I have recently thought about how to classify what theorists actually do and I came up with three broad approaches: 1) Model analysis, 2) Constraint driven modeling and 3) Data driven modeling. By model, I mean a set of equations (and inequalities) that are proposed to govern or mimic the behavior of some biological system. Often, a given research project will involve more than one category. Model analysis is trying to understand what the equations do. For example, there could exist some set of differential equations and the goal is to figure out what the solutions of these equations are or look like. Constraint driven modeling is trying to explain a phenomenon starting from another set of phenomena. For example, trying to explain the rhythms in EEG measurements by exploring networks of coupled spiking neurons. Finally, data driven modeling, is looking directly for patterns in the data itself and not worry about where the data may have come from. An example would be trying to find systematic differences in the DNA sequence between people with and without a certain disease.
I have spent most of my scientific career in Approach 1). What I have done a lot in the past is to construct approximate solutions to dynamical systems and then compare them to numerical simulations. Thus, I never had to worry too much about data and statistics or even real phenomena itself. In fact, even when I first moved into biology in the early nineties, I still did mostly the same thing. (The lone exception was my work on posture control, which did involve paying attention to data). Computational neuroscience is a mature enough field that one can focus exclusively on analyzing existing models. I started moving more towards Approach 2) when I began studying localized persistent neural activity or bumps. My first few papers on the subject were mostly analyzing models but there was a more exploratory nature to them than my previous work. Instead of trying to explicitly compute a quantity, it was more about exploring what networks of neurons can do. The work on binocular rivalry and visual competition were attempts to explain a cognitive phenomenon using the constraints imposed by the properties of neurons and synapses. However, I was still only trying to explain the data qualitatively.
That changed when I started my work on modeling the acute inflammatory response. Now, I was just given data with very few biological constraints. I basically took what the immunologists told me and constructed the simplest model possible that could account for the data. Given that my knowledge of statistics was minimal, I simply used the “eye test” as a basis of whether or not the model worked or not. The model somehow fit the data and did bring insights to the phenomenon but it was not done in a systematic way. When I arrived at NIH, I was introduced to Bayesian inference and this really opened my eyes. I realized that when one doesn’t have strong biological or physical constraints, Approach 2) is not that useful. It is easy to cobble together a system of differential equations to explain any data. This is how I ended up moving more towards Approach 3). Instead of just coming up with some set of ODEs that can explain the data, what we did was to explore classes of models that could explain a given set of data and use Bayesian model comparison to decide which was better. This approach was used in the work on quantifying insulin’s effect on free fatty acid dynamics. While that work involved some elements of Approach 2) in that we utilized some constraints, my work on protein sequences is almost all within Approach 3). The work on obesity and body weight change involves all three Approaches. The conservation of energy and the vast separation of time scales put a lot of strong constraints on the dynamics so one can get surprisingly far using Approach 1) and 2).
When I was younger, some my fellow graduate students would lament that they missed out on the glory days of the 1930’s when quantum mechanics was discovered. It is true that when a field matures, it starts to move from Approach 3) to 2) and 1). Theoretical physics is almost exclusively in 1) and 2). Even string theory is basically all in Approach 1) and 2). They are trying to explain all the known forces using the constraints of quantum mechanics and general relativity. The romantic periods of physics involved Approach 3). There was Galileo, Kepler and Newton inventing classical mechanics. Lavoisier, Carnot, Thompson and so forth coming up with conservation laws and thermodynamics. Faraday and Maxwell defining electrodynamics. Einstein invented the “Thought experiment” version of Approach 3) to dream up Special and General Relativity. The last true romantic period in physics was the invention of quantum mechanics. Progress since then has basically been in Approaches 1) and 2). However, Approach 3) is alive and well in biology and data mining. The theoretical glory days of these fields might be now.