Models will play a central role in the representation, storage, manipulation, and transmission of knowledge in systems biology. Models that are capable of fulfilling all these purposes will likely differ from the familiar styles deployed with great success in the physical sciences. "Classical" flavors of models may be viewed on a continuum between two major types:

• Models that are of heuristic nature.
  Although formal (mathematical), these models are not primarily intended for data analysis. They represent highly idealized or stylized situations aimed at discovering necessary and sufficient conditions for specific behaviors. Such models pursue a commitment to explanatory principles more than quantitative prediction. They are thought-experiments whose complexity often demands a computational infrastructure for execution.

• Models that aim at being realistic.
  Models of this kind are designed to capture as many detailed mechanistic features as are needed for generating quantitative fits with experimental data. Success is cast in terms of quantitative prediction, that is, the computation of numerical ranges for critical system variables and parameters. Models of this kind are often hailed as providing guidance for new experiments aimed at modifying system dynamics, such as the identification of drug targets. Realistic models are important in assessing when we know enough about a system to effect specific interventions at a given experimental resolution.

In spectacular instances, both types of models may predict missing components, interactions, or processes that would, when added, bring a model into qualitative or quantitative agreement with data (as in the golden days of high-energy physics). The ideal gas and the Ising model of a magnet are classic examples of powerful heuristic models in physics. Hopfield’s “kinetic proof reading”, Wolynes' spin-glass framing of protein folding, or Bialek's predictive information are instances of potent heuristic models in biology. Oftentimes heuristic and realistic flavors are blended, as in the Bayesian reconstruction of influence networks. Still, matters are not that simple. A population geneticist might consider a model that tracks an observed gene frequency dynamics with quantitative accuracy as realistic. Yet, to a molecular biologist the same model will appear as heuristic. Successful examples of realistic models in biology are rare at present, if there are any at all. Maybe that's because we don't know enough (but when do we?). Or maybe we need to rethink what is real.

Certain kinds of models do not fit neatly into the scheme I just described. These models are qualitative sketches of biological processes (like Russ Harmer's diagram at the top of this page). They are drawings that specify which components or processes inhibit or stimulate which other components or processes in, say, a gene-regulatory network or signaling pathway. The static nature of a drawing is clearly a severe limitation in the depiction of complex and dynamical relationships. Yet, the spirit of such sketches is to succinctly specify systems whose full details and potential states are oftentimes beyond comprehension. These models are interesting mixtures of several modalities, such as arrows germane to dynamics (e.g. feedback), arrows that depict causality ("this phosphorylates that"), and a layout (e.g. "top to bottom") that conveys a sense of temporal (or logical) progression towards some observable of interest. How can we bridge the gap between models of the classical kind – blends between heuristic and realistic flavors – and a sketch like this?

A model in molecular biology should perhaps be more like a datastructure that contains a transparent, formal, and executable representation of the mechanistic facts it rests upon. A case of particular interest are facts about molecular interactions that underlie cellular signaling systems. A model should be an environment in which data that is about interaction directly instructs the execution of these interactions on a system of (virtual) molecules. Furthermore, a model must be equipped with analytical tools for revealing and navigating the causal organization that results from a particular set of interactions. This organization shapes dynamics in non-intuitive ways. Such a model seems to resemble the notion of a distributed and asynchronous program in computer science. If so, then modeling is not unlike programming. Conversely, if a program is to be a biological model, it cannot be written in an arbitrary language. The static analysis of the program must provide insight into how it behaves (its dynamics) and why it behaves the way it does. This is analogous to the static analysis of a system of differential equations, wherein one computes, say, the eigenvalues of the Jacobian to reason about stability.

The concepts that make such an approach actually possible are familiar to computer science, in particular to a branch of computer science known as concurrency. Computer scientists Vincent Danos, Jérôme Feret, Jean Krivine, and I have joined forces with several other researchers to design a computational environment that makes this vision a practical reality. However, the transfer of perspective from concurrency to biology is neither simple to execute – several sophisticated software tools had to be written – nor easy to grasp, as it deals with unfamiliar concepts whose clarification took a long time even within their domain of origin.

For another, complementary approach to modeling in systems biology, check out my colleague Jeremy Gunawardena's project on "Little b".

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