```
#' Discriminate between beta-sharing clones and dual-alpha TCR clones (optimized
#' for common clones)
#'
#' \code{dual_top()} distinguishes between clones that share a common beta
#' chain and dual TCR clones with two productive alpha chains. The procedure
#' calculates the likelihood that two (alpha, beta) pairs (with common a beta
#' chain) come from two distinct clones sharing the same beta chain vs the
#' likelihood that the two pairs derive from a dual TCR-alpha clone.
#' A significant difference between the two likelihoods is indicative of a
#' dual alpha clone, and these clones are returned as dual clones.
#'
#' @param alpha Matrix recording which alpha chains appear in each well of the
#' data. See \code{\link{create_data}}.
#' @param beta Matrix recording which beta chains appear in the each well of the
#' data. See \code{\link{create_data}}.
#' @param pair A matrix where each row is a beta/alpha pair, column 1 and 2 are
#' the beta indices, and column 3 and 4 are the alpha indices, and column 5
#' is the proportion of replicates the clone was found in (or equal to -1 if
#' the clone is dual)
#' @param error The mean error "dropped" chain rate due to PCR or sequencing
#' errors.
#' @param numb_cells The number of cells per well in each column of the plates.
#' Should be a vector of 12 elements.
#'
#' @return A matrix of dual-alpha clones, where col 1 and 2 are beta indices of
#' the clone (which should be equal) and col 3 and 4 are alpha indices of the
#' clone (which are different).
#'
#' @export
dual_top <- function(alpha, beta, pair, error, numb_cells) {
number_plates <- nrow(alpha)/96 # number of plates
max_beta <- ncol(beta) # determine maximum beta index
sample_size_well <- numb_cells[, 1] # number of cells per well
numb_sample <- numb_cells[, 2] # number of wells w/ sample size
# Determine the wells with the small sample sizes, which is necessary to
# determine top clone duals properly
small <- which(sample_size_well < 50) # find the sample sizes < 50 cells
if (length(small) == 0 ) return(matrix(nrow = 0, ncol = 3))
if (length(small) > 1) {
if (any(small == 1)) {
small_wells <- c(1:numb_sample[small[1]])
for (i in 2:length(small)) {
j <- small[i]
small_wells <- c(small_wells,
(sum(numb_sample[1:(j-1)]) + 1):sum(numb_sample[1:j])
)
}
} else {
small_wells <- vector()
for (i in 1:length(small)) {
j <- small[i]
small_wells <- c(small_wells,
(sum(numb_sample[1:(j-1)]) + 1):sum(numb_sample[1:j])
)
}
}
} else {
small_wells <- 1:numb_sample[small]
}
# look at only the wells with the small sample size
alpha <- alpha[small_wells, ]
beta <- beta[small_wells, ]
# pre-allocate matrix to record the indices of the candidate dual TCR clones,
# the shared and dual likelihoods, and the estimated frequency of the
# candidate dual
rec <- matrix(nrow = 0, ncol = 6)
colnames(rec) <- c("beta", "alpha1", "alpha2", "shared_LL",
"dual_LL", "dual_freq")
#
freq <- pair
freq <- freq[freq[, 9] > .8,]
freq <- freq[order(freq[, "MLE"], decreasing = TRUE), ]
freq <- freq[!is.na(freq[, "MLE"]), ]
for (clon in 1:max_beta) {
x <- freq[freq[, "beta1"] == clon, , drop = FALSE] # find clones with the beta index
numb_cand <- nrow(x) # find number of alphas associated with beta
if (numb_cand > 1) { # if more than 1 alpha
combos <- utils::combn(numb_cand, 2) # find all combos of pairs
for (ind in 1:ncol(combos)) { # check each combo
ind_beta <- clon
ind_alph1 <- x[combos[1, ind], "alpha1"]
ind_alph2 <- x[combos[2, ind], "alpha1"]
f1 <- x[combos[1, ind], "MLE"] # freq est of beta alpha1
f2 <- x[combos[2, ind], "MLE"] # freq est of beta alpha2
exp_plates <- 0 # expected number of plates
# Determing which wells that contain the clone a clone is counted to be in a
# well if their component chains are found in the same well
sample_size_well <- numb_cells[, 1] # number of cells per well
numb_sample <- numb_cells[, 2] # number of wells w/ sample size
sample_size_well <- sample_size_well[small]
numb_sample <- numb_sample[small]
numb_distinct <- length(sample_size_well)
well_clone <- rep(0, numb_distinct)
well_clone <- matrix(ncol = 5, nrow = numb_distinct)
colnames(well_clone) <- c("ba1", "ba2", "a1a2", "ba1a2", "none")
for (size in 1:numb_distinct) {
ind1 <- cumsum(numb_sample[1:size])[size] - numb_sample[size] + 1
ind2 <- cumsum(numb_sample[1:size])[size]
well_clone[size, "ba1"] <- sum(beta[ind1:ind2, ind_beta] == 1 &
alpha[ind1:ind2, ind_alph1] == 1 &
alpha[ind1:ind2, ind_alph2] == 0)
well_clone[size, "ba2"] <- sum(beta[ind1:ind2, ind_beta] == 1 &
alpha[ind1:ind2, ind_alph1] == 0 &
alpha[ind1:ind2, ind_alph2] == 1)
well_clone[size, "a1a2"] <- sum(beta[ind1:ind2, ind_beta] == 0 &
alpha[ind1:ind2, ind_alph1] == 1 &
alpha[ind1:ind2, ind_alph2] == 1)
well_clone[size, "ba1a2"] <- sum(beta[ind1:ind2, ind_beta] == 1 &
alpha[ind1:ind2, ind_alph1] == 1 &
alpha[ind1:ind2, ind_alph2] == 1)
well_clone[size, "none"] <- numb_sample[size] - sum(well_clone[size, 1:4])
}
binomial_coeff <- list()
for (i in 1:numb_distinct) {
binomial_coeff[[i]] <- choose(sample_size_well[i], 1:sample_size_well[i])
}
multinomial_coeff <- list()
for(i in 1:numb_distinct) {
cells_per_well <- sample_size_well[i]
multi_mat <- matrix(0, nrow = cells_per_well, ncol = cells_per_well)
for (j in 1:(cells_per_well-1)) {
for (k in 1:(cells_per_well - j)) {
# print(c(i, j, k))
multi_mat[j, k] <- multicool::multinom(c(j, k, sample_size_well[i] - j - k),
counts = TRUE)
}
}
multinomial_coeff[[i]] <- multi_mat
}
shared_LL <- dual_discrim_shared_likelihood(f1, f2, .15, numb_wells = well_clone, numb_cells = sample_size_well, binomials = binomial_coeff, multinomials = multinomial_coeff)
dual_LL <- stats::optimize(dual_discrim_dual_likelihood, interval = c(0, .4), err = .15, numb_wells = well_clone,
numb_cells = sample_size_well, binomials = binomial_coeff)
dual_LL_LL <- dual_LL$objective
dual_LL_freq <- dual_LL$minimum
rec <- rbind(rec, c(clon, ind_alph1, ind_alph2, shared_LL, dual_LL_LL, dual_LL_freq))
}
}
}
rec <- as.data.frame(rec)
rec <- dplyr::mutate(rec, diff = shared_LL - dual_LL)
filt_rec <- dplyr::filter(rec, diff > 10)
filt_rec <- dplyr::filter(filt_rec, shared_LL > 40 & shared_LL < 100)
dual_cand <- filt_rec[, c(1, 1:3), drop = FALSE]
names(dual_cand) <- c("beta1", "beta2", "alpha1", "alpha2")
dual_cand
}
```

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