Lets take a simple case:
The gene product of gene A positively regulates gene B.
Even if no parameters are known, one can hypothesize the steady state behavior of B will probably be a sigmoid function of A. The exact shape of the curve cannot be infered without additional information.
Lets take a less specific case:
Gene A regulates gene B, but the type of regulation is unknown.
Now, there are two relationships that are possible: a sigmoid function (positive regulation) or an inverted sigmoid function (negative regulation). Again the exact shape of each cannot be known.
Lets extend the situation: A regulates B and C, and B regulates C.
Now, there are 2x2x2 possibilities. However, the number of different shapes that the 8 different combinations can make is probably not 8. It can be more in the case that this topology is highly versatile in the types of functions it can realize. It can be less than 8 if many versions of this toplogy produce similar behaviors. It is also possible that a few versions of this general toplogy are very interesting in the variety of functions they can realize, but the other versions are similar to one another. If this last situation is the real situation, then it is possible to make some inferences about the dynamical behavior with just the topological information. Here is how:
For a given general topology, i.e. where the regulation types are not known:
- Generate all the different "versions" of this topology
- Analyze each version by varying the parameters. Look for steady state behaviors as well as other interesting qualitative behaviors.
- Classify each version of the topology by its qualitative behaviors.
- Hypothesize possible uses for each qualitative behaviour, especially in the context of where the original toplogy came from.
The above approach is not specific to genetic networks. If it works for one type of network, it should work for the others.