• scLANE
  • Installation
  • Model structure
• Usage
  • Libraries
  • Input data
  • Trajectory DE testing
  • Downstream analysis & visualization
• Conclusions & best practices
• Contact information
• References

scLANE

Installation

You can install the most recent version of scLANE using:

remotes::install_github("jr-leary7/scLANE")

Model structure

The scLANE package enables users to accurately determine differential expression of genes over pseudotime or latent time, and to characterize gene’s dynamics using interpretable model coefficients. scLANE builds upon the marge modeling framework(GitHub, paper), allowing users to characterize their trajectory’s effects on gene expression using negative binomial GLMs, GEEs, or GLMMs depending on the experimental design & biological questions of interest. This modeling framework is an extension of the Multivariate Adapative Regression Splines (MARS) method, which builds nonlinear models out of piecewise linear components. scLANE is agnostic with respect to the ordering estimation method used, and can be implemented downstream of any pseudotime or RNA velocity method.

A quickstart guide on how to use scLANE with simulated data continues below, and a more detailed vignette showcasing its performance on real data can be found here.

Usage

Our method relies on a relatively simple test in order to define whether a given gene is differentially expressed (or “dynamic”) over the provided trajectory. While the exact structure of the test differs by model mode, the concept is the same: the spline-based NB GLM / GEE / GLMM is treated as the alternate model, and a null model is fit using the corresponding model mode. If the GLM mode is used, then the null model is simply an intercept-only NB GLM; the GEE mode fits an intercept-only model with the same working correlation structure as the alternate model, and if the GLMM mode is used then the null model is an intercept-only model with random intercepts for each subject. The alternate hypothesis is that at least one of the estimated coefficients is significantly different from zero. We predict a given gene to be dynamic if the adjusted p-value of the test is less than the default $\alpha = 0.01$ threshold, and classify it as static otherwise.

Libraries

library(dplyr)
library(scLANE)
library(ggplot2)

Input data

We read a previously-simulated dataset comprised of cells from 3 subjects exhibiting a homogeneous trajectory structure from the Zenodo repository. The underlying true pseudotime values are stored in the colData slot of the SingleCellExperiment object under the name cell_time_normed.

sim_data <- readRDS(url("https://zenodo.org/records/8433077/files/scLANE_sim_data.Rds"))

The PCA embeddings show us a pretty simple trajectory that’s strongly correlated with the first principal component.

data.frame(sim_data@int_colData$reducedDims@listData$PCA[, 1:2]) %>% 
  mutate(pseudotime = sim_data$cell_time_normed) %>% 
  ggplot(aes(x = PC1, y = PC2, color = pseudotime)) + 
  geom_point(size = 2, alpha = 0.75, stroke = 0) + 
  scale_color_gradientn(colors = viridisLite::plasma(n = 20)) + 
  labs(x = "PC 1", y = "PC 2", color = "Pseudotime") + 
  theme_scLANE(umap = TRUE)

We also see that the data are not clustered by subject, which indicates that gene dynamics are mostly homogeneous across subjects.

data.frame(sim_data@int_colData$reducedDims@listData$PCA[, 1:2]) %>% 
  mutate(subject = sim_data$subject) %>% 
  ggplot(aes(x = PC1, y = PC2, color = subject)) + 
  geom_point(size = 2, alpha = 0.75, stroke = 0) + 
  labs(x = "PC 1", y = "PC 2", color = "Subject ID") + 
  theme_scLANE(umap = TRUE)

Trajectory DE testing

Since we have multi-subject data, we can use any of the three model modes to run our DE testing. We’ll start with the simplest model, the GLM, then work our way through the other options in order of increasing complexity. We first prepare our inputs - a dataframe containing our cell ordering, a set of genes to build models for, and a vector of per-cell size factors to be used as offsets during estimation. In reality, it’s usually unnecessary to fit a model for every single gene in a dataset, as trajectories are usually estimated using a subset of the entire set of genes (usually a few thousand most highly variable genes). For the purpose of demonstration, we’ll select 50 genes each from the dynamic and non-dynamic populations.

Note: In this case we’re working with a single pseudotime lineage, though in real datasets several lineages often exist; in order to fit models for a subset of lineages simply remove the corresponding columns from the cell ordering dataframe passed as input to testDynamic().

set.seed(312)
gene_sample <- c(sample(rownames(sim_data)[rowData(sim_data)$geneStatus_overall == "Dynamic"], size = 50), 
                 sample(rownames(sim_data)[rowData(sim_data)$geneStatus_overall == "NotDynamic"], size = 50))
order_df <- data.frame(X = sim_data$cell_time_normed)
cell_offset <- createCellOffset(sim_data)

GLM mode

Running testDynamic() provides us with a nested list containing model output & DE test results for each gene over each pseudotime / latent time lineage. In this case, since we have a true cell ordering we only have one lineage. Parallel processing is turned on by default, and we use 4 cores here to speed up runtime.

scLANE_models_glm <- testDynamic(sim_data, 
                                 pt = order_df, 
                                 genes = gene_sample, 
                                 size.factor.offset = cell_offset, 
                                 n.cores = 4L, 
                                 verbose = FALSE)
#> Registered S3 method overwritten by 'bit':
#>   method   from  
#>   print.ri gamlss
#> scLANE testing completed for 100 genes across 1 lineage in 19.707 secs

After the function finishes running, we use getResultsDE() to generate a sorted table of DE test results, with one row for each gene & lineage. The GLM mode uses a simple likelihood ratio test to compare the null & alternate models, with the test statistic assumed to be asymptotically Chi-squared distributed.

scLANE_res_glm <- getResultsDE(scLANE_models_glm)
select(scLANE_res_glm, Gene, Lineage, Test_Stat, P_Val, P_Val_Adj, Gene_Dynamic_Overall) %>% 
  slice_sample(n = 5) %>% 
  knitr::kable(format = "pipe", 
               digits = 3, 
               col.names = c("Gene", "Lineage", "LRT stat.", "P-value", "Adj. p-value", "Predicted dynamic status"))

Gene	Lineage	LRT stat.	P-value	Adj. p-value	Predicted dynamic status
MFSD2B	A	216.750	0.000	0.000	1
TTC5	A	5.481	0.019	0.346	0
SMG1	A	8.736	0.013	0.254	0
TMCO3	A	167.311	0.000	0.000	1
FOXD3	A	4.282	0.039	0.475	0

GEE mode

The function call is essentially the same when using the GLM mode, with the exception of needing to provide a sorted vector of subject IDs & a desired correlation structure. We also need to flip the is.gee flag in order to indicate that we’d like to fit estimating equations models (instead of mixed models). Since fitting GEEs is more computationally complex than fitting GLMs, DE testing with the GEE mode takes a bit longer. Using more cores and / or running the tests on an HPC cluster speeds things up considerably.

scLANE_models_gee <- testDynamic(sim_data, 
                                 pt = order_df, 
                                 genes = gene_sample, 
                                 size.factor.offset = cell_offset, 
                                 is.gee = TRUE, 
                                 id.vec = sim_data$subject, 
                                 cor.structure = "ar1", 
                                 n.cores = 4L, 
                                 verbose = FALSE)
#> scLANE testing completed for 100 genes across 1 lineage in 1.638 mins

We again generate the table of DE test results. The variance of the estimated coefficients is determined using the sandwich estimator, and a Wald test is used to compare the null & alternate models.

scLANE_res_gee <- getResultsDE(scLANE_models_gee)
select(scLANE_res_gee, Gene, Lineage, Test_Stat, P_Val, P_Val_Adj, Gene_Dynamic_Overall) %>% 
  slice_sample(n = 5) %>% 
  knitr::kable("pipe", 
               digits = 3, 
               col.names = c("Gene", "Lineage", "Wald stat.", "P-value", "Adj. p-value", "Predicted dynamic status"))

Gene	Lineage	Wald stat.	P-value	Adj. p-value	Predicted dynamic status
BAD	A	136315.561	0	0	1
MPLKIP	A	29.814	0	0	1
LY6G5C	A	NA	NA	NA	0
PCF11	A	4336.078	0	0	1
WAPAL	A	2761.705	0	0	1

GLMM mode

We re-run the DE tests a final time using the GLMM mode. This is the most complex model architecture we support, and is the trickiest to interpret. We recommend using it when you’re most interested in how a trajectory differs between subjects e.g., if the subjects belong to groups like Treatment & Control, and you expect the Treatment group to experience a different progression through the biological process. Executing the function with the GLMM mode differs only in that we switch the is.glmm flag to TRUE and no longer need to specify a working correlation structure.

scLANE_models_glmm <- testDynamic(sim_data, 
                                  pt = order_df, 
                                  genes = gene_sample, 
                                  size.factor.offset = cell_offset, 
                                  n.potential.basis.fns = 3, 
                                  is.glmm = TRUE, 
                                  id.vec = sim_data$subject, 
                                  n.cores = 4L, 
                                  verbose = FALSE)
#> scLANE testing completed for 100 genes across 1 lineage in 4.52 mins

Note: The GLMM mode is still under development, as we are working on further reducing runtime and increasing the odds of the underlying optimization process converging successfully. As such, updates will be frequent and functionality / results may shift slightly.

Like the GLM mode, the GLMM mode uses a likelihood ratio test to compare the null & alternate models.

scLANE_res_glmm <- getResultsDE(scLANE_models_glmm)
select(scLANE_res_glmm, Gene, Lineage, Test_Stat, P_Val, P_Val_Adj, Gene_Dynamic_Overall) %>% 
  slice_sample(n = 5) %>% 
  knitr::kable("pipe", 
               digits = 3, 
               col.names = c("Gene", "Lineage", "LRT stat.", "P-value", "Adj. p-value", "Predicted dynamic status"))

Gene	Lineage	LRT stat.	P-value	Adj. p-value	Predicted dynamic status
TIMP1	A	172.327	0.000	0	1
NPC2	A	128.963	0.000	0	1
ARL8A	A	4.819	0.998	1	0
SFMBT2	A	2.454	1.000	1	0
TRAPPC1	A	89.370	0.000	0	1

Downstream analysis & visualization

Model comparison

We can use the plotModels() to visually compare different types of models. It takes as input the results from testDynamic(), as well as a few specifications for which models & lineages should be plotted. While more complex visualizations can be created from our model output, this function gives us a good first glance at which models fit the underlying trend the best. Here we show the output generated using the GLM mode, split by model type. The intercept-only model shows the null hypothesis against which the scLANE model is compared using the likelihood ratio test and the GLM displays the inadequacy of monotonic modeling architectures for nonlinear dynamics. A GAM shows essentially the same trend as the scLANE model, though the fitted trend from scLANE is more interpretable.

plotModels(scLANE_models_glm, 
           gene = scLANE_res_glm$Gene[1], 
           pt = order_df, 
           expr.mat = sim_data, 
           size.factor.offset = cell_offset, 
           plot.null = TRUE, 
           plot.glm = TRUE, 
           plot.gam = TRUE, 
           plot.scLANE = TRUE)

When plotting the models generated using the GLMM mode, we split by lineage & color the points by subject ID instead of by lineage. The gene in question highlights the utility of the scLANE model, since the gene dynamics differ significantly by subject.

plotModels(scLANE_models_glmm, 
           gene = scLANE_res_glmm$Gene[1], 
           pt = order_df, 
           expr.mat = sim_data, 
           size.factor.offset = cell_offset, 
           id.vec = sim_data$subject, 
           is.glmm = TRUE, 
           plot.glm = TRUE,
           plot.gam = TRUE, 
           plot.scLANE = TRUE)

Coefficient summaries

A key feature of scLANE is the ability to obtain a quantitative, interpretable coefficient for the effect of pseudotime on gene expression. This functionality is currently available for the GLM & GEE frameworks, and each coefficient carries the interpretation of a generalized linear model.

scLANE_models_glm[["JARID2"]]$Lineage_A$Gene_Dynamics %>% 
  knitr::kable("pipe", 
               digits = 2, 
               col.names = c("Gene", "Lineage", "Breakpoint", "First Slope", "Second Slope", "First Trend", "Second Trend"))

Gene	Lineage	Breakpoint	First Slope	Second Slope	First Trend	Second Trend
JARID2	A	0.1	-38.09	3.93	-1	1

Coefficients can also be plotted like so:

plotModelCoefs(scLANE_models_glm, 
               gene = "JARID2", 
               pt = order_df, 
               expr.mat = sim_data,
               size.factor.offset = cell_offset)

Knot distribution

Lastly, we can pull the locations in pseudotime of all the knots fitted by scLANE. Visualizing this distribution gives us some idea of where transcriptional switches are occurring in the set of genes classified as dynamic.

dyn_genes <- filter(scLANE_res_glm, Gene_Dynamic_Overall == 1) %>% 
             pull(Gene)
knot_dist <- getKnotDist(scLANE_models_glm, dyn.genes = dyn_genes)
ggplot(knot_dist, aes(x = knot)) + 
  geom_histogram(aes(y = after_stat(density)), 
                 color = "black", 
                 fill = "white", 
                 linewidth = 0.5) + 
  geom_density(color = "forestgreen", 
               fill = "forestgreen", 
               alpha = 0.5, 
               linewidth = 0.75) + 
  labs(x = "Knot Location", y = "Density") + 
  theme_scLANE()
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Smoothed dynamics matrix

We can extract matrix of the fitted values for each dynamic gene using the smoothedCountsMatrix() function.

smoothed_dynamics <- smoothedCountsMatrix(scLANE_models_glm, 
                                          size.factor.offset = cell_offset, 
                                          pt = order_df, 
                                          genes = dyn_genes)

The smoothed dynamics can then be used to generate expression cascade heatmaps, cluster genes, etc. For more information on downstream analysis of gene dynamics, see the corresponding vignette.

Conclusions & best practices

In general, starting with the GLM mode is probably your best bet unless you have a strong prior belief that expression trends will differ significantly between subjects. If that is the case, you should use the GEE mode if you’re interested in population-level estimates, but are worried about wrongly predicting differential expression when differences in expression are actually caused by inter-subject variation. If you’re interested in generating subject-specific estimates then the GLMM mode should be used; take care when interpreting the fixed vs. random effects though, and consult a biostatistician if necessary.

If you have a large dataset (10,000+ cells), you should start with the GLM mode, since standard error estimates don’t differ much between modeling methods given high enough n. In addition, running the tests on an HPC cluster with 4+ CPUs and 64+ GB of RAM will help your computations to complete swiftly. Datasets with smaller numbers of cells or fewer genes of interest may be easily analyzed in an R session on a local machine.

Contact information

This package is developed & maintained by Jack Leary. Feel free to reach out by opening an issue or by email (j.leary@ufl.edu) if more detailed assistance is needed.

References

1. Bacher, R. et al. Enhancing biological signals and detection rates in single-cell RNA-seq experiments with cDNA library equalization. Nucleic Acids Research (2021).

2. Warton, D. & J. Stoklosa. A generalized estimating equation approach to multivariate adaptive regression splines. Journal of Computational and Graphical Statistics (2018).

3. Nelder, J. & R. Wedderburn. Generalized linear models. Journal of the Royal Statistical Society (1972).

4. Liang, K. & S. Zeger. Longitudinal data analysis using generalized linear models. Biometrika (1986).

5. Laird, N. & J. Ware. Random-effects models for longitudinal data. Biometrics (1988).