From Topology to Response

From Santa Fe Institute Events Wiki

The original proposal

Imagine a small (3-7 nodes) network where every node represents a protein species, and every (directed) edge the activation relation between the proteins (i.e. A ---> B means that the protein A can react with B and activate it). Furthermore, assume that there are two numbers associated with every node: the total number of protein molecules of the given type and the fraction of the active forms. Finally, let two nodes, R and E, be special and call them the Receptor and the Effector. What you have is a crude model of intracellular signalling.

This paper considers such models and exhaustively classifies all the possible topologies (i.e. wirings) with respect to the activation pattern of the Effector in response to a standardized signal sent by the Receptor. The goal of our project would be to do the same experiment using different tools, and potentially obtain different results. The main difference would be to use stochastic (rather than deterministic) dynamics to determine the response. As the signalling systems operate with relatively low numbers of molecules, stochastic effects may be important. If we do this and have time left, we can try pushing it further and consider the issues of robustness and evolvability of these networks.

To put a nasty spin on the project, I propose that we use an obscure computational technique called model checking to get the response profile of a network; partly just because we can, but partly also because it nicely deals away with the need of explicitely simulating and averaging of stochastic models.

Now, a couple of final remarks:

  • Don't think of it as a network project. All networks involved will be rather trivial.
  • The project group should include a biologist (to do sanity checks) and somebody familiar with parallel computing.
  • Model checking is (very) expensive computationally, we will probably need a cluster.
  • I have all the original results from the paper mentioned.
  • The tool to use would probably be PRISM.



  • (17 June) We now have a generator of PRISM-digestible topologies.
  • (24 June) We've found the steady states of 3-point topologies and got some idea of the computational burden of the project.
  • (29 June) We've encoded common dynamic responses as LTL formulae and uncovered a serious bug PRISM! Stay tuned...
  • (29 June) The project has been frozen, as we have to wait for the PRISM people to fix the bug. No refunds.
  • (30 June) We're back in the game! The PRISM people have fixed the bug in their software and we fixed a bug in our model. We now move to characterize all 3-point topologies.