MATCHER: manifold alignment reveals correspondence between single cell transcriptome and epigenome dynamics

Genome Biology

Welch JD, Hartemink AJ, Prins JF. MATCHER: manifold alignment reveals correspondence between single cell transcriptome and epigenome dynamics. Genome Biol. 2017 Jul 24;18(1):138. doi: 10.1186/s13059-017-1269-0. PMID: 28738873; PMCID: PMC5525279.

MATCHER identifies correlations between epigenome and transcriptome dynamics to reveal the sequential changes cells undergo during biological processes. It works on both sampling of the transcriptome and epigenome from different cells and from the same cells. It is based on the hypothesis that

cells undergoing a common process are sequenced using multiple genomic techniques, examining any of the genomic quantities should reveal the same underlying biological process.

By projecting a low-dimensional representation of each measure on a common plane, the different measures can be compared. If all the measures from from the same cell or sampling event, they can be aligned with correspondence. A similar system can be used to integrate video, audio and written transcripts of a speech. If not they are aligned using geometric information without correspondence. MATCHER is designed for alignment without correspondence since getting multiple measures from a single cell can be difficult.

Modelling

MATCHER uses a Gaussian process latent variable model (GPLVM), a non-linear model of high-dimensional data as a function of latent variables to infer a pseudotime for each measure. A PCA can be considered a linear version of this model. GPL VMs are also generative and can predict missing observations in one measure given data at both measures at other points along the manifold.

All these measures are then mapped onto a “master time” between 0 and 1 using a learned monotonic warping function. This provides a common plane of comparison between different data measures. This is what allows integrating data even when the different measures came from different cells instead of the same cell.

Assumptions

1. The data lie on a 1D manifold.

2. Each measure changes as a response to the same underlying biological process.

3. The process flows in one direction without reversals, branches or cycles.

4. They cells are from the same population and cell type.

These assumptions leave orientation (one measure increases while another decreases), scale and time warping (genomic measures change at different rates) as the remaining sources of differences between the different measures. Correct orientation needs an informed prior since it cannot be inferred from data while scale differences can be addressed by normalizing the manifold coordinates. Time warping is addressed by learning a monotonic warping function for each data type. For branching trajectories, each branch could be assigned cells and aligned separately.

Analysis

Using simulated data they showed that MATCHER could accurately infer master time across warping functions and noise levels. With real data of DNA methylation and gene expression from the same cells, MATCHER could infer master time values that were highly concordant. It was also able to infer correlations between the measures that closely matched the true correlations.

Using gene expression, chromatin accessibility and histone modification data, MATCHER inferred positive correlations, confirming on a single-cell level, findings from bulk data. Chromatin was being remodeled to prime lineage-specific genes and shut down pluripotency genes.

Between DNA methylation and gene expression they found that master time tracked together well until a master time of 0.3 when coupling decreased. Based on statistical tests on the data, they hypothesized that

specific *de novo* DNA methylation changes are required to trigger a key step
in the process of gene expression changes during the transition from ground
state pluripotency to a primed state, but after this point in the process,
the sequential gene expression changes proceed somewhat independently from
the DNA methylation changes.

Examining relative ordering showed that DNA methylation changes lagged behind gene expression changes. DNA methylation pseudotime was bimodal suggesting that there were two metastable states that cells could rapidly travel between. Once the methylation changes required to push cells out of a certain transcriptomic space, DNA methylation profiles stabilize. The decoupling is only partial - DNA methylation and gene expression still correlate, but are only somewhat predictive of each other. This could be because there are other factors that regulate gene expression. In iPSC reprogramming, there is higher concordance and both gene expression and methylation master time densities are bimodal. This does show that getting the individual genomic measures from the same cell provides information about the system that MATCHER cannot infer. While individual master times can sometimes be discordant, a shared master time showed greater correlation when shared data is available to get a shared cell ordering.