Cell2State: Learning Cell State Representations From Barcoded Single-Cell Gene-Expression Transitions 

Abstract: Genetic barcoding coupled with single-cell sequencing technology enables direct measurement of cell-to-cell transitions and gene-expression evolution over a long timespan. This new type of data reveals explicit state transitions of cell dynamics. Motivated by dimension reduction methods for dynamical systems, we develop a *cell-to-state* (cell2state) learning method that, through learning from such multi-modal data, maps single-cell gene expression profiles to low-dimensional state vectors that are predictive of cell dynamics. We evaluate the cell2state method using barcoded stem cell dataset (Biddy et al. (2018)) and simulation studies, compared with baseline approaches using features that are not dynamic-aware. We demonstrate the merits of cell2state in challenging downstream tasks including cell state prediction and finding dynamically stable clusters. Further, our method reveals potentiallatent meta-states of the underlying evolution process. For each of the meta-states, we identify a set of marker genes and development pathways that are biologically meaningful and potentially expand existing knowledge.

Reviews and author responses:

The authors introduce cell2state, an algorithm that incorporates both genetic barcoding coupled with single-cell sequenced data to model explicit state transitions of cell dynamics over time. Single-cell gene expression profiles are mapped to low-dimensional state vectors that are predictive of cell dynamics. Cell2state is evaluated using barcoded stem cell dataset (Biddy et al. (2018)) and simulation studies are also presented. The model demonstrates better results for cell state prediction, finding dynamically stable clusters, and reveals potential latent meta-states of the underlying cellular evolution process. 
 Strength: The paper deals with a very relevant and challenging problem in biology that of lineage tracing along with states.
Weakness: Paper is very hard to read. There is no consistency to notation and variables used. I worry that the main claims might be incorrect but tidying up the notation might help alleviate some of these concerns. 
   Page 2, 1st paragraph: shouldn’t the lossless encoding of states be I(\Phi(X),\Phi(X’)) instead of I(\Phi(X),X’)? 

Figure 1 has variables X’ and \lambda. What are these? Also in this figure, label an example of X(t) and X(t+1). 

What is Definition 1 stating? What is the growth rate and what is y? 

Shouldn't EXP[N|X(t)]  be EXP[all N descendants of X(t)|X(t)]?

Definition 2 states ‘p’ but uses ‘f’ in the equation. 

The ‘p’ in definition 1 is not the same as the ‘p’ in Assumption 1. Please maintain consistency of variables used. 

Can 1 cell map to more than one latent meta states?

Last line of page 3: \Phi(X(t)) is the low-dim embedding of X(t) and not X(t+1). Check notational consistency. 

Section 3.1: what is \Pi? 
Section 3.1 - what is the lifting of dimensions? The data is reduced using PCA, then lifted to high-dim using another Gaussian kernel. Would this not add too many 'and' irrelevant dimensions to an already noisy dataset? 
Section 3.1: how do you define the function space H? 

Section 3.2: what is X’? 
Section 3.2 - what is P^hat? 
It is worth dedicating more explanation to the cell2state algorithm, the tetrahedron structures, what these mean before Section 3.3. Section 5 could go to the Supplementary to make space for relevant material in the main paper. 

In Page 2, summary 3rd point, the authors claim their model would perform with <=7 dimensions. I could not find details to this in the Experiments section. 


The authors develop a novel approach to learn a low dimensional embedding of transcriptomic state of cells using data from cell barcoding experiments, which can capture the single cell RNAseq profiles of cells and their descendants. The main contributions of the paper can be summarized as: 
1) A novel approach to learn latent representation of the transcriptomic state of cells by utilizing knowledge of 'true' cell lineage 
2) A mathematical analysis of the distortion of the learned embedding under certain reasonable assumptions 
3) Experiments on simulated and real data to validate the proposed approach. The strengths of the paper according to me are the following: 
1) The authors propose a novel way to identify the transcriptomic state of cells 
2) The proposed approach is based on sound mathematical intuitions 
3) Contingent on certain assumptions holding (more on this in the weakness), the approach can be theoretically shown to work reasonably well
4) The experimental validation is quite reasonable

The weaknesses of the paper (according to me) are the following: 
1) It is entirely unclear to me who the target audience for the paper is. It reads to a degree like a paper I would find in a life sciences journal, but it also contains aspects of a traditional machine learning paper. This leads to a paper that in my humble opinion would be truly appreciated by a very small number of computational biology researchers who are also sufficiently proficient in machine learning. However, this is largely a problem with the writing of the paper. I would suggest the authors either introduce more biological contexts in the paper (if their goal is to introduce the machine learning audience to an interdisciplinary problem) or focus on the methodological aspects of the paper and introduce the biological details as an application. 
2) Assumption 1 is central to the mathematical formulation used in the paper and is a pretty reasonable assumption in my view. However, it is quite unacceptable that the reasonableness of the assumption is not discussed in any depth, given how central it is to the paper. I would suggest citing some papers that explore the assumption in more detail. 
3) The simulated experiment need to be better motivated. Currently, it reads like the data generation process simply meets the assumption of the cell2state algorithm and hence it works well. The authors should at least explain why this is a reasonable approach to generated synthetic data and ideally cite other papers that have generated synthetic data using a similar approach.  The paper presents an approach to infer cell state from a relatively new type of biological dataset. The work is both important in it's scope and novel in terms of approach. However, the paper has some big writing issues in my opinion. A lot of the biological context is not appropriately introduced for a non life sciences audience and some justifications are missing/lacking. 

Kernel-based embedding of barcoded single-cell data that preserves mutual information between barcoded pairs.  This manuscript proposes a kernel-based embedding technique to map high-dimensional single-cell gene expression feature vectors to a low-dimensional space so that information is preserved in pairs of single-cell expression pairs that are measured from barcoded parent-descendant pairs. The proposed method uses barcoded single-cell data.  Even though each cell can be measured only once, the method builds on the assumption that dividing cells are phenotypically (approximately) similar, and descendants of the same cell lineage reveals dynamics of cell transitions. Overall, the proposed method aims to embed the single-cell pairs so that information between barcoded cell pairs is preserved. The kernel-based feature embedding is implemented with a combination of random Fourier features and with a more more traditional PCA/SVD dimension reduction techniques. Additionally authors provide bounds for distance distortion of state embeddings as well as information loss of the embedding (the details of the proofs I did not check in details). The main drawbacks of this manuscript include 
i) a non-specific description of the methods in the main texts which leaves a number of technical aspects partly unclear, and
ii) description of somewhat unconventional analysis results without any comparisons to previous methods.   It is difficult to grasp the true novelty and practical benefits of the proposed method based on the presented results without any comparisons.

Authors proposed cell2state that could embed barcoded scRNA-seq trajectories into low-dimensional representation. Authors provided theoretic analysis of the embedding learnt by cell2state and demonstrated that the learnt embedding was almost lossless.

Authors applied this embedding framework on one barcoded scRNA-seq dataset (Biddy, et al., 2018) and demonstrated the learnt embeddings clearly distinguished different cell states. Furthermore, the learnt embeddings were able to substantially improve various downstream tasks other than identifying cell subpopulation.
 Major Comments:

(1) (Fig. 3ik) Why does the error increase dramatically when gamma (kernel width) increases over 10^2?

(2) Based on Fig 3d and 3e, it is clear that Day-21 raw data is more helpful to identify cell subpopulation compared with Day-12 raw data. I'm curious to see the difference between Day-21 cell2state and Day-21 raw data embedding. Also, it is not fair to compare cell2state embedding and raw data embedding from single time point (Day-12 or Day-21) as cell2state utilize raw data from both time point to generate the representation. Instead authors can first concatenate Day-12 and Day-21 data along the dimension of cell: Just concatenate the expression profile of cell at Day-12 and the expression profile of corresponding descendant together. There will be missing profiles as cells were not perfectly paired and authors can impute the missing profiles based on nearest neighbors with respect to Day-12. Then authors can perform PCA/kernel PCA+UMAP to generate embedding for Day-12 based on this joint gene expression profile. This serves a simple baseline model as it utilizes the same input as that to cell2state. Authors can compare Day-12 cell2state to this joint embedding to see if cell2state generates better embeddings given the same input.

(3) What does the color scale stand for in Fig.4b? For a better visualization, this panel can be rotated 90 degrees as well.

(4) 2000 random Fourier features were selected based on algorithm 1. I'm wondering if this number of random features is sufficient to approximate the kernel. Is 2000 an optimized number after tuning in the parameter space?


Minor Comments:

(1) The color scale in Fig. 3a is hard to distinguish. The gradient is helpful to illustrate the nature of the data, but it is more helpful to distinguish them here in panel a.

(2) It is hard to make sense of Fig. 3b. It is more clear to just illustrate the general trend of cell transition instead of drawing all individual connections here.

(3) It is better to explain the 366G abbreviation in the caption of Fig. 3 or in the corresponding section (section 4.2.2).
 Although authors demonstrated that cell2state embedding is lossless and helpful to achieve a superior performance combined with a simple linear classification model, authors didn't directly compare cell2state with any other compatible embedding methods. This makes it hard to evaluate the novelty of the proposed embedding framework. Authors mentioned state representation learning and other related fields in the background section. I would suggest authors to pick up similar embedding methods as a baseline model for comparison.

Meta-review: While the problem tackled in this paper is interesting, there is a consensus among reviewers that the writing of the paper does not allow the reader to fully understand the method developed, nor the biological context and results obtained by the method. We encourage the authors to take into account the reviewers' comments to prepare a future improved version of the manuscript.

Decision: Reject