cl <- clustirr(s = tcr_reps, meta = meta, control = list(gmi = 0.7))

3.5.1 Inspect the content of clust_irrs

We can look at the similarity scores between CDR3 sequences of TCR repertoire a. Each row is a pair of CDR3 sequences from the repertoire annotated with the following metrics:

• max_len: length of the longer CDR3 sequence in the pair
• max_clen: length of the longer CDR3 core sequence in the pair
• weight: $\omega$ = BLOSUM62 score of the complete CDR3 alignment
• cweight= $\omega_c$: BLOSUM62 score of CDR3 cores
• nweight = $\bar{\omega}$: normalized weight by max_len
• ncweight = $\bar{\omega}_c$: normalized cweight by max_clen

The results for CDR3$\alpha$ sequence pairs from repertoire a:

kable(head(cl$clust_irrs[["a"]]@clust$CDR3a), digits = 2)

… the same table for CDR3$\beta$ sequence pairs from repertoire a:

kable(head(cl$clust_irrs[["a"]]@clust$CDR3b), digits = 2)

Notice that very similar CDR3$\alpha$ or CDR3$\beta$ pairs have high normalized alignment scores ($\bar{\omega}$). We have similar tables for repertoire b and c. These are used internally to construct graphs in the next step.

3.5.2 Inspect graphs with plot_graph

We can use the function plot_graph for interactive visualization of relatively small graphs.

The function clust_irr performs automatic annotation of TCR clones based on multiple databases (DBs), including: VDJdb, TCR3d, McPAS-TCR. Each TCR clone recieves two types of annotations (per chain and per database):

• Ag_species: the name of the antigen species recognized by the clone’s CDR3

• Ag_gene: the name of the antigen gene recognized by clone’s CDR3

Hence, in the plot we can highlight TCR clones that recognize certain antigenic species or genes (see dropdown menu), or use the hoovering function to look at the CDR3 sequences of nodes.

Do this now!

plot_graph(cl, select_by = "Ag_species", as_visnet = TRUE)

Notice that even in this small case study–where each TCR repertoire contains only 500 TCR clones–we observe that the joint graph is complex! This complexity makes qualitative analyses impractical. To address this, ClustIRR focuses on quantitative analyses (see the next steps).

3.5.3 You can evaluate $J$ with igraph

We can use igraph functions to inspect various properties of the graph in cl$graph. For instance, below, we extract the edge attributes and visualize the distributions of the edge attributes ncweight and nweight for all CDR3$\alpha$ and CDR3$\beta$ sequence pairs.

# data.frame of edges and their attributes
e <- igraph::as_data_frame(x = cl$graph, what = "edges")

ggplot(data = e)+
  geom_density(aes(ncweight, col = chain))+
  geom_density(aes(nweight, col = chain), linetype = "dashed")+
  xlab(label = "edge weight (solid = ncweight, dashed = nweight)")+
  theme(legend.position = "top")

Can you guess why we observe trimodal distributions?

• Top mode: weights of identical CDR3 sequence pairs from the different TCR repertoires

• Middle mode: weights of CDR3 sequences with same lengths

• Bottom mode: weights of CDR3 sequences with different lengths -> scores penalized by gap cost

gcd <- detect_communities(graph = cl$graph, 
                          algorithm = "leiden",
                          metric = "average",
                          resolution = 1,
                          iterations = 100,
                          weight = "ncweight",
                          chains = c("CDR3a", "CDR3b"))

3.6.1 Inspecting the outputs of detect_communities

The function detect_communities generates a complex output. Lets investigate its elements:

names(gcd)

[1] "community_occupancy_matrix" "community_summary"         
[3] "node_summary"               "graph"                     
[5] "graph_structure_quality"    "input_config"              

The main element is community_occupancy_matrix, which contains the number of T-cells in each community (row) and repertoire (column). Here we have three repertoires (three columns) and about 260 communities. This matrix is the main input of the function dco (step 5.), to detect differences in the community occupancy between repertoires.

dim(gcd$community_occupancy_matrix)

[1] 261   3

head(gcd$community_occupancy_matrix)

   a  b  c
1 10 10 10
2  2  2  2
3  2  2  2
4  5  7  9
5 28 31 34
6  5  5  5

3.6.2 Visualizing community abundance matrices with get_honeycombs

honeycomb <- get_honeycombs(com = gcd$community_occupancy_matrix)

In the honeycomb plots shown below, several communities (black dots) appear far from the diagonal. This indicates that these communities contain more cells in repertoires b and c (y-axes in panels A and B) compared to repertoire a (x-axes in panels A and B). Meanwhile, the same points are generally close to the diagonal in panel C but remain slightly more abundant in repertoire c (y-axis) compared to b (x-axis).

In step 5, ClustIRR will provide a quantitative answer to the question: Which communities are differentially abundant between pairs of repertoires?

Importantly, the color of the hexagons encodes the density of communities in the 2D scatterplots: dark hexagons indicate high a frequency of communities, while light hexagons represent sparsely populated regions.

wrap_plots(honeycomb, nrow = 1)+
    plot_annotation(tag_levels = 'A')

Also see community_summary. In the data.frame wide we provide community summaries in each community across all TCR repertoires, including:

• clones_a, clone_b, clone_c, clones_n: the frequency of clones in the community coming from repertoire a, b, c and in total (n)
• cells_a, cells_b, cells_c, cells_n: the frequency of cell in the community coming from repertoires a, b, c and in total (n)
• w: average inter-clone similarity
• ncweight_CDR3a/b, nweight_CDR3a/b: raw and normalized similarity for CDR3$\alpha$ and CDR3$\beta$ sequences
• n_CDR3a, n_CDR3b: number of edges between CDR3$\alpha$ and CDR3$\beta$ sequences

kable(head(gcd$community_summary$wide), digits = 1, row.names = FALSE)

In the data.frame tall we provide community and repertoire summaries in each row.

kable(head(gcd$community_summary$tall), digits = 1, row.names = FALSE)

Node-specific (TCR clone-specific) summaries are provided in node_summary

kable(head(gcd$node_summary), digits = 1, row.names = FALSE)

3.6.3 Special functions: decoding communities with decode_community

Community with ID=8 contains 42 TCR clones. These are connected based on their CDR3$\beta$ sequences.

ns_com_8 <- gcd$node_summary[gcd$node_summary$community == 8, ]

table(ns_com_8$sample)

 a  b  c 
14 14 14 

We can extract it and visualize it using igraph:

par(mai = c(0,0,0,0))
plot(subgraph(graph = gcd$graph, vids = which(V(gcd$graph)$community == 8)))

Furthermore, we can “decompose” this graph using decode_community based on the attributes of the edges (edge_filter) and nodes (node_filter).

# we can pick from these edge attributes
edge_attr_names(graph = gcd$graph)

[1] "nweight"  "ncweight" "chain"    "w"       

The following edge-filter will instruct ClustIRR to keep edges with with edge attributes: nweight $>=$ 8 AND ncweight $>=$ 8

edge_filter <- rbind(data.frame(name = "nweight", value = 8, operation = ">="),
                     data.frame(name = "ncweight", value = 8, operation = ">="))

# we can pick from these node attributes
vertex_attr_names(graph = gcd$graph)

 [1] "name"             "clone_id"         "Ag_gene"          "Ag_species"      
 [5] "info_tcr3d_CDR3a" "db_tcr3d_CDR3a"   "info_tcr3d_CDR3b" "db_tcr3d_CDR3b"  
 [9] "info_mcpas_CDR3a" "db_mcpas_CDR3a"   "info_mcpas_CDR3b" "db_mcpas_CDR3b"  
[13] "info_vdjdb_CDR3a" "db_vdjdb_CDR3a"   "info_vdjdb_CDR3b" "db_vdjdb_CDR3b"  
[17] "clone_size"       "sample"           "CDR3b"            "CDR3a"           
[21] "cell"             "HLA_A"            "age"              "TRAV"            
[25] "TRAJ"             "TRBV"             "TRBJ"             "id"              
[29] "community"       

The following node-filter will instruct ClustIRR to retain edges between nodes that have shared node attributed with respect to ALL of the following node attributes:

node_filter <- data.frame(name = c("TRBV", "TRAV"))

c8 <- decode_communities(community_id = 8, 
                         graph = gcd$graph,
                         edge_filter = edge_filter,
                         node_filter = node_filter)

par(mar = c(0, 0, 0, 0))
plot(c8$community, vertex.size = 10)

kable(as_data_frame(x = c8$community, what = "vertices")
      [, c("name", "component_id", "CDR3b", "TRBV", 
           "TRBJ", "CDR3a", "TRAV", "TRAJ")],
      row.names = FALSE)

… or we can summarize the properties of each component in the next table as rows with:

• component id, community id (=8 in this example because this is what we selected)
• mean edge weights (for all core and complete CDR3 pairs)
• number of nodes, number of edges and expected number edges if the component were a clique
• diameter of the component

kable(c8$component_stats, row.names = FALSE)

3.8.1 Visualizing the distribution of $\beta$ with get_beta_violins

beta_violins <- get_beta_violins(node_summary = gcd$node_summary,
                                 beta = d$posterior_summary$beta,
                                 ag_species = NULL,
                                 db = "vdjdb",
                                 db_dist = 0,
                                 chain = "both")

beta_violins$violins

[[1]]

3.8.2 Compare $\beta$s of clones specific for CMV, EBV, flu or MLANA?

beta_violins <- get_beta_violins(node_summary = gcd$node_summary,
                                 beta = d$posterior_summary$beta,
                                 ag_species = c("CMV", "EBV", "Influenza"),
                                 ag_genes = c("MLANA"),
                                 db = "vdjdb",
                                 db_dist = 0,
                                 chain = "both")

patchwork::wrap_plots(beta_violins$violins, ncol = 2)

3.8.3 Compare $\beta$ between repertoires with get_beta_scatterplot

beta_scatterplots <- get_beta_scatterplot(node_summary = gcd$node_summary,
                                          beta = d$posterior_summary$beta,
                                          ag_species = c("CMV"),
                                          db = "vdjdb",
                                          db_dist = 0,
                                          chain = "both")

patchwork::wrap_plots(beta_scatterplots$scatterplots[[1]], ncol = 3)

3.8.4 Posterior predictive checks

Before we can start interpreting the model results, we have to make sure that the model is valid. One standard approach is to check whether our model can retrodict the observed data (community occupancy matrix) which was used to fit model parameters.

General idea of posterior predictive checks:

1. fit model based on data $y$
2. simulate new data $\hat{y}$
3. compare $y$ and $\hat{y}$

ClustIRR provides $y$ and $\hat{y}$ of each repertoire, which we can visualize with ggplot:

ggplot(data = d$posterior_summary$y_hat)+
  facet_wrap(facets = ~sample, nrow = 1, scales = "free")+
  geom_abline(intercept = 0, slope = 1, linetype = "dashed", col = "gray")+
  geom_errorbar(aes(x = y_obs, y = mean, ymin = L95, ymax = H95),
                col = "darkgray", width=0)+
  geom_point(aes(x = y_obs, y = mean), size = 0.8)+
  xlab(label = "observed y")+
  ylab(label = "predicted y (and 95% HDI)")

3.8.5 Differential community abundance results $\rightarrow$ par. $\delta$

Given two repertoires, $a$ and $b$, we can quantify the differential community occupancy (DCO):

$$\begin{align} \delta^{a-b}_i = \beta^a_i - \beta^b_i \end{align}$$

Importantly, ClustIRR always computes both contrasts ($a$ vs. $b$ and $b$ vs. $a$): $\delta^{a-b}_i$ and $\delta^{b-a}_i$.

ggplot(data = d$posterior_summary$delta)+
    facet_wrap(facets = ~contrast, ncol = 2)+
    geom_errorbar(aes(x = community, y = mean, ymin = L95, ymax = H95), 
                  col = "lightgray", width = 0)+
    geom_point(aes(x = community, y = mean), shape = 21, fill = "black", 
               stroke = 0.4, col = "white", size = 1.25)+
    theme(legend.position = "top")+
    ylab(label = expression(delta))+
    scale_x_continuous(expand = c(0,0))

Given two repertoires, $a$ and $b$, ClustIRR also quantifies absolute differences in community probabilities:

$$\begin{align} \epsilon^{a-b} = \mathrm{softmax}(\alpha + \beta^a) - \mathrm{softmax}(\alpha + \beta^b) \end{align}$$

Again, both contrasts are computed: $\epsilon^{a-b}_i$ and $\epsilon^{b-a}_i$.

ggplot(data = d$posterior_summary$epsilon)+
    facet_wrap(facets = ~contrast, ncol = 2)+
    geom_errorbar(aes(x = community, y = mean, ymin = L95, ymax = H95), 
                  col = "lightgray", width = 0)+
    geom_point(aes(x = community, y = mean), shape = 21, fill = "black", 
               stroke = 0.4, col = "white", size = 1.25)+
    theme(legend.position = "top")+
    ylab(label = expression(epsilon))+
    scale_x_continuous(expand = c(0,0))