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Bayesian Weighting Schemes

Week 2 Progress Report

Week 2 was spent further looking into Bayesian Weighting Schemes and in particular how they were applied in a specific paper titled Top-Down Network Analysis to Drive Bottom-Up Modeling of Physiological Processes by Poirel et. al. This was the original LINKER paper that PATHLINKER was built upon. I also spent a very decent amount of time looking at other interactomes and curating a working list of interactomes and how they weight their interactomes. So far I have only done this in detail for the HIPPIE interactome but more work is still needed. Besides research, I also worked on a document about Bayesian Weighting that aims to elucidate some of the mathematical set up and notation for the paper mentioned above as it suffered from some convoluted mathematical notation. Hopefully, this will be useful to people trying to read this paper in the future. Other tasks involved debugging code, presenting learned material and sorting through papers to find relevant papers.

Summer Week 1: Prime Nodes

This week, I got caught up with the state of the project. Anna and Miriam had cleaned up and optimized our code to the point where it could be submitted and run in a reasonable amount of time. However, there still remained the problem of nodes only connected to positives. Since positives are held at a constant score of 1.0, and negatives at a constant 0.0, any nodes only connected to a positive will have a score of 1.0, which misrepresents how a gene fits within the polygenic nature of schizophrenia and cell motility.

To solve this, we decided to make three networks, each one identical to the one we were previously testing. However, there are two key differences.

  1. The positives are divided between the three networks.
  2. The three nodes in each networks representing their gene are also connected to a prime node that is only connected to those three nodes. The prime node’s score is the node by which we judge a gene.

This reduces the edge cases where a gene is only connected to a positive or a negative, since the gene cannot be connected to only one node. This also allows us to evaluate positive nodes within the context of all other positives. If a positive node is found to be positive in other networks, then the score will be high. Even the neighbor positives within the same network will diffuse the positivity through their prime nodes down to other networks, increasing the score for the neighbor of the positive and therefore increasing the score for the positive.

One thing to note is that the AUC seems to be relatively stable despite the network threshold or the prime node implementation. However, my guess is that this is probably due to the positives generally being only vaguely functionally related. Also, only 116 SZ genes are in the 0.200 network, reducing the polygenic power of our method. One thing to try is to add more genes from other studies. I will research other studies to find more gene lists and p-values.

Week 1

Sol, Usman, and I have started working on summer research to modify the PathLinker algorithm.

This week, we plan to finish the code implementing Dijkstra’s algorithm on toy datasets, which was used as a warmup exercise in order to acclimatize us back into working and coding. In addition, I’ve been assigned to understand Yen’s k-shortest paths algorithm, which is one of the foundations of PathLinker.

Week 23

I ran the bulk-BLASTer to find good homology targets from our results

Derek Applewhite, our cell biology advisor, noted that several top genes could be novel to flies, and several genes could be novel to cell motility.

Miriam and I will continue to work out the bugs in the verification system for our process.

Week 23

This week, my goals have been relatively simple and short. There are a couple of bugs in my code that I need to sort out. I haven’t been able to collect any data about how “good” our method is due to these bugs, but once I do, we will hopefully be able to see that the results we are getting are not random.

Week 22

Since the last time I wrote a blog post, I have mainly been working on one way of verifying our algorithm; essentially, we need to make sure that our method is actually good at doing what it’s supposed to be doing. Although there are several ways to verify an algorithm, some of which Alex has been working on, I am working on something called “k-fold cross validation.”

This method of verification works by removing (or “hiding”) 1/k-th of your positives, then running your method and seeing where the hidden positives are ranked. You randomly choose the 1/k positives to hide and do this several times. You can also use the distribution of scores you get from each run to see how your method (with all positives) compares – are you getting significant results or are you getting what is expected from randomly choosing positives?

My first attempt at this was just a test run, and there were a few mistakes that I made. First, I chose to sample half instead of choosing a more reasonable number of positives such as 1/4 or 1/5. I also didn’t randomly choose positives to hide – I simply deleted the second half of the positives, and in doing so, might have removed an entire cell motility pathway or two from the positives. This would have produced biased results.

This coming week, my goal is to randomly sample 1/4 of positives multiple times, as well as implement some plotting functions in order to visualize the distribution of scores.

Week 22

So we have a BLASTer to see which genes in humans are homologous to genes in drosophila melanogaster, our model organism for cell motility. It works- it just takes a couple of hours to get an output file for 20 genes. Should be no problem to run overnight.

Miriam has been working on a way to verify that the network is working. Currently, she has been eliminating some positives while keeping others, looking at how high up the eliminated positives are in the result. It should be fruitful.

We also looked at how other functionally similar genes we were certain about were similar. We found that all of the gene interactions we thought of as functionally similar had strong edges in the networks. This validates the network as a whole as biologically sound and will further validate our results.

Week 21

Although we had the bio qual, we still managed to do a little bit of work. One of the sources for our positive set was a little suspect, so we decided to take it out and see the impact on the results. We found that there was a drastic change. Since we were relatively confident that the other positives were good, if the suspect one was good, then the results wouldn’t change as much if we ran the whole network through. What we found was that it was indeed not very good. The output file was dramatically different. But we need a way to quantify the change

This upcoming week, we will also be developing a program to find how conserved our output genes are in fruit flies, which are our model organism

No Post

I am taking the biology junior qualifying exam this weekend, so there will be no blog post. The junior qualifying exam is a cumulative exam each student must take their junior year for their major. Each student must pass it in order to be able to move on to writing a thesis their senior year and graduate.

Week 20

I took a pathway that I know pretty well, NMDA-based long term potentiation (the process by which neurons become more sensitive to neurotransmitters in response to glutamatergic activity). I made some positives for both the first part of the pathway, the channel proteins that bind to and Ca2+ associated proteins, and the last part of the pathway, which involves nuclear proteins involved with transcribing growth factors and new channel proteins.

A protein centrally implicated in LTP, CaMKII, was used as the reference ranked 21 out of ~15,000. It’s good, but it could be improved. It might be better if we allowed for more precision.

Upcoming tasks will include further verifications, but will probably be postponed, since both of us are taking the biology junior qualifying exam, which is a cumulative exam that we need to pass to graduate.