After reading a string of disheartening reviews on the supposedly important future directions of biological research, I’m convinced that the older generation of biologists, those who made their careers in heyday of molecular biology during the 60’s, 70’s, 80’s, have turned biology into an innumerate outlier among the natural sciences.
Yes, they have been fantastically successful, and I’m not arguing that they should have approached the problems of their day any differently. But so many senior molecular biologists seem to have a congenital inability to grasp the roles played quantitative theories in science. One of those roles, perhaps the most important one for theories in most of the natural sciences, is this: to explain the behavior of systems as a consequence of the interactions of the system components. ‘Consequence’ is the key word here: you haven’t explained the behavior of a system by describing the behavior and listing the parts. You haven’t explained the behavior of the system by describing what occurs when knock you out individual parts. And you haven’t explained the behavior of the system by putting all of the interactions between parts into a big network diagram.
This seems to be an unusually difficult point to grasp for many molecular biologists, but a simple example from physics may offer some clarity. Let’s think about how physicists explain the solar system. Instead of qualitatively describing the motions of all of the planets around the sun, and concluding with some verbal statement like “the sun is an attracting and organizing force,” physicists have a quantitative theory of gravitation, either Newton’s original law or Einstein’s General Relativity. These are genuine causal theories; with them, physicists can explain how the behavior of the solar system arises as a consequence of the gravitational interactions between the planets. They can explain the various oddities in the orbits, and they can explain things such as why all of the planets don’t just fall right into the sun. They can do this because they have numbers, they have a quantitative theory that is rigorous and specific enough to allow you to actually deduce consequences, an advantage that most purely verbal theories don’t offer. Nature is quantitative. Mass matters, velocity matters, charge matters, pH matters, the affinity between proteins matters, the number of molecules in a system matters, the volume of a cell matters; nature’s components exist in quantitative relationships, and we can only understand the consequences of those relationships by thinking in numbers.
This is why one of the biggest fundamental challenges facing those who study life at the cellular level is to go quantitative. We need quantitative data and quantitative theories. The past decades of research have been in large part one of cartography (and I’m not using that term derisively!); the pioneering molecular and cellular biologists, with and without genomic tools, have done a tremendous job mapping the molecular interior of the cell, and identifying the the core cellular processes on which life runs. As these maps become increasingly complete, our task is to understand dynamics, or behavior. But it is shocking that so many successful molecular biologists lack the imagination to see what the next task is; what many of them seem to be claiming is that we need more of the same.
Here is Sydney Brenner, who after making a persuasive argument for a molecular understanding says that we achieve this by making a giant map of the cell:
The whole may therefore be pictured as a communication system, with devices transforming and passing information to each other. Even a biosynthetic enzyme pathway can be viewed in this way, with the substrate as the input message to an enzyme and the product, the output message, which itself may be an input message to another enzyme. This suggests that everything can be represented as a graph, with the devices at the vertices and their communicating messages as the arcs…
This model of a cell also allows us to deal with questions of cell regulation. Today, if we are asked to predict the effect of a drug for a receptor on the heart, our response is to kill an animal and test the drug directly by demonstration. However, if we knew the graph of devices through which the drug exerted its effects (for example, the membrane receptor-G protein device that transforms the binding of the natural ligand into an internal signal resulting in the synthesis of cyclic AMP, which acts on another device to release calcium ions and which in turn leads to changes in the molecular complex causing contraction), we could calculate the effects by knowing what each device does and how many devices there are in the cell.
“Sequences and consequences,” Phil. Trans. R. Soc. B 12 January 2010 vol. 365 no. 1537 207-212
To be fair, Brenner does suggest that mathematics needs to be involved in the graph representations, but he views these equations as something you can just formulaically plug in at each edge in the network. Your understanding is also formulaic, coming in the form of a prediction produced by your giant, incomprehensible computer model. That may be sufficient for predicting the consequences of new drugs, but that’s not the same thing building your understanding of a specific cellular subsystem with a model that is grounded in principles of physical chemistry. (Incidentally, Brenner writes that “we can represent the functions [within the network map] as electronic circuits or mathematical equations.” Uh… a circuit diagram is basically a schematic representation of mathematical equations. The diagram is meaningless without the math behind it.)
While I’m picking on Nobel Laureates, let’s turn to Paul Nurse, who pioneered our understanding of the machinery underlying cell division, but who also doesn’t seem to appreciate the role of quantitative theory and its possibilities for explaining the behavior of the system as a consequence of its parts. After badly misapplying the scientific term ‘ensemble’ to genomic data (and it gets worse… in the next sentence he uses the words ‘canonical ensemble’ in a sense that has nothing to do with their normal scientific meaning!), Nurse exhibits a very poor understanding of what quantitative models are and how they are used, in both biology and physics:
However, two major problems are often encountered when generating mathematical models for cell biology: the complexity of the pathways being modeled and the difficulty of estimating the appropriate values for rate constants and the concentration of components. Biochemical pathways are often complex with many redundant functions, reflecting the fact that evolution does not always lead to, from an engineer’s point of view, the most efficient and economic solutions. Natural selection acts on pre-existing cells often by making additions to previously operational pathways, and these additions increase redundancy. In this respect modeling in biology may differ from physics where the aesthetic is to search for the simplest and most elegant model to explain a phenomenon. In biology, there are often more elements in a model than are strictly necessary and some act redundantly. The number of elements also increases the degrees of freedom available, reducing confidence in the outcome of the modeling process.
“The Cell in the Era of Systems Biology,” Cell, Volume 144, Issue 6, 18 March 2011, Pages 850–854
This feeling that biology is too complex and evolutionarily contingent for quantitative models might be cured by taking a look at some of the complex systems that physicists can successfully explain. Perhaps part of molecular biologists’ aversion to quantitative models comes from the distorted view of physics we get by only taking the introductory courses that cover the mathematically simplest theories in physics, such as wave theory, Newton’s laws, and Maxwell’s equations. If we spent more time learning more advanced formulations and applications of classical mechanics, or non-linear dynamics, our skepticism might moderate.
So if you’re looking for an inspiring vision of what biologists are going to do in the future, don’t turn to the writings of those who built their careers doing classic molecular biology. It was certainly a smart move to forget reaction rates and free energies when so much could be learned by, in the unfortunate words of Erwin Chargaff, “practicing biochemistry without a license”; but now these scientists have forgotten how to do quantitative science. There are all sorts of interesting questions out there now that can only be answered by thinking about the quantitative relationships between system components, questions about the response curves of signal transduction pathways, the consequences of noise and small numbers for transcriptional systems, the readout of non-coding information in the genome, the spontaneous synchronization of cellular processes, and the counterintuitive behavior of gene regulatory networks. We know in large part what happens in biology, but we don’t know why.
Some further reading:
One more disappointing review:
“Yeast: An Experimental Organism for 21st Century Biology” David Botstein and Gerald R. Fink, Genetics November 1, 2011 vol. 189 no. 3 695-704
Physicists dealing with the problem of many poorly known parameters (PDF).
Albert Einstein:
My interest in science was always essentially limited to the study of principles, which best explains my conduct in its entirety. That I have published so little is attributable to the same circumstance, for the burning desire to grasp principles has caused me to spend most of my time on fruitless endeavors.
Math matters in economics too:
Talking to yourself in plain English, it’s not too hard to find yourself making plausible-sounding arguments that don’t actually hang together…
But take an NK model like Mike Woodford’s (pdf) — a model in which everyone maximizes given a budget constraint, in which by construction all the accounting identities are honored, and in which it is assumed that everyone perfectly anticipates future taxes and all that — and you find immediately that a temporary rise in G produces a rise in Y, with none of either the Ricardian effects Lucas declares important nor the kind of adding-up constraints that Cochrane or Fama or Sumner seem to think are decisive. If your verbal reasoning led you to think that expansionary fiscal policy can’t be expansionary as a matter of logic, well, your logic was wrong.
– Paul Krugman
The Finch and Pea 