Alignment of Single-Cell Trajectories by tuMap Enables High-Resolution Quantitative Comparison of Cancer Samples

Summary

Single-cell technologies allow characterization of cancer samples as continuous developmental trajectories. Yet, the obtained temporal resolution cannot be leveraged for a comparative analysis due to the large phenotypic heterogeneity existing between patients. Here we present the tuMap algorithm that exploits high-dimensional single-cell data of cancer samples exhibiting an underlying developmental structure to align them with the healthy development, yielding the tuMap pseudotime axis that allows their systematic, meaningful comparison. We applied tuMap on single-cell mass cytometry data of acute lymphoblastic and myeloid leukemia to reveal associations between the tuMap pseudotime axis and clinics that outperforms cellular assignment into developmental populations. Application of the tuMap algorithm on single-cell RNA sequencing data further identified gene signatures of stem cells residing at the very early parts of the cancer trajectories. The quantitative framework provided by tuMap allows generation of metrics for cancer patients evaluation.

Graphical Abstract

eTOC blurb

Single-cell technologies provide unprecedentedly large amounts of data, of which only a small fraction is utilized. Trajectory inference methodologies leverage the detailed information to gain temporal resolution in process characterization. Yet, in cancer, patient heterogeneity prevents quantitative comparison of the processes occurring in different patients, an essential step for clinical reasoning and mechanistic understanding. We present the tuMap algorithm that overcomes inter-patient variability and aligns cancer patient trajectories to a single axis, thus providing a continuous framework for cancer comparison.

Introduction

Many tissues maintain a stoichiometric homeostasis through a persistent developmental process of stem cells differentiating into mature cells(Gehart and Clevers, 2019; Gonzales and Fuchs, 2017; Pinho and Frenette, 2019). The tight regulations placed on cellular proliferation, differentiation, and apoptosis processes result with balanced cellular abundances along with a robust and appropriate response to stimuli(Hunter Arielle Glatman Zaretsky and Engiles, 2013; Joost et al., 2018). Recently, due to the advancement in high-throughput single-cell ‘omics’ technologies, such developmental processes have been characterized in a highly rigorous manner(Haensel et al., 2020; Herring et al., 2018; Law et al., 2019). The high-dimensional data obtained on single-cells are leveraged to order the cells by similarity along a continuum, a pseudotime trajectory, representing the underlying developmental process and enabling characterization of markers’ expression dynamics along the process with an unprecedented high temporal resolution(Bendall et al., 2014). The conservation of developmental processes across healthy individuals allows averaging of multiple samples taken from different individuals to assemble one common trajectory(Chen et al., 2020; Wang et al., 2020; Zhang et al., 2020). Apart of the highly detailed characterization of the process itself, the common continuum along which single-cells of different individuals are positioned allows for a systematic and meaningful comparison of different samples with respect to multiple features(Abstract, 2019; Bendall et al., 2011; Good et al., 2018; Menon et al., 2018; Oetjen et al., 2018).

Akin to the healthy tissue, recent studies revealed that cancers such as: leukemia(Lapidot et al., 1994), breast cancer(Al-Hajj et al., 2003), and colorectal cancer(O’Brien et al., 2007) also exhibit a hierarchical structure, harboring a quiescent population of stem cells that fuels the tumor growth and more differentiated cells . Single-cell profiling applied on cancer tissues revealed the large variation existing between patients with respect to genes’ and markers’ expression(Izar et al., 2020; Puram et al., 2017; Tirosh et al., 2016), hindering identification of common cell populations that exist across samples that may facilitate cross-samples comparison. However, recently developed methodologies leverage the high-dimensional data on single-cells to assign cells from the cancer tissue into developmental populations along the healthy axis by their phenotypic similarity(Good et al., 2018; van Galen et al., 2019). While such stratification methodologies provide a comparative framework across samples to yield clinically meaningful associations, it may miss the clinical significance of intermediate cell types that are located along the differentiation continuum.

Hematopoiesis is one of the most intensively characterized biological system in terms of developmental trajectories using single-cell data generated using both CyTOF(Bendall et al., 2014, 2011; Levine et al., 2015) and single-cell RNA sequencing(Watcham et al., 2019). Genetic mutations in progenitor cells alter the normal development, yielding an accumulation of cells from a specific developmental stage called: “blasts”(Leonard et al., 2017), that may be related to the myeloid or the lymphoid lineage, resulting with either myeloid or lymphoid leukemia, respectively(De Kouchkovsky and Abdul-Hay, 2016). Recent studies used single-cell mass cytometry and gene expression technologies to unravel the large intra- and inter-tumor heterogeneity existing in myeloid and lymphoblastic leukemias(Ferrell et al., 2016, 2014; Good et al., 2018; Han et al., 2015; Levine et al., 2015; Zheng et al., 2017). Despite this heterogeneity, some studies identified a correspondence between the phenotypes of malignant and healthy cells, allowing classification of malignant cells by their relation to normal hematopoietic development with clinical implications(Corces et al., 2016; van Galen et al., 2019), such as disease relapse(Good et al., 2018). However, these approaches are categorical and limited to predefined developmental stages, ignoring the continuous nature of hematopoiesis that might embed clinical relevance.

Here, we demonstrate the inherent limitations associated with developmental trajectory inference in cancer samples for a systematic cross-samples comparison. To resolve this, we present tuMap, a computational algorithm that robustly aligns single cells of cancer samples to the healthy developmental axis to yield the tuMap pseudotime axis which allows a systematic high-resolution comparison across patients, within a patient over time and against the healthy counterpart. We showcase the power of a continuous quantitative comparison framework by studying two mass cytometry (CyTOF) bone marrow datasets, one in acute lymphoblastic leukemia (ALL)(Good et al., 2018) and a second in acute myeloid leukemia (AML), in each case revealing clinically significant intermediate regions along the trajectory that are obscured under a stratification paradigm of discrete well-defined cell populations. Finally, we leverage the high resolution of the tuMap pseudotime axis of AML single-cell RNA sequencing data(van Galen et al., 2019) to identify extremely early cells and derive candidate leukemic stem cell genes.

Results

Cancer patients exhibit high inter-individual heterogeneity, barring systematic comparison.

The high resolution obtained from characterization of developmental processes as a continuum can be leveraged through an appropriate comparative analysis to reveal the clinical relevance of transitional cell states. In healthy individuals, this comparison is traditionally performed by combining data of multiple individuals to calculate a unified trajectory(Abstract, 2019; Bendall et al., 2011; Chen et al., 2020; Good et al., 2018; Menon et al., 2018; Oetjen et al., 2018; Wang et al., 2020; Zhang et al., 2020). To validate this approach and check its relevance to cancer, we utilized a published dataset that profiled bone marrow samples from 5 healthy individuals and 60 acute lymphoblastic leukemia (ALL) patients for developmental and signaling markers at a single cell resolution by CyTOF(Good et al., 2018) (Methods). Single cells from the healthy and ALL samples were originally assigned to the main healthy B-cell subpopulations based on the expression values of 11 developmental markers by using either manual gating or a nearest neighbor classifier, for healthy and ALL samples, respectively. We leveraged the high dimensional expression data to project the healthy cells on a 2-dimensional PCA space on which most of the variation in B-cell populations’ positions was attributed to cell-population identity rather than the individual (Fig. 1A, Supp. Fig. 1A-B). In accordance, a trajectory assembled by combining all the individuals together reliably reflects B-cell development, with a high correlation between B-cell populations’ positioning along it and the known developmental ordering (Methods, Supp. Fig. 1C-D, Spearman r = 0.94, 0.95±0.04, for overall and per each individual healthy sample, respectively). This coherency between healthy individuals with respect to the B-cell developmental axis can be explained by the tight regulation placed on the inter-marker correlation network under physiologic conditions, justifying the approach of pooling healthy samples together to assemble one averaged trajectory (Fig 1B, left, Methods).

Figure 1: Incoherencies of single-cells’ markers’ expression profiles in ALL samples relative to the healthy suggest using a supervised, individualized trajectory inference approach.

(A) The first two principal components of 10,000 bone marrow single cells expression profiles from the 5 healthy individuals using the B-cells developmental markers that were sampled with inverse relation to their assigned cell-populations’ frequency. The averaged position of each cell population in each individual is colored by individual ID (blue, red, green, orange, and purple) and maturation degree (light to dark colors for immature to mature cell populations), with dashed lines linking developmentally adjacent cell populations. Contour lines correspond to single-cell density in the 2-dimensional space. (B) Circos plots depicting the inter-marker correlation network across healthy (left) and ALL (right) samples. The tracks’ colors denote the median inter-marker correlation across samples whereas the tracks’ widths denote the percentage of samples exhibiting an absolute inter-marker correlation above 0.3. (C) Spearman correlation values between the mean cell populations’ expected ordering and their mean pseudotime values along the average PAGA trajectory assembled by pooling of healthy (n=5 individuals) and either 5 or 60 ALL patients (Kruskal-Wallis test P=1.1610⁻¹⁵, Conover’s post-hoc P = 0.026, 2.710⁻⁶, 4.710⁻¹⁰, for: Healthy-ALL5, Healthy-ALL60, and ALL5-ALL60, respectively). *** denotes P < 0.001.

In contrast, analyzing ALL data reveals an obliteration of these markers’ co-expression network in cancer patients (Fig. 1B, right, t test P = 3.32∙10⁻¹⁸, n = 275, 3,300 marker-pairs*number of individuals, for healthy and ALL, respectively). This pronounced deviation from the healthy hinders projection of the patient’s cells onto the healthy PCA space to position them along the developmental axis, a procedure that strongly relies on inter-marker relationships learnt from the healthy (Supp. Fig. 2A). Furthermore, combining data of multiple ALL patients to assemble an averaged trajectory fails to capture the healthy developmental axis within each sample, a problem that is aggravated with increased sample number, possibly due to patient-specific markers’ alterations (Fig. 1C, Supp. Fig. 2B-C, Methods, Spearman correlation with developmental population order = 0.58±0.46, 0.16±0.14, for n = 5*100, 60 samples, respectively). These findings highlight the fact that in cancer, fundamental assumptions necessary for standard trajectory building are violated independently in each patient, making it impossible to quantitatively compare them to one another using standard means.

tuMap aligns cancer samples to a healthy developmental axis for quantitative comparison.

We set out to provide a quantitative framework for comparative analysis of different patients’ tumor development dynamics. The two major problems barring assembly such a framework are: (a) What is the common framework through which samples are compared to one another, and (b) How to overcome the large difference in marker expression while preserving the individual-level resolution. To develop this framework, we first set out to test whether we can flush out the remnants of healthy development in the cancer samples, as this may form the common comparative axes we seek. We evaluated, per patient, multiple published trajectory inference algorithms(Cannoodt et al., n.d.; Macnair and Claassen, 2019; Street et al., 2018; Wolf et al., 2019) using a modified version of the corDist function introduced by Saelens et al(Saelens et al., 2019) (Supp. Fig. 3A, Methods). The healthy developmental axis was indeed observable in most cases, suggesting that remnants of healthy development are still detectable in this cancer context. We noted that the psupertime algorithm(Macnair and Claassen, 2019), a semi-supervised trajectory inference approach that relies on cellular classification into cell populations followed by optimization of their ordering, performed better than unsupervised methodologies(Cannoodt et al., n.d.; Street et al., 2018; Wolf et al., 2019) (Supp. Fig. 3B-I, Methods). Specifically, psupertime captured the healthy developmental axis in the ALL cancer samples better, exhibited a high robustness to noise in markers’ expression levels and was highly reproducible between runs, suggesting it may be a good choice for downstream modeling of individual trajectories in this case. Characterizing marker behavior, we realized that while trajectory alignment algorithms such as our own cellAlign(Alpert et al., 2018a) can potentially be used to derive a common axis overcoming unbalanced cellular density in patients’ trajectories, their assumptions of similar markers expression dynamics along the trajectories being aligned are not met in cancer data. Specifically, we observed discordances between the ALL and healthy samples with respect to marker expression dynamics in a patient-specific manner, emphasizing the need for a comparative approach that allows for patient-specific behavior (Fig. 2A, Kruskal-Wallis rank sum test P = 1.1610⁻¹⁵, Fig. 2B, Supp. Fig. 4A, Methods).

Figure 2: The tuMap algorithm tailors the trajectory-alignment process based on patient-specific markers alterations.

(A) Mean Euclidean distance between single cells markers’ expression profiles of healthy samples (left, n = 5), ALL samples (middle, n = 60) and permutes ALL samples (right, n = 60) and the interpolated markers’ expression along the averaged healthy trajectory (Kruskal-Wallis rank sum test P = 1.1610⁻¹⁵) (B) Interpolated, scaled expression of the markers: CD34 and CD19 along the trajectories of 3 ALL patients (UPN94, UPN20, and UPN17; low and high expression are colored blue and red, respectively), and along the averaged healthy sample (top; CD34 and CD19 corresponds to green and red lines, respectively). Left: alignment distance between each marker’s expression profile per patient and the averaged healthy trajectory. (C) The tuMap algorithm schematics. For the averaged healthy and cancer patient’s samples ordered along two developmental trajectories in the high-dimensional markers’ space, the tuMap algorithm first calculates per marker its degree of conservation in expression dynamics along the cancer sample’s trajectory relative to the averaged healthy trajectory. The resulting markers’ conservation scores are then transformed into weights, which are used for weighted alignment between the cancer sample and the averaged healthy trajectory, allowing for pseudotime scaling.

To provide a quantitative framework for comparative analysis of different patients’ tumors while preserving the individual-level resolution, we developed the tuMap alignment algorithm. tuMap takes as input multiple cancer samples, each ordered along a developmental trajectory assembled per patient separately and a reference backbone, best being the averaged healthy. To overcome the inconsistencies in markers’ expression dynamics typically observed in cancer, tuMap applies a weighted alignment that attenuates the effect of those markers with disrupted expression dynamics relative to the healthy while enhancing the effect of those markers with conserved expression. Specifically, for each cancer sample, the tuMap algorithm applies the following sequential steps (Fig. 2C, Methods for detailed breakdown of tuMap): (A) Quantifies the overall similarity between the expression dynamics of single markers along the cancer relative to the averaged healthy trajectory by using the distance derived from single-marker alignments; (B) Assigns patient-specific set of weights for each marker that are inversely associated with this distance by using a transformation function (Supp. Fig. 4B-E); (C) Calculates the pairwise dissimilarity matrix between the cancer sample’s trajectory and the averaged healthy trajectory, using the identified marker weights; (D) Identifies the optimal alignment of the cancer sample to the healthy trajectory; Finally, (E) tuMap uses the resulting alignment to map single cells from the cancer sample to their approximate location along the healthy development to obtain tuMap pseudotime values which are similarly scaled across cancer samples, allowing for cross-samples comparison. tuMap further provides the typical mapping error along the tuMap trajectory that is inherent to the weighted alignment process.

tuMap characterization of B-cell development axis in ALL improves relapse prediction.

To validate tuMap performance, we tested it on simulated data of healthy samples in which we noised single-marker expression values. Specifically, per ALL patient and per marker, we sampled the single-cell marker’s expression values from its observed distribution in the patient, followed by trajectory assembly and alignment with the averaged healthy trajectory using either cellAlign, tuMap or weighted alignment with random assignments of markers’ weights. For each of the resulting alignments, we assessed the alignment quality by calculating the distance between the aligned elements using the remaining un-noised markers (alignment distance, see Methods). The alignments induced by the tuMap algorithm exhibited significantly better quality as compared to the random weights’ assignment, a trend that was not observed for cellAlign alignments (Fig. 3A top, Supp. Fig. 5A, t-test P = 1.24410⁻⁶⁶, n = 660 combinations of 11 markers and 60 ALL patients). Focusing on the simulations using random weights, we observed that the alignment quality was inversely associated with the weight assigned to the noised marker. That is, simulations in which the noised marker was assigned with a large weight yielded worse alignments as compared to those simulations that attenuated its influence on the alignment (Fig. 3A bottom, Supp. Fig. 5B).

Figure 3: By attenuating the effect of noised markers, the tuMap algorithm achieves high quality alignments that allow for cross-sample comparison, facilitating relapse prediction in ALL.

(A) Top: The alignment-distances resulting from tuMap and cellAlign (dashed lines) alignments relative to their distribution under a random assignment of markers’ weights following permutation-based noising the expression of CD19 in one ALL patient (“UPN1”). Bottom: The random weights assigned to CD19 are shown as color gradient (blue to yellow for low to high weights, respectively) ordered by the resulting alignment-distances. (B) A violin plot showing the distribution of markers’ weights as calculated across ALL patients (n=60) overlayed by the actual values of markers’ weights (grey dots). (C) Cellular density along the tuMap pseudotime axis of the 60 ALL patients, ordered by the tuMap-pseudotime location of the highest density. Left: Density plot of B-cell populations along the averaged healthy pseudotime axis. (D) iAUC values obtained using signaling responses either along the tuMap axis (light-blue) or by discrete B-cell populations (blue) as predictors of relapse using cox-regularized models under different alpha values for the best lambda inferred through cross-validation.

We next applied tuMap on the ALL dataset by calculating tuMap pseudotime values per single cell along the ALL trajectories with relatively low mapping errors (Supp. Fig. 5C, Methods). The markers’ weights assigned by the tuMap algorithm reflect the tendency of these markers to preserve their expression dynamics along the ALL trajectories as compared to the averaged healthy. We observed that some markers, including IgMi, IgMs, CD20, CD19 and CD34, were assigned with relatively higher weights as compared to the other markers, yet exhibited a high degree of variability across-patients (Fig. 3B, Supp. Fig. 5D). The standardization of the tuMap pseudotime axis across patients allows for a meaningful comparative analysis with respect to B-cell developmental stages. To illustrate this principle, we calculated the cellular density distributions along the tuMap pseudotime axis across patients and observed peaks in density that spanned the early pseudotime regions, reflecting the clonal expansion of immature B-cells (Fig. 3C). Yet, the high resolution obtained from cellular ordering along the tuMap pseudotime continuum demonstrated the large variation across patients with respect to the exact developmental stage of the clonally expanded B-cells that was obscured when using a simple stratification of cells into populations.

To demonstrate the added clinical value unveiled by cellular mapping to the tuMap pseudotime continuum as compared to discrete populations, we utilized the longitudinal clinical information about relapse occurrence that was shown to be accurately predicted by a set of six signaling responses at baseline and under stimulations(Good et al., 2018). To compare the clinical predictive value of these responses across methodologies, we quantified the expression levels of these signaling molecules at 50 points along the tuMap pseudotime axes of ALL patients at baseline and following stimulations (see Methods). We next calculated regularized survival models to predict relapse occurrence on the training cohort using the two sets of signaling responses calculated either by discrete developmental B-cell populations or along the tuMap pseudotime axis, and evaluated their predictive performance using the integrated AUC(Uno et al., 2007) (iAUC) and c-statistic(Uno et al., 2011) on the test cohort (Methods). The signaling responses along the tuMap pseudotime axis yielded better iAUC and c-statistic values as compared to the model that used equivalent signaling responses by discrete B-cell populations under different levels of regularization (Fig. 3D, Supp. Fig. 5E). Taken together, this indicates that the high-resolution characterization of signaling responses along the tuMap axis can uncover clinically meaningful information that may be masked through averaging by coarse-grained cellular grouping into cell populations.

Cellular density along tuMap pseudotime axis predicts survival in AML.

We next sought to demonstrate tuMap performance in facilitating a systematic cancer samples’ comparison by applying it on bone marrow samples from patients diagnosed with acute myeloid leukemia (AML), a hematologic malignancy that involves the myeloid lineage. For this, we used single-cell mass cytometry (CyTOF) to profile human bone marrow aspirates collected from nine healthy individuals and 21 AML patients that were sampled longitudinally at the time of AML diagnosis and 14 days following initiation of an induction therapy. For one patient we profiled an additional sample during disease remission, and for six patients we profiled an additional bone marrow sample at the time of AML relapse diagnosis (Fig. 4A, Methods, Supp. Table 1 for demographics, Supp. Tables 2-3).

Figure 4: Application of the tuMap algorithm on AML bone marrow samples reveals predictors of survival.

(A) AML CyTOF study design: human bone marrow aspirates of nine healthy individuals and 21 AML patients sampled at the time of AML diagnosis and 14 days following an induction therapy were profiled by CyTOF. For six patients, additional samples from relapse diagnosis were profiled, whereas for one patient, an additional sample from remission was profiled. (B) A PCA 2-dimensional embedding of the developing monocytic cell populations: monoblasts (yellow), promonocytes (pink) and monocytes (red), for 10,000 cells sampled with inverse relation to the cell populations’ abundances. (C) Left: The dynamics of stemness index as calculated for one AML patient at multiple time points during the disease course: AML diagnosis, 14 days following initiation of an induction therapy, disease remission, and disease relapse. Right: Boxplots of the stemness indices distributions across all AML patients sampled at AML diagnosis, 14 days following an induction therapy and relapse diagnosis (paired t-test P = 0.04, 0.04, n = 19, 6 samples with paired day 14 and either diagnosis or relapse samples, respectively). Actual values overlay the boxplots as grey dots. Asterisk denotes P < 0.05. (D) Kaplan-Meier survival curve for n = 19 AML patients with matched diagnosis and day 14 samples stratified by the median risk as derived from the COX regularized model (log-rank test P = 1.7810⁻⁵, n = 10, 9, low risk (yellow) and high risk (brown) patients, respectively).

We manually gated the monocytic developmental cell populations from the healthy samples using their known markers’ expression profiles (Methods, Supp. Fig. 6). As expected, the monocytic cell populations of the healthy samples were ordered along a continuous trajectory that reflects the normal differentiation process from monoblasts to mature monocytes (Fig. 4B, Supp. Fig. 7A). The markers’ expression dynamics along the averaged trajectory matched their known trends through differentiation, with downregulation of the stemness markers: CD34 and CD117 and an upregulation of the terminal differentiation markers such as: CD14 and CD64 (Supp. Fig. 7B). In addition, healthy individuals exhibited relatively conserved cellular density distributions along the averaged trajectory, reflecting the tight regulations that are placed on the stoichiometry of the monocytic differentiation process under physiologically normal conditions (Supp. Fig. 7C).

We next sought to leverage the tuMap algorithm to characterize the monocytic differentiation process occurring in the leukemic samples to derive clinical associations. Similar to the approach we followed in the analysis of ALL CyTOF data, we defined the markers’ expression profiles of the healthy myeloid cell populations and then applied a developmental classifier that assigns single cells from the AML samples to the closest healthy population (Supp. Fig. 6A, Supp. Fig. 8, Supp. Fig. 9A, Methods). We extracted only those cells assigned to the monocytic cell populations to generate a developmental trajectory per sample in a semi-supervised manner, following which we applied the tuMap algorithm to derive per sample the tuMap pseudotime axis (Methods). Similar to ALL, the markers’ weights assigned by the tuMap algorithm exhibited a large variability across samples, reflecting the markers’ relative tendency to preserve their expression dynamics along the monocytic differentiation process in AML (Supp. Fig. 9B). Furthermore, and in contrast to the healthy samples, we observed a large variation across the AML samples with respect to the cellular density along the tuMap pseudotime axis (Supp. Fig. 9C).

To quantify these differences in cellular density between patients and understand its clinical meaningfulness, we leveraged the cross-sample standardization of the tuMap pseudotime axis to calculate per sample the earth movers’ distance (EMD) between the cellular density distribution along tuMap pseudotime relative to that calculated along the averaged healthy pseudotime (Methods). The resulting EMD values reflect the extent of deviation of the AML patient from healthy development and specifically, the overall degree of cellular maturation in the sample. That is, samples with a high EMD value exhibit a high abundance of immature, stem cells and vice versa. We thus defined the stemness index of a sample as the EMD of the cellular density distribution along the tuMap axis relative to the healthy cellular density distribution, allowing for a meaningful developmental characterization of AML samples. We observed that the diagnosis and relapse samples exhibited large stemness indices, which were significantly reduced 14 days following induction therapy, reflecting a response to the given treatment that was reversed when the disease relapsed (Fig. 4C, paired t-test P = 0.04, 0.04, n = 19, 6 samples with paired day 14 and either diagnosis or relapse samples, respectively). This suggested a potential linkage between the cellular density distributions along the tuMap axis and clinical outcome.

To study this hypothesis, we calculated a regularized cox proportional hazard model correlating patients’ overall survival with age at AML diagnosis, gender, and cellular density along the tuMap pseudotime axis at diagnosis and 14 days following initiation of treatment (Methods, Supp. Table 4). Stratification of patients by the median risk value as predicted by the model yielded two groups whose survival rates significantly differed (Fig. 4D, log-rank test P = 1.7810⁵, n = 19 patients with matched diagnosis and day-14 samples). Apart of age at AML diagnosis, the optimal survival model identified cellular density at specific regions along the tuMap trajectory at day 14 and not day 0 to be predictive of survival. Furthermore, a similar stratification of AML patients into groups based on their median age alone yielded a less significant difference in overall survival (log-rank test P = 0.004, n = 19 patients), emphasizing the importance in post-treatment patients’ monitoring for clinical evaluation. Studying the cellular density distributions along the tuMap pseudotime axis of day-14 samples revealed that patients assigned to the low-risk group exhibited an enrichment of mature cells following therapy, in contrast to those patients assigned to the high-risk group, reflecting a favorable response to therapy (Supp. Fig. 9D). To compare the predictive performance of the tuMap approach to the one that relies on cellular assignment into discrete cell populations, we calculated a similar survival model using the frequencies of the main monocytic cell populations (monoblasts, promonocytes and mature monocytes). The resulting model was less predictive to the overall patients’ survival (log rank test P = 0.0018, n = 19 patients with matched diagnosis and day-14 samples), highlighting the added value obtained by the continuous characterization of the involved cell lineage in clinical predictions.

Alignment of single-cell gene-expression bone marrow samples of AML patients by tuMap reveals differential gene regulations at the very early stages of leukemic development.

To demonstrate tuMap utility and performance on single-cell RNA sequencing data, we used a publicly available dataset of bone marrow aspirates from healthy individuals and AML patients sampled at multiple time points during their disease course(van Galen et al., 2019). The original publication leveraged single-cell gene expression to assign single cells to the main bone marrow cell populations and single-cell genotyping to classify cells from the AML samples as either malignant or normal. Similar to the approach we applied in the AML CyTOF dataset, we used those cells assigned to the monocytic developmental lineage that were further identified as either being normal or malignant from the healthy and 9 AML diagnostic samples, respectively (Methods).

We first utilized this rich dataset to characterize the trajectory of monocytic development in the healthy samples using the set of genes that assemble the gene-signatures of the main monocytic cell populations, as identified by the original publication (Fig. 5A, Supp. Fig. 10A, Methods). The expression patterns of these genes changed continuously along the averaged healthy trajectory, peaking at the pseudotime regions that correspond to the respective cell populations (Supp. Fig. 10B).

Figure 5: Alignment of single-cell gene-expression bone marrow samples of AML patients by tuMap reveals differential gene regulation at very early leukemic cells.

(A) A PCA 2-dimensional plot of the developing healthy monocyte cell populations: HSC, progenitors, GMP, promonocytes and monocytes. (B) Genes’ weights assigned by tuMap for those genes related to the HSC-Prog and Myeloid gene-signatures across 9 AML patients (t test P = 3.210⁻²⁸, n = 279, 279, gene-sample combinations, for HSC-Prog and Myeloid signatures, respectively). Actual values overlay the boxplots as grey dots. *** denotes P < 0.001. (C) Mean difference in gene expression between early cells of AML and healthy samples when using either the tuMap trajectory (x-axis) or discrete populations (cells labeled as either HSC or progenitor populations). Genes are colored red, blue, and green based on their difference in expression between AML and healthy relative to the 0.25 threshold resulting from each methodology. Genes are colored red, blue, and green based on their mean difference and its directionality relative to the 0.25 threshold resulting from each methodology. Dashed line denotes equal effect size by both methodologies. DE: differentially expressed. (D) Mean expression levels of the two genes: MSI2 and CD164 by single cells assigned to the early regions of the tuMap pseudotime axis for 9 AML patients either with (yellow, n=4) or without (green, n=5) FLT3-IDT mutation.

In accordance with our previous analysis on the CyTOF data, as compared to the healthy, gene-expression variability among malignant AML cells was significantly more attributed to the patient, justifying the individualized trajectory approach we apply on AML samples (Supp. Fig. 10C, Methods, t-test P = 3.04∙10⁻⁶⁸, n = 126 combinations of 4 AML samples). We assembled developmental trajectories for each AML diagnosis sample individually, with a strong correspondence between the positions of cell populations along the resulting trajectories relative to their positions along the averaged healthy pseudotime axis (corDist = 0.91±0.05, Supp. Fig. 10D, Methods). We next derived the tuMap pseudotime axis of the AML samples that enables a meaningful comparison across AML samples and relative to the healthy trajectory (Methods). We observed that the weights assigned by tuMap to those genes constituting the signature of mature myeloid cells were significantly higher as compared to those genes constituting the signature of progenitor cells (Fig. 5B, t test P = 3.2∙10⁻²⁸, n = 279, 279 gene-sample combinations, for HSC-Progenitors and Myeloid gene-signatures, respectively). This suggests an underlying mechanism in cellular maturation in AML that differentially affects the stemness and maturation genes, such that the process of myeloid specialization is relatively conserved in contrast to the processes of pluripotency decay.

To characterize more deeply the effect of AML on the gene expression patterns of stem cells, we sought to leverage the continuous nature of the tuMap trajectory to isolate very early cellular forms of the myeloid compartment. To showcase this capability, we calculated the median, scaled expression of cell-cycle genes by single cells distributed along the early parts of the healthy trajectory (Methods). In agreement with the known quiescent nature of the early stem cells(Guan et al., 2003), we observed a positive correlation in the expression of cell-cycle genes by single-cells from both HSC and progenitor populations along the healthy trajectory, such that the earliest cells exhibited lower expression of cell cycle genes as compared to those assigned to later parts of the trajectory (Supp. Fig. 10E, Pearson’s r = 0.43, 0.6, for HSC and progenitor cells, respectively). We next sought to leverage the tuMap framework to reveal gene-expression differences between the leukemic stem cells and the healthy counterpart. For this, we calculated the mean expression of each gene in those single cells assigned to these early regions of the healthy and tuMap trajectories for healthy and AML samples, respectively. Similarly, we computed gene expression difference effect size values when cells were designated as early population based on discrete labeling. Comparison of these two ways of identifying early cells showed that despite being highly correlated (Pearson’s r = 0.76) the effect size values obtained through the continuous tuMap methodology were remarkably bigger than those of the discrete labeling approach, facilitating identification of 173 differentially expressed genes undetectable otherwise (Fig. 5C). This analysis suggests that the sensitivity of the tuMap pseudotime axis to identify early developmental stages can be used to reveal leukemic stem cells’ properties driven by the tumor’s genetic background. To test this, we compared the average expression of genes in early parts of the tuMap pseudotime axis between those AML patients harboring the FLT3-IDT mutation relative to those without it (Methods). We identified two genes that exhibited the highest difference in mean expression values in the early regions of the tuMap pseudotime axis between the groups: MSI2 is an RNA-binding protein that regulates the expression of FLT3 gene(Hattori et al., 2017), with known high expression levels associated with FLT3-IDT positive(Thol et al., 2013), and CD164, a hematopoiesis regulator(Zannettino et al., 1998), which was shown to be involved in multiple cancers(Chen et al., 2017; Havens et al., 2006; Huang et al., 2013; Wang et al., 2019) through regulation on proliferation and survival genes and promotes stem-cell activity, suggesting a potential leukemic stem cell marker specific to the FLT-IDT AML cases (Fig. 5D). These results emphasize the capability of tuMap to accurately delineate cell populations at very specific developmental stages, enhancing identification of gene-signatures.

Discussion

Cancer is characterized by a significant inter-patient variability driven by the patient’s specific unique genetic profile, hindering a meaningful systematic cross-sample comparison, and highlights the need in a personalized approach. Here, we developed the tuMap algorithm that aligns cancer single cells samples with the healthy developmental axis to yield the tuMap pseudotime axis that is similarly scaled across samples thus allowing a systematic comparison. tuMap is robust to the noise introduced by patient-specific alterations of markers’ expression profiles by using a high dimensional alignment that emphasizes the effect of the conserved markers while attenuating the effect of the non-conserved markers. Thus, the tuMap algorithm can be used both for cross-sample comparison of the different features, such as signaling responses, along the axis and for deriving the exact developmental stage of single cells within the cancer sample to provide a meaningful insight into the comparative result. Of note, tuMap is an alignment algorithm, thus should be applied on cancer and healthy trajectories assembled a priory irrespective of the trajectory-inference methodology used, yet in the manuscript we recommend using a semi-supervised trajectory inference approach that yields trajectories that reflect the normal development.

Developmental classification of cancer cells has been demonstrated before, where the cellular assignment to discrete cell populations provided a ground truth for cross-samples comparison. To demonstrate the added value provided by cellular mapping to the continuous tuMap pseudotime axis, we contrasted both methodologies on single-cell mass cytometry datasets of bone marrow aspirates from ALL(Good et al., 2018) and AML patients. In both cases, we identified regions along the tuMap pseudotime axis that predict outcome better than stratification into cell populations, probably as a result from elimination of features’ averaging across cells assigned to a certain cell population. Using a single-cell RNA sequencing dataset, we showed that the tuMap pseudotime axis can be used to identify very early leukemic stem cells, thus enabling differential gene-expression analysis that highlights candidate leukemic stem cell markers.

tuMap is well suited for cancers that develop in tissues exhibiting an internal cellular hierarchy with cells encompassing different stages of the differentiation process. This nature of tissue composition can be found mostly in hematologic malignancies as these typically arise from progenitor cells with a characteristic and well-defined developmental trajectory reflecting maturation. Yet, recent studies have identified an underlying correspondence between cancer samples and healthy development also in solid tumors such as glioblastoma(Couturier et al., 2020) and renal tumors(Young et al., 2018), suggesting that the tuMap algorithm can be applied also to non-hematological malignancies. Of note, the tuMap algorithm assigns weights to markers by their relative tendency to preserve their expression dynamics along the sample’s trajectory relative to the healthy. In some cases, the markers’ expression dynamics are extremely abnormal, yielding a meaningless alignment. tuMap provides two measures to avoid such cases: (1) by reporting the alignment error to identify those cases where the alignment is based on a very small set of markers assigned with high weights, and (2) by outputting the alignment-based distance that can be high in those cases where no marker exhibits a conserved expression. We note that increasing the breadth of the markers measured per cell by more sophisticated marker selection strategies or applying a preliminary step in which the markers are chosen a priori based on their conservation with the healthy might reduce such cases.

Fine modifications of the tuMap algorithm can expand its applicability. In some cases, the scarcity of the healthy material may hinder a high-resolution characterization of the averaged healthy reference. An optional solution involves alignment of the cancer samples one to another to obtain a consensus trajectory that includes the information embedded in each sample, similar to multiple sequence alignment(Thompson et al., 2011). In addition, the current version of the tuMap algorithm assumes that the healthy samples can be represented by a linear developmental trajectory. We believe that combining the principles of tuMap and branched-trajectories alignment tools(Do et al., 2019) can yield trajectory alignment algorithms that are capable to systematically compare cancer samples exhibiting a branched developmental axis.

The standardization of the tuMap pseudotime axis across patients allows to derive molecular events at a precise developmental stage that may explain differences in clinical outcome. In addition, one can infer per sample the cascade of activation of specific pathways along the tuMap pseudotime and to compare it across patients. Associations between these traits and specific mutations may unravel the pathogenesis of cancer development under different genetic background. Such information can be utilized to target specifically the molecular pathway identified as clinically relevant in a certain developmental stage, allowing for a personalized therapy.

In the recent years, high-throughput profiling of cancer samples by single-cell technologies such as single-cell RNA sequencing and mass cytometry continues to grow, allowing for a high-resolution characterization of developmental processes that are frequently abnormal in cancer. A comparative framework for these samples is an essential tool for patients’ tumors’ characterization to forward a deeper understanding of molecular dynamic mechanisms and fine-tuned clinical metrics that are the building blocks of a cancer precision medicine era.

STAR METHODS

RESOURCE AVAILABILITY

Lead contact

Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Shai S. Shen-Orr (shenorr@technion.ac.il).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• AML mass cytometry data generated during this study are available at: https://data.mendeley.com/datasets/my928cxv7f/3. The DOI is listed in the key resources table. This paper further analyzes existing, publicly available data. The accession numbers for the datasets are listed in the key resources table.

• All original code has been deposited at: https://data.mendeley.com/datasets/my928cxv7f/3 and is publicly available as of the date of publication. DOIs are listed in the key resources table.

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

EXPERIMENTAL MODEL AND SUBJECT DETAILS

Bone marrow samples were collected in the department of hematology at Rambam Medical Center, Haifa, Israel. All the participants gave a written informed consent, and the study was approved by the local ethical requirements and the declaration of Helsinki (IRB number: 0076–15-RMB). Patient identifiers were anonymized before data analysis. The clinical data of the AML patients are provided in Supp. Table 4, and summary statistics regarding the age and gender of the healthy individuals and AML patients are provided in Supp. Table 1.

METHOD DETAILS

Sample collection of AML patients.

Mononuclear cells were separated by centrifugation over a layer of Lymphoprep™ (Axis Shield) and then were stored in freezing medium (90% fetal bovine serum, Biological Industries, 10% Dimethyl Sulfoxide, Sigma) in liquid nitrogen until being processed. CyTOF profiling. Primary conjugates of mass cytometry antibodies were prepared using the MaxPar X8 labeling kit (DVS Sciences) according to the manufacturer protocol and optimal concentration per antibody was determined by titration (antibodies’ details are provided in Supp. Table 2). Frozen AML and healthy bone marrow samples were washed twice in warm cell culture media (RPMI-1640 media supplemented with 10% fetal bovine serum (Biological Industries), 1% Penicillin-Streptomycin-Glutamin) with Pierce™ universal nuclease for cell lysis (1: 10,000 dilution, ThermoFisher) and stained in 1mL cell culture media with Rhodium intercalator (DVS Sciences, 1:2,000 dilution for 20 minutes at room temperature) to discriminate between dead and live cells. The cells were then washed twice with cell staining media (CSM, phosphate buffered saline + 0.5% bovine serum albumin, both from Sigma) and stained with the antibodies cocktail in 100uL CSM at room temperature, followed by another CSM wash and fixation with formaldehyde (Pierce, 1.6%, in 1mL at room temperature). The samples were preserved in formaldehyde until acquisition day. Before acquisition, the cells were washed in once in CSM and stained with Iridium (DVS Sciences, 1:2,000 dilution in 0.5mL for 20 minutes at room temperature). Finally, the samples were washed 3 times with DDW immediately prior to acquisition with CyTOF1 machine (DVS Sciences). The cells in each sample were counted and diluted to 1 million cells in 1mL DDW. 630uL from each sample were filtered through cell strainer and added to 70uL EQ Four Elements Calibration Beads (DVS Sciences) for normalization. The CyTOF machine was tuned according to the manufacturer instruction with a tuning solution (DVS Sciences). The resulting FCS files were normalized(Finck et al., 2013) and gated in cytobank.org(Kotecha et al., 2010).

QUANTIFICATION AND STATISTICAL ANALYSIS

ALL data analysis.

WHealthy and ALL Lineage- bone marrow samples were downloaded from Github (https://github.com/kara-davis-lab/DDPR/releases).

Healthy data preprocessing.

We followed the gating scheme provided by the original manuscript to gate the baseline files of the healthy to the main 15 B-cell populations (in Cytobank.org), followed by concatenating all the populations into one file and applying asinh transformation with cofactor of 5.

ALL data preprocessing.

Baseline Lin- ALL samples, as well as those stimulated by one of the four perturbations used for the clinical predictive model (i.e., BCR cross-linking, IL7, TSLP, and pervanadate) were concatenated. The fcs files of the different cohorts were normalized by quantile normalization using the normalization factors provided by the authors of the original publication.

Inter-marker correlation.

Single cells in each healthy sample were clustered using the Phenograph algorithm with k=20 (R package cytofkit(Chen et al., 2016)), followed by calculation of the median markers’ expression in each cluster and inter-marker correlation matrix across clusters.

Projection of noised data on healthy PCA.

To simulate ALL data, we applied permutations per developmental marker (i.e., CD34, CD38, CD19, TdT, CD179a, CD179b, CD127, CD24, CD20, IgHi, and IgHs) independently across cells used for trajectory assembly of the averaged healthy samples. Next, we projected the noised data on the healthy PCA space and assigned each cell with the PAGA pseudotime of its closest neighbor on the 2-dimensional PCA space. For robustness assessment, we computed Spearman correlation between the original and new PAGA pseudotime values. To contrast these correlations with the supervised trajectory building technique, we inferred a developmental trajectory under the noised data, as detailed below, and similarly calculated the Spearman correlation values between the pseudotime values achieved with or without noise.

Marker expression variance analysis.

For the healthy individuals, we sampled 10,000 cells per individual with an inverse relation to the assigned population’s frequency, and calculated an ANOVA model regressing the developmental markers’ expression against the assigned population and individual ID. To achieve a fair comparison between the healthy and ALL samples, we performed 100 simulations, in each we sampled 5 ALL individuals and performed similar downstream analysis as detailed for the healthy.

Assembly of averaged trajectories.

For the healthy trajectory, we used only those cells assigned by manual gating to one of the developmental populations, as defined by the original publication: hematopoietic stem cells, Progenitor 1–3, Pre-Pro-B, ProB1–2, PreB1–2, Immature B1–2, and Mature B. For the ALL samples, we first assigned the cells to the main healthy population using the classifier provided by the authors of the original publication and extracted only those cell populations that span the healthy developmental trajectory, as detailed above. We next applied the PAGA algorithm (Reticulate R package, scanpy Python package) on the expression levels of the developmental markers, as defined by the original publication (CD34, CD38, CD19, TdT, CD179a, CD179b, CD127, CD24, CD20, IgHi, IgHs). To obtain a trajectory that best reflects the healthy development, the number of neighbors (k) used by the PAGA algorithm was optimized to obtain the maximal correlation between cell populations’ ordering along the axis as compared to their known ordering, for k = {20, 30, 40, 50, 60, 70, 100}. For a fair comparison between the healthy and ALL despite the different number of samples (n = 5, 60 samples for healthy and ALL, respectively) and the different number of cells per sample, we used all the cells from the healthy samples whereas for the ALL samples, we applied 100 iterations, in each we sampled 5 ALL patients and from each patient we sampled 15,000 cells with an inverse relation to the cell populations’ abundance. Due to computational considerations and algorithmic complexity, to assemble an averaged trajectory of all the 60 ALL samples, we subsampled 5,000 cells per ALL sample with an inverse relation to the cell populations’ abundance. The resulting pseudotime values were scaled to 0–1 range and the trajectory’s directionality was set as the direction along which CD34 expression declines along the trajectory.

Assembly of individual trajectories.

We used those cells assigned to the same developmental populations and the same set markers as detailed above for the averaged trajectory case. To normalize the number of cells used for trajectory assembly across samples, we sampled 10,000 cells from each sample (both healthy and ALL) with inverse relation to the cell populations abundance. To obtain the optimal individual trajectory that best reflects the healthy development, we applied parameters optimization of the number of clusters for Slingshot (k={1,2,3,4,5,6,7,8}, 5 repetitions for each, slingshot R package) and Scorpius (k={4,5,6,7,8,9,10,11,12}, 5 repetitions for each, SCORPIUS R package) algorithms and the number of neighbors for the PAGA algorithm (k = {10, 15, 20, 30, 40, 50, 60, 70, 100}, 5 repetitions for each, Reticulate R package, scanpy Python package). Of note, in ~50% of the runs, the Slingshot algorithm yielded branched trajectories which we eliminated from the optimization process and downstream analysis. To reduce the number of these cases and guarantee at least one non-branched trajectory per sample, we used lower values of k and included k=1 in the parameters’ set used in the optimization process. The optimal parameter was chosen to maximize the corDist relative to the averaged optimal healthy trajectory assembled using the respective algorithm, where the corDist is the Pearson correlation between the absolute difference in median positions of each two cell-populations along the two trajectories (Supp. Fig. 3A). The resulting pseudotime values were scaled to 0–1 range and the trajectory’s directionality was set as the direction along which CD34 expression declines along the trajectory.

Assembly of ALL trajectories with Psupertime.

The cells were first classified into developmental cell populations, as detailed above. Classified cells were then assigned with ordinal numbers that reflect the relative ordering of their assigned cell-populations along the developmental axis (for instance, “HSC” and “mature B” cell populations were assigned with 1 and 12, respectively). We then applied the psupertime algorithm using the psupertime R package with the developmental markers detailed above using “best” penalization methodology for choosing the optimal lambda for regularization and the cross-entropy loss function. The resulting pseudotime values were trimmed to have terminal regions’ cellular density above 0.5% and were scaled to 0–1 range.

Assessment of conservation of markers’ expression dynamics in healthy, ALL samples and random data.

To obtain a fair comparison across conditions, we subsampled 10,000 cells per sample (both healthy and ALL) with an inverse relation to the assigned cell populations’ abundance, with which we inferred a trajectory in a supervised approach, as detailed above. For each cell, we chose the closest healthy cell with respect to the averaged-healthy pseudotime axis and calculated either the high dimensional distance with respect to the developmental markers (Fig. 2A) or marker-specific distance (Supp. Fig. 4A). As a negative control, for each ALL sample we generated 10 random expression datasets using permutations applied on each marker across cells and ran a similar analysis.

The tuMap algorithm.

The tuMap algorithm takes as input single cells from the healthy and cancer samples ordered along two pseudotemporal axes, and a processed high dimensional expression matrix of markers with an established relevance to the developmental process. Similar to the cellAlign algorithm, in order to remove the effects of the noise in markers’ expression and the biased cellular distribution along the trajectories on the alignment, we recommend to interpolate the expression of markers along both trajectories prior to the alignment process(Alpert et al., 2018b). The tuMap algorithm estimates the tuMap pseudotime values per cell by applying three sequential steps: markers’ weighting, assembly of the dissimilarity matrix and pseudotime scaling, as detailed below. Markers’ weighting. tuMap first assesses the conservation of markers’ expression dynamics along the healthy and the cancer trajectory by single-marker alignment performed by the cellAlign algorithm. The resulting alignment-based distances between the two trajectories per marker are then transformed to obtain weights that are inversely related to the distance. The tuMap algorithm provides two classes of transformation functions: sigmoidal and non-sigmoidal. The non-sigmoidal transformation calculates the marker’s weight as a multiplicative inverse function of the marker’s alignment-based distance as follows:

$$w_{marker}=\frac{1}{\alpha +align\_dis{t}_{marker}}$$

The markers’ weights are then normalized such that their sum equals to 1: $w_{marker}\to \frac{w_{marker}}{{\displaystyle {\sum }_{m\in markers}{w}_m}}$. Of note, a titration of the α parameter changes the distributions of resulting markers’ weights: Increasing the value of alpha yields a more uniform distribution of weights, resulting with alignments that resemble the cellAlign alignments, whereas decreasing the value of alpha strongly biases the markers’ weights distribution to prioritize those markers with low alignment-based distance (Supp. Fig. 4B-C). The second transformation function provided by the tuMap algorithm is the sigmoidal transformation:

$$w_{marker}=\frac{1}{1+e^{align\_dis{t}_{marker}-\alpha }}$$

This transformation exhibits an inflexion point whose location depends on the value of alpha and reaches saturation levels of either 0 or 1 with increasing or decreasing marker’s alignment-distance, respectively. Thus, similar to the non-sigmoidal transformation function, titration of the alpha parameter affects the markers’ weights: Increasing the value of alpha yields a more uniform distribution of weights, resulting with alignments that resemble the cellAlign alignments, whereas decreasing the value of alpha assigns similarly high weights to those markers with low alignment distance and similarly low weights to those markers with high alignment distance (Supp. Fig. 4D-E).

Assembly of the dissimilarity matrix.

tuMap utilizes the markers’ weights to assemble a dissimilarity matrix whose elements equal to the pairwise weighted Euclidean distance between the interpolated points. Formally, for the two interpolated points x = (x₁, x₂,. . , x_M), and y = (y₁, y₂, . . , y_M), and markers’ weights: {w₁,w₂,. . , w_M}, the weighted pairwise distance is:

$$d_{\left(x,y\right)}=\sqrt{w_1\cdot {\left(x_1-y_1\right)}^2+w_2\cdot {\left(x_2-y_2\right)}^2+\cdots +w_M\cdot {\left(x_M-y_M\right)}^2}.$$

This pairwise dissimilarity matrix is used as an input to the cellAlign algorithm to identify the path with the lowest cost that connects the healthy and cancer elements along both trajectories. To find the optimal alignment along the dissimilarity matrix, cellAlign offers the user the choice between different step functions that determine the relationships between consequent alignment steps. The symmetric1 step function penalizes a diagonal step equally to a horizonal or vertical step, thus prioritizes diagonal steps and is more robust to subtle differences in distance between adjacent elements in the dissimilarity matrix. The symmetric2 step function penalizes a diagonal step twice as much as a horizonal or vertical step, thus allows the alignment to pass through low-cost regions even under longer alignments.

Pseudotime scaling.

The resulting alignment is used to scale the pseudotime values of the cells along the patient’s trajectory to the ones along the healthy trajectory to obtain the standardized tuMap pseudotime axis in two steps. First, each cell along the patient’s trajectory is assigned to the closest interpolated point of the patient’s trajectory with respect to the pseudotime axis. Second, the assigned interpolated point is assigned to the median pseudotime position of interpolated points along the healthy individual’s trajectory that are aligned to this patient’s interpolated point.

Estimation of tuMap alignment error.

The weights tuMap places on the markers decrease the dimensionality of the alignment, introducing an error in the estimation of tuMap pseudotime. The tuMap algorithm allows the user to estimate the mapping error along the trajectory per patient by aligning trajectories assembled individually from healthy individuals relative to the averaged healthy. Given the strong correspondence between the individual and averaged healthy trajectories the obtained tuMap pseudotime values should be similar to those along the averaged healthy trajectory. Specifically, to calculate the typical mapping error, the tuMap algorithm aligns trajectories of healthy individuals with the averaged healthy trajectory using the same markers’ weights used for the patient’s alignment. The difference between the location of each cell along the averaged healthy trajectory and the mapped pseudotime is defined as the mapping error, and this value is then interpolated and averaged across patients to achieve a smooth measure along the trajectory.

Comparison of tuMap and cellAlign algorithms.

Per ALL patient, we simulated data of one-marker’s perturbation that relies on the marker’s expression distribution in the sample. For this, we used the healthy expression data from which we sampled 5,000 random cells to alleviate computational complexity. For each marker independently, we replaced its expression values with those that were sampled randomly from the marker’s expression distribution in the patient. We then re-classified the single cells from the noised dataset to the healthy developmental cell populations and used these cell populations to assemble a trajectory in a supervised manner, as detailed above, with a non-sigmoidal transformation using the parameter α = 1, and symmetric1 step pattern. The resulting trajectories were aligned to the healthy trajectory using all the developmental markers either with cellAlign, tuMap or 100 weighted alignments under random assignments of markers’ weights as sampled from a uniform distribution. The alignment weights were normalized to have a sum of 1, similar to the tuMap algorithm’s markers’ weighting principles. For each alignment, we assessed the alignment quality as the alignment-based distance: the sum of high-dimensional distances between the aligned interpolated points using only the non-noised markers. Per marker and per patient, we calculated the percentage of random weights assignments that yielded a better alignment quality (i.e., lower alignment distance) as compared to the alignments resulted from either the tuMap or cellAlign algorithms.

Application of tuMap on ALL data.

Expression values of the developmental markers along the ALL trajectories were interpolated and scaled (n=200 interpolated points and window size of 0.05). Markers’ weighting and tuMap pseudotime assembly were calculated as detailed above, using the non-sigmoidal transformation with α = 1, and symmetric1 step function.

ALL clinical association analysis.

Signaling dynamics along the tuMap axis.

To achieve equivalent predictor data as the original publication, we estimated the expression values of the 9 measured signaling molecules: pAkt, pPLCg1–2, pSTAT5, pIkaros, p4EBP1, pSyk, pCreb, pErk and pS6 along the tuMap pseudotime axes of each patient at baseline and under each perturbation of relevance (Pervanadate, IL-7, BCR Cross-link and TSLP) relative to baseline. To achieve smooth and un-noised expression along the tuMap trajectories, we defined per patient 50 equally spaced points along the tuMap pseudotime axis. Per point, we defined a window around it whose size equals to the difference between every two adjacent points and calculated the percentage of cells within this window with positive expression of the signaling molecule, similar to the original publication and using the same expression threshold (10). Similar to the original publication, we normalized the signaling molecules’ expression values along the tuMap trajectories of the samples under the four perturbations to those values measured at baseline as per sliding window.

Survival analysis.

To achieve equivalent sets of predictors for comparison between tuMap continuous axis and the assignment into discrete populations, we used as predictors only the expression values of 9 signaling molecules at baseline and following 4 perturbations, as mentioned above, either along the trajectory or in the 12 developmental cell populations, as provided by the original publication. For the survival models, we followed the original publication and used the data of 54 patients with available clinical information along with their stratification into training (n = 44 patients) and test (n = 10 patients) cohorts. We preprocessed the predictors data using similar steps taken by the original publication, specifically: we replaced missing values with the median value across patients, we removed those predictors which got zero values across all patients and scaled the predictors’ expression by subtraction of the mean and division by the standard deviation. Similar to the original publication, we used weighted lasso models to overcome the imbalance between the number of patients who experienced relapse versus those who did not. We calculated cross-validation Cox survival models under different values of alpha to identify per alpha the optimal lambda value (chosen as the value yielding the minimal cross-validation error; glmnet R package) and assessed the integrated iAUC(Uno et al., 2007) and C-statistic(Uno et al., 2011) per alpha (survAUC R package) for the test-set.

tuMap application on the AML CyTOF dataset.

Gating of healthy and AML samples.

Gating was performed using cytobank software. Healthy and AML bone marrow samples were gated to exclude B cells, T cells and NK cells, followed by inclusion of only the HLADR⁺ cells, a fraction that includes the monocytic cell populations without contamination of thromboblasts, and myelocytes (see Supp. Fig. 6 and 8 for healthy and AML gating schemes). The healthy samples were subjected to an additional gating step to identify erythroblasts, monocytic and plasmacytoid dendritic cells, monoblasts, promonocytes and monocytes.

Trajectory assembly.

To build a classifier of the bone marrow myeloid cells, we calculated per healthy cell population (erythroblast, mDC, pDC, monoblast, promonocyte and monocyte) the mean expression and covariance matrix of those markers that are typically expressed by these cell types, specifically: CD34, CD123, CD33, CD64, CD11c, CD14, CD13, CD117, CD71, and CD11b. These matrices were used to calculate the Mahalanobis distance of each single cell from the respective healthy population, such that each cell was assigned to the cell population whose Mahalanobis distance from the cell is minimal. Cells whose Mahalanobis distance from the closest healthy population exceeded the number of markers used for classification (10), were tagged as unclassified and were removed from downstream analysis. Contrasting single cells’ predicted classifications as resulted from the classifier versus the gold standard classification achieved through manual gating, resulted with classification accuracy of 74% (see Supp. Fig. 9A for confusion matrix, caret R package). Only those cell subsets classified as: monoblasts, promonocytes and monocytes, the developmental populations along the monocytic lineage, were used for trajectory building. Two samples with an insufficient number of cells (< 50) classified as related those cell populations constituting the monocytic lineage were excluded from the trajectory building analysis (patient 12 day-14, patient 20 day-14). We used the psupertime algorithm on the classified cell populations to generate a trajectory per AML sample, as described above for the ALL dataset, using those markers expressed by different stages of the monocytic developmental axis based on the literature, specifically: CD34, CD117, CD33, CD64, CD13, CD14, and CD11b. We applied the tuMap algorithm using the same parameters as described above for the ALL dataset.

Survival analysis.

Density along the tuMap trajectory on the healthy and the AML tuMap pseudotime axis were calculated using the density function with 128 equally spaced points between 0 and 1 pseudotime range. Earth movers’ distances between the AML samples and healthy density vectors were calculated using the emd function (emdist R package). A regularized Cox proportional hazard model was applied using cv.glmnet function (glmnet R package) with alpha = 1, and 5 cross-validation folds with the following predictors: diagnosis age, gender, density calculated on 128 equally spaced points between 0–1 pseudotime axis on diagnosis and day 14 (a total of 258 predictors). The model was applied only on those 19 patients for whom the day 14 sample was not excluded due to insufficient number of cells (i.e., excluding n = 2 patients, as detailed above). The best lambda yielding the minimal cross-validation error was used to calculate a regularized COX model under the same set of parameters and on the same patients (cv.glmnet and glmnet functions, glmnet R package). The resulting model was used to calculate the predicted risk for each patient (predict function, glmnet R package), and the patients were stratified into 2 groups based on the median risk calculated across patients. The log-rank test for differences in survival between the 2 groups was calculated using the survdiff function (survival R package).

tuMap application on the AML scRNAseq dataset.

Processed gene-expression and cellular annotation data of bone marrow aspirates were downloaded from GEO website (GSE116256).

Sample filtering.

We used the four healthy bone marrow samples (named: “BM1–4”), and diagnosis bone marrow samples of 9 out of 16 AML patients which have a sufficient number of mature and immature cells, based on the original publication’s annotations file. Specifically, for healthy samples we used the cells assigned to the monocytic developmental cell populations: “HSC”, “Prog”, “GMP”, “ProMono” and “Mono”, whereas for the AML samples we used those cells classified both as malignant and as related to the monocytic lineage: “HSC-like”, “Prog-like”, “GMP-like”, “ProMono-like” and “Mono-like”. For 4 patients, no cells were classified as the above populations (samples: “AML314”, “AML371”, “AML722”, and “AML977”); For 2 patients there was an insufficient representation of the ProMono-like and Mono-like populations (samples: “AML420”, and “AML916”); For one patient, there was an insufficient representation of the HSC-like and Prog-like populations (sample: “AML556”). This filtering step resulted with the following remaining AML samples: “AML1012”, “AML210”, “AML328”, “AML329”, “AML419”, “AML475”, “AML707”, “AML870”, and “AML921”.

Gene-expression data preprocessing.

Guided by the tutorial of Seurat R package (https://satijalab.org/seurat/v3.2/pbmc3k_tutorial.html), gene-expression values were normalized by the total counts per cell and then log-transformed with a scale factor of 10,000. For the combined healthy samples and per AML diagnosis file, we filtered out those genes exhibiting a non-zero expression value by less than 1% of the cells. To avoid the effect of dropouts on the alignment process, we imputed the expression of the genes in the dataset prior to alignment using the function magic (Rmagic R package)(Dijk et al., 2018) with the default set of parameters.

Variability analysis.

We regressed the raw (i.e., non-imputed) expression values per gene against the individual ID and the cell population, and calculated the variability explained by each using ANOVA. The set of genes used in this analysis for the healthy and AML included those reported by the original study as assembling the gene-signatures of the developing cell populations, respectively (for healthy: HSC-Prog, GMP, and Myeloid; for AML: HSC-Prog-like, GMP-like, and Myeloid-like). These sets of genes were further filtered to include only those genes that exist in the averaged healthy gene-expression data and in each AML patient’s gene-expression data following the gene-filtering applied in the preprocessing step, detailed above. To normalize the effect of the different number of samples in AML as compared to the healthy (n = 9, 4, respectively) on the resulting variability, we performed it multiple times on AML samples, each time with sampling of 4 out of 9 different AML samples, and reported the average percentage of explained variability across genes.

Trajectory assembly.

We used the psupertime supervised trajectory inference algorithm on the imputed gene expression data of single cells assigned to monocytic developmental cell populations and using the genes assembling these cell-populations’ signature genes provided by the original article for the healthy samples to generate a trajectory, as detailed above. Specifically, for the healthy samples, we used the developmental cell populations: HSC, Progenitors, GMP, Promonocytes and Monocytes, whereas for the AML samples we used the developmental cell populations: HSC-like, Progenitors-like, GMP-like, Promonocytes-like and Monocytes-like. For both the healthy and AML samples, we used the gene-signatures of healthy developmental cell populations provided by the original article to assemble the trajectory. Of note, to achieve uniform trajectory building conditions across patients, the set of genes was filtered to include only those genes that remained in all the AML samples following the gene filtering applied in the preprocessing step, detailed above. Genes’ weights and tuMap pseudotime axes per sample were calculated as described above for the CyTOF datasets.

Cell cycle genes expression dynamics.

We used those genes annotated as related to cell cycle genes by KEGG and scaled their imputed expression values across the healthy cells. We then calculated the median scaled value per cell across genes as a representative to the overall expression of the cell cycle genes by each cell.

Differential expression analysis.

We defined early cells along the trajectory as those with either averaged pseudotime or tuMap pseudotime values smaller than 0.05, for healthy and AML samples, respectively. Similarly, early cells by populations were defined as those classified as HSC/HSC-like and Prog/Prog-like, for healthy and AML samples, respectively, similar to the approach applied in the original publication. For the combined healthy samples and per AML sample, we calculated the mean expression of each gene by the early cells as defined either by the tuMap trajectory or by cell populations. Because of the strong conservation of gene-expression patterns in healthy individuals, we used this mean value as a representative to the averaged healthy gene-expression levels, whereas for the AML samples, we averaged these expression values across patients to obtain the overall expression of each gene by early cells in AML. The gene-specific effect-size representing the differential expression of each gene between AML and healthy samples was calculated as the difference in the overall expression of the gene in AML relative to its expression level in the healthy. For differential expression analysis between FLT3-IDT positive and negative patients, we used the mean expression level per gene by early cells of AML patients as defined by the tuMap pseudotime axis, calculated as detailed above. We averaged the resulting expression values per gene across the AML samples that were either positive or negative to the FLT3-IDT mutation (genetic information was provided from the original publication), yielding an effect size per gene. Those two genes with the largest effect size are reported (MSI2 and CD164).

ADDITIONAL RESOURCES

The tuMap algorithm is available as a R package in GitHub (https://github.com/shenorrLab/tuMap/) along with a tutorial that allows replication of the AML CyTOF analysis (Fig. 4, Supp. Fig. 7, and Supp. Fig. 9). This repository has been archived at Zenodo (DOI: 10.5281/zenodo.5167077).

KEY RESOURCES TABLE

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
CD4 (RPA-T4)	BioLegend	Cat# 300502, RRID:AB_314069
CD34 (581)	BioLegend	Cat# 343502, RRID:AB_1731898
CD9 (HI9a)	BioLegend	Cat# 312102, RRID:AB_314907
CD41 (HIP8)	BioLegend	Cat# 303702, RRID:AB_314372
CD90 (5E10)	BioLegend	Cat# 328102, RRID:AB_940393
PD-1 (EH12.2H7)	BioLegend	Cat# 329902, RRID:AB_940488
HLADR (L243)	BioLegend	Cat# 307602, RRID:AB_314680
CD61 (VI-PL2)	BioLegend	Cat# 336402, RRID:AB_1227584
CD7 (CD7–6B7)	BioLegend	Cat# 343102, RRID:AB_1659214
CD3 (UCHT1)	BioLegend	Cat# 300402, RRID:AB_314056
CD56 (NCAM16.2)	BD Bioscience	Cat# 559043, RRID: AB_397180
CD45RA (HI100)	BioLegend	Cat# 304102, RRID:AB_314406
CD64 (10.1)	BioLegend	Cat# 305002, RRID:AB_314486
CD13 (WM15)	BioLegend	Cat# 301702, RRID:AB_314178
TIM-3 (F38–2E2)	BioLegend	Cat# 345002, RRID:AB_2116574
CD117 (104D2)	BioLegend	Cat# 313202, RRID:AB_314981
CD16 (3G8)	BioLegend	Cat# 302002, RRID:AB_314202
CD71 (CY1G4)	BioLegend	Cat# 334102, RRID:AB_1134247
CD138 (MI15)	BioLegend	Cat# 356502, RRID:AB_2561790
CD57 (HNK1)	BioLegend	Cat# 359602, RRID:AB_2562403
CD45 (HI30)	BioLegend	Cat# 304002, RRID:AB_314390
CD8a (RPA-T8)	BioLegend	Cat# 301002, RRID:AB_314120
CD19 (HIB19)	BioLegend	Cat# 302202, RRID:AB_314232
CXCR4 (44708)	R and D Systems	Cat# FAB171B, RRID:AB_357077
CD33 (WM53)	BioLegend	Cat# 303402, RRID:AB_314346
PD-L1 (29E.2A3)	BioLegend	Cat# 329702, RRID:AB_940372
CD11c (Bu15)	BioLegend	Cat# 337202, RRID:AB_1236381
CD14 (M5E2)	BioLegend	Cat# 301802, RRID:AB_314184
CD127 (A019D5)	BioLegend	Cat# 351302, RRID:AB_10718513
CD28 (CD28.2)	BioLegend	Cat# 302902, RRID:AB_314304
CD15 (W6D3)	BioLegend	Cat# 323002, RRID:AB_756008
CD11b (ICRF44)	BioLegend	Cat# 301302, RRID:AB_314154
CD38 (HIT2)	BioLegend	Cat# 303502, RRID:AB_314354
CD96 (NK92.39)	BioLegend	Cat# 338402, RRID:AB_1279386
CD25 (BC96)	BioLegend	Cat# 302602, RRID:AB_314272
Biological Samples
Bone marrow aspirates taken from 9 healthy individuals and AML patients at AML diagnosis, 14 days following induction therapy and relapse.	Rambam Health Care Capus	NA
Chemicals, Peptides, and Recombinant Proteins
MaxPar Intercalator - Rh(500uM)	DVS sciences	Cat# 201103A
Fetal Bovine Serum	Biological Industries	Cat# 04–121-1A
Lymphoprep	Axis Shield	Cat# 1114547–1
Dimethyl Sulfoxide	Sigma	Cat# D2650
RPMI-1680	Sigma	Cat# R8758
Pierce™ universal nuclease for cell lysis	Thermo Fisher Scientific	Cat# 88700
Bovine serum albumine	Sigma	Cat# A4378–5G
Pierce™ 16% formaldehyde	Thermo Fisher Scientific	Cat# 28906
MaxPar Intercalator - Ir(125uM)	DVS Sciences	Cat# 201192A
EQ four elements calibration beads	DVS Sciences	Cat# 201078
Deposited Data
FCS files of ALL and Healthy bone marrow samples	Good et al, 2018; https://github.com/kara-davis-lab/DDPR/releases	NA
Cellular features within B-cells developmental populations in ALL bone marrow samples.	Good et al, 2018, Table S5	NA
Clinical information of AML patients related to the AML CyTOF dataset	This study, Table S4	DOI: 10.17632/my928cxv7f.3
Single-cell RNA sequencing data of AML patients and cellular annotations into cell populations and cellular classification as healthy and malignant	van-Galen et al, 2019, GEO	GSE116256
Genetic information about AML samples related to the AML scRNAseq dataset	van-Galen et al, 2019, Table S1	NA
Raw and gated FCS files of the AML CyTOF dataset	This study	DOI: 10.17632/my928cxv7f.3
Software and Algorithms
R	https://www.cran.r-project.org	v4.0.3
R Studio	https://www.rstudio.com/	NA
tuMap (R package)	This study, https://github.com/shenorrLab/tuMap/	DOI: 10.5281/zenodo.5167076
cytofkit (R package)	Chen et al, 2016	v1.6.5
scanpy (python package)	https://github.com/theislab/scanpy	NA
slingshot (R package)	Street et al, 2018	v1.9.1
scorpius (R package)	Cannoodt et al, 2016	v1.0.7
psupertime (R package)	Macnair et al, 2019; https://github.com/wmacnair/psupertime	v0.2.6
glmnet (R package)	https://cran.r-project.org/web/packages/glmnet/index.html	v4.0–2
survAUC (R package)	https://cran.r-project.org/web/packages/survAUC/index.html	v1.0–5
caret (R package)	https://cran.r-project.org/web/packages/caret/index.html	v6.0–86
emdist (R package)	https://cran.r-project.org/web/packages/emdist/index.html	v0.3–1
survival (R package)	https://cran.r-project.org/web/packages/survival/index.html	v3.2–7
Rmagic (R package)	Dijk et al, 2018	v2.0.3
circlize (R package)	https://jokergoo.github.io/circlize_book/book/	v0.4.11
Cytobank premium	https://www.cytobank.org	NA
Biobase (R package)	https://www.bioconductor.org/packages/release/bioc/html/Biobase.html	v2.48.0
cellAlign (R package)	Alpert et al, 2018	v0.1.0
Original code used to generate this study’s figures (R scripts)	This study	DOI: 10.17632/my928cxv7f.3
Other
CyTOF 1	DVS Sciences	NA

Highlights.

• High diversity in cancer hinders quantitative comparison and mechanistic insight

• tuMap aligns cancer sample trajectories to a reference, quantifying dynamics

• tuMap provides a comparative framework for cancer sample dynamics and regulation

• tuMap reveals clinical associations, masked under standard classification