Upon first glance, which of the below diagrams1 makes the most sense to you?
Figure 1
Figure 2
As it happens, both diagrams describe the same generic biological process. They are drawn from a report concerning the study of the changing levels of the kinase, R, over time.
S, the “signal”, is the level of mRNA from which R is transcribed. As well as being the response, R is involved in a positive feedback loop. R activates the protein E by phosphorylation and EP in turn enhances the rate of synthesis of R.
When this report including these two figures was shown to (a small sample of) biologists and to (an equally small sample of) mathematicians, mathematicians gravitated towards the first picture and were able to quickly and easily understand how the time evolution of R could be described using the accompanying equations. They baulked at the second diagram, describing it as “confusing” – to the bemusement of biologists who are familiar with diagrams involving many more interacting molecules.
Those with a background in biology, on the other hand, seemed more comfortable with the second picture. Whilst some of them shied away from the equations, a verbal description of the behaviour of the system (“changing the level of S affects the steady-state level of R”) was intuitive and the visual representation in Figure 2 was a means of leading them into the discussion which followed.
What can we learn from this anecdotal observation of colleagues proof-reading my undergraduate dissertation? As I plunge headlong into multidisciplinary postgraduate study, my peers and I are becoming acutely aware of the knowledge each of us brings – and the understanding that each of us lack. But the difference between students with contrasting backgrounds is not just in the facts and methods each can remember. How we represent the world to ourselves seems different too. Learning to bridge the gap in perception – to see what we are understanding through the eyes of someone from a different discipline, as opposed to complaining to the mathematicians “…but biology is just not like that…” will be significant in our future success. Hopefully, as biologists, we will learn how to usefully use mathematics to describe and investigate biological processes. Perhaps I can convert a few people without training into biology to drawing colourful diagrams alongside their equations too – they might find a way to open biologists’ eyes.
1 Images were created using PGF/TikZ
Hi Erika,
There’s been a bit of a discussion over here about similar ideas.
Anna and her incredible star trek socks… was asking (I paraphrase) “how maths could really be useful in biology”.
I tried to argue that it allows us to be more exact in the type of relationships we want to find/test/hypothesise between variables.
I think the two images above are really interesting in this respect (except the text in the 2nd one is too small for me after a couple of beers). I was drawn to the first one, as there was little unnecessary detail surrounding it, but I’m a fully fledged, hated maths in high school, biologist (Zoology, Bsc. [Hons.]).
I also wandered exactly how each parameter interacted with the others in the system, which after reading on, would have been described by the equations. You didn’t give us a chance to decide whether the equations were just as useful at describing what was going on as the text accompanying the 2nd fig.
Anyhoo, it’s grand to have someone else around here who’s not scared of discussing the virtues of maths (in moderation)!
I am scared of maths and am not afraid to admit it. I think my brain is tuned in a totally different way, which Erika demonstrated quite aptly in this post. The first figure made literally no sense at all to me. It’s amazing.
Welcome to NN Blogs, Erika! As you can tell already, your blog (along with Mike’s) will fill a much-needed niche. Maybe the two of you can teach me math. Please do. It’s sad.
And leave Star Trek out of this! Sheesh.
Welcome aboard Erika! I couldn’t decide – both figures have info that the other lacks. The top one shows an equilibrium reaction not present below; and the lower one clearly represents a cell, a context not evident from Fig. 1.
But on the wider issue – I am firmly of the camp that no-one, no-one, should be allowed onto a UG science degree program in the UK without A-level maths. I’m not yet in the majority but I hope it’s coming!
And on a technical, blogging point, most people don’t use the lower text entry box when composing blogs since this imposes an extra click on your readers (and there are some testy types around here).
I quite liked maths in high school, but reached my limit of understanding towards the end of my A Level course. I could probably make myself understand the first diagram if I had to, but I would much rather use the second one!
Stephen, I use the lower box sometimes – on longer entries, or if I’m trying to prevent people from seeing the “punchline” before they’ve read the rest of the text. It also forces people reading the post in Google Reader (and presumably other RSS readers) to click through to the actual post, increasing the amount of comments!
For me, the first figure makes it easier to understand the feedback mechanism, but the second figure puts it in biological context. I have no preference for either: they complement each other well.
(Disclaimer: I did my PhD in cell biology and my undergrad in chemistry, so I’m familiar with both styles of figures and not scared of arrows with kinetic constants next to it.)
Welcome Erika,
At first glance I am a fan of figure 2 (die-hard Biologist, don’t know what A Level means, seriously). However, if I were making a more concerted effort to understand the reaction/process then the first figure tells me more information. So, context rears it’s ugly head. What are you trying to convey to the specific audience you are speaking too. I think that sometimes a confusing/complex/unfamiliar type of display can be good to tweek your audience into paying attention. Good luck with the blog and the research.
Ooh!
6 comments already – this is exciting!
As several of you have pointed out, with the context missing the figures are difficult to interpret, and not quite all the information is included on each.
The point I was trying to make was that it seems to me that the way people with a background in biology or a background in mathematics, entering this field of “systems biology”, seem to interpret information differently – the way they filter evidence differs.
When I am presented with a paper with some biology in it, and some maths, I will read the biology and skip over the maths, and then if it looks interesting I might sit down with a pen and paper and try to follow the mathematical argument. My colleagues with a background in mathematics work the other way around, starting with the mathematical reasoning and glossing over the biology unless they think they need to know it. This difference is clearly in part a matter of training and what we are familiar with, but it also seems to me that there is some sort of personality-driven difference in the way we interpret problems.
@Cath: Stephen, I use the lower box sometimes…
Thanks for the…
…tip!
I use the lower box for footnotes only. No one reads my blog, so it doesn’t matter.
Erika, the top diagram made immediate sense to me, but that’s probably because my undergraduate degree was Biochemistry, with an emphasis on physical chemistry. I do find the biological-type figures a bit confusing, sometimes.