Life depends on the interaction of tens of thousands of genes and their protein products, orchestrated by the regulatory logic of each genome. If we are to comprehend this logic, we must hope that it can be dissected into a series of interlinked modules or networks, each of which can be studied in relative isolation. But even then the complexity of a single module can be daunting. As our knowledge increases, diagrams of gene regulatory networks look increasingly like explosions in a spaghetti factory. We need fresh methods to explore the behaviour of such networks.
On page 188of this issue1, von Dassow and colleagues describe how they have taken a computational approach to the problem. Their starting point is the network of genes that makes body segments in the fruitfly Drosophila (Fig. 1). In the past 20 years, genetic analysis has produced a wealth of experimental data on segmentation, and a textbook model of how dynamic intercellular signalling maintains a stable boundary between cells that are in distinct states2, 3 (see Box 1).
Figure 1: Segmentation (in this case abnormal) in the Drosophila embryo.
Normally the segment-polarity gene network generates a linear array of 14 segments, each bounded by a stripe of cells expressing the engrailed gene. This 'two-tailed' embryo shows how the segment-polarity network can make regular patterns, even with abnormal inputs. Signals from the mutant mother have triggered two arrays of segments to form back-to-back. Where they meet, a circular segment boundary has formed (here revealed by staining for Engrailed protein).
High resolution image and legend (24K)From these data, von Dassow et al. abstracted a set of key interactions which, they hoped, would constitute a discrete developmental module. To make it computationally tractable they had to simplify it further. Their final model has 136 coupled equations with nearly 50 free parameters for such values as half-lives, diffusion constants and binding coefficients of the gene products involved. For virtually none of these are real values known. So the authors had to use random sampling and statistical methods to explore the properties of this model over the plausible range of parameter values. The boxed item in the paper (page 189) shows the proteins and type of equations involved.
The prime result is counterintuitive: a random search of parameter space identified a surprisingly high frequency of 'solutions' that allowed the model to generate the correct pattern of segment gene expression; correct, that is, in the sense of resembling the pattern actually observed in developing Drosophila embryos. The values of parameters in these solutions do not converge on a single set of optimal values — the value of almost every parameter can range over orders of magnitude and still be compatible with a correct solution. It is the organization of the gene network that provides stability, not the fine-tuning of molecular interactions.
It is revealing, though, that when the group first built the model it did not work at all. Despite their best efforts to distil a logically complete model from data in the literature, and from discussions with experimental workers, no parameter set provided a correct solution. Certain essential linkages in the network were missing. In a confession of humility that is all too rare among scientists, the authors point out that "Biologists' maps of gene networks are rapidly outgrowing our ability to comprehend genetic mechanisms using human intuition alone, as shown by our initial failure".
With hindsight, logical gaps in the textbook model are not difficult to spot, but no textbook or review had highlighted them. For example, it was not clear why the engrailed gene is not activated in front of, as well as behind, the cells expressing wingless (Box 1). Von Dassow and colleagues have plugged this and other gaps with plausible assumptions based on hints already buried in the experimental literature; in this case, that the gene transcription factor CiD represses engrailed transcription in the absence of signalling from another protein called Hedgehog. This highlights a key aspect of the work: the model is so closely tied to real data that its inadequacies immediately define a programme of experimental work to test these assumptions.
With the segmentation gene network implemented in silico, it becomes possible to explore how different sorts of variation affect its output. The effects of varying parameter values over small ranges are equivalent to those of minor mutations; small changes in the inputs used to trigger patterning mimic the natural variation in development seen from embryo to embryo. On both of these counts, the network is satisfactorily robust. Most small changes in parameter values have little effect — only at rare thresholds does the behaviour of the model switch from one stable state to another.
Initial conditions can also be varied more widely, to explore how this gene network might behave in different developmental contexts. For example, the model was designed with a precise periodic input to trigger activity of the segment-polarity genes throughout the whole length of the body. This mimics what happens in Drosophila (Box 1). In many other insects, however, segmentation spreads through a field of cells from head to tail (much as it does during early patterning in vertebrate embryos). In these cases, the segment-polarity system seems to be conserved4, but the upstream triggers may not be5, 6. Von Dassow et al. are quite happy with this: their model will generate the same segment pattern with a variety of different inputs, and the inputs can be much less precise than those known from Drosophila.
Our understanding of gene networks is at an early stage. We perceive their complexity only after it has been filtered by the limitations of the techniques used to study them. Genome databases and DNA-chip technology, which enables huge numbers of genes to be screened for activity, will undoubtedly provide more, and much more complicated, data than anything produced by Drosophila genetics. If a relatively simple gene network such as the segment-polarity system is hard to understand intuitively, we can be certain that modelling will be essential to make sense of the flood of new data.
But this will not be elegant theoretical modelling: rather, it will be rooted in the arbitrary complexity of evolved organisms. The task will require a breed of biologist–mathematician as familiar with handling differential equations as with the limitations of messy experimental data. There will be plenty of vacancies, and, on present showing, not many qualified applicants.
