How to compare experimental and theoretical results

The decision letter from the journal was very supportive it was clear our paper (Kirkegaard et al., 2016) would be published but one of the referees definitely did not like the w

How to compare experimental and theoretical results

The decision letter from the journal was very supportive  it was clear our paper (Kirkegaard et al., 2016) would be published  but one of the referees definitely did not like the way we had combined experimental biology and physical calculations in our paper: The data should be described and the inferences drawn, and the modelling relegated to its proper place as quantitative verification of the inferences that can be made directly from the data.

And this was not an isolated case; a referee of another paper had said: Instead, the authors should let the data speak for itself, and postpone heavier theoretical analysis for later, perhaps in the Discussion. Many of my colleagues have experienced the same reaction to papers mixing theory and experiment. What were we doing wrong? Why was it not OK, according to these referees, to present the observations and the theory in a back-and-forth dialogue within the Results section?

While I was bemused by these statements (relegated!), they resonated with my long experience with some in the biology community, namely that they see the significance of theory very differently from the way physicists understand it. For many biologists, theoretical results are simply not Results. Indeed, I suspect to many they are seen as a matter of opinion, without any intrinsic significance. In essence, they dont add anything new. Hence the belief in the canonical Results/Discussion dichotomy in which theory (or modelling, as it is often called) plays second fiddle, or third.

In contrast, physicists are brought up to think by means of mathematical models: harmonic oscillators, random walks, idealized electrical circuits and so on are among the tools in our toolbox, whether we do experiment or theory. We use them as solvable examples in which a well-defined set of assumptions leads to precise outcomes, and where the dependence of the outcomes on the variousparameters in the model can be interpreted. This approach allows us to estimate what is important and what is not in any setting. Models also help us to think about problems: If this is the underlying physics, then A should vary with B quadratically, or under these assumptions, the data should collapse like this or, when we spot something is not quite right, here I argue that these claims are in conflict with basic laws of physics (Meister, 2016).

The role of theory is also intimately connected with predictions. While I know biologists who would say who cares about a prediction in the absence of experiment?, physicists are brought up to celebrate them  they are the stuff of legend, from Diracs prediction of antiparticles and Einsteins prediction of the bending of starlight, to the work by many that predicted the Higgs particle. We view predictions as motivations for experiment and as a means to move the discipline forward. Of course, sometimes they turn out to be wrong, but that is often how science works. Even if theoretical work does not take the form of a prediction, per se, it may still be very useful to design experiments with theory in mind, as emphasized by Bialek (2018), who has described many historical examples of the role theory has played in biology, from Rayleighs work on hearing to Watson and Crick.

My purpose here is to push back against the view that theory is not a Result. I argue for the unabashed inclusion of mathematical formulations and pedagogy within the body of papers published in eLife and other primarily biological journals. By interleaving the experimental and theoretical results it is possible to tell a story, and I firmly believe this makes for much more interesting and readable papers. It is also faithful to the scientific method, in which one goes back and forth with experiment and hypothesis.

Readers may be interested to learn that biological information, background and results are now routinely included in papers published in physics journals, although this has not always been the case: I vividly recall a situation several decades ago when a colleague, a high-energy physicist, saw a preprint about pattern formation in the slime mold Dictyostelium discoideum on my desk and asked: Why would any physicist study something as ridiculous as that? But by now many physicists do exactly that, and many physics journals are full of discussions of cAMP signaling, spiral waves, and chemotaxis (Goldstein, 1996; Rappel et al., 1999; Gholami et al., 2015). If we really take interdisciplinary research seriously then I assert there has to be a prominent place for theory within biology papers, both as Results in papers that combine experiment and theory, and as Results in theory papers.

This is nothing new. If you have not already done so, I highly recommend reading the celebrated paper by Hodgkin and Huxley (1952) to see experiments and theory interleaved. Theory is not relegated to the discussion, or worse, to supplementary material, but instead is incorporated into the body of the paper as if it is the most natural thing to do. And this was in the Journal of Physiology. The same structure is found in the Michaelis-Menten paper, which was published (in German) in a biochemistry journal (Michaelis and Menten, 1913; Michaelis et al., 2011). If this was appropriate a century ago, why must details of mathematical models now be relegated to the back of papers (see, for example, Paulick et al. (2017), Ferreira et al. (2017), and Streichan et al. (2018))?

Many readers will appreciate that the issue I am raising about quantitative descriptions of living systems is closely associated with the tension that exists between the stereotypes of the biologist, who wants to incorporate all the complexity of a particular system, and the physicist who seeks generality and minimalism. As has been emphasized in other recent opinion pieces (Shou et al., 2015; Riveline and Kruse, 2017), the role of theory in biology has been growing and this development requires new ways of training scientists on both sides of the physics/biology divide. Less attention has been paid to providing concrete examples for the biology community of how physicists think about understanding data, and this essays goal, in part, is to address this lacuna.

Well aware of the risks of trying to speak for an entire community, below I take the reader through an example of how (at least some) physicists might go about describing a well-known phenomenon that shows up everywhere in biology  from the functioning of cellular receptors to bacterial chemotaxis, the propagation of action potentials, and fluorescence recovery after photobleaching (FRAP) experiments  namely, diffusion. Employing poetic license, I imagine that we are at a point in time when the diffusion equation itself was not known, nor was Ficks Law, so both the experimental observations and theoretical analysis presented below are new and worthy of being described as Results.

I compose two versions of a Results section to indicate various ways of presenting the data and theory interleaved in a compact presentation that (I hope) is widely understandable by the community. The first version involves a microscopic model that is a caricature of the biological system, but contains the essential ingredients to display the behavior observed on the large scale. The way in which microscopic parameters enter into the macroscopic answer turns out to be general (or, as physicists say, universal), a key take-home lesson. The second version  which is probably more challenging  involves the use of dimensional analysis, one of the most powerful methods of analyzing natural phenomena. Here, relationships between various quantities are deduced by examining the units in which they are measured (mass, length, time, charge, etc.). Introduced long ago, particularly in the work of Clerk-Maxwell, 1869, this technique can often lead to exact answers to problems, up to the proverbial factors of two.

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