The Systems Biology of COVID-19 and the SARS-CoV-2 virus. The class will build a foundation that includes the emergence of complexity, simple biological subsystems, their reductionist and equivalent toy and organ-chip models, and the measurements required to specify model architecture and parameters. Applications to biology, physiology, medicine, chemical and biological defense, pharmacology, drug discovery, and toxicology. UGrad: PHYS 240 01 and BME 290B; Grad: PHYS 326 and BME 395C.
Chinowsky_TheorSysBio_PCRC_100616
ReplyDelete0. Knew
Admittedly, I have very little experience with anything beyond basic statistics. However, the previous papers have covered GRNs to such an extent that I feel reasonably comfortable with network dynamics and understand the challenges of modeling a genome based network.
1. Learned
This paper covers a vast amount of networking and statistical models that may be useful for gene network modeling. The review starts with concepts of conditional independence models, which covers the range of coexpression networks, where correlation is used to construct a network. This unfortunately cannot account for non-linear gene dependencies, but this can be remedied by use of other functions. Full conditional models differ from coexpression networks by asking the question “can a correlation be explained by all other genes in the model”. A invertible matrix Σ that contains vertices i and j is used to define the Gaussian graphical model (GGM). The inverted matrix is used to show correlation, but only after correcting for the influence of every other gene in the model. However, this type of modeling works best when a large sample size is used compared to the number of variables—something that is difficult to do for genome wide networks. The paper further introduces Bayesian networks, which can be used to build networks for independencies of all orders. The DAG structure used for Bayesian networks does imply ordered variables, and Bayesian networks are inherently acyclic, which is problematic for biology, with appears to be very cyclic. The bottom line is that this paper presents a vast amount of ways to go about network reconstruction, depending on exactly what you are trying to model—this is nicely summed up in Figure 8.
2. Pressing
While this paper presents a lot of very helpful theory, it gives few examples. What are real-life biological instances where one might choose one type of modeling over another?
3. Presentation
Honestly, a presentation on just one of the modeling types presented in this paper would be super helpful.
4. Thoughts
This was a very very dense review paper. I felt like I couldn’t comprehend the full scope of the paper, and would have to read it several more times to even begin to understand all of the nuances presented.
I think a lot of examples can be found in the references. For example, at the end of the section on low-order conditional independence it gives some examples/references for how these ideas can and have been implemented.
DeleteThe paper last week is an example of a network with discrete nodes (discrete in the sense that their probability distributions take a discrete number of different values). In particular, since each gene only had two states (on or off), the probability distribution for each node would consist of P(off) and P(on).
DeleteBen Terrones
ReplyDeleteSysBio16 Asgn_13_Class_13_Article_15_2016_10_06
0. KNEW:
I knew about gene networks and how perturbations are used to study gene interactions. I also knew about coexpression networks and using a threshold to decide if genes are connected. I knew that mutual information is also used to build networks and permutations are used to measure noise and assign significance.
1. LEARNED:
I learned that there are two solutions to assigning dependencies in coexpression networks: Perturbing certain genes to see how that affects other genes or using statistical methods to see which possibility is more likely. I learned about GGM’s and their benefits compared to correlation networks as well as some issues such as using GGM’s in a p>>N scenario. There are also low-order conditional independence models, which ask if the relationship between two genes can be explained by a third gene as opposed to the GGM’s which attempt to explain the relationship using all other genes. The author then discussed Bayesian networks and the related local probability distributions. Overall they go into an incredibly dense discussion of how to create these networks and using known information, how to decide which method to use.
2. PRESSING ?:
There were a couple places in the paper (page 6, large paragraph on page 11) where they mentioned that the statistical methods are sometimes useless without the experimental perturbation data. So I’m wondering why would you not get this experimental data? It seems like it almost always improves the construction of the network. Is it because of the amount of time/work it would take to get this data for a large number of genes? This seems like a really dumb question.
3. PRESENTATION:
I agree with Colbie in that it would be helpful to see an example of one of these models and a walk through of the construction of the network.
4. THOUGHTS:
This paper was difficult to get through because of how dense it was and how unfamiliar I am with the methods discussed.
From my understanding, obtaining perturbation data does bring more understating like you said, but maybe you just don't always need it or are interested in it. Maybe if you just want to construct a network based on conditional independence of some given order without worrying about cause and effect or whether or not an effect is directly or indirectly caused by a change in gene expression of a particular gene. Many of the reasons the authors give for using perturbation data is to determine these things, but there are still other cited examples that have accomplished things without this data. Maybe other people have other views on this though?
DeleteIt turns out that, at least if you construct a network in one of the ways they say to in the paper, you can never fully pick apart causes from effects (see the section called 'Markov equivalence' on pg. 6). This means that a network of relationships (without specifying what caused what) is the best you can do in general---so you need the perturbation data to turn all of those links into arrows.
DeleteStatistical tests can give you an idea about causation, but with absolutely no causation data in your input, they can't tell you much.
Anyway, I think the main reason you might not get perturbation data is that it is practically not feasible to do so for every gene/protein/whatever in your network. Perturbation experiments (where you delete a gene and observe what happens, or upregulate/downregulate a gene by adding some chemical, or mutate a gene so that it is more active) are time-consuming, and very complicated when you're trying to pick apart cause and effect from thousands of moving parts.
Maybe in specific cases it might be easy to figure out a way to get particular kinds of perturbation data. But in general I think it's a tough problem, which is why we're trying to split the burden between causation experimentally and statistically.
0. Knew:
ReplyDeleteI knew about gene expression networks and difficulties in assigning causation in these models. We've discussed some of the statistics used to derive these models, but it was good to get a better understanding of some of the background mathematics (although this was difficult to grasp from reading 1 paper).
1. Learned:
As I mentioned in 0, it was good to get a background of some of the mathematics behind model development. The usefulness of some of the expressions still isn't completely clear to me. I learned that for most of these models, p >> N (this maybe should have occurred to me sooner). Some of these notations were new to me and could be helpful in the future.
2. Pressing ?:
Similar to Ben's question... can you link cause and effect without experimental data? It seems to me that these models lower the amount of data needed, but still need quite a bit, correct?
3. Presentation:
development of structure priors and examples of their applications
4. Thoughts:
Seems like this was not an easy paper to write. They considered a bunch of different modeling techniques that are used.. not sure how they chose what to include and what to leave out. I couldn't grasp all of the expressions, but still think the author's did a good job explaining them in the text. Figure 8 was a good way to tie it all together!
2. Yeah that's my understanding. The statistical models only look at conditional independence which doesn't give a directionality.I could be wrong though.
Delete0. Knew:
ReplyDeleteI knew about coexpression networks from previous papers. I knew about using perturbations to determine dynamic properties of GRN. I have looked a little bit into Bayesian probability, but not in how it relates to Bayesian networks.
1. Learned:
I learned about the many different ways one can infer a cellular network. The paper is mainly divided into two parts. The first part looks at statistical methods (no interventions) for building networks (the left side of figure 8). This includes a large section covering Bayesian networks. Bayesian networks consider all orders of conditional independence, where a random variable X is conditionally independent of Y given Z if “learning” about Y with prior knowledge of Z gives us no new information about X. Some statistical models that are discussed that are simpler than Bayesian networks are full conditional models where all other genes are considered to draw an edge between genes and low (first) order conditional models that only consider a third gene.
The second part pf the paper looks at using interventions, such as perturbations, to gain further insight into how to build networks (the right side of figure 8). The idea is that if we can break it, we can understand it. Perturbation data goes beyond statistical models by distinguishing between cause and effect and between direct and indirect effects. Some of these include ideal/soft interventions, Boolean networks, and nested effects models.
2. Pressing Questions:
When the author discusses cyclic versus acyclic graphs, are cyclic graphs ones that are one giant cycle or just a graph that includes cycles? And going the other way, do acyclic graphs have no cycles at all, or just include sections that are not cycles?
3. Presentation Topic:
I would love a presentation on Bayesian probability theory (I am not sure how in depth John will go into today).
4. Thoughts:
I agree with previous comments: this paper was very dense, but with many read-throughs I think I grasp the main points.
We'll see!
Delete0 Knew
ReplyDeleteI was familiar with many of the concepts from the first half of the paper, including co-expression networks and conditional interdependence, from the papers we've read so far in class. Of note, many of the papers we've read thus far are cited in this review. I had also heard of Bayesian Networks for the first time last week during Eric Horvitz's lecture at VUMC, I wasn't expecting to see them again so soon!
1 Learned
I really appreciated this reviews discussion of and comparison of the various approaches to network inference - in particular it addresses the benefits of each method, the statistical and computational costs of each method, and applications of the methods to real problems in biology.
2 Pressing questions
Many of the decisions around model construction and simplification appear to be statistically or computationally driven. Do biological principals have a role in simplifying model analysis, for instance the decision about whether to regard a variable as continuous (requiring gaussian models) or discrete.
3 Presentation Topics
What are hidden variables? Can we review strong and weak criteron? (Page 3, "comparison to correlation networks")
4 Thoughts
If one of the goals of systems biology is to create a comprehensive map of the molecular interactions in a cell, how can graphical networks from different models be integrated, a la KEGG but without all the citations? If I study beta cell networks and someone else studies B cell networks, can we combine our data sets / models to generate a more robust model of "biology." I would argue this represents a fundamental limitation to systems biology. In molecular biology insights about one transcription factor/gene pair can inform another study, so that each investigator builds upon a collective set of knowledge. In systems-bio, the "standing on the shoulder of giants" seems limited to the model construction, but not the models themselves. What is the goal here? To learn new statistics or to learn new biology?
Biological principles probably do play a role, as they did in the mathematical model we talked about last class; for example, in that paper, gene expression was considered to be binary, because the biological data was mostly expressed in two forms (very high and very low). Having binary gene expression data, of course, simplifies model computations immensely.
DeleteOf course, that may not be the case for some other variable of biological interest---it may turn out the data for it doesn't read either very high or very low. In that case a continuous model is more appropriate.
Hidden variables are things we can't see that may explain relationships between the things we can see. For example, though it could look like two genes are related, the biological reality could be that they are not linked to each other, but instead both to some gene we didn't know about.
That is a good point about integrating different models. I wonder about that too. But it is probably the case that not all models should be integrated---models that are trying to describe different things in principle are unrelated to each other.
My thought is that it is not models that should be integrated, but what you find out from the models. Model A may tell you about the existence of gene A, and model B may tell you about the existence of gene B. Those two genes are new pieces of knowledge, and can be incorporated into new, more accurate models afterward.
So the cycle might look like: Model -> Find something -> Model -> Find something -> etc.
Even though the models are not always the same, you are standing on the shoulders of giants in the sense that you are always informed by the techniques and approaches people have tried before when you are building your model.
0. KNEW
ReplyDeleteI have a small understanding of gene regulatory networks and perturbations and some of the methods to define them, like coexpression networks using the mutual information threshold.
1. LEARNED
A fundamental method of defining networks is the creation of coexpression networks (does not show underlying biological mechanisms). These dependencies can be defined either via perturbations or conducting statistical methods that utilize the concept of conditional independence.
Full conditional dependence models (Markov networks, undirected graphical models) ask, 'can the correlation between two genes be explained by all other genes in the model?' We need to have p (# samples) >> N (# of genes).
Low-order conditional independence models ask, "Can the correlation between two genes be explained by a single third gene?" Nice if the number of samples is smaller than the number of genes.
Much of the rest of the paper is over my head.
2. QUESTIONS
On page three the authors state that 'Full conditional models become especially simple in a Gaussian setting.' Why is that the case?
What is a directed versus undirected graph?
3. PRESENTATION
There's a large amount of linear algebra terminology used in this paper and is inherently utilized in gene regulatory networks. It may be a good idea to cover very basic definitions, such as vector spaces, rank, basis, and eigenvectors.
4. THOUGHTS
A difficult paper to read. I would definitely need to go through this a couple times to get a grasp of the underlying concepts needed to explain the models, especially related to statistics and linear algebra.
I think the simplification they are referring to is saying that vertices are adjacent if kij is not equal to 0 where kij relates to the covariance matrix.
DeleteIn directed graphs the edges are arrows, where in undirected graphs the edges are just lines (no directionality).
Natalie Hawken
ReplyDeleteAsgn 13, Article 15: Inferring cellular networks--a review
0. KNEW
I knew about knock-out experiments and how they are used to determine gene/protein function and connections to other proteins. From previous papers, I knew a bit about pair-wise mutual information, coexpression networks, and Gaussian distributions. I knew how computational limitations create the need for these methods of paring down the data to the most important measures.
1. LEARNED
I learned a lot about dealing with the validity of results. I didn't know that for most of these tests, it would be ideal to have more samples for each gene than the total number of genes, and that this lack of data can lead to statistical errors. I understand the idea behind conditional independence and how different conditions are used to create different models (full conditional models, low-order, Bayesian, etc). I learned how researchers break up the data to pieces to make the calculations smaller via local probability distributions (LPDs) and then can put the pieces back together. I found it interesting how the researchers manipulated the time variable in order to create cyclic networks via the acyclical Bayesian networks. I found it interesting that these networks used previously found connections to increase the speed of computation through using structure priors, search heuristics, etc. I found the idea of "what I cannot break, I do not understand" to be particularly helpful in figuring out why we need to do all of this perturbation experiments.
2. MOST PRESSING QUESTIONS
What is the DAG?
Why are there so many types of LPDs and which ones are the best to use? How does a regression tree differ from a Boolean LPD, or kinetic modelling LPD, etc, etc? (pg 6)
What is overfitting? (pg 7)
What is the marginal likelihood measure and how is it calculated? (pg 7)
3. PRESENTATION TOPICS
I didn’t understand any of the Boolean network stuff (pg 11). How are these networks assembled and how are they different from the other types of networks? How does the "sparse Bayesian regression based on a Gaussian linear model" work and what does that even mean (pg 11)?
A lot of the network methods talk about "learning". What does this mean? How does the network/model learn? What is it learning? (pg 6).
Go over the difference between ideal interventions and soft interventions and discuss the pro/cons of both (pg 12).
4. THOUGHTS
Because this paper went over so many different analysis techniques and didn’t give a lot of examples, I was left more confused and with more questions than when I started. I was talking to my roommate who is a CS major, and she could understand what all of the techniques were, but I don't think I have enough base knowledge to fully get a grasp of this paper. I'm hoping the class discussion will be able to explain all these ideas in a simpler way.
Here are some answers to a few questions. We will probably discuss more in class.
DeleteThe DAG (directed acyclic graph) is your network of genes with connections. It looks like a bunch of dots representing genes, and arrows representing relationships. It is 'directed' because the arrows tell you what causes what.
At the end of the day we're doing modeling, so you can choose whatever probability distributions (LPD) you want as long as they give you reasonable answers. Typically people choose mathematically simple ones (like Gaussian bell curves) since they are easy to work with.
With enough free parameters, a model can fit any data you want. But if you needed 100 parameters to get a fit, your model probably wasn't that good of a fit in the first place. We want to avoid 'overfitting', or only getting a good fit because we have enough free parameters in our model, because that means our model is probably not realistic.
Learning just refers to doing some tests to figure out if two genes should be linked or not. So the way to think about it might be 'learning what your network should look like'.
Class 13. Article 15 F. Markowetz and R. Spang. Inferring cellular networks - a review.
ReplyDelete0. KNEW:
We've been talking about constructing networks for a while, so, morally speaking, we are already intimately familiar with the problem here: how do you construct a biologically faithful network from limited experimental data? I am familiar with Bayesian reasoning and the associated math. I also am familiar with some of the problems one might encounter when doing statistical modeling (overfitting, searching through model space for an appropriate model, incorporating the information you have in the best possible way).
1. LEARNED:
The main thing I learned were Markowetz and Spang's bird's-eye view of how researchers have been reconstructing biological networks. As before, we take some biological data (e.g. microarray data) as an input, and through that try to figure out relationships between different genes/proteins/etc. The basic idea is that we assume correlated (in some way) nodes are related, so we link them up if they pass whatever requirements we have imposed for a link to be reasonable.
The coexpression network idea is the primitive version of this, wherein you take nodes to be connected if the correlation number you compute is higher than some threshold you decide. It can't pick apart causal relationships, which is a problem, of course.
Bayesian networks are a more restrictive (that is, will contain less connections in general) and more refined construction in the same spirit, wherein you say that two nodes should be connected if their correlation cannot be explain by any subset of the other nodes. The technical advantage of them is that you can conceptualize the probability of your nodes taking certain values as a product of the probabilities of the independent sections taking certain values.
Your model can have nodes with continuous or discrete probability distributions depending on what, in that context, is biologically relevant. Discrete and continuous distributions may be freely mixed in the same model.
To choose a good model, you can assign some score to a given model (for example, how closely it fits the data) and search through model space to choose the best one. Since it is computationally difficult in general to comb through all of model space, various tricks (like using structure priors) can be used to restrict your search to reasonable-seeming models.
2. QUESTIONS:
Ben made an interesting point above, which is: why isn't perturbation data being collected? I suspect it is because of the difficulty of running such experiments in general (mutation/deletion genetic experiments, biochemical experiments) when you have a huge network with lots of moving parts.
My question on that front is: how much perturbation data is it reasonable to expect to have when you're constructing a model? And related to that: is there some way to automate these sorts of experiments in particular cases?
3. PRESENTATION:
I will be giving the presentation...so yeah.
4. THOUGHTS:
Once again, it is interesting to see how everybody's different backgrounds play a role. I was really confused before, and now other people are confused.
Sylvia Morrow
ReplyDeleteAsgn13_F. Markowetz and R. Spang. Inferring cellular networks - a review.
0. KNEW: The basics of causal/correlation relationships.
1. LEARNED: A vague idea of the strategies of intervention/perturbation that can determine causal relationships. That there are perturbation data statistical methods that can be used to help with finding the most likely relationships. Correllation matrices look for correlation extremes - highly correlated or not correlated at all. In this context bootstrapping is random sampling with replacements and then finding bootstrap networkds.
2. PRESSING ?:
--the paper says you need p>>N where N is the number of samples. I think I'm misunderstanding what N means because I would think you would want more samples for better statistics?
--how accurate is the idea that "biological data are high-dimensional but sparse" (pg 4)
--Can a biological LPD truly be discrete? Or are some LPDs just well-approximated by discrete functions?
3. PRESENTATION:
--Bayesian networks
4. THOUGHTS: Ran out of time and had to skim some of the math details. It was a bit above my head.
The paper says in most situations p>>N, which is not good for GGNs. So there are other methods mentioned to get around this.
DeleteI think in this paper "sparse" is used in a graph theory context where it means very few edges compared to nodes (which depends on the context). So I think it is accurate to have high dimensional data (many nodes) with a small number of edges compared to that dimensionality, especially in Bayesian networks.
Article 13a
ReplyDeleteInferring cellular networks – a review
0 (Knew): I knew some of the basic probability and statistics terms used in the paper, as well as the basics of various attempted methods of developing quantitative expressions for gene regulation networks, from previous papers.
1 (Learned): I learned about the basics of Bayesian networks, and I was made aware of the incredibly helpful figure, Figure 8. While I can't explain it completely right now, and will need to examine it more closely, it seems to be an incredibly helpful image.
2 (Questions): What is the virtue of the "single third gene" tactic? I'm still lost on this.
3 (Presentation): Basically a 3 slide presentation on every result of Fig. 8.
4 (Comments): Pretty thick, bulky paper.
2. I know one reason for first order conditional independence is that it is computationally favorable since we are looking at three genes at a time instead of all of them. It is also favorable when p>>N, which the paper describes as not good for GGNs in previous sections.
Delete0. KNEW:
ReplyDeleteI was familiar with the general need for creating functional networks of genes. I was familiar with the notation they describe throughout the paper and why they used what they did. I knew about coexpression networks. I knew what pair-wise mutual information is. I knew about cross validation. I knew the independence condition.
1. LEARNED:
I learned about the ideas of time-lag in coexpression networks and differential coexpression. I realized the direct vs indirect correlation problem, although this is pretty obvious. I learned how perturbing can be useful for establishing directions in networks. I learned what Markov networks are.
2. PRESSING ?:
What software packages implement Markov networks?
Does RTA satisfy the N>>p?
3. PRESENTATION:
Use analogies like the one given: “Knowing Z, reading Y is irrelevant for reading X”
4. THOUGHTS:
Easy to read paper except the math really lost me.
0. Knew: I knew about gene regulatory networks from the previous articles and discussions we have had.
ReplyDelete1. Learned: I learned more about conditional dependence and perturbation experiments. I learned about the different conditional dependence models and about the problems they have (the information they leave out, etc). I learned about why Bayesian networks are so useful, but that their major drawback is their acyclicity. I learned about the guilt-by-association heuristic idea.
2. Pressing Questions: I am not too clear on dependency structures and how they differ from coexpression networks (p.2).
If genes don't follow the same regulatory regime, then the guilt-by-association heuristic is dismantled; how is this situation handled? With more or better models (I am sure this is one way).? (p.2)
3. Presentation: Bayesian networks and Markov equivalence
4.Thoughts: For the most part, the explanations in this paper were decent, and the figures were not too confusing. I think the paper makes sense; we are looking to find functions for each gene and to infer cellular networks using different methods. The equations were a little confusing, but I appreciate that the article tried to explain them.
The guilt by association heuristic is partially remedied through these probabilistic and interventional models the paper discusses.
Delete0 Knew
ReplyDeleteFamiliar (as the others noted) with GRNs (goals, challenges and hopefully some of the nuance between) and also Bayesian networks and most of the statistics from a quant finance perspective. It was interesting to see the concepts applied to systems biology
1 Learned
Logic of using Bayesian networks to infer cellular networks (..rather than econometric/financial data)
2 Pressing
How does the structural EM algorithm overcome/attempt to overcome the issue of hidden variables?
3 Presentation
Regularization
Quick run-through of the DAG on n edges equation, and maybe definitions of some of the linear algebra to make sure we're all on the same page for class discussion
4 Thoughts
The paper was dense, but it was nice to see the logic/math behind the concepts we've been discussing recently. I'm interested to see how the course progresses now that we've reached this point. Also really enjoyed the figures in this paper. They conveyed the logic in a more accessible manner than Huang's cell mountain.