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Cell-size conventions for a single-cell reference

Source: R/01_02_single_cell_generate_synthetic_networks.R
rescale_single_cell_moments.Rd

Turns nonnegative gene-by-cell-type moments into the reference used by the single-cell mixture. Column \(j\) of the supplied mean, of total \(s_{0j}=\mathbf{1}^{\top}\boldsymbol{\mu}_{\cdot j}\), is normalised to a composition \(\boldsymbol{\theta}_{\cdot j}=\boldsymbol{\mu}_{\cdot j}/s_{0j}\), and its covariance to the per-transcript covariance \(\boldsymbol{\Sigma}^{\theta}_{j}=\boldsymbol{\Sigma}_j/s_{0j}^{2}\). A cell of size \(S_j\) is \(S_j\) times a unit cell in every gene, so the generator draws cells from \(\mathcal{N}(S_j\boldsymbol{\theta}_{\cdot j}, S_j^{2}\boldsymbol{\Sigma}^{\theta}_{j})\): the size enters the mean linearly and the covariance quadratically, and the overlap between two types of equal size does not depend on that size. Two conventions are available for the fit; the default is the raw-covariance, cell-fraction model of the article.

  • cellular_raw (default). Mean \(\tilde{\boldsymbol{\mu}}_{\cdot j}=S_j\boldsymbol{\theta}_{\cdot j}\) and covariance \(S_j^{2}\boldsymbol{\Sigma}^{\theta}_{j}\), the generator itself. Keeping \(S_j\) in the mean makes the fitted composition a cell fraction, not a transcript fraction.

  • transcript_raw. Library-normalised mean \(\boldsymbol{\theta}_{\cdot j}\) and covariance \(S_j\boldsymbol{\Sigma}^{\theta}_{j}\): dividing the bulk by its scale leaves the covariance \(\propto\sum_j q_j S_j\boldsymbol{\Sigma}^{\theta}_{j}\) in the transcript fractions \(\boldsymbol{q}\), which is the fitted composition. The physical generator is still the cellular model: generative_mean and generative_sigma are the moments simulate_bulk_from_cells() should draw from.

Usage

rescale_single_cell_moments(
  moments,
  cell_size,
  reference = c("cellular_raw", "transcript_raw")
)

Arguments

moments

List with mean_profiles (\(G\times J\)) and covariance_matrices (\(G\times G\times J\)), as returned by simulate_hierarchical_grn_moments() with nonnegative = TRUE.

cell_size

Positive cell sizes \(S_j\). A scalar is repeated once per cell type. For two types the scenarios use \((1, 1)\) and \((1, 5)\); \((1, 2, 5)\) is the same idea for three types.

reference

cellular_raw or transcript_raw.

Value

A list with the matrices passed to the estimator (mean_signature_matrix, Sigma), the cellular generator (generative_mean, generative_sigma), cell_size, composition (\(\boldsymbol{\theta}\)), reference and estimand ("cellular" or "transcript").

See also

simulate_hierarchical_grn_moments(), simulate_bulk_from_cells(), single_cell_scenario_design()

Examples

mu <- cbind(c(2, 2, 0, 0), c(0, 0, 1, 1))
sigma <- array(rep(diag(4), 2), dim = c(4, 4, 2))
moments <- list(mean_profiles = mu, covariance_matrices = sigma)
ref <- rescale_single_cell_moments(moments, c(1, 5))
colSums(ref$generative_mean)
#> [1] 1 5