ConvexML: Scalable and accurate inference of single-cell chronograms from CRISPR/Cas9 lineage tracing data

CRISPR/Cas9 gene editing technology has enabled lineage tracing for
thousands of cells in vivo. However, most of the analysis of CRISPR/Cas9
lineage tracing data have so far been limited to the reconstruction of
single-cell tree topologies, which depict lineage relationships between
cells, but not the amount of time that has passed between ancestral cell
states and the present. Time-resolved trees, known as chronograms, would
allow one to study the evolutionary dynamics of cell populations at an
unprecedented level of resolution. Indeed, time-resolved trees would
reveal the timing of events on the tree, the relative fitness of subclones,
and the dynamics underlying phenotypic changes in the cell population –
among other important applications. In this work, we introduce the first
scalable and accurate method to refine any given single-cell tree topology
into a single-cell chronogram by estimating its branch lengths. To do
this, we leverage a statistical model of CRISPR/Cas9 cutting with missing
data, paired with a conservative version of maximum parsimony that
reconstructs only the ancestral states which we are confident about. As
part of our method, we propose a novel approach to represent and handle
missing data – specifically, double-resection events – which greatly
simplifies and speeds up branch length estimation without compromising
quality. All this leads to a convex maximum likelihood estimation (MLE)
problem that can be readily solved in seconds with off-the-shelf convex
optimization solvers. To stabilize estimates in low-information regimes,
we propose a simple penalized version of MLE using a minimum branch length
and pseudocounts. We benchmark our method using simulations and show that
it performs well on several tasks, outperforming more naive baselines. Our
method, which we name 'ConvexML', is available through the
cassiopeia open source Python package.