So FBA can be formulated as

where Z is the biological objective function, c is a vector of coefficients that define how much each reaction contribute to the objective. v is the vector of fluxes of each reaction, and it is unknown. S is a m*n matrix. It contains the stoichiometry of the metabolic networks. and are the lower bounds and upper bounds of .

Then FVA can be formulated as

Note that now is a known value. So this means that we already know the optimal of the biological objective, but we want to find out the range (min, max) of certain fluxes that fit the optimal solution. This gives the variability of . For example, in certain conditions, some reactions might changes but without changing the outcome. FVA analysis will be able to identify such reactions.

This paper applied FVA to the analysis of the metabolic network in photosynthetic PNSB. The authors tested their model in several conditions. This paper is particularly interesting to me because of the methods FVA. The original paper of FVA is published in 2003. (pubmed)

There are several interesting things in their work. First, they developed a new algorithm to merge the gene expression data from different cell lines given the same compound. This aggregation algorithm uses several techniques such as Spearman’s footrule, Borda Merging Method and the Kruskal Algorithm.

Secondly, they calculated the drug similarity based on the merged list of gene ranks from the previous step based on results from Gene Set Enrichment Analysis (GSEA). This is because the list of expressions are different for two different compounds.

Thirdly, they compared the drug similarity measure with chemical similarity measures using fingerprints or electrotopological descriptors. The results are quite uncorralted with very low pearson correlation coefficient. An interesting extension of this could be the activity cliffs – very similar compounds that having completely different biological activity profile.

One limitation of this method is that you need to have a gene expression profile of a compound to be able to use it, similar to the original connectivity map approach. The other concern is that for compounds that have inconsistent effects on different cell lines. But as the authors mentioned, “when no information on the drug MoA is available a priori, the best strategy is still
to merge profiles from multiple cell lines”.

Iorio, F. et al. Discovery of drug mode of action and drug repositioning from transcriptional responses. Proceedings of the National Academy of Sciences 107, 14621 -14626 (2010). doi:10.1073/pnas.1000138107

Cephalosporins disrupts the synthesis of the peptidoglycan layer of bacterial cell walls. The petidoglycan layer is important for cell wall structural integrity. The final transpeptidation step in the synthesis of the peptidoglycan is facilitated by transpeptidases known as penicillin-binding proteins (PBPs). PBPs bind to the D-Ala-D-Ala at the end of muropeptides (peptidoglycan precursors) to crosslink the peptidoglycan. Beta-lactam antibiotics mimic this site and competitively inhibit PBP crosslinking of peptidoglycan.

This week’s molecule is BPA, or bisphenol-A. New York time has a long article about the research over this controversial chemical, mended with some political background. Details at In Feast of Data on BPA Plastic, No Final Answer – NYTimes.com

From the article, there is no decisive results to testify BPA’s effects on human bodies. But it doesn’t mean there is no results. Rather, scientists are still debating over whether BPA is toxic or not, mainly because unreproducible results. Part of the reasons of the conflicting results, as the article pointed out, is that “different laboratories have studied the chemical in different ways”. The conflicting results have even produced conflicts between scientists. It’s interesting to read that “researchers who study it argue bitterly at conferences”, and “At one such meeting, scientists in the audience said, “We don’t want to hear you two speak until you get this straightened out,” “.

The articles goes on with recent development in the research, and mentioned some efforts in reconciling the disputes. One biggest dispute is that low dosage of BPA turns out to have worse effects in animal studies than higher dosages. From endocrinologists’ point of view, it makes sense because BPA is no regular toxicant, but it “acts like a hormone”, and “hormones can act at extremely low doses”.

So much about the article, and here is the chemistry about BPA.

BPA has two phenol functional groups, and it is used to make polycarbonate plastic that are used in almost everything we use that are plastic, including food containers and baby bottles (in some states in the USA, BPA bottles is already banned in Canada, as well as some states in the US).

Why is BPA toxic? Because it can bind to estrogen receptors, though the binding is much weaker than the body’s own estrogen. Estrogen is assotiated with many horrible diseases, such as cancers, obesity, immune system diseases, and behavior problems. BPA could also bind to receptors for male hormone and thyroid hormone. DES (diethylstibestrol) is a disastrous example of an endocrine disruptor, as mentioned in the NYTimes article. It was used as a drug to prevent miscarriage for pregnant women in 1950s. It could bind to estrogen receptors much stronger than BPA, and has caused sever problems such as cancers, and even affects the offsprings of the womens who took it. What’s this chemical?

(Images: BPA, Estrone, and DES. Curtosey of wikipedia)

I talked to Alex Pico, my direct mentor on the Express Reader plugin, also Scooter and Daniele. The face to face meeting turns out to be very efficient and we clarified several uncertainties in the project design. It’s also interesting to learn some history of the Cytoscape, and link faces to some familiar names in mailing lists.

One of the interesting talk is about a cytoscape plugin that can explore open linked data (LOD), given by Eric Neumann. He talked about a SPARQL plugin that can be used to query LOD data, and gave quite a few case studies on how to use the plugin to query and visualize data that are related to drug discovery.  It was related to the work that is being done in the Wild’s group I worked with last year (chem2bio2rdf). Although I am not actively involved in that project any more, it’s exciting to see that the data could be potentially put into real use.

Dr Lee Hood gave a inspiring talk on the future role of systems biology to P4 medicine (predictive, preventive, personalized, participatory). There are several other interesting talks and fun posters too.

Finally, the location of the meeting was in a big research building that was belong to Pfizer, and was recently bought to UM, but was still pretty much vacant. It’s a huge building and very nice facilities, but so quiet as we are the only group of people in it.

Update on 9/3: It seems the videos of all talks are uploaded now (http://cytoscape.wodaklab.org/wiki/CytoscapeRetreat2010)

> a
a
[,1] [,2] [,3]
[1,] 0 2 1
[2,] 2 0 3
[3,] 1 3 0
> g1
g1
Vertices: 3
Edges: 6
Directed: TRUE
Edges:

[0] 0 -> 1
[1] 0 -> 2
[2] 1 -> 0
[3] 1 -> 2
[4] 2 -> 0
[5] 2 -> 1
> E(g1)$weight
[1] 2 1 2 3 1 3
> E(g1)
Edge sequence:

[0] 0 -> 1
[1] 0 -> 2
[2] 1 -> 0
[3] 1 -> 2
[4] 2 -> 0
[5] 2 -> 1
> get.adjacency(g1, attr="weight")
[,1] [,2] [,3]
[1,] 0 2 1
[2,] 2 0 3
[3,] 1 3 0

An interesting paper published on JCIM. The authors created a GMM (Gaussian mixture model) based on properties of active compounds over targets, and used the model to generate more molecules that are likely to be active. Each compound is represented based on properties extracted from a graph representation of it, and PCA conducted to reduce dimensionality. Then they sample from the built GMM, and map the samples back to a molecule.

Testing this method on DUD data sets, they authors showed that molecules generated using this method are similar to the compounds in the input sets, and docking results show that the molecules are likely to be active against a target of the input molecules.

Generative Models for Chemical Structures – Journal of Chemical Information and Modeling (ACS Publications)

N = 100;
x = linspace(-pi, pi, N);
y = sin(x);
plot(x, y, 'r');
hold on;

% add 10% noise based on gaussian
scale = 0.1;
n1 = randn(1, N); % noise with mean=0 and std=1;
y1 = y + n1.*y*scale;
plot(x, y1, 'g');

% mask signal with noise
n2 = 0.1*randn(1,N)*sqrt(max(abs(y))); % noise with mean=0 and %std=max(amplitude);
y2 = y + n2;
plot(x, y2, 'b');

% Of course we can combine the two
y3 = y1 + n2;
plot(x, y3, 'm');

The final result looks like this:

We can also try to add noise to a more complicated synthetic data. For example, the famous swiss roll data^[1] in manifold learning. First, we can generate the dataset by this function:




Plot a scatter plot of will give us a swiss roll dataset. For example, the following matlab code will create this figure.

N = 500;
r = linspace(0,1,N);
t = (3*pi/2)*(1+2*r);
x = t.*cos(t);
y = t.*sin(t);
z = 20*rand(1,N);
scatter3(x, y, z, 12, t, 'filled');

Now after adding noise. the standard deviation of the noise is 2% of smallest dimension of the bounding box enclosing the data (as discussed in ^[2])

mindim = min(max(y)-min(y), max(x)-min(x));
x = x+0.02*randn(1,N)*sqrt(mindim);
y = y+0.02*randn(1,N)*sqrt(mindim);
scatter3(x, y, z, 12, t, 'filled');

1. Tenenbaum, J.B., Silva, V.D. & Langford, J.C. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290, 2319-2323 (2000).
2. Balasubramanian, M., Schwartz, E.L., Tenenbaum, J.B., de Silva, V. & Langford, J.C. The Isomap Algorithm and Topological Stability. Science 295, 7a (2002).

Cartoon courtesy of xkcd