Text

manuscripts/03.results.md

@@ -2,11 +2,15 @@
 
 ### Profiling the binding effects of mixed-composition immune complexes
 
-To determine the effect of having multiple Fc forms present within an immune complex (IC), we started with a controlled and simplified _in vitro_ system. Like in previous work, we employed a panel of CHO cell lines expressing one of six individual hFcγRs [@pmid:23509345; @pmid:29960887]. ICs were formed by immobilizing anti-2,4,6-trinitrophenol (TNP) IgG on BSA-TNP complexes having an average valency of 4 or 33 (Fig. {@fig:mixBind}A). Binding was then quantified after incubation with the cells, using a constant IC concentration of 1 nM. Unlike our previous work using a single IgG isotype, we assembled ICs from mixtures of hIgG isotypes. Combinations of hFcγRs, IgG mixtures, and valency resulted in XXX distinct experimental conditions.
+To determine the effect of having multiple Fc forms present within an immune complex (IC), we started with a controlled and simplified _in vitro_ system. Like in previous work, we employed a panel of CHO cell lines expressing one of six individual hFcγRs [@pmid:23509345; @pmid:29960887]. ICs were formed by immobilizing anti-2,4,6-trinitrophenol (TNP) IgG on BSA-TNP complexes having an average valency of 4 or 33 (Fig. {@fig:mixBind}A). Binding was then quantified after incubation with the cells, using a constant IC concentration of 1 nM. Unlike our previous work using a single IgG isotype, we assembled ICs from mixtures of each pair of hIgG isotype. Combinations of hFcγRs, IgG pairs, and valency resulted in 72 distinct experimental conditions (Fig. {@fig:S1}).
 
 Inspection of the resulting binding data revealed several expected patterns. Among the conditions with only one IgG present, a strong correlation exists between binding amount and the affinity of IgG-FcγR interaction [@pmid:19018092] (Fig. {@fig:mixBind}). The higher valency ICs universally showed greater binding signal compared to their matching lower-valency counterparts (Fig. {@fig:mixBind}). Finally, mixtures between isotype extremes showed a monotonic shift with composition (Fig. {@fig:mixBind}). These patterns, along with their reproducibility (Fig. {@fig:mixBind}), gave us confidence in the quality of the binding measurements.
 
-A few unexpected trends were observed among the binding measurements as well. We observed appreciable binding from IgG2-FcγRI interactions, despite this combination being reported as non-binding [@pmid:19018092] (Fig. {@fig:mixBind}). Similarly, we saw an increase in binding with transition from IgG4 to IgG1 with FcγRIIIA-158F, even though these two isotypes are documented to have identical affinity [@pmid:19018092] (Fig. {@fig:mixBind}). These two observations are consistent with our completely independent, previous binding measurements using this same system [@pmid:29960887]. Each of the affinities involved is very weak, and avidity is a well-known strategy to quantify weak interactions more robustly. Therefore, these binding patterns likely reflect differences in affinity that could not be accurately quantified due to their weak interactions in monovalent form [@pmid:19018092]. In all, these data support that a TNP-based IC system provides a controlled _in vitro_ system in which we can profile the effects of mixed IC composition on binding to effector cell populations.
+A few unexpected trends were observed among the binding measurements as well. We observed appreciable binding from IgG2-FcγRI interactions, despite this combination being reported as non-binding [@pmid:19018092] (Fig. {@fig:mixBind}). Similarly, we saw an increase in binding with transition from IgG4 to IgG1 with FcγRIIIA-158F, even though these two isotypes are documented to have identical affinity [@pmid:19018092] (Fig. {@fig:mixBind}b). These two observations are consistent with our completely independent, previous binding measurements using this same system [@pmid:29960887]. Each of the affinities involved is very weak, and avidity is a well-known strategy to quantify weak interactions more robustly. Therefore, these binding patterns likely reflect differences in affinity that could not be accurately quantified due to their weak interactions in monovalent form [@pmid:19018092]. 
+
+To better visualize the binding measurements, we performed principal component analysis (PCA), with each IgG dose given the isotype mixture and valency as a sample and each receptor as a feature, and technical replicates averaged. We found that two components can explain almost 90% of the variance (Fig. {@fig:mixBind}f). 
+
+In all, these data support that a TNP-based IC system provides a controlled _in vitro_ system in which we can profile the effects of mixed IC composition on binding to effector cell populations.
 
 ![**Experimental IC mixture binding data** a-r) Quantification of hIgG subclass TNP-4-BSA and TNP-33-BSA IC binding to CHO cells expressing the indicated hFcγRs. Relative fluorescent units (RFU) of different multivalent immune complexes consisting of various IgG mixtures binding to different human immune cell receptors;](figure1.svg "Figure 1"){#fig:mixBind width="100%"}
 

manuscripts/06.methods.md

@@ -6,7 +6,7 @@ All analysis was implemented in Julia, and can be found at <https://github.com/m
 
 ### Generalized multi-ligand, multi-receptor multivalent binding model
 
-To model polyclonal antibody immune complexes (ICs), we extended our previous binding model to account for ICs of mixed IgG composition [@pmid:29960887].
+To model polyclonal antibody immune complexes (ICs), we employed a multivalent binding model to account for ICs of mixed IgG composition [@pmid:29960887; @DOI:10.1101/2021.03.10.434776].
 
 We define $N_L$ as the number of distinct monomer Fcs, $N_R$ the number of FcRs, and the association constant of monovalent Fc-FcR binding between Fc $i$ and FcR $j$ as $K_{a,ij}$. Multivalent binding interactions after the initial interaction have an association constant of $K_x^* K_{a,ij}$, proportional to their corresponding monovalent affinity. The concentration of complexes is $L_0$, and the complexes consist of random ligand monomer assortments according to their relative proportion. The proportion of ligand $i$ in all monomers is $C_i$. By this setup, we know $\sum_{i=1}^{N_L} C_i = 1$. $R_{\mathrm{tot},i}$ is the total number of receptor $i$ expressed on the cell surface, and $R_{\mathrm{eq},i}$ the number of unbound receptors $i$ on a cell at the equilibrium state during the ligand complex-receptor interaction.
 

manuscripts/80.supplement.md

@@ -2,8 +2,8 @@
 
 Add supplemental figures.
 
-![Supplemental figure 1](figureS1.svg "Figure S1"){#fig:S1 width="100%"}
+![**Experimental IC mixture binding data** Quantification of hIgG subclass TNP-4-BSA and TNP-33-BSA IC binding to CHO cells expressing the indicated hFcγRs. Relative fluorescent units (RFU) of different multivalent immune complexes consisting of various IgG mixtures binding to different human immune cell receptors.](figureS1.svg "Figure S1"){#fig:S1 width="100%" tag="S1"}
 
-![Supplemental figure 2](figureS2.svg "Figure S2"){#fig:S2 width="100%"}
+![Supplemental figure 2](figureS2.svg "Figure S2"){#fig:S2 width="100%" tag="S2"}
 <div id="refs"></div>
 

src/figures/figure1.jl

@@ -112,6 +112,7 @@ function figure1()
     score_plot = plot_PCA_score(score_df)
     loading_plot = plot(loading_df, x = "PC 1", y = "PC 2", color = "Cell", label = "Cell", Geom.point, Geom.label, Guide.title("Loading"))
 
-    pl = plotGrid((2, 4), [nothing, pl1, pl2, pl3, nothing, vars, score_plot, loading_plot]; widths = [1 1 1 1; 1 0.8 1.1 1.1])
+    pl = plotGrid((2, 4), [nothing, pl1, pl2, pl3, nothing, vars, score_plot, loading_plot]; widths = [1 1 1 1; 1 0.8 1.1 1.1],
+        sublabels = [1 1 1 1 0 1 1 1])
     return draw(SVG("figure1.svg", 18inch, 8inch), pl)
 end

src/figures/figureCommon.jl

@@ -26,7 +26,7 @@ function setGadflyTheme()
 end
 
 
-function plotGrid(grid_dim = (1, 1), pls = [], ptitle = nothing; widths = [], heights = [], sublabel = true)
+function plotGrid(grid_dim = (1, 1), pls = [], ptitle = nothing; widths = [], heights = [], sublabels = true)
     @assert length(grid_dim) == 2
     nplots = prod(grid_dim)
     if length(pls) != nplots
@@ -54,6 +54,15 @@ function plotGrid(grid_dim = (1, 1), pls = [], ptitle = nothing; widths = [], he
         grid[i] = Vector{Union{Plot, Compose.Context}}(fill(context(), grid_dim[2]))
     end
 
+    if sublabels == true
+        sublabels = ones(nplots)
+    elseif sublabels == false
+        sublabels = zeros(nplots)
+    else
+        @assert length(sublabels) == nplots
+    end
+    sublabels = sublabels .> 0
+
     for i = 1:nplots
         xi = (i - 1) % grid_dim[2] + 1
         yi = (i - 1) ÷ grid_dim[2] + 1
@@ -63,7 +72,7 @@ function plotGrid(grid_dim = (1, 1), pls = [], ptitle = nothing; widths = [], he
                     context(0, 0, widths[yi, xi], 1),
                     (
                         context(),
-                        text(0.0, 0.0, sublabel ? 'a' - 1 + i : "", hleft, vtop),
+                        text(0.0, 0.0, sublabels[i] ? 'a' - 1 + i : "", hleft, vtop),
                         font("Helvetica-Bold"),
                         fontsize(30pt),
                         fill(colorant"black"),
@@ -74,7 +83,7 @@ function plotGrid(grid_dim = (1, 1), pls = [], ptitle = nothing; widths = [], he
                     context(0, 0, widths[yi, xi], 1),
                     (
                         context(),
-                        text(0.0, 0.0, sublabel ? 'a' - 1 + i : "", hleft, vtop),
+                        text(0.0, 0.0, sublabels[i] ? 'a' - 1 + i : "", hleft, vtop),
                         font("Helvetica-Bold"),
                         fontsize(30pt),
                         fill(colorant"black"),

src/mixture.jl

@@ -68,7 +68,7 @@ function plotMixSubplots(splot::Function, df = loadMixData(); avg = false, kwarg
             pls[(j - 1) * lpairs + (i - 1) + 1] = splot(ndf; kwargs...)
         end
     end
-    return plotGrid((lcells, lpairs), pls; sublabel = false)
+    return plotGrid((lcells, lpairs), pls; sublabels = false)
 
 end