In a time-course experiment, an expression matrix is obtained
for each time point. The exploratory analysis described above can
be applied to all time-points together in order to learn about
general trends in expression over time. But, in order to learn
about the different developmental trajectories and gene regulatory
networks controlling differentiation, we must perform trajectory
analysis.
The first goal of trajectory analysis is to infer ancestor–descendant relationships between pairs of time-points. This is crucial
because scRNA-seq kills cells; therefore, we cannot use it to directly
measure the change in gene expression of any individual cell over
time. Live-cell imaging with fluorescent reporters can address this,
but only for a handful of genes at a time. Many algorithms have
been proposed to recover trajectories from scRNA-seq data.
Waddington-OT is the only algorithm developed to date that is
capable of modeling cell growth and development in a scRNA-seq
time-course. All other algorithms either cannot incorporate known
information about time of collection, or assume that all cells grow
at the same rate (and therefore give rise to the same number of
descendants). Waddington-OT infers ancestor-descendant relationships between pairs of time-points by leveraging a classical
mathematical tool called optimal transport (OT). Intuitively, OT
is based on the principle that cells can’t change expression of all
genes by large amounts in a short period of time. Therefore, cells
are connected to “putative descendants” in a way that minimizes
the total net change in expression over time. Each cell is allocated a
certain amount of “descendant mass” according to an estimate of
its proliferative ability and apoptosis rate (i.e., more proliferative
cells are connected to more descendants). These growth rates are
initially based on gene signatures of cell cycle and apoptosis, but are
ultimately learned from data. The output of this first step of trajectory analysis is a “transport matrix” connecting each pair of timepoints. The transport matrix has a row for each cell at time 1 and a
column for each cell at time 2. The entries of the matrix indicate the
amount of descendant mass each cell from time 1 gives rise to at
time 2 (if we hadn’t killed the cells).
After inferring ancestor–descendant relationships, the second
goal of trajectory analysis is to infer gene regulatory networks
controlling development and differentiation. To do this,
Waddington-OT looks for transcription factors that are most predictive of transitions to various cell sets. For example, in iPSC
reprogramming which transcription factors are responsible for
pushing cells toward the stem cell state? Waddington-OT also
allows us to analyze the shared ancestry connecting pairs of cell
sets. This allows us to answer—does this pair of cell sets share a
common ancestor near the beginning of the time-course and when
does the pair diverge? We can then look for transcription factors
that explain the bifurcation.
Methods for in Vivo EMT at Single Cell Resolution
311
for each time point. The exploratory analysis described above can
be applied to all time-points together in order to learn about
general trends in expression over time. But, in order to learn
about the different developmental trajectories and gene regulatory
networks controlling differentiation, we must perform trajectory
analysis.
The first goal of trajectory analysis is to infer ancestor–descendant relationships between pairs of time-points. This is crucial
because scRNA-seq kills cells; therefore, we cannot use it to directly
measure the change in gene expression of any individual cell over
time. Live-cell imaging with fluorescent reporters can address this,
but only for a handful of genes at a time. Many algorithms have
been proposed to recover trajectories from scRNA-seq data.
Waddington-OT is the only algorithm developed to date that is
capable of modeling cell growth and development in a scRNA-seq
time-course. All other algorithms either cannot incorporate known
information about time of collection, or assume that all cells grow
at the same rate (and therefore give rise to the same number of
descendants). Waddington-OT infers ancestor-descendant relationships between pairs of time-points by leveraging a classical
mathematical tool called optimal transport (OT). Intuitively, OT
is based on the principle that cells can’t change expression of all
genes by large amounts in a short period of time. Therefore, cells
are connected to “putative descendants” in a way that minimizes
the total net change in expression over time. Each cell is allocated a
certain amount of “descendant mass” according to an estimate of
its proliferative ability and apoptosis rate (i.e., more proliferative
cells are connected to more descendants). These growth rates are
initially based on gene signatures of cell cycle and apoptosis, but are
ultimately learned from data. The output of this first step of trajectory analysis is a “transport matrix” connecting each pair of timepoints. The transport matrix has a row for each cell at time 1 and a
column for each cell at time 2. The entries of the matrix indicate the
amount of descendant mass each cell from time 1 gives rise to at
time 2 (if we hadn’t killed the cells).
After inferring ancestor–descendant relationships, the second
goal of trajectory analysis is to infer gene regulatory networks
controlling development and differentiation. To do this,
Waddington-OT looks for transcription factors that are most predictive of transitions to various cell sets. For example, in iPSC
reprogramming which transcription factors are responsible for
pushing cells toward the stem cell state? Waddington-OT also
allows us to analyze the shared ancestry connecting pairs of cell
sets. This allows us to answer—does this pair of cell sets share a
common ancestor near the beginning of the time-course and when
does the pair diverge? We can then look for transcription factors
that explain the bifurcation.
Methods for in Vivo EMT at Single Cell Resolution
311