Modeling and E. coli that Count

I have used the term "biological system" quite often in my past posts. When I talked about abstraction, I used the term to refer to the highest level in the hierarchy. But it's often used more generally. I'll offer you a definition that to me seems reasonable, but you can be the judge of how airtight it is. A biological system is a chemical and physical system whose components reside within or are derived from a life form. I was going to restrict life forms to those that have come about by evolution, but I think that synthetic biology opens the door to my broader definition (i.e., building systems that have no homology with natural ones).

So now we're dealing with chemistry and physics, the stereotypically "mathy" sciences. It turns out that there are tons of mathematical models that we can use to describe chemical and physical systems. These models not only increase our understanding of the system, but also allow us to make predictions about their behavior. Now, to be fair, mathematical biology is a discipline in its own right. Math and biology needn't rely on chemistry or physics to mediate their cooperation. However, since I will be focusing on molecular biology (as opposed to population dynamics) I want to start from the bottom-up. That means chemistry.

Engineers use models all the time. A civil engineer designing a suspension bridge will be using a model that considers parameters such as the strength of the cable, the weight of the bridge, the load of the passing traffic, etc. As engineers themselves, synthetic biologists also make use of the benefits modeling tools have to offer, though obviously they aren't too concerned with cable strengths!

A great example of applying modeling techniques to synthetic biology is the work done by Friedland et al., a group of collaborators in Boston/Cambridge, Massachusetts, in 2009. The team built devices housed within E. coli cells that can count to two or three, and they used models whose predictions closely matched their experiments' results. Scientists dream for such outcomes! For the sake of brevity I will focus on only one of the several devices they built.

This device "counts" by producing GFP only after the E. coli cells in which it resides have been exposed to two distinct pulses of the sugar arabinose. If the E. coli are only given one pulse, then they will not glow green. To pulse the cells, one simply adds arabinose for a set amount of time, centrifuges the culture, removes the liquid, and resuspends the pellet of cells in fresh media lacking arabinose. So their device uses an input of two arabinose pulses and an output of GFP. What's in between?

To make their device work, the team relied on a combination of regulation mechanisms (you can follow along with the figure above). Besides GFP, the other protein in their system was T7 RNA polymerase. It acts just like ordinary RNA polymerase, except it only transcribes genes regulated by the T7 promoter. They fitted both the T7 RNA polymerase and GFP genes with cis-repressors, a feature that when transcribed into mRNA blocks ribosomes from performing translation by kinking the mRNA strand at the front end. Along with these parts, they also used the pBAD promoter (switched on in the presence of arabinose) to control the production of a RNA molecule that disables the cis-respressors by directly binding to them. So with each pulse of arabinose, the cis-repressors in the cell are disabled. The really clever part of their design is the use of T7 RNA polymerase. They used a constitutive promoter to constantly churn out T7 RNA polymerase mRNA, but used the T7 promoter to control GFP. So the first pulse of arabinose allows the translation of T7 RNA polymerase mRNA into T7 RNA polymerase enzymes. These enzymes bind to the T7 promoter and produce GFP mRNA. When arabinose is pulsed a second time, the GFP mRNA is translated into GFP protein, causing the cells to glow. The E. coli have just counted to two!

Now comes the modeling. By considering all the players in the system (e.g., promoters, proteins, mRNA, ribosomes, etc.) and their chemistry (e.g., how long they last before degrading) we can produce a series of equations and a model that predict how much GFP is produced after the two arabinose pulses. We can also ask what would happen if cells receive only the first pulse or the second pulse. You might expect that no GFP would be produced in these two cases, but we're not dealing with an airtight system. For instance, the mRNAs might occasionally unkink themselves spontaneously, just in time for the passing ribosome to latch on. The team was able to fit their model to the results of the experiment quite well, as you can see at right. In the graph the points represent data from their experiments, and the solid lines represent model predictions. Prediction and observation came close for all three categories: both pulses, first pulse only, and second pulse only. The cells that got both pulses really churned out GFP and therefore glowed a much brighter green.

This is only one example of how modeling is used in synthetic biology. As we learn more about synthetic biology, our ambitions are bound to grow. We will have the ability to build large and intricate systems, fitted with delicate regulation mechanisms. Using modeling will allow us to test our designs before we build them, weeding out those with unseen flaws. This is what any competent engineer would do. What's the use in building ten bridges in ten different ways to see which one stands up the best? Clearly it's a waste of money and resources that would be better spent on something else. Right now biology still builds a lot of bridges.

Image Credit: Friedland, A. E. et al. (Figures 1A and 2A)

References and Further Reading:

Campbell, A.M. What is Synthetic Biology? (2009).

Friedland, A. E. et al. Synthetic Gene Networks that Count. Science 324, 1199–1202 (2009).