Math is everywhere in today's society, and advanced mathematics have fueled the engineering efforts which underly almost all technology. In the past, biology may have been a refuge for scientists that were math-adverse. This is not longer true; instead, biologists should openly embrace higher mathematics and employ these techniques in a variety of ways. Perhaps the most relevant application to the synthetic biologists is for developing mathematical models of gene expression and cellular behavior.
Biologists make models all the time: any hypothesis, for example, is a reflection of some model held by the scientist which describes how a certain system works. Many times, this model may be implicit in a description for a biological process. More powerful models are explicitly formulated using the language of mathematics. Leveraging mathematics allows quantitative predictions of a cell's behavior or gene expression pattern to be made with great precision. Engineering the metabolism of a cell by modulating expression of many different genes requires sophisticated and (as much as possible) accurate models.
How then, is the a biologist with limited mathematical training to understand models of gene expression, let alone craft ones themselves? Diving into advanced literature on the subject can lead one to practically drown in a sea of differential equations, boolean logic, and matrices. I must even admit to having trouble staying afloat at first: my formal mathematics education stopped at 'Calculus II for Bio Majors" at Cook College, Rutgers (a course which covered matrices but not differential equations). Fortunately, my brother is quiet adept at this sort of math and has provided me with some excellent tutorials.
Even if you don't have a skilled mathematician in the family, there are resources to help you learn gene expression modeling (or any modeling of a biological system). Below I feature links to several of these resources. The resource which I have found to have the best blend of exhaustive yet accessible explanation is a thesis from 2010 written by Hosam Abdel Aleem. I'm sure there are other articles and publications out there that are as good, if not even better, than Dr. Aleem's work, but his is a delightful read and quiet approachable (it's also freely available).
An Algebraic Approach to Modelling the Regulation of Gene Expression
This thesis throughly explains the philosophy behind modeling, as well as how to construct mathematical models of gene expression in detail. The author covers not only modeling by differential equations (continuous), but also boolean models (binary) and his own methods (discrete but with multiple values). I highly recommend this read to anybody that is interested in modeling gene expression but doesn't know where to start.
In future posts, I will provide more detail of my own experience learning some of this material, including some step by step examples of how to create a model, solve or analyze the associated equations, and calculate the results. Until that time, I'd like to wish all of my readers a very Happy Thanksgiving!
For more links to resources for mathematical modeling of gene expression, select 'Read More'. Did I miss an important resource, or do you have a favorite method for modeling transcription and translation? Please share your thoughts below as a comment!