BiTSC ²: Bayesian inference of tumor clonal tree by joint analysis of single-cell SNV and CNA data

Abstract

The rapid development of single-cell DNA sequencing (scDNA-seq) technology has greatly enhanced the resolution of tumor cell profiling, providing an unprecedented perspective in characterizing intra-tumoral heterogeneity and understanding tumor progression and metastasis. However, prominent algorithms for constructing tumor phylogeny based on scDNA-seq data usually only take single nucleotide variations (SNVs) as markers, failing to consider the effect caused by copy number alterations (CNAs). Here, we propose BiTSC, Bayesian inference of Tumor clonal Tree by joint analysis of Single-Cell SNV and CNA data. BiTSC takes raw reads from scDNA-seq as input, accounts for the overlapping of CNA and SNV, models allelic dropout rate, sequencing errors and missing rate, as well as assigns single cells into subclones. By applying Markov Chain Monte Carlo sampling, BiTSC can simultaneously estimate the subclonal scCNA and scSNV genotype matrices, subclonal assignments and tumor subclonal evolutionary tree. In comparison with existing methods on synthetic and real tumor data, BiTSC shows high accuracy in genotype recovery, subclonal assignment and tree reconstruction. BiTSC also performs robustly in dealing with scDNA-seq data with low sequencing depth and variant missing rate. BiTSC software is available at https://github.com/ucasdp/BiTSC2.

Introduction

The rapid development of single-cell DNA sequencing (scDNA-seq) technology has provided a refined perspective for unveiling the evolutionary mechanisms underlying cancer progression and characterizing intra-tumor heterogeneity (ITH) [1, 2]. Although promising, the major single-cell whole-genome amplification methods, e.g. DOP-PCR, MDA and MALBAC, still encounter various technical bottlenecks. These limitations will result in a high incidence of errors, such as missing bases, false positives or false negatives in the sequenced single-cell DNA, which poses additional challenges for the downstream ITH inferences [3].

Early single-cell studies utilize information from single-cell single nucleotide variant (scSNV) or single-cell copy number alteration (scCNA) to infer tumor evolution with classic phylogenetic methods [4–7]. In recent years, many computational methods have emerged for inferring the evolutionary histories of tumors from single-cell data. CHISEL [8], SCICoNE [9] and MEDALT [10] are the few methods that perform scCNA detection and also infer evolutionary histories. RobustClone [11] is a model free method that takes raw scSNV or scCNA genotype matrix as input to recover clone genotypes and infer tumor clone tree. BEAM is a Bayesian evolution-aware method based on scSNV data, which improves the quality of single-cell sequences by using the intrinsic evolutionary information under a classic molecular phylogenetic framework [12]. Many other methods based on scSNV data build maximum likelihood or Bayesian-based models to account for sequencing noise as well as reconstruct tumor clone/cell tree. SCITE [13], OncoNEM [14], SCI [15], CellPhy [16] make infinite site assumption in their models, that is, mutation may only occur once at any locus and only binary genotypes are allowed in scSNV sites. SiFit [17] and SiCloneFit [18] construct their models under the finite site assumption, which allows mutations to happen more than once at any locus.

These single-cell based methods can only take into account one source of information, either from scSNV or scCNA. In fact, these two types of markers all play important role in tumor generation, progression and metastasis, and they constitute crucial traits in characterizing tumor heterogeneity [19]. Evolutionary inference with only one type of markers may lead to biased estimate. For example, suppose there is a true evolutionary process as shown in Figure 1A. The tumor tree has five subclones, where the root node subclone1 is comprised of normal cells only, and the other nodes are cancerous subclones caused by point mutations and/or CNAs on three loci A, B and C. The SNV and CNA genotypes of these subclones are shown in Figure 1B. The two SNVs occur at loci A and B give rise to subclone2. The loss of the mutant copy on locus B further generates subclone4 based on the genotype of subclone2. If one infers the tumor clone tree with only SNV data , one will most probably recover a linear evolutionary history as in Figure 1C. However, this is biased as it misses the identification of the two extra subclones (3 and 5), which respectively generated by a copy loss at locus A and a copy gain at locus C. Also, ignoring the CNA-driven loss of SNV at locus B in subclone4 may lead to misplacement of cells in subclone4 as the ancestor of cells in subclone2 and 5 on the SNV-based clone tree (Figure 1C). In such case, the full history can only be resolved by taking into account of information from both SNV () and CNA ().

Figure 1.

ScDNA-seq data display tumor heterogeneity. (A) Joint tumor phylogeny tree by SNV and CNA, where the gray node represents normal cells and the other nodes are cancerous cells. The letters A, B, and C are mutation loci. The bars under each letter represent alleles, and the bars with red stars and triangles are mutated. (B) The SNV genotype matrix, , and the CNA genotype matrix, , where rows represent loci and columns are subclones. (C) The phylogeny tree generally obtained by SNV-based algorithms. (D) Three possible scenarios for the overlapping relationship of SNV and CNA along the tree.

In fact, joint analysis of SNV and CNA in characterizing ITH is common with bulk sequencing. PyClone [20] applies Bayesian clustering to identify tumor clones/subclones based on SNVs and clonal CNAs (CNAs carried by all cancer cells). It provides insights to temporal ordering of mutations and subclones, but does not make inference to the tree structure. PhyloWGS [21] also employs a Bayesian framework with a tree structured stick breaking process as prior, which infers subclone cluster as well as the tree relationship of the subclones. Canopy [22] is a Markov Chain Monte Carlo (MCMC) algorithm for tumor evolution history inference, which accounts for both point mutations and raw copy number (CN) information. Recently, [23] proposed a unified Bayesian feature allocation model, SIFA, on raw bulk sequencing reads. It provides a generating model that incorporates SNV and CNA to infer tumor phylogenetic tree.

To the best of our knowledge, the only method for tumor tree inference from scDNA-seq data that integrates SNV and CNA information is SCARLET [24]. SCARLET optimizes for a loss-supported phylogeny. It inputs a copy number tree constructed with existing methods and then refines such tree by resolving the multifurcations using point mutation profiles of the observed cells [24].

In this study, we propose Bayesian inference of Tumor clone Tree by joint analysis of Single-Cell SNV and CNA, termed BiTSC. It is the first method that fully models SNV and CNA states from raw reads of scDNA-seq data. It generalizes the SIFA model to account for the overlapping of CNA and SNV states comprehensively, and models allelic dropout (ADO) rate, missing rate and sequencing errors in scDNA-seq data. BiTSC takes the observed total reads and mutant reads at multiple loci in single cells as input and assigns cells to subclones. By applying MCMC sampling, BiTSC can simultaneously estimate the subclonal CNA and SNV genotypes, the overlapping relationship of CNA and SNV, the subclonal assignments of cells and the tumor evolutionary tree. In comparison with existing methods on synthetic and real tumor data, BiTSC shows high accuracy in genotype recovery, subclonal assignment and clone tree reconstruction. It is worth noting that BiTSC is also robust in dealing with scDNA-seq data with low sequencing depth.

Methods

Overview of BiTSC

We give a brief introduction to BiTSC in this section, the general flowchart is shown in Figure 2. The definitions of all parameters in Figure 2B and examples of main parameters in Figure 1A can refer to Table S1, and the more model details can be found in following subsection and in supplementary notes.

Figure 2.

Overview of the computational framework of BiTSC that identifies subclones, recovers subclonal genotypes of CNA and SNV, as well as reconstructs subclonal evolutionary trees using tumor scDNA-seq read count data. (A)The input of the algorithm, total reads matrix and mutant reads matrix . (B) The probabilistic graphical model shows the dependency among parameters, where the shade nodes stand for observed or fixed values, the unshaded nodes represent the latent parameters. (C) The inference output of the algorithm, mainly containing subclone assignment (), subclonal phylogenetic tree (), genotype matrix of CNA () and SNV (), phase indicator and other parameters, such as missing rate (), ADO rate () and so on.

BiTSC is a Bayesian model, which takes input of raw total and mutant read counts matrices and measured at loci of cells (Figure 2A). Due to the sharing of genetic information among homogeneous cells, we assume that there are latent subclones in the cells drawn for sequencing (). Here, we define subclone as a group of cells with identical genotypes and distinct subclones differ in SNV or CNA markers on at least one of the measured loci. We further assume the latent states follow a categorical distribution with parameter representing the prevalence of subclones and denote the state of cell by (the blue box in Figure 2B). BiTSC employs a tree coupled generating model to generate the raw total and mutant read count matrices, where the point mutation profiles and the CN profiles of subclones are jointly modeled, with their context and relationships coupled by the clone tree (the green box in Figure 2B).

We consider three possible scenarios for the overlapping relationship of SNV and CNA along the tree: (i) CNA event happens before SNV on the same lineage; (ii) CNA and SNV occur in the same genomic region but on separate branches of the tree, thus affecting distinct clones; (iii) SNV happens before CNA on the same lineage (Figure 1D). For the first two scenarios, the overlapping of SNV and CNA does not affect the number of mutant alleles. For scenario (iii), we introduce an phase indication vector of length (the green box in Figure 2B), where indicates CNA happened on the mutant allele at locus , thus affecting the number of mutant copy, and otherwise (Figure 1D). For example, in the toy model in Figure 1A, the phase indicator for locus B is , since the copy loss on this locus occurs on mutant allele, which gives rise to subclone4. For locus A, the SNV arises in subclone2, which is parallel to the CNA occurring in subclone3. In such case, CNA does not affect the number of the mutant copy, thus . For locus C, as there is only a CNA event, so . Then the phase indicator for the toy model in Figure 1A (Table S1).

In addition, as single-cell sequencing data is prone to high technical errors, our model also accounts for sequencing error rate (), missing rate () and ADO rate (Figure 2B).

The ultimate goal of BiTSC is to infer the subclone prevalence , the subclone assignment of cells (a vector of length ), the SNV and CNA genotypes of subclones and , the subclone tree , the missing rate and also ADO rate (Figure 2C). By assigning priors to , , , , , , and (the dispersion parameters for generating total reads and mutant reads ), and given read depths of the sequencing cells , and a sequencing error rate , these can be estimated from a posterior distribution , which corresponds to (Figure 2, see below and supplementary notes for details).

Tree coupled generating model of genotypes

The subclone genotypes and are generated according to the SNV and CNA origin matrices , and the clone tree as well as phase indicator (the green box in the Figure 2B). By assuming a total of subclones on the tree, is represented by a length- vector, where indicates the parent of subclone is . We fix subclone to normal cell and place it at the root of the tree (). We assign a uniform prior to all possible trees with nodes.

As the first model for joint analysis of CNA and SNV states from the raw reads of scDNA-seq data, considering the complexity of the model, BiTSC assumes CNA and SNV mutations arise independently. And each mutation (including SNV and CNA) originates only once in a specific subclone besides normal subclone. In general, the mutation will be inherited by all descendant subclones after its origination, with the exception that the mutant allele is affected by subsequent overlapping CNA (with phase indicator ), resulting in the increase or loss of such mutation at the locus. We use and to represent the originations of SNV and CNA changes at locus , that is, indicates mutation at locus occurs from subclone and gains mutant copies, and indicates the CNA arises in subclone and gains (or losses if is negative) normal or mutant copies.

For SNV state, we take the prior of as , where is the somatic point mutation rate and is predetermined within range of , represents the maximum number of possible mutant copies [23]. In this study, we restrict . However, such restriction may be relaxed if multiple mutations are allowed to hit one site. The specification of the mutation probability is independent of , which makes it equally likely for the SNV to originate from any subclones (besides the normal subclone).

For CNAs, since they span genome intervals, if the genomic segmentation information is available, it will improve the inference of CNA status. There are many existing methods that can be applied to estimate the segment information, such as HMMcopy, copynumber, etc.[25, 26]. We thus model CNA status in segment level in a way similar to SIFA [23]. We sort the loci according to their chromosomal positions and divide the genome into segments, . If loci and are located on the same segment, we assume they share the same CNA status. We let represent no CNA event at locus . For each genome segment, , we assign a prior probability for no CNA, and uniform prior probabilities for other possible combinations of and (e.g., , for ), with as the maximum possible number of total copies. The probability is further generated from a prior distribution with given hyperparameters.

The independent origination of SNVs () and CNAs () coupled with the structure of the -node clone tree and phase indicator will derive the genotype matrices and . The elements represent the number of mutant copies at the -th locus of the -th subclone, and represent the total number of copies at the -th locus of the -th subclone. The CN matrix can be obtained according to and . The point mutation matrix is determined by , and . For example, for locus B in Figure 1A, SNV and CNA with a copy loss arise in subclone2 and sublcone4 on the clone tree , respectively. Then , thus the CNA genotypes on locue are (Table S1). For SNV, and the CNA occurs on the mutant allele, thus and (Table S1).

The optimal number of subclones is selected based on a modified Bayesian Information Criterion (BIC, see Supplementary Note 4 for details).

Zero-inflated modeling of single-cell sequencing reads

Next, we introduce the likelihood model of observing the total reads and the mutant reads at locus of cell .

By given the latent subclone state , e.g. , the total reads should be positively correlated with CN and the cell-specific diploid average coverage (which should be given a priori) for cell [23, 27, 28]. Here, we model the total reads by negative binomial distribution [29] as:

We parameterize the mean of negative binomial distribution to be , which is equal to when the total CN of the single cell is . The is the dispersion parameter that can control nonuniformity degree of coverage across the genome and that . The distribution reduces to Poisson as .

Since there often exist three major sources of noises in scDNA-seq, namely missing base, ADO or sequencing error, especially at low sequencing depth. We model them explicitly by introducing the zero-inflation parameter , the ADO rate and the sequencing error rate . For total reads , we apply the zero-inflated negative binomial (ZINB) distribution, which introduces an additional probability when no reads are observed (e.g. ), in order to control the amount of excessive zero reads due to missing [30]. Also, we model the false positives when all copies are lost, e.g. , by a small probability due to sequencing error. Moreover, the allelic amplification bias in scDNA-seq may result in random nonamplification of one allele, often referred as ADO [15]. To account for ADO events for each cell, we introduce the mixture probability with ADO rate for the likelihood of the total reads. Finally, the ZINB likelihood of , which accounts for various sources of noises can thus be defined as in Eq. 1,

(1)

where,

We then denote the expected probability of observing a mutant allele at locus for cell as . We model the likelihood of observing reads of the mutant allele by beta-binomial distribution [15] as:

(2)

where is the mean frequency of observing mutant reads and is the overdispersion term determining the shape of the distribution, which decreases with increasing variance [15].

The integrated likelihood model of mutant reads that also accounts for ADO rate and sequencing error can be similarly defined as in Eq. 3. For modeling sequencing error in mutant counts, we assume that if mutation is absent in cell , i.e. and/or , the probability of observing a variant read corresponds to the per-nucleotide rate of sequencing error . If mutation presents in cell and , the probability of sampling the mutant allele type is corrected by sequencing errors in producing any of the other two bases [15]. If mutation presents with , that is, , there will also be a small probability of sequencing error. In addition, ADO may happen when there is at least one copy present on the locus (). When ADO happens in the case of , there will be two possibilities, with probability to drop the mutant allele or with probability to drop the wild-type allele. The probability of sampling a mutant read will also vary according to the ADO events. We denote as the probability of sampling a mutant read without ADO events. and denote the probability of sampling a mutant read with an ADO event on the mutant allele and on the wild-type allele, respectively.

(3)

where , , , and

Inference

We apply the MCMC procedure to estimate the unknown parameters in BiTSC. The posteriors of the unknowns are sampled with differed strategies. Here we only briefly introduce our sampling procedures; the sampling details of each parameter can be found in Supplementary Note 1.

For genotype origin matrices and , we update one locus at a time by applying Gibbs sampler, where new states are sampled from the full conditional distribution. If the CNAs are in a segmented form, then at each step we will update all loci within the same segment. The hyper-parameter of is also sampled by Gibbs sampler. Under scenarios where CNA happens after SNV at overlapping locus , we calculate the full conditional distribution by integrating over all possible values of phase indicator . That is with probability the subsequent CNA happens on the wild-type allele () and with probability the CNA occurs on the mutant allele (, see Supplementary Note 1 for details). After performing Gibbs sampling on and , we estimate each element of with the maximum probability at each locus.

For the dispersion parameters and of the negative binomial distribution and beta-binomial distribution, we use Metropolis sampling with Gamma prior [31]. For missing rate and ADO rate , since it is difficult to sample from its full conditional distribution, we adopt Metropolis sampling step with a uniform proposal of and in the interval . We apply a mixed sampling strategy for as in [23], where the tree is updated by randomly applying a Metropolis–Hastings sampler or a slice sampler.

In sampling of the subclone prevalence, instead of updating the entire vector at once, we sample additional Gamma parameters , one at a time. And let . This move is equivalent to sampling with prior , and often leads to better mixing of the MCMC [23]. Each is updated by Metropolis–Hastings sampling with a Gamma proposal and an adaptive step size. Each element of is taken from the Categorical distribution with parameter . We employ Gibbs sampling to update each one by one.

In order to avoid Markov Chain being trapped at some local optimum states, we adopt the parallel tempering technique, which runs multiple chains with different temperatures and exchanges samples between them [23, 32]. We use heuristic initialization for each parallel chain before MCMC sampling (Supplementary Note 2). The derivation of the fully conditional distribution for all model parameters can refer to Supplementary Note 3. The optimal number of subclones is selected by performing a modified BIC (Supplementary Note 4). We use the posterior mode for , , , and as the final estimates. We obtain the inference of with the maximum probability at each locus, as well as and according to the final estimates of , , and .

Benchmark BiTSC

Simulation data

To test the ability of BiTSC in identification of subclones that generated by only CNA changes, we simulated 10 datasets, denoted as G1. Figure S1 shows the ground truth of the datasets, which contains the phylogenetic tree and subclonal genotype matrices of CNA and SNV. We also simulated another 10 datasets, named G2, to assess the accuracy of BiTSC and the competing algorithms when the overlapping CNA affects the state of SNVs in cells. Figure S2 shows the ground truth information of G2. There are CNA driven-loss of SNVs and CNA driven-gain of SNVs events in subclone4 and subclone5, respectively.

We also systematically evaluate BiTSC in scenarios when topological structure of the clone tree can be fully recovered by SNV markers (Figure S3). We simulate 150 datasets with variant number of cells (), sequencing depths (), missing rate () as well as the number of loci () and the number of subclones (). The 150 datasets are divided into five groups (denoted G3–G7), each of which contains 30 datasets. In each group we change one parameter and keep other parameters fixed. Under each parameter setting, we generate 10 replicates with different total reads matrix and mutant reads matrix . In addition to the variable parameter, we set the default parameters in each group as follows: number of cells () is 100, number of loci () is 100, ADO rate () is 10%, missing rate () is 20%, sequencing depths of all single cells () are 3, and the number of subclones () is 4. The ground truth (including genotype matrices , and tree structure ) of G3–G5 is shown in Figure S4, and the ground truth of G6 and G7 is shown in Figure S5 and S6, respectively. To simulate coverage heterogeneity caused by amplification noise under different sequencing depths [3], we set the divergence parameter of negative binomial distribution, when generating total reads. Under the ground truth of G5, we show examples of simulated data of total reads under different sequencing depths. The large variance of simulated data shows high false positive and false negative rates due to nonuniform amplification (Figure S7). The detailed simulation process can be found in Supplementary Note 5, and the specific parameter settings of G3–G7 can refer to Table S2.

Real data

In addition to simulation data, we also test BiTSC on two sets of real scDNA-seq data. One is from the metastatic colorectal cancer patient CRC2 in [33], which includes 141 cells from the primary colorectal tumor and 45 cells from a matched liver metastasis by single cell DNA target sequencing of 1000 cancer genes with an average sequencing depth of 137. The sequencing data are available in NCBI Sequence Read Archive under accession number SRP074289. The other one is the single nuclei exome sequencing data of estrogen-receptor positive (ER1/PR1/Her22−) breast cancer (ERBC) patient in [5] and [34], denoted as ERBC dataset. We use the 55 cells, include 45 tumor cells and 10 matched normal cells, studied in [34]. The data are available in Sequence Read Archive under accession number SRA053195.

Evaluations

We compare the performance of our algorithm to RobustClone, SCITE[11, 13], BEAM [11, 12], SiFit [11, 17] and SCARLET [24], five recent algorithms that perform single cell DNA genotype recovery and tumor tree analysis. Our evaluation metrics include: (1) the error rate of the recovered scSNV genotype matrix; (2) adjusted Rand Index (ARI) [35, 36], the similarity of subclone assignment between ground truth and the estimates (details can refer to Supplementary Note 6); (3) MP3 similarity [37], the similarity measure of the reconstructed tree and the true tree. Since RobustClone and BEAM do not make explicit infinite site assumption, we choose MP3 similarity as the metric for tree reconstruction, which allows mutations to occur multiple times on the tree.

Results

BiTSC jointly infers both SNV and CNA states

Since BiTSC models both single-cell SNV and CNA data jointly, we design two sets simulations: one set corresponds to the case where CNAs do not affect SNV states but induce extra observable subclone genotype(s) on the tree (Figure S1 and G1, scenario (iii) in Figure 1D with ); the other set includes CNAs that overlap with SNVs and result in gain or loss of mutant copies (Figure S2 and G2, scenario (iii) in Figure 1D with ). We simulate ten replicates for each setting. We compare the performance of BiTSC to SCARLET, the only algorithm of tumor tree inference that accounts for SNV loss caused by CNA. In addition, we also add RobustClone, SCITE, BEAM and SiFit, four recent methods to infer clone/cell/mutation tree with only one source of marker (SNV), in the comparison. As SCARLET needs an inferred CN tree for summarization of supported loss set as input, we provide it with the true CN tree. We provide BiTSC the real segmentation information. The prior settings and the MCMC configurations of BiTSC for analyzing these simulation datasets are in Tables S3 and S4. We perform BiTSC with the number of subclones in range from 3 to 10, and select the best fitted according to the modified BIC (Methods and Supplementary Note 4).

In the first group (G1) of simulations, we use a simple bifurcation structure as ground truth, which includes a branch of clone derived by a CN change (Figure S1). Figure 3A shows the comparison results of simulations in G1. For tree reconstruction, we apply MP3 similarity [37]. BiTSC and RobustClone all display satisfactory accuracies (Figure 3A). Since MP3 measures tree similarity based only on SNV triplet structures, the CNA- (only) induced lineage in the simulation does not affect the measurement. Thus, RobustClone shows slightly less variance in performance. However, SCARLET shows large variance for tree reconstruction. The subclone assignment results of BiTSC are more consistent with the ground truth than that of RobustClone, SCITE, BEAM and SiFit, which only analyze one source of data (SNV)(Figure 3A). Since SiFit and SCITE do not output subclone assignment information, we apply K-medoids clustering based on the distance of cell along their reconstructed cell lineage tree (SiFit) or mutation tree (SCITE) to cluster cells into subclones as shown in [11]. As SCARLET does not cluster cell with two source markers in its final output, we exclude it in the evaluation of subclone assignment. Among all compared algorithms, only BiTSC is able to reliably recover the CNA states with accuracy of 100% (Figure S8). For SNV genotype recovery, BiTSC also shows higher accuracy than others (Figure 3A).

Figure 3.

Comparison of performance on G1 and G2 for scSNV genotype recovery, subclone assignment and tree reconstruction. (A) The violin plot of BiTSC with real segments as input, SCARLET with true CN tree and supported loss set as input, RobustClone, SCITE, BEAM and SiFit for error rate of recovered scSNV genotype matrix, ARI of subclone assignment and MP3 similarity on G1 dataset, where 0, 1 and 1 indicate best performance for error rate, ARI and MP3 similarity, respectively. (B) The violin plot of BiTSC with real segments as input, SCARLET with true CN tree and supported loss set as input, RobustClone, SCITE, BEAM and SiFit for error rate of recovered scSNV genotype matrix, ARI of subclone assignment and MP3 similarity on G2 dataset, where 0, 1 and 1 indicate best performance for error rate, ARI and MP3 distance, respectively.

Next, we evaluate BiTSC under more complex scenario. In this group, the data are generated from a tumor tree with six subclones, in which SNV states are partly affected by overlapping CNAs (gain and/or loss of mutant copy caused by CNAs, Figure S2). Both BiTSC and SCARLET show their advantages in joint modeling of the two sources of data (Figure 3B, Figure S9). BiTSC performs best in tree reconstruction. In most cases, it almost fully recovers the true tree structure. SCARLET, owing to the given CNA information, also shows consistent performance. We note that, in this comparison we only provide BiTSC the segmentation information, and it has higher MP3 similarity than SCARLET in 9 out of 10 simulations. In addition, BiTSC is able to successfully recover the CN profiles with mean accuracy of 99.32%, thus resulting in a more accurate subclone assignment (Figure 3B, Figure S9). More importantly, BiTSC can also correctly infer the phase indicator (fully recovered in 7 out of 10 simulations), which reflects the detailed overlapping relationship of SNVs and CNAs (Figure S10).

The SNV recovery errors of BiTSC are significantly lower than other methods. The results are comparable for RobustClone, SCITE, BEAM, SiFit and SCARLET, where SCARLET is slightly better than the other four single source only methods. Although SCARLET accounts for CNA information in its algorithm, the CNA states as well as the CN tree have to be inferred by extra methods and packages. When providing true segmentation information to BiTSC, it outperforms SCARLET (Figure 3B). We also apply BiTSC without real segmentation information (each locus as independent segment), it still shows comparable tree reconstruction performance and excellent genotype recovery ability (Figure S11).

BiTSC recovers SNV genotypes and assigns cells with high accuracy on synthetic datasets

We further conduct five groups of simulations where CNA states do not explicitly affect SNV states and clone tree topology. In other words, in these sets of simulations, CNAs do not provide much extra information to the tree reconstruction (Figures S4–S6, including scenarios (i) and (ii) in Figure 1D with ). We compare BiTSC mainly to the four single source methods, RobustClone, SCITE, BEAM and SiFit. We evaluate their performance under change of settings such as, number of cells, sequencing depth, missing rate, number of loci and number of subclones (see Methods for details). Still, we provide BiTSC the real segmentation information. The prior settings together with MCMC and model selection configurations of BiTSC can refer to Tables S3 and S4 and Supplementary Note 4.

Figure 4 shows the detailed comparison performance of 5 algorithms in G3–G7 with three measurements. The overall benchmarks at differed settings are displayed in Figure S12. In general, compared with the other four algorithms, BiTSC has high accuracy in recovering SNV genotypes (top row in Figure 4 and Figure S12), high robustness in subclone assignments (2nd row in Figure 4 and Figure S12), and high power in clone tree reconstruction (3rd row in Figure 4 and Figure S12).

Figure 4.

Comparison of detailed performance on G3-G7 for scSNV genotype recovery, subclone assignment and tree reconstruction among BiTSC with real segments as input, RobustClone, SCITE, BEAM and SiFit, where 0, 1 and 1 indicate best performance for error rate, ARI and MP3 similarity, respectively.

Specifically, BiTSC recovers SNV genotypes with little error rate in almost all simulation settings where the default sequencing depth () is set to 3. The accuracies of RobustClone and BEAM get significantly improved as the sequencing depths increase (G4 in Figure 4). The accuracies of SCITE and SiFit also show improved performance with increasing the sequencing depths (G4 in Figure 4). For default depth, RobustClone, SCITE, BEAM get lower error rates when more cells () are sampled and/or more loci () are sequenced, but shows reduced accuracy as the missing rates () and the number of subclones rise. Different from these three algorithms, SiFit shows increasing error rates with more cells ().

The subclone assignment results of BiTSC, RobustClone and SCITE are mostly consistent with the ground truth. BEAM and SiFit are slightly less consistent (2nd row in Figure S12), but BEAM gets improved with the increase of number of cells (), number of loci () and/or sequencing depths () and SiFit performs better with less cells (), more loci () and/or deeper sequencing depths () (2nd row in Figure 4). The tree reconstruction accuracies, which are measured in MP3 similarity, are almost over 0.9 in all cases for BiTSC. For RobustClone, the tree reconstruction performance is also good in simulations with moderate missing rates and fewer subclones. The MP3 similarities between real tree and tree recovered by SCITE mostly near 0.5, but the similarity increases with the increase of sequencing depth(), number of loci () and number of subclones (). BEAM and SiFit are very sensitive to number of cell, sequencing depth and number of loci. And BEAM only performs satisfactorily in scenarios with sequencing depth over 5.

In the above comparisons BiTSC was given the real segmentation information as input. Reliable segmentation may offer extra information and jointly updating CNA states of multiple loci with in the same segment could greatly improve the likelihood of the model. However, this information may not always be reliably estimated. In that case, we can either take the more refined raw bins (the bins after binning step before segmentation and CNA calling) as segments or use locus specific segments (each gene/SNV locus as a segment). Here we additionally evaluate BiTSC under locus-specific configuration, where the are updated one locus at a time. Although the performance results of BiTSC reduce slightly as compared with cases where correct segmentation information is provided, the overall accuracies are still consistently good (Figures S13 and S14).

BiTSC recovers single-cell phylogeny of metastatic colorectal cancer

We apply BiTSC to real scDNA-seq data of colorectal cancer patient CRC2 in [33], which includes both primary and metastatic samples. After filtering for some low-coverage data, the sequencing data of 182 single cells with 36 SNV loci were retained for further analysis. We directly input the raw reads covering these loci to BiTSC and use locus-specific segment setting for CNAs. The cell-specific sequencing depth of each single cells can be found in the Supplementary Table S4 in [33]. The priors and MCMC settings for running BiTSC are shown in Tables S5 and S6.

BiTSC fits a clone tree with 8 subclones as shown in Figure 5A (see Figure S15 for the BIC values). Figure 5B displays the prevalence of cells in each subclone. The metastatic aneuploid cells are mainly distributed in subclones 7 and 8, whereas the primary aneuploid cells are predominantly clustered in subclone5 (Figure 5C). Although the cells occupied the other subclones were labeled diploid in [33], we still find considerable CNA events occurring in these targeted genes (Figure 5D). Extensive point mutations are identified in primary (subclone5) and metastatic (subclones 7 and 8) tumor cells (Figure 5E).

Figure 5.

BiTSC reconstructs tumor phylogeny of metastatic colorectal cancer. (A) The phylogeny tree of metastatic colorectal cancer reconstructed by BiTSC. (B) The subclone assignment. (C) The number of overlapped cells contained in subclones identified by BiTSC and cells contained in the targeted region, where PD stands for Primary Diploid, PA stands for Primary Aneuploid, MD stands for Metastatic Diploid, and MA stands for Metastatic Aneuploid in [33]. (D) The CNA subclonal genotype matrix estimated by BiTSC, where LINGO2: 1–5 represent different loci in the genomic region of LINGO2 on the chromosome, as well as SPEN:1-2 and APC:1-2. (E) The SNV subclonal genotype matrix estimated by BiTSC.

Interestingly, our inferred tumor clone tree and genotypes show that metastatic cells (subclones 7 and 8) mainly share the same CNA events on PTPRD and LINGO2:3, which arise from primary sites (subclone5). Contrary to the polyclonal seeding (i.e. two independent clones with different mutations migrate from primary colon cancer to liver metastases at different time points) conclusion based on SCITE tree in the original study [33], our result indicates that the liver metastasis from colon is a single event, which supports the monoclonal seeding hypothesis and is consistent with the inference based on the SCARLET tree (Figure S16) [24].

Besides the metastatic lineage, we also identified another lineages with unique mutations. The lineage leads to subclone6, which consists of a small proportion of cells that carries point mutations on CIITA and PIK3CG. Such lineage was also identified by SCITE and SCARLET trees (Figure S16AB).

BiTSC recovers single-cell phylogeny of breast cancer

We additionally perform BiTSC on the ERBC dataset, which contains 55 cells. The raw single-cell sequencing dataset are retrieved from the Sequence Read Archive (No. 053195) in FASTQ format [5, 34]. The information of mean sequencing depths for individual samples can refer to Table S1 of [34]. We adopt the pipeline given by [34] in their Supplementary Note to preprocess the raw data (Supplementary Note 7 for brief steps). After preprocessing, a total of 1137 gold-standard SNV loci with their raw mutant and total reads are extracted and used for downstream analysis. The priors and MCMC settings for running BiTSC are shown in Tables S6 and S7.

We apply BiTSC to the processed ERBC dataset and infer a best fit clone tree with 9 subclones (Figure 6A). The BIC values for 3–10 subclones can be found in Figure S17. Subclones 1, 2 and 3 are inferred to be ancestor clones with no cells assigned in. Subclones 4 and 8 contain only normal cells, and subclones 5 and 6 are tumor only clones. With only one cell assigned to subclone5, the majority of tumor cells are concentrated in subclone6. The other tumor cells are distributed in subclones 7 and 9. Note that BiTSC is not aim for labeling tumor or normal cells; the labels of tumor cell or normal cell are from [5] according to the sampling sites. The normal cells are most possibly from matched adjacent normal tissue, which may already possess many somatic mutations. In the study by [34], they also identified many somatic mutations in the normal cells with the same dataset (Figure 6 in [34]). Figure 6BC show the inferred CNA and SNV genotype matrices by BiTSC ( and ). From the results we can see some CN events shared by most subclones (3–9 and 4–9, Figure 6B), which confirming the findings that somatic CNAs are acquired early on during breast cancer development [5]. We further find many loci with increased CN occur on the mutant alleles in the major tumor clone (subclone6). In addition, there are also some CNA-driven loss of mutations in subclones 7 and 9 (Figure 6BC). We then investigate previously reported non-synonymous mutations in [5, 34]. We find that all these mutations are inferred to have overlapped copy gains, to some extent, in the same region (Figure 6D). Moreover, by combining CNA and SNV genotypes together with the phase indicator, we infer that the copy gain happened in DNM3 and PIK3CA in tumor subclone6 possibly occurred on their mutant allele (Figure 6DE).

Figure 6.

BiTSC reconstructs tumor phylogeny of breast cancer. (A) The phylogeny tree of breast cancer reconstructed by BiTSC. (B) The CNA subclonal genotype matrix estimated by BiTSC. (C) The SNV subclonal genotype matrix estimated by BiTSC. (D) The CNA subclonal genotype matrix of 10 previously reported nonsynonymous mutations. (E) The SNV subclonal genotype matrix of 10 previously reported nonsynonymous mutations.

Discussion

Computational method based scDNA-seq data for tumor ITH and evolutionary history inference can provide important insights to the understanding of tumor progression and metastasis mechanism and provide guidance to tumor treatment and response. Most of such methods only utilize one source of information, either SNV or CNA, which may lead to biased estimation of the true evolution history of cancer. In this study, we propose BiTSC, a Bayesian-based method that integrates SNV and CNA markers from scDNA-seq data to jointly infer tumor clone tree. BiTSC is a unified Bayesian framework, which takes the raw total reads and mutant reads of single cells generated by sequencing as input and takes into account sequencing errors and models ADO rate, as well as missing rate. It also optimizes SNV and CNA subclonal genotype matrices, assigns cells to subclones and constructs subclonal tree. It can also estimate the overlapping relationship between CNA and SNV. BiTSC has a high accuracy for subclone assignment and SNV subclonal genotypes matrix recovery compared with existing methods such as RobustClone, BEAM and SCARLET. BiTSC can handle low-depth single-cell sequencing data with strong performance. BiTSC also provides high accurate and robust estimation of the missing rate in scDNA-seq data (Figure S18).

The simulations designed in this study simplified the SNV distribution along the chromosomes. While in reality SNVs occur randomly on all genomic regions, they were simulated in a neatly arranged manner. Since we assume SNVs arise independently between different loci and infer the genotype of SNV locus by locus. As long as the SNVs generated are informative in distinguishing subclones, whether they occur randomly on chromosomes will not affect the inference of our model. We have tested BiTSC on an exemplar simulation with 10 replicates, where SNVs randomly and uniformly occur on all genomic regions (Figure S19A). BiTSC can fully recover the SNV and CNA genotypes of cells and accurately assign cells into subclones (results not show). Moreover, SNVs could be also sparsely and nonuniformly distributed within each CNA segment. We additionally performed an simulation with sparsely distributed SNVs as in Figure S19B. BiTSC also works robustly, when provided the CNA segment information, BiTSC could fully recover the SNV and CNA genotypes of cells and accurately assign cells into subclones (results not show).

In general, BiTSC prefers to update all the loci in the same CNA segment together, since loci in the same segment share CNA status. There are many existing methods can be applied to perform segmentation, for example, HMMcopy, copy number, etc. [26]. In cases when segment information can not be reliably obtained, BiTSC can also update and locus by locus in the same way as updating and . In the results on synthetic data, we show that the accuracy and robustness of updating one locus at a time are still higher than RobustClone and BEAM in most cases (see Section 3.2, Figure S11, Figures S13 and S14). In this way, BiTSC may provide a raw estimation of CNA segments based on the inferred CNA genotype matrix .

At a given number of subclones, BiTSC will place each cell into the most likely subclones according to their mutation profiles (both SNV and CNA) and make inference to subclone genotypes. The number of subclones is determined by model selection procedure. In some cases, BiTSC may recover a few empty subclones under the selected number of . These subclones are possibly latent subclones, that are either un-sampled or extinct ancestors of all other descendent subclones. Such subclones may be pruned in the final results if only the observed subclones are being interested.

The full probabilistic model in BiTSC describes the generating process in a comprehensive manner. Especially, we purposed the phase indicator, which reflects the overlapping relationship of SNV and CNA in the same genomic region. Under such setting, our model can detect both gains and losses of mutant copy due to CNA. In contrast, the stepwise construct and refine approach (i.e. SCARLET) could not recover gains of mutant copy from the data. In addition, the optimization of SCARLET may fall into local optimum with integer-linear programming and the subtree root may be misplaced during the refinement [24]. For example, in the toy model of Figure 1A, SCARLET misplaces cells in subclone4 as the siblings of cells in subclone2. Thus, it failed to reconstruct the most parsimonious tree as shown in ground truth (Figure S20). In contrast, BiTSC can fully recover the topological structure in the true tree.

Indeed, different values of will indicate whether CNA affects the CN of the mutant allele on overlapping locus. This will affect the genotype matrix , thereby affecting the likelihood computation of mutant reads (Eq. 3), and further affecting the sampling of parameters , , and (the posterior computation in Supplementary Note 3). In the example of Figure 1A, the CNA occurs on the mutant allele on locus under the ground truth, then and the mutation states are (the 2nd row of in Table S1). However, if the phase indicator is erroneously estimated as , the SNV states of locus B will be derived as . Thus, it will directly affect the likelihood computation in Eq. 3 in turn impact the sampling of other parameters.

Despite the application of phase indicator and the comprehensive design of BiTSC, its model assumptions are still a simplified version of the reality. In our model, we assume SNV and/or CNA mutations occur independently among different loci and each mutation (including SNV and CNA) originates only once in a specific subclone, i.e. the infinite site assumption. In practice, however, such assumption may be violated. Multiple (point) mutations may hit the same site in the genome. Moreover, CN changes may happen in overlap or nested regions on the genome [22]. In addition, the effects of epistatic interactions among genes may induce extra correlations between different SNVs or CNAs. These complications are beyond the discussion of our present model. However, working on relaxing one or more assumptions in joint modeling of single cell SNV and/or CNA data can be a promising future direction.

Key Points

• We proposed Bayesian method, BiTSC, for tumor clone tree inference by joint analysis of single-cell SNV and CNA data.

• BiTSC employs a tree coupled generating model that accounts for allelic dropout rate, sequencing errors and missing rate, as well as assigns single cells into subclones.

• BiTSC involves phase indicator in its model that models the overlapping relationship of SNV and CNA on the tumor tree.

• BiTSC shows high accuracy in genotype recovery, subclonal assignment and tree reconstruction on synthetic and real tumor data.

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Author contributions statement

Z.C., F.G., L.W. and L.M. conceived the model, Z.C. conducted the experiments, Z.C., W.L. and L.M. analyzed the results. Z.C., F.G., L.W. and L.M. wrote and reviewed the manuscript.

Author Biographies

Ziwei Chen is a Phd candidate in Academy of Mathematics and System Sciences, Chinese Academy of Sciences. Her research focuses on computational biology, systems biology, and data science.

Fuzhou Gong is a professor in the National Center for Mathematics and Interdisciplinary Sciences at Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He is also a faculty member in the School of Mathematical Sciences at University of Chinese Academy of Sciences, China. His research focuses on probability theory, stochastic analysis, and applied mathematics.

Lin Wan is a professor in the National Center for Mathematics and Interdisciplinary Sciences at Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He is also a faculty member in the School of Mathematical Sciences at University of Chinese Academy of Sciences, China. His research focuses on computational biology, systems biology, and data science.

Liang Ma is an assistant professor in Key Laboratory of Zoological Systematics and Evolution at Institute of Zoology, Chinese Academy of Sciences. His research focuses on computational biology, statistical learning, evolution and population genetics.