cells exhibit: regulation, switching, and oscillation.
From experience, undergraduate mathematics students are often familiar enough with ideas in ecology or epidemiology to follow the biological aspects of our models well enough without too much extra detail. However, many have little knowledge of cell dynamics and genetics. So, before we start introducing the models themselves we will have a short primer of what it is we are trying to model (and I hope any biologists will forgive me my simplifications and mistakes!)
All living things are made of cells – self-contained structures bounded by a cell membrane (and sometimes also a cell wall). Many organisms exist predominantly as single cells (e.g. bacteria, amoebae), while others exist as patterned collections of cells (e.g. animals, most plants). While different cells possess and maintain a well-defined identity, they are far from static structures, and depend on balanced dynamical processes. Mathematical modelling plays an important role in understanding these dynamical processes and how they are regulated in cells.
Unicellular organisms encounter variable environments, and therefore need to be able to adapt their behaviour. For example, a bacterium living in your gut will have to adapt its metabolism to whatever food you present it with, an example where a cell must switch between different behaviours. Multicellular organisms often develop from a single cell through sequential rounds of cell division. However, the cells in multicellular organisms do not remain identical to each other, but take on stable and well-defined characteristics, so we can talk about skin cells, liver cells, muscle cells, blood cells, etc. in a meaningful way. This adoption of distinct well-defined characters is called differentiation, and again requires cells to be able to switch their behaviour.
How do cells manage to change or switch their state in a coherent way? They use a combination of information from their environment and internal mechanisms. Central to the internal mechanisms are what we call gene regulatory networks. Almost all cells contain large structures centred on DNA (deoxyribonucleic acid), basically a set of long, linear sequences of letters (A, C, G and T). This sequence is highly stable, is accurately copied during cell division, and is identical in all cells of a multicellular organism. The full DNA sequence in a cell is referred to as the genome.
How is the genome involved in the regulation of the state of a cell, either stably maintaining it or switching it? A key concept is that of the gene, and the basic unit of dynamics that we will concern ourselves with here is the expression of a gene. For our purposes, a gene is a defined subset of the DNA sequence that