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• Description on how each Rmulti is calculated in the multi-receptor model.
• The range of concentration
• Maybe indicate the direction of increase in concentration on 3E

We should calculate the likelihood of each receptor expression observation given the model prediction and sigCoef2. Currently the likelihood distribution is being calculated from the data and the model prediction is being used as the observation.

Now that we have most of the pieces together, it would be helpful to create a function that assembles this figure and outputs a PDF.

Setup PCA for dataset at varying concentrations and avidities.

In most immune cells, a high-affinity activating FcgR is paired with expression of a low-affinity inhibitory receptor. Removing the inhibitory receptor often leads to autoimmunity, and a common notion is that the inhibition is important for blocking activation from "incorrect" contexts. With a two-receptor model, we would be able to directly address this for differing immune complex compositions.

Make a plot of experimental binding results vs. the affinities of the receptors.

• The scale of weightings for 4E
• How the fraction was calculated in 4H (might not be necessary)
• Description of 4I (modulating individual receptor affinities), and an avidity legend

We could use a new class file for calculating the binding for the mouse Ig-FcgR pairs. On loading it should load the affinities like StoneMod. Then, given which Ig, the avidity, and the concentration of immune complex, it provides the amount of binding to each FcgR.

This should reuse StoneMod code where possible. It may be helpful to move the StoneMod method outside of the StoneMod class. The same binding model applies, and this function doesn't rely on any member variables, and so it should be possible to reuse.

The last step would be to write a few unit tests for these steps. I.e. check that the affinities were loaded correctly, calculate reasonable binding numbers for a few terms, give proper errors when, for example, negative values are passed as parameters, etc.

Compare the distribution of receptor expression fits to the measured values, to see how well the model fits and if any are wildly divergent. This should involve a plot that visually shows this, as we will want to show the evidence.

With an MCMC chain, we really have an ensemble of predictions more so than a single one. That means that we can provide confidences in our predictions, rather than just a single best fit. In order to assemble these, one needs take the following steps:

1. Assemble predictions for each step in the MCMC chain (map)
2. Combine these into a single large table of predictions
3. Create summary statistics given the large number of observations (reduce)

• Explain what is done in Figure 3H (what the curves mean)
• A legend for the receptors
• Maybe indicate switch from human receptors to murine receptors

We should rigorously show that we can predict antibody efficacy and that we can do better than affinities alone.

Should put together one plot of strictly the A/I ratio vs. efficacy as shown in Nimmerjahn & Ravetch.

Having the figure functions plot on their own is helpful for debugging, but we will also want these to be placed within large figures. Having the functions operate on the axis labels passed to them would enable this.

Alexa pointed out there might be some inconsistencies.

How the activity index is calculated in multi-receptor model

It'd probably be helpful to dig up the murine affinities of each FcgR-IgG pair so that we can map our predictions to effects seen in murine models. The following paper seems to have some of them, but getting the raw values and mapping them to their source may require some digging.

The function of Fcγ receptors in dendritic cells and macrophages

We will need to present a new plot of the data from Anja since this isn't published previously. This can be processed data with the raw data presented in a supplementary table.

These captions don't give an accurate idea of what is being modeled.

It would be helpful to add the IgA, IgD, IgE, and IgM affinities, to the extent that we can find them quantified.

Parallel to binding, we can also plot the inferred crosslinks, receptor bound, etc, of the model.

In looking through a few other papers with FcgR-IgG binding data, the affinities reported vary sometimes more than 10-fold. We should probably find a few sources of Ka values and do a more rigorous comparison of the various sources. These values are really important to the ultimate predictions.

Still needs indication for where the receptors start, and which color is which receptor.

Description for murine PCA and human PCA

After this plot is finished, we should make sure the chain does indeed converge.

Results seem suspicious since there should be considerable inhibitory receptor binding.

This is the output from explained_variance_score, which is usually already calculated. So, it just needs to be placed on the figure.

How the murine affinities PCA was done

Now that we have most of the pieces together, it would be helpful to create a function that assembles this figure and outputs a PDF.

The MCMC chain is a list of parameter sets. It'd be helpful to have a function that collects the model predictions for each parameter set and aggregates these into a large table. From there, these can be manipulated to provide confidence intervals for each prediction.

This function would optionally be made parallel, depending upon how long it takes to make each prediction call.

I'm wondering if, with the murine in vivo modeling, whether we should be keeping the IC or IgG concentration constant.

Now that we have a model that works for predicting effect function, one application would be to vary avidity and look at the predicted metastasis effects for each antibody class.

Cells generally express more than one FcgR type, and so developing a model for how these receptors operate coordinately would be extremely powerful. This will involve a number of steps, starting with going back to the original Perelson manuscript to re-derive the multivalent binding model.