How DNA is like a Magnet

Now that we have piles and piles of widely available genome sequence, one of our main tasks as biologists is to figure out how to read what’s in there. Protein-coding sequences have long been relatively easy to read, ever since the genetic code was worked out. Non-coding regulatory sequences – enhancers and promoters – are much more difficult to interpret, obviously. Usually our first task is to identify the individual binding sites for gene-regulating proteins in these sequences. But then what? Well, most people stop there, happy to have identified the necessary parts of the gene regulating machinery, but many of us are interested in learning the underlying logic by which this machinery operates – we want to learn the grammar of regulatory DNA. The question is, how does a particular combination of regulatory binding sites give rise to a particular pattern of gene expression? In my biased opinion, this the real secret of life – how your cells read information in your DNA in order to turn on the right genes at the right place in the right time.

So, how do we read non-coding, regulatory DNA? One way that has proven very useful is take an approach from the 1920’s that was developed to understand the physics of magnets. No, I’m not talking about the pseudoscience of biomagents; I’m talking about Ising models.

Ising models are named after German physicist Ernst Ising (pronounced ‘eesing’, not ‘eyesing’), who, after writing one of the best scientific papers of the 1920’s, basically quit physics. (The fact that he was a Jew living Nazi Germany didn’t help his career – he eventually became one of the many talented Jewish scientists that fled to the United States.)

Ising was thinking about a simplified model of magnets. In this model, a magnet is a one-dimensional array of atoms whose magnetic moments point either ‘up’ or ‘down’. The direction of these magnetic moments can be influenced by an external magnetic field, and in the Ising model we also assume that atoms exert an influence on their neighbor’s magnetic moment. The Ising model incorporates these two phenomena to predict when you will observe spontaneous magnetization in the array of atoms – when the magnetic moments of all atoms in the array are pointing in the same direction.

What does this have to do with DNA? The Ising model is not really just about magnets. Abstractly, you can think of an array of atoms that are spin up or spin down as an array of binary digits, with 0 representing ‘up’, and 1 representing ‘down’. But an array of 1’s and 0’s (as we all know) can represent just about anything. So the one-dimensional Ising model is about anything that you can represent as a string of 1’s and 0’s, where an external field and nearest neighbor interactions influence the probability of being a 1 or a 0… clearly a huge category.

That category includes gene regulation. You can think of your non-coding DNA as an array of transcription factor binding sites that are either unoccupied (0) or bound by protein (1). The external field in this case is determined by the concentration and affinity of the transcription factors. You use the Ising model to determine the occupancy state of your promoter/enhancer, and from that you try to predict when and where the downstream gene will be on. This is basically the process I followed to predict where stripes of gene expression are positioned in developing embryos, building on work that has used Ising models to predict the behavior of gene circuits in a variety of contexts, including E. coli and that old workhorse of gene regulation studies, bacteriophage lambda.

Why is this cool? 1) It’s a chance to fruitfully apply an elegant physical model to biology (it’s a rare day when biologists use Hamiltonians). 2) It is yet another example how very, very different systems in nature seem to follow an analogous mathematical logic. 3) This is one example of how we deal with complexity in biology. Gene regulation is subject to multiple inputs that lead to very non-linear and non-intuitive consequences, and so we need quantitative models to make sense of how these complex effects result in the remarkable patterns that are absolutely crucial for successful living.

Check out this nice tutorial on the math behind Ising models (PDF).

Author: Mike White

Genomes, Books, and Science Fiction

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