Wednesday, July 22, 2009

Automatic analysis and construction of feed-forward regulatory networks

Given the assumption that transcriptional regulation is sigmoid shaped, i.e. the steady state diagram of the inducer vs. the target protein has a sigmoid shape (or inverted in the case of a repressor), it might be possible to automatically determine the steady state diagram of a regulatory network with no feedback controls. It might also be possible to generate a feed forward network for a given steady state diagram.

Lets take a simple case, where a transcription factor "a" indirectly upregulates and downregulates the target gene "X", as shown below. Then there are two regulation curves associated with "a". If we assume that a repressor will dominate over an activator, then we can determine what the the final steady state diagram of "X" will be as a function of "a" by looking at the dissociation constants (the center of the sigmoid curves).

The same method can be used to construct networks that have more complex steady state behaviors. For example, suppose "a" and "b" regulate "X" such that the activity of "X" is described by the yellow regions (1,2,3) in the diagram below. Then, it is possible to identify the network that will satisfy each piece and then put the pieces together. The shape of the sigmoid is determined by the dissociation constants.

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.

Friday, March 13, 2009

Modular vs non-modular evolution

A simple experiment:

simulated evolution using "modules" vs simulated evolution without "modules"

Questions to answer:
1) What kind of fitness landscape might favor modules, if any?
2) Does stochasticity play a role?
3) What is the affect on rate of evolution?

Sunday, March 8, 2009

Measuring with limited instruments

At the present, instruments for measuring events inside a cell are limited. Although there are techniques using fluorophores to detect molecular events, they are not as quick and simple as GFP. 

So the question: is it possible to place GFPs at specific locations such that those different measurements will provide sufficient information for calculating some un-measurable point? 

Put in a different way: given a system, find a way to measure parameter X using a minimum number of other parameters (from a limited set of parameters). 

Tuesday, February 17, 2009

Borrowing sub-systems from another orgnanism

Engineering a cell is mostly done at the genetic level because that is where the tools are available. However, it is possible to borrow an entire system from another organism, such that the controls of the system are at the genetic level. 

Consider a system with various proteins, including a few transcription factors. Now, lets take the system as a whole and consider the fact that we can control the concentrations of each of the members of the system, and we can take as "output" the concentrations of all the transcription factors in the system. As long as the entire system does not interact with the host machinery, this can be a generic strategy for borrowing systems, rather than genes, from other organisms. 

Sunday, February 15, 2009

Borrowing phosphorylation cycle from another organism

Perhaps it is not neccessary to engineer proteins themselved in order to engineer a cell at the protein level. 

Suppose organism Y has a system composed of a kinase, phosphatase, and transcription factor(s) that is controlled via phosphorylation. This entire system can be transplanted into organism X (e.g. E. coli), with each component under the control of different promoters. 

This will give some control at the protein level, because the equilibrium concentrations of the phosphorylated and unphosphorylated proteins can be controlled by regulating the levels of the kinase and phosphotase. Of course, the control is still at the transcription level, but the phosphorylation will serve as a fast-acting system -- i.e. producing a few kinases will activate many transcription factors. 

Saturday, February 14, 2009

Feed forwards

Apparently, the dynamical system involving only feed forward neural networks (not artificial) converge to a single point. Feedback is required in order to create complex effects, such as convergence to a complex attractors, etc. The structure of genetic networks is similar, and E. coli's regulatory network is largely composed of feed forward networks and very little feedback (except self-loops). Is it possible that for a single input pattern, the cell is adapted to respond in the same way every time, somewhat like a neural network learning an input pattern? 

Is it possible that the genetic network "sets up" the community of proteins in the cell. The community of proteins determine the dynamics of the cell. In this is the case, then the genetic network is a system that takes input from the environment and produces a dynamical system, or  machine, as the output. The dynamical system is designed to survive in the particular input environment. Here is an somewhat odd example (completely hypothetical) :

Lets consider a Venus fly trap or some similar plant...

input: bug lands inside the plant's mouth.
processing: some transcription factor triggered
output: production of several insect digestion enzymes

The output proteins may not just be for digestion itself. They might together form a small machine, such as an oscillator that is responsible for closing the mouth, or some other mechanics that is responsible for carrying out the whole digestion process. By identifying the machine that is the "output" it may be possible to learn behavior pattern is needed to cope to particular environmental signals. 

Tuesday, February 10, 2009

Using broken transcription factors as AND logic

Yeast-2-Hybrid is a technique where gene X is placed under the control of a transcription factor TF, but TF will only become active when proteins A and B interact with each other. This same concept can use used to create a transcriptional AND gate:

gene A --> protein A
gene B --> protein B

TF is only active when proteins A and B are present. Hence, gene X =  gene A && gene B