Tuesday, May 5, 2009

Inference from topology

Changing parameters of a system can drastically change its behavior in some situations. But even so, it might be possible to deduce certain dynamical properties from topology...

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:
  1. Generate all the different "versions" of this topology
  2. Analyze each version by varying the parameters. Look for steady state behaviors as well as other interesting qualitative behaviors. 
  3. Classify each version of the topology by its qualitative behaviors.
  4. 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. 

Monday, May 4, 2009

Cell-wide Control

Identifying multiple stable states of a cell and the key regulatory motifs controlling those states might be an efficient way to have control of the whole cell's dynamics. This is essentially like identifying all the switches in a circuit. Of course, some switches affect one another; such cases would need to be resolved.

If the switching points in a cellular network are identified, the cell can be rewired so that some states follow after another or that some states affect another -- small connections can create grand effects.

Implications of Network Motifs on Evolution

There are claims that "modularity" may be advantageous to evolution. An analogy for supporting this hypothesis are logic gates in digital electronics. Rate of evolution of digital electronics has increased due to the fact that logic gates can be reused in different ways to form complex circuits.

Taking the analogy to biology...

Task at hand: need to identify the equivalent of logic gates in biology.
Once the above task is complete, redraw biological networks using the "modules".

I anticipate the following features would characterize biological modules:
(1) They are common in biological networks but hard to find because they will be intertwined with each other, i.e. may or may not be as obvious as looking for high frequency sub-graphs
(2) Individual modules will have a defined behavior...but this "defined behavior" may be difficult to identify.
(3) They will be highly flexible in the types of functions they can produce when connected with each other.
(4) Different physical networks, i.e. genetic networks, signaling networks, metabolic networks, RNA networks, will probably have different modules.

Negative and Positive Autoregulation at the Interface

The scenario:

stimulus ----> A ----> B and A regulates itself

The steady state of B as a function of A is a signmoid curve.

Consider two cases:

1) A negatively regulates itself and A has a basal level of production. In this scenario, the steady state value of A will remain not-too-low and not-too-high (due to negative regulation). Therefore, in the sigmoid curve of B vs. A, A remains in the somewhat-linear region of the curve.

2) A positively regulates itself and has no basal level of production. In this scenario, the steady state of A is either low of high, so B is low or high (possible amplified).

case (1) is one where the stimulus can linearly control B, and case (2) is one where the stimulus has a threshold above which B is active.