Update talk.md

docs/micom/talk.md

@@ -294,7 +294,7 @@ Harcombe et al. 2013, https://doi.org/10.1371/journal.pcbi.1003091
 
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-As noted previosly classical FBA works fairly well when predicting the growth rates of individual bacteria. Here we see the results of a studying that compared empirically measured fluxes with those predicted by FBA across a series of evolved E. coli strains. We see that the predictions agree well with the empirical estimates and the evolved strains are able to achieve growth rates that are 90-95% of the theoretical maximum.
+Classical FBA works fairly well when predicting the growth rates of individual bacteria. Here we see the results of a studying that compared empirically measured fluxes with those predicted by FBA across a series of evolved E. coli strains. We see that the predictions agree well with the empirical estimates and the evolved strains are able to achieve growth rates that are 90-95% of the theoretical maximum.
 
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@@ -311,7 +311,15 @@ Senne de Oliveira Lino et al. 2021, https://doi.org/10.1038/s41467-021-21844-7
 
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+Its when we consider communtities that things start to break down. Classical FBA doesn't do so great here. One of the issues is that given multiple taxa, optimal community biomass may be achieved by various linear combinations of the  growth rates of the individual taxa. That is, there is a non-unique solution space for the growth rates and fluxes. So you might have a solution where the optimal community biomass is achieved by only one organism growing. Additionally, experimental results suggest optimizing community biomass may be a slightly flawed approach, as empiraclly many communities achieve lower overall biomass as diversity increases due to competitive interactions as shown by the figure on the right.
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+<!-- .slide: data-background="var(--primary)" class="dark" -->
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+## Let's return to the models we've built
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+:computer: Let's switch to the notebook!
 
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@@ -321,7 +329,7 @@ Note:
 
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-In practice, getting a community-wide growth rate using classic FBA doesn't work very well. Let's set up an example to illustrate, wherein we have two identical microbes in our community, lets say theyre both e coli, at the exact same abundances. If we know that the maximum community growth is 1, we see that there are actually an infinite number of solutions to this. We could have equal growth rates of 1 for each, which comes out to a community growth rate of 1, based on our definition in the last slide. Alternatively, we could have a growth rate of 2 for the orange one and zero for the blue one. This would still satisfy our maximum community growth rate of 1, despite the fact that 50% of the taxa aren't growing. There is actually an infinite number of solutions to this, represented by this red line in the first graph This isn't good, since this introduces a lot of ambiguity and increases the size of the flux cone to include non-biologically relevant solutions. So that's not what we want. Intuitively, we know that idenitcal strains should grow at the same growth rate. To overcome this, MICOM introduces a regularization technique that reduces the solution space back to a relevant one. If we make the assumption that we mentioned earlier, which is biologically intuitive, that any taxon present in a sample should be able to grow, the regularization strategy should return a solution in which most of the taxa are growing, omitting those terminal solutions in which some taxa aren't growing at all. What's called an L2 regularization scheme actually achieves this well, by minimizing the sum of the squares of the individual growth rates. This basically penalizes really high growth rates, and rather finds a solution along that maximal growth rate line that distributes the growth across as many taxa as possible. Indeed, we see that incorpoating this L2 strategy onto our example here, we end up with a solution in which both taxa are growing at the same rate, minimizing the L2 parameter and matching our intuition. Thinking biologically, though, it also makes sense that for every bacteria in a community to be able to grow, optimal growth rate might not be achieved. An idealistic maximal growth rate might only occur when some bacteria are growing at the expense of others, and the biologically relevant growth rate may be suboptimal, falling below this maximal growth rate. In MICOM, we can model this by incorporating cooperative tradeoff wherein we define the fraction of the maximal community growth rate for which we want to conduct the L2 regularization. In this example we can set a tradeoff of 80% optimal growth, and we see slightly lower growth rates. Methods for choosing a tradeoff parameter is covered at the end of the course notebook, if you are interested.
+This is where cooperative trade off flux balance comes in. This approach is able to generate unique, biologically relevant, solutions to the community growth rate problem posed just a moment ago. Lets try to understand how. First, lets consider the growth curves on the left. As many of us are famililar, bacteria and other organisms typically start at low biomass and low growth rate and increase their biomass until they've consumed all their resources. In doing so, they typically achieve a maximum growth rate somewhere along the way- as shown in the grey region, that eventually returns to zero or close to zero. This growth rate trajectory can be mapped in a growth cone as shown below. Dynamic models typically are able to capture this trajectory while classical FBA can provide a solution somewhere in the optimal region of the growth cone but would not be able to contrain it. ctFBA introduced a biological meaninful contraint by minimizing the distance between the point of zero growth and the theoretical maximum, as shown on the right. This approximates the trajectory expected empiraclly. This constrain is achieved using an L2 style regularization that minimized the sum of the squared growth rates ofthe community. Additionally, ctFBA allows for suboptimal community biomass, which helps balance the tradeoff between individual growth rates with that of community.
 
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@@ -343,7 +351,7 @@ https://doi.org/10.1128/mSystems.00606-19
 
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-The age-old question. Here, we can results from a sample micom community, with the number of taxa growing at various tradeoff values. For reference, any growthrate below 10^-6 is effectively no growth. If we take no regularization step (no L2 parameter minimization), there is a super small number of taxa growing at high growth rate, and nearly all the taxa effectively not growing at all. Obviously, this is not what's actually happening in the microbiome, and this solution is not relevant to the system. If we apply the L2 regularization strategy at the maximal community growth rate, we see that a lot more taxa are able to grow - thats the L2 reguluarization distributing growth across as many taxa as possible. Like I mentioned, though, this maximal growth rate might not be achievable with all taxa growing. Lowering the tradeoff value just a little to 0.7, we see that almost all the taxa are able to grow, echoing what we expect to see in the microbial community. This result by itself statisfies our assumption that taxa present in the sample should be able to grow. The team also validated predicted growth rates by comparing them with actual growth rates. For these data, the team had metagenomes. Its been shown by the Segal lab that coverage profiles of metagenomic reads for fast growing bacteria can be used to estimate the growth rate. You can do this by measuring the decay in read coverage from the origin of replication. Using this method, the team could measure growth rates in vitro, and compare these to growth rates predicted by MICOM. You can see in this panel on the right that without regularization, or at high tradeoff values with regularization, the predicted growth rate did not correlate with calculated growth rate. Lowering the tradeoff value slightly showed a much stronger correlation with calculated growth rate, serving to validate this method. So, in short, cooperative tradeoff with L2 regularization helps us reach a solution wherein most taxa are able to grow, and the growth rates look a lot more like they do in real life.
+The age-old question. Here, we see results from the orignal micom publication validating the ctFBA approach described. On the left we see distributions of individual taxa across a large number of communities and conditions. What we see is that if dont integrate a  regularization step (no L2 parameter minimization), there is a very small number of taxa that can achieve high growth rates, and a majority effectively not growing at all. Obviously, this is not what's actually happening in the microbiome, and this solution is not relevant to the system. If we apply the L2 regularization strategy and require the community to achieve its theoretical maximal growth rate, we see that a lot more taxa are able to grow - that is the L2 reguluarization better distributes growth across the individual communitu members. However, as previously noted, this maximal growth rate might not be achievable with all taxa growing. Lowering the tradeoff value just a little to 0.7, we see that almost all the taxa are able to grow, echoing what we expect to see in the microbial community. This result by itself statisfies our assumption that taxa present in the sample should be able to grow. The team also validated predicted growth rates by comparing them with replication rate, which is generally proportional with growth rate. For these data, the team had metagenomes. Its been shown that coverage profiles of metagenomic reads for fast growing bacteria can be used as a proxy for growth rate. You can do this by measuring the decay in read coverage from the origin of replication. Using this method, the team could estiamte  growth rates in vitro, and compare these to growth rates predicted by MICOM. You can see in this panel on the right that without regularization, or at high tradeoff values with regularization, the predicted growth rate did not correlate with calculated growth rate. Lowering the tradeoff value slightly showed a much stronger correlation with calculated growth rate, thus showing that ctFBA provides a biologically meaninful solution to the community growth rate problem. So, in short, cooperative tradeoff with L2 regularization helps us reach a solution wherein most taxa are able to grow, and the growth rates are a much closer to what you would expect.
 
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@@ -370,13 +378,6 @@ This is a visualization of a standard metagenome-scale metabolic model. Each pin
 
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-## Let's return to the models we've built
-
-:computer: Let's switch to the notebook!
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-<!-- .slide: data-background="var(--primary)" class="dark" -->
-
 ## Before we look at our results...
 
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@@ -393,8 +394,7 @@ Visualize growth rates of individual taxa per sample
 
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-First and foremost, we'll take a look at growth rates of the indivual taxa in each of our models. MICOM has a built in function for this, so it will be very easy to build. Here we have a scatter plot with log scaled growth rate on the y axis, for each taxa on the x axis. This plot is a great way to check that your models are growing correctly at a typical growth rate, like what we see here. It can also tell you which microbes are doing well and have high growth rates in the dietary context you have used to simulate the models. For instance, here we see that prevotella has a high growth rate, and seems to be thriving. We'll see in our results that the growth rates for individual taxa differ quite a bit, since the dietary context has changed. This echoes one of our primary points, which is that the diet is a major factor in the metabolic activity of the microbiome, and it is important to choose a representative diet.
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+First and foremost, we'll take a look at growth rates of the indivual taxa in each of our models. MICOM has a built in function for this, so it will be very easy to build. Here we have a scatter plot with log scaled growth rate on the y axis, for each taxa on the x axis. This plot is a great way to check that your models are growing correctly at a typical growth rate, like what we see here. It can also tell you which microbes are doing well and have high growth rates in the dietary context you have used to simulate the models. For instance, here we see that prevotella has a high growth rate, and seems to be thriving. We'll see in our results that the growth rates for individual taxa can differ quite a bit. This echoes one of our primary points, which is that context is a major factor in the metabolic activity of the microbiome, and it is important to consider.
 
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@@ -407,7 +407,7 @@ The context-dependent way in which a microbial taxon uses its environment
 
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-Next, we'll look at a visualization of the niche space of each taxon in each sample. The niche space represents the context-dependent way in which a taxon uses it's environment - in this case, how it uses the metabolites available to it. Since plotting all the metabolic exchanges wouldn't be possible, we'll use tSNE to make the plot. This technique takes high dimensional data and reduces it to two dimensions, such that similar points are closer together and less similar points are spaced farther apart. This gives us an idea of the metabolic niche each taxon falls into, and how similar or different it is from the other taxa in the community. Like I mentioned, niche space is context dependent. Some taxa change their metabolic behavior depending on what metabolites are present in their environment, allowing them to survive in multiple niche spaces. This adaptation can be helpful for their survival. We will see when comparing the relative positions of taxa between the matched and unmatched dietary contexts, many will change their predicted metabolic behavior and occupy a different niche space, underscoring the need for accurate diets to obtain accurate predictions.
+Next, we'll look at a visualization of the niche space of each taxon in each sample. The niche space represents the context-dependent way in which a taxon uses it's environment - in this case, how it uses the metabolites available to it. Since plotting all the metabolic exchanges wouldn't be possible, we'll use tSNE to make the plot. This technique takes high dimensional data and reduces it to two dimensions, such that similar points are closer together and less similar points are spaced farther apart. This gives us an idea of the metabolic niche each taxon falls into, and how similar or different it is from the other taxa in the community. Like I mentioned, niche space is context dependent. Some taxa change their metabolic behavior depending on what metabolites are present in their environment, allowing them to survive in multiple niche spaces. This adaptation can be helpful for their survival. In example niche plot shown I've used UMAP to accomplish the dimensionality reduction, which is fairly similar to tSNE conceptually. Here I'm shown the results for individual taxa across thousands of samples. Interestingly, what we see is that individual taxa often cluster into one or just a few decrete locations, suggeting the often select from a finite number of metabolic strategies.
 
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@@ -419,7 +419,7 @@ Metabolite exchanges are highly dependent on environmental context and can provi
 
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-Finally, we'll take a look at the metabolic exports predicted from the growth of each metabolic model. As shown here, we'll construct a heatmap illustrating the amount of different metabolites produced and exported from taxa in each sample. In this case, each row represents a metabolite, and each column represents one of our samples, with cells colored in a logarithmic color map. While MICOM does have a built in tool to build heatmaps like the one shown here, we'll use this opportunity to take our output and build a visualization in another package, in this case we will use Seaborn. This will additionally allow us to plot the results of growth on both diets on a single plot. Similar to the niche space, the metabolic activity of any taxon in a community, and therefore its exchanges, is dependent on the context in which it grows - in this case, we'll look at exports from the microbiome between both the matched and unmatched diets we've used for modeling. Since the environmental context in these two growth simulations is so disparate, we expect to see very different exchange fluxes between each of the two media. Again, since we are interested in determining the most biologically relevant set of growth rates and fluxes, correct matching of diet with sample is crucial.
+Finally, we'll take a look at the metabolic imports predicted from the growth of each metabolic model. As shown here, we'll construct a heatmap illustrating the amount of different metabolites produced and exported from taxa in each sample. In this case, each row represents a metabolite, and each column represents one of our samples, with cells colored in a logarithmic color map. While MICOM does have a built in tool to build heatmaps like the one shown here, we'll use this opportunity to take our output and build a visualization in another package, in this case we will use Seaborn. This will additionally allow us to plot the results of growth on both diets on a single plot. Similar to the niche space, the metabolic activity of any taxon in a community, and therefore its exchanges, is dependent on the context in which it grows 
 
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