The second approach to this problem is one that I've pioneered, and it's got great strengths but great weaknesses. It turns out that if you want to model genes as if they're little lightbulbs, which they're not, but if you want to model them that way, then the appropriate rules that talk about turning genes on and off are called Boolean functions. If you have K inputs to a gene, there's only a finite number of different Boolean functions.
So what I started doing years ago was wondering if you just made genetic networks with the connections at random with the logic that each gene follows is assigned at random, would there be class of networks that just behaved in ways that looked like real biologic networks? Are there classes of networks where all I do is tell you all I know about the number of inputs, and some biases on the rules by which genes regulate one another -- and it turns out that a whole class of networks, regardless of the details, behaves with the kind of order that you see in normal development?
SA: How would you identify the different networks as one class or another?
There are two classes of networks: one class behaves in an ordered regime and the other class behaves in a chaotic regime, and then there is a phase transition, dubbed the edge of chaos, between the two regimes. The ordered regime shows lots and lots of parallels to the behavior of real genetic systems undergoing real development. To give an example, if I make a network with two inputs per gene and that's all I tell you, and I make a huge network, with 50,000 or 100,000 genes, and everybody¿s got two inputs, but it's a scrambled mess of a network in terms of the connections -- it's a scrambled spaghetti network, and the logic assigned to every gene is assigned at random, so the logic is completely scrambled -- that whole system nevertheless behaves with extraordinary order. And the order is deeply parallel to the behavior of real cell types.
Even with 10 inputs per gene, networks pass from the chaotic regime into the ordered regime if you bias the rules with canalizing functions. The data is very good that genes are regulated by canalizing functions. There is one caveat. It could be that among the known genes that are published, it's predominantly the case that they are governed by canalizing functions because such genes have phenotypic effects that are easy to find, and there's lot of things that are noncanalizing functions, but you just can't find them easily genetically. So one of the things that we'll have to do is take random genes out of the human genome or the yeast genome or the fly genome and see what kind of control rules govern them.
SA: What would be the implication if it did turn out that most were governed by canalizing functions?
What we've done is made large networks of genes, modeled genes mathematically, in which we've biased the control rules to ask whether or not such networks are in the ordered or chaotic regime, and they are measurably in the ordered regime. The implication is that natural selection has tuned the fractions of genes governed by canalizing functions such that cells are in the ordered regime.
The way you do this is you make an ensemble of all possible networks with the known biases, number of input per genes and biases on the rules. And you sample thousands of networks drawn at random from that ensemble, and the conclusions that you draw are conclusions for typical members of the ensemble. This is a very unusual pattern of reasoning in biology. It's precisely the pattern of reasoning that happens in statistics with things like spin glasses, which are disordered magnetic materials. The preeminent place it has been used is in statistical physics. The weakness of this ensemble approach, this ensemble of networks, is that you can never deduce from it that gene A regulates gene F because you're making statistical models. The strength is that you can deduce lots of things about genetic regulatory nets that you can't get to if you make little circuits and try to do the electrical engineering approach.