Deciphering Cell Cycle Dynamics and Cell States in Single-cell RNA-seq data with SPAE

20 Rapid advances in single-cell RNA sequencing (scRNA-seq) technology have enabled 21 the investigation of gene expression changes at the single -cell level, particularly for 22 elucidating the heterogeneity among cells and complex biological processes. This 23 technique reveals subtle molecular differences within individual cells, thereby offering 24 a unique viewpoint for the investigation of cell cycle progression, cellular 25 differentiation, and disease pathogenesis. However, accurately identifying and 26 analyzing cell cycle dynamics in scRNA-seq data remains challenging due to the 27 complexity of the data and the subtle differences between cell states. To address this 28 challenge, we developed the integrated Sinusoidal and Piecewise AutoEncoder (SPAE), 29 an autoencoder -based piecewise linear model, for characterizing the cell cycle 30 dynamics and cell states in scRNA-seq data. Compared with existing methods, SPAE 31 demonstrates substantially improved accuracy and robustness in cell cycle 32 characterization. Additionally, SPAE can accurately predict cancer cell cycle transitions 33 and effectively facilitate the removal of cell cycle effects from gene expression data . 34 SPAE is available for non-commercial use at https://github.com/YaJahn/SPAE. 35 36

scRNA-seq; Autoencoder; Cell cycle dynamics; Cell cycle effects 37 38

39 In recent years, the field of biomedical research has experienced significant 40 advancements due to the development of single -cell RNA sequencing (scRNA-seq) 41 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint technology [1-3]. This technology represents a significant transition from tissue level 42 to single-cell level, providing a unique perspective for a deeper understanding of cell 43 heterogeneity [4]. Moreover, scRNA -seq has demonstrated immense potential in 44 studying two fundamental biological processes: the cell cycle and cell differentiation 45 [5-7]. 46 The cell cycle, a fundamental framework in cellular fate, is essential for 47 organismal growth and development. Its stages , G1, S, G2, and M phases , are 48 interconnected by complex molecular events and regulatory networks. Precise 49 regulation of these stages is crucial for maintaining tissue homeostasis and enabling 50 developmental adaptation [8, 9]. Moreover, it is intricately associated with cell states 51 and plays a pivotal role in tumorigenesis. Consequently, accurate identification and 52 comprehension of cell cycle stages are imperative for the in -depth exploration of 53 cellular behaviors [10, 11]. 54 scRNA-seq enables precise quantification of gene expression at the individual-cell 55 level, thereby offering novel and comprehensive insights into the cell cycle [12, 13]. 56 Despite the rich dataset s provided by scRNA -seq for cell cycle analysis, the 57 interpretation of these data presents several challenges. A primary hurdle is the accurate 58 inference of specific cell cycle stages from the scRNA -seq data. Traditional 59 experimental methods, though able to identify cell cycle stages, are not only time -60 consuming and labor -intensive but also lack the capability for the quantitative 61 measurement of cell cycle phase [14]. Moreover, the technical variability and data 62 sparsity inherent to scRNA -seq [15], compounded by the transient and overlapping 63 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint nature of cell cycle stages, significantly complicate the analysis [16]. This complexity 64 underscores the need for advanced methodologies to accurately interpret cell cycle 65 dynamics from scRNA-seq data. 66 Addressing the challenges associated with scRNA -seq data interpretation, the 67 scientific community has recently introduced several computational methodologies. 68 These encompass supervised machine learning methods, which predominantly utilize 69 known cell cycle genes. For instance, cyclone [5] and the CellCycleScoring function in 70 Seurat [17] are notable examples. These methods employ annotated cell cycle genes for 71 predicting the cell cycle phases (G1, S, or G2/M) of individual cells. Additionally, 72 reCAT [18] is an innovative approach combining the Travelling Salesman Problem and 73 Hidden Markov Model to reconstruct cell cycle pseudotime series. However, a 74 significant limitation of these methods is their dependency on datasets with pre -75 annotated cell cycle genes and experimental labels, which constrains their broader 76 application. 77 To circumvent these constraints, unsupervised techniques have been developed. 78 CCPE [19] is a representative linear autoencoder-based model for cell cycle analysis. It 79 projects single-cell gene expression profiles into a low -dimensional latent space using 80 a linear encoder and reconstructs the input with a linear decoder. A helical structure is 81 then fitted in the latent space to capture the continuous cyclic trajectory of the cell cycle. 82 While CCPE performs well when the data distribution is approximately linear, its linear 83 encoder limits its ability to model nonlinear or multi-stage cell cycle transitions, which 84 motivated the development of SPAE. Other unsupervised methods include Cyclum [20] 85 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint and CYCLOPS [21]. Cyclum utilizes an autoencoder model that integrates both linear 86 and non-linear elements within the hidden layer, aimed at inferring the pseudotime of 87 cellular cyclical processes. Conversely, CYCLOPS employs a linear -projection 88 autoencoder, mapping data onto a closed elliptical curve in a low -dimensional space, 89 offering a fresh perspective in understanding cell cycle dynamics. However, it ’s 90 important to note that CYCLOPS, while designed to simulate circadian rhythms, 91 incorporates complex operations such as square roots and division in its neural network, 92 potentially posing challenges in optimization. Moreover, tools like cyclone and reCAT, 93 while useful, do not effectively eliminate cell cycle effects from expression data, 94 highlighting the need for continued advancements in this field. 95 In this study, we present a novel computational framework, the Integrated 96 Sinusoidal and Piecewise AutoEncoder (SPAE), designed to concurrently analyze cell 97 cycle dynamics and cell states from single-cell RNA-seq data. The motivation behind 98 SPAE arises from the need to more accurately capture both the cyclic and piecewise 99 linear characteristics of cellular processes observed in scRNA -seq data. Existing 100 models such as CCPE [19] use a purely linear encoder, which limits their ability to 101 represent complex nonlinear gene expression trajectories, while models like Cyclum 102 rely on sinusoidal transformations, they cannot explicitly distinguish multiple cell states 103 that deviate from a single smooth cycle. To overcome these limitations, SPAE 104 integrates two complementary components: a nonlinear component to represent the 105 periodic nature of the cell cycle and a piecewise linear component to model transitions 106 between distinct cellular states that often follow locally linear patterns in gene 107 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint expression space. This combination allows SPAE to more faithfully reconstruct cyclic 108 and branching trajectories while simultaneously assigning cells to specific states. We 109 rigorously assessed SPAE ’s efficacy in estimating cell cycle pseudotime and 110 determining cell stage classifications. Our comparative analysis includes established 111 methodologies such as CCPE, cyclone, Seurat, Cyclum, CYCLOPS, and reCAT. 112 Furthermore, we demonstrate SPAE’s utility in predicting cancer cell cycle transitions 113 and in mitigating the confounding effects of cell cycle variations. 114 115

116 Datasets 117 We utilized datasets presented in Table 1 and Table 2 to assess the performance of 118 SPAE. The Quartz -Seq dataset of mouse embryonic stem cells (mESCs) [22], 119 sequenced through Quartz -Seq technology, provided cell cycle stage and gene 120 expression data for 33,412 genes. The H1 human embryonic stem cells (hESCs) [23] 121 dataset utilized a fluorescence ubiquitination -based cell cycle indicator to stage 247 122 cells. For the E-MTAB-2805 mESCs dataset [6], 288 mouse embryonic stem cells were 123 sequenced using the HiSeq 2000 sequencing system, covering 38,293 genes. To assess 124 model robustness under different dropout rates, we utilized the E-MTAB-2805 mESCs 125 dataset, which initially had a dropout rate of 2 4%. We first applied the MAGIC [24] 126 model to impute the missing data, and subsequently introduced artificial dropout rates 127 of 0%, 20%, 50%, and 70%. Additionally, the nutlin-treated multiple cancer cell lines 128 dataset [25] included single-cell RNA-seq data from 24 cancer cell lines , treated with 129 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint DMSO or nutlin on the 10× Genomics platform, highlighting cell cycle arrest induced 130 by nutlin in cells expressing wild -type TP53. The FELINE Breast Cancer Single -Cell 131 Genomics dataset [26] comprised patients with ER+ breast cancer undergoing 132 neoadjuvant endocrine therapy (letrozole) with or without a CDK4/6 inhibitor 133 (ribociclib), sampled at the start of treatment, after 14 days, and after 180 days of 134 treatment, using 10× technology for single-nucleus RNA sequencing. 135 Moreover, to evaluate SPAE ’s performance in removing cell cycle effects, we 136 analyzed datasets from mouse embryonic stem cell , human myoblasts (hMyo), and 137 breast cancer . The mouse embryonic stem cell dataset [27] utilized droplet 138 microfluidics for high-throughput barcoding and RNA sequencing of individual cells. 139 This dataset focused on the impact of leukemia inhibitory factor withdrawal. It included 140 data from different stages of mouse embryonic stem cells at different stages: 141 undifferentiated, and 2, 4, and 7 days post LIF withdrawal. The scRNA -seq data of 142 human myoblasts [7], developed by Trapnell et al. (2014), included differentiating 143 myoblasts sampled at various time points, namely at 0, 24, 48, and 72 hours. At 0 hours 144 (0h), myoblast cells are actively proliferating and remain undifferentiated, with 145 transcriptional profiles dominated by cell cycle and proliferation -associated genes. By 146 24 hours (24h), after switching to a differentiation -induction medium, the cells begin 147 exiting the cell cycle and initiating early differentiation programs, marked by 148 downregulation of cell cycle genes and upregulation of early myogenic markers like 149 MYOD1. At 48 hours (48h), the cells show active differentiation with increased 150 expression of muscle-specific genes such as MYOG (myogenin), reflecting a transition 151 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint from proliferative myoblasts to early muscle precursors. By 72 hours (72h), the 152 differentiation process is largely complete, with transcriptional profiles dominated by 153 late myogenic markers like MYH genes, indicating mature muscle cells with a 154 heterogeneous mix of late differentiation states. These time points correspond to critical 155 stages in an experimental setup where the growth medium was changed to an induction 156 medium, triggering the transition of proliferating myoblasts into a differentiation 157 program. This process promotes the differentiation of myoblasts into more specialized 158 cell types, allowing the capture of dynamic transcriptional changes associated with cell 159 fate transitions. Breast cancer dataset [28] involves high throughput sequencing of 160 MDA-MB-231 breast tumor cells, exploring the role of CSL (CBF1/RBP -161 Jkappa/Suppressor of Hairless/LAG-1) in cancer. It includes four cell types: CSLKO1 162 and CSLKO2 (CSL gene knockouts) and WT1 and WT2 (wild-type controls). 163 164 SPAE model 165 SPAE models the distinct cell states using a piecewise linear regression framework . 166 Piecewise linear regression is a modeling approach in which the relationship between 167 variables is represented by multiple linear segments with different slopes across distinct 168 regimes [29]. The mathematical formulation, including the continuity constraints and 169

function, is detailed in Supplementary Note 1 . In SPAE, we employ an 170 autoencoder-based piecewise linear model in which the encoder consists of both 171 nonlinear and piecewise linear components. In the nonlinear component, we use a 172 standard multi-layer perceptron with hyperbolic tangent activation functions to map the 173 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint transcriptome profile 𝑋 to 𝑧𝑐 which represents the pseudotime along the cell cycle 174 process ( Figure 1). The p iecewise linear component assigned cells into different 175 clusters. Suppose we have 𝑘 clusters, the gate function in our piecewise linear model 176 determined which cluster a cell 𝑥𝑛 belongs to, defined as 177 𝑔𝑖(𝑥𝑛) = {𝑥𝑛, 𝑐𝑒𝑙𝑙 𝑛 𝑏𝑒𝑙𝑜𝑛𝑔𝑠 𝑡𝑜 𝑐𝑙𝑢𝑠𝑡𝑒𝑟 𝑖 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 , (𝑖 = 1, … , 𝑘) (1) 178 The transformations of the encoder can be represented as 179 𝑧𝑛 = [𝑧𝑛 𝑐 𝑧𝑛 𝑝] = [𝑤3 𝑁𝐿tanh (𝑤2 𝑁𝐿 tanh(𝑤1 𝑁𝐿𝑥𝑛 + 𝑏1 𝑁𝐿) + 𝑏2 𝑁𝐿) ∑ (𝑤𝑖 𝑝𝑥𝑛 + 𝑏𝑖 𝑝) ∙ 𝑔𝑖(𝑤𝑖 𝑝𝑥𝑛 + 𝑏𝑖 𝑝)𝑘 𝑖=1 ] (2) 180 Where 𝑤𝑁𝐿 (collection of 𝑤1 𝑁𝐿 , 𝑤2 𝑁𝐿 , 𝑤3 𝑁𝐿 ) and 𝑏𝑁𝐿 are the weight and 181 bias matrices of the nonline encoder, 𝑤𝑝 represents weight in the piecewise linear 182 component. In the decoder, we used 𝑉 as the weight matrix of the decoder and 183 performed linear transformations, as follows 184 𝑥𝑛̂ = 𝑥̂𝑛 𝑛𝑜𝑛𝑙𝑖𝑛𝑒𝑎𝑟 + 𝑥̂𝑛 𝑝𝑖𝑒𝑐𝑒𝑤𝑖𝑠𝑒 185 = [𝑉𝑛𝑜𝑛𝑙𝑖𝑛𝑒𝑎𝑟 𝑉𝑝𝑖𝑒𝑐𝑒𝑤𝑖𝑠𝑒] [ 𝑠𝑖𝑛𝑧𝑐 𝑐𝑜𝑠𝑧𝑐 ∑ (𝑤𝑖 𝑝𝑥𝑛 + 𝑏𝑖 𝑝) ∙ 𝑔𝑖(𝑤𝑖 𝑝𝑥𝑛 + 𝑏𝑖 𝑝)𝑘 𝑖=1 ] (3) 186 = 𝑉𝑧𝑛 187 The optimization problem using the least square error is formulated as 188 min 𝑤𝑁𝐿,𝑤𝑝,𝑉 ∑ ‖𝑥𝑛 − 𝑥𝑛̂‖2𝑁 𝑛=1 + 𝜆‖𝑤𝑁𝐿‖2 + ∑ 𝛼𝑖‖𝑤𝑖 𝑝‖ 2 + 𝛽‖𝑉‖2𝑘 𝑖=1 (4) 189 Where 𝜆, 𝛼𝑖, and 𝛽 are regularization coefficients controlling the complexity of the 190 nonlinear encoder, the piecewise linear component, and the decoder, respectively. 191 Specifically, 𝜆 ∥ 𝑤𝑁𝐿 ∥2 ensures the smoothness of the learned latent manifold by 192 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint regularizing the nonlinear weights, while 𝛼𝑖 constrains the slope parameters of each 193 cell state. To train the model, we employ an alternating optimization strategy that 194 iterates between refining the piecewise thresholds and updating the autoencoder 195 weights. Detailed descriptions of the initialization and the two -step optimization 196 algorithm are provided in Supplementary Note 2. 197 198

199 Overview of SPAE 200 As illustrated in Figure 1, SPAE integrates an autoencoder to analyze single-cell RNA 201 sequencing (scRNA-seq) data by capturing both cell cycle dynamics and different cell 202 types. The model consists of two key components: a nonlinear encoder for cell cycle 203 estimation and a piecewise linear regression model for identifying distinct cell types 204 based on their gene expression profiles. In the encoder, a multi -layer perceptron with 205 hyperbolic tangent activation functions reduces the data ’ s dimensionality while 206 mapping cells along a pseudotime trajectory, capturing their progression through the 207 cell cycle. To account for the periodicity of the cell cycle, SPAE employs sine and 208 cosine functions in the decoder, allowing for precise estimation of pseudotime and cell 209 cycle phases. Once the cyclic behavior is modeled, SPAE integrates a piecewise linear 210 regression model, which allows the program to treat inferred cycle processes as 211 confounding factors and, after discounting confounding cell cycle effects, to make 212 predictions for multiple cell types. 213 214 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint SPAE accurately infers cell cycle pseudotime 215 To assess the performance of SPAE in predicting cell cycle pseudotime, we compared 216 SPAE with Cyclum, CYCLOPS, and reCAT [18, 20, 21], and the widely used trajectory 217 inference tool Monocle using the scRNA -seq data of mESCs. Figure 2A shows the 218 distribution of cell cycle pseudotime estimated by each method. We calculated 219 statistical measurements using the interquartile distances between boxplots, which 220 helped quantify the separation of pseudotime of cells in different cell cycle phases. 221 Specifically, we measured the distance between the lower quartile of the inferred cell 222 cycle pseudotime in the S phase and the upper quartile of the pseudotime in the G1 223 phase, as well as the distance between the lower quartile of the pseudotime in the G2/M 224 phase and the upper quartile of the pseudotime in the S phase. Both SPAE and Cyclum 225 retain the correct cell cycle order, from G1 to S and then to G2/M. CYCLOPS 226 effectively distinguishes between S and G2/M phases, while reCAT can distinguish G1 227 and S phases but not G2/M. Compared to Cyclum, SPAE exhibits superior performance 228 in separating S phase and G2/M phase. To quantitatively validate these observations, 229 we calculated Spearman’s rank correlation coefficient ( ρ)[30] between each method’s 230 inferred pseudotime and the true, biologically ordered cell -cycle stages. Our results 231 demonstrate that SPAE achieves the strongest monotonic correlation with the true cell-232 cycle order (ρ = 0.866, P = 1.90×10⁻¹¹), substantially outperforming other methods such 233 as Cyclum (ρ = 0.699, P=2.96×10⁻⁶), reCAT (ρ = 0.591, P = 1.87×10⁻⁴), Monocle (ρ 234 = 0.468, P=0.004587) and CYCLOPS ( ρ = -0.276, P = 0.1087). Notably, while 235 Monocle is effective for branching trajectories, its lower correlation here suggests 236 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint

in capturing the closed-loop topology of the cell cycle compared to SPAE. 237 These statistics confirm that SPAE most accurately reconstructs the biological sequence 238 of cell-cycle stages, effectively capturing the continuous transition consistent with the 239 visual patterns in Figure 2A. We calculated the Pearson correlation between the gene 240 expression and cell cycle pseudotime inferred by SPAE. The genes with the highest 241 correlation with cell cycle pseudotime were Aurora kinase A ( Aurka), cell division 242 cycle associated 2 ( Cdca2) and karyopherin alpha 2 ( Kpna2). The correlation 243 coefficients of Aurka, Cdca2, and Kpna2 are 0.73, 0.73, and 0.71, respectively (Figure 244 2B). Aurka is a kinase that plays an important role in cell cycle regulation and control. 245 It affects the cell cycle mainly by regulating chromosome separation in the preparatory 246 phase of cell division. Aurka maintains the stability of the cell cycle by interacting with 247 other cell cycle proteins [31]. Cdca2 has a crucial role in controlling the G1/S transition, 248 which is a critical stage in the cell cycle. Cdca2 depletion led to cell cycle arrest at the 249 G1 phase, suggesting that Cdca2 is required for proper cell cycle progression [32]. 250 Kpna2 is also involved in cell cycle regulation and restriction of cell cycle progression 251 [33]. To complete the comparison, we extend this analysis to CYCLOPS, Cyclum, 252 reCAT and Monocle, showing the Pearson correlation between gene expression and 253 inferred cell cycle pseudotime for the top six genes identified by each method 254 (Supplementary Figure S 1-S4). Notably, most of the top genes identified by 255 CYCLOPS, Cyclum, and reCAT have little to no direct involvement in the cell cycle, 256 which suggests a potential limitation in these methods for capturing key cell cycle -257 related dynamics. Additionally, we included specific plots comparing the Pearson 258 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint correlation for Aurka, Cdca2, and Kpna2 between all methods. While SPAE 259 consistently identified these genes as highly correlated with cell cycle pseudotime (with 260 correlations of 0.73, 0.73, and 0.71, respectively), their correlations were significantly 261 lower in CYCLOPS, Cyclum, and reCAT (Supplementary Figure S 1B-S3B). For 262 instance, Monocle showed weaker correlations for key regulators like Aurka (R = 0.55) 263 and Cdca2 (R = 0.58), although it maintained a comparable correlation for Kpna2 (R = 264 0.77) (Supplementary Figure S 4B). This indicates that general-purpose tools like 265 Monocle and other specific methods may fail to capture the importance of these well -266 known cell cycle regulators, further highlighting SPAE ’s strength in identifying 267 biologically relevant genes associated with cell cycle progression. Figure 2C displays 268 a heatmap illustrating several G2/M phase marker genes with relatively high 269 correlations to cell cycle pseudotime estimated by SPAE, which are all highly expressed 270 in the G2/M phase. 271 272 SPAE demonstrates superior accuracy and robustness in cell cycle 273 characterization 274 To evaluate SPAE ’s performance in predicting cell cycle progression, we follow the 275 comparison strategy in Cyclum [20]. SPAE was compared with several models, 276 including CCPE, Cyclum, CYCLOPS, cyclone, Seurat, and reCAT. The continuous 277 pseudotime generated by SPAE, CCPE, Cyclum, and CYCLOPS was converted into 278 discrete cell cycle phases using a three -component Gaussian mixture model. The 279 performance was evaluated using seven classification metrics including Accuracy, 280 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint Precision, Recall, F -score, Rand Index (RI), Normalized Mutual Information (NMI), 281 and Adjusted Rand Index (ARI), across three datasets (mESCs Quartz-Seq, E-MTAB-282 2805 mESCs, and H1 hESCs). To account for the stochasticity of machine learning 283 models, we evaluated each method ten times on each dataset and then calculated the 284 average values for each performance metric. The radar plots demonstrate SPAE ’s 285 outstanding performance in the analysis of H1 hESCs dataset, with the clustering 286 metrics achieving the highest values among all methods ( Figure 3A, where 0.2, 0.4, 287 0.6, and 0.8 represent different thresholds). In the E -MTAB-2805 dataset analysis, 288 SPAE led in all individual metrics, showcasing its superior performance compared to 289 other models (Figure 3B) . Furthermore, in the analysis of the m ESCs Quartz Seq 290 dataset, SPAE continued to demonstrate strong performance ( Supplementary Figure 291 S5), confirming its robustness across different datasets. 292 We further evaluated the performance of SPAE under different sample sizes by 293 subsampling the scRNA-seq data from the H1 hESC dataset with fewer cells or genes. 294 We conducted an analysis on seven sub-datasets with a diverse range of gene numbers, 295 extending from 50 to 600, and five sub -datasets with a range of cellular numbers, 296 extending from 10 to 100. Our results indicated a gradual increase in the median value 297 of clustering metrics for SPAE , CYCLOPS and Cyclum with increasing number of 298 genes ( Figure 3C , Supplementary Figure S 6). The findings of our analysis 299 demonstrated the superiority of SPAE over CYCLOPS and Cyclum in terms of seven 300 clustering metrics. In particular, SPAE exhibited a greater accuracy in predicting cell 301 cycle stages using fewer genes compared to CYCLOPS and Cyclum. Moreover, SPAE 302 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint displayed better performance with smaller numbers of cells compared to CYCLOPS 303 and Cyclum. As the number of cells increased, the performance of SPAE declined 304 gradually and reached a stable point ( Figure 3D , Supplementary Figure S 7). 305 Conversely, the performance of Cyclum and CYCLOPS exhibited fluctuations but 306 consistently remained below that of SPAE . However, we did not include cyclone, 307 Seurat, and reCAT in Figures 3C -D due to their poor performance in the context of 308 subsampling. When randomly sampling cells, the accuracy of all performance metrics 309 for these methods was extremely low. Additionally, when randomly sampling genes, 310 the number of selected genes was often too small, and many of the genes were not 311 marker genes used by these models, resulting in their failure to produce any meaningful 312 results. Therefore, we believe including these methods in the subsampling analysis 313 would not provide valuable insights, as their performance was not comparable to SPAE, 314 Cyclum and CYCLOPS under these conditions. Our analysis suggests that SPAE is 315 more robust and exhibits higher prediction accuracy for sub -datasets with smaller 316 numbers of genes or cells. A comprehensive comparison of the algorithmic features and 317 architectures of these methods is provided in Supplementary Table S1. 318 319 SPAE is robust to dropout events in the E-MTAB-2805 mESCs dataset 320 To assess SPAE’s robustness against dropout events in scRNA-seq, we utilized the E-321 MTAB-2805 mESCs dataset, which initially had a dropout rate of 24%. We first applied 322 the MAGIC [24] model to impute the missing data, and subsequently introduced 323 artificial dropout rates of 0%, 20%, 50%, and 70%. Our analysis indicated that SPAE’s 324 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint performance was influenced by the dropout rate. However, the evaluation of the 325 clustering metrics in Figure 4 revealed that SPAE outperformed Cyclum, and 326 CYCLOPS when the dropout rate was below 70%. At a dropout rate of 70% , all 327

(SPAE, Cyclum and CYCLOPS) were no longer performant in estimating the 328 cell cycle stages based on precision, recall and F1 score. For lower levels of dropout 329 events, however, SPAE ’s clustering metric values remained higher than those of 330 Cyclum and CYCLOPS. Therefore, our findings suggest that the SPAE is in general 331 more robust to dropout events compared to Cyclum and CYCLOPS, albeit at higher 332 levels of dropout events none of the methods were able to obtain sufficient information 333 to deliver performant cell cycle stage estimation. 334 335 SPAE identifies differentially expressed genes enriched in key cell cycle pathways 336 Performing differential gene expression analysis based on inferred cell cycle phases 337 allows us to uncover variations in gene expression across distinct cell cycle stages. 338 Using the DESeq2 package [34] within R/Bioconductor, we identified differentially 339 expressed genes (DEGs) from cell cycle stages as inferred by SPAE. Subsequently, we 340 compared these findings to those obtained from Cyclum , CYCLOPS, cyclone, Seurat, 341 and reCAT using the E -MTAB-2805 mESCs dataset, applying stringent criteria 342 (P.adjusted ≤ 0.05 and |log2FC| ≥ 1). Our gene set enrichment analysis [35] unveiled 343 that DEGs identified by SPAE are predominantly related to cell cycle pathways and 344 rank highly in enrichment analysis. Furthermore, these DEGs exhibited enrichment in 345 biological processes closely associated with the cell cycle, encompassing pathways 346 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint such as the p53 signaling pathway, progesterone -mediated oocyte maturation. 347 Contrastingly, DEGs identified by Cyclum showed minimal relevance to the cell cycle, 348 highlighting a significant difference (Figure 5A ). CYCLOPS, cyclone, Seurat, and 349 reCAT also exhibit some degree of cell cycle relevance, these methods are less effective 350 and exhibit lower correlations compared to SPAE, failing to capture key pathways 351 closely related to the cell cycle with the same level of significance (Supplementary 352 Figure S8). We also explored the expression patterns of four genes enriched in the cell 353 cycle pathway, Cdc20, Fzr1, Cdk1 and Ccnb1, which are G2/M phase marker genes 354 (Figure 5B). These genes were identified through a rigorous two-step selection process. 355 First, differential gene expression (DEG) analysis was conducted using the DESeq2 356 package in R/Bioconductor, based on cell cycle stages inferred by SPAE from the E -357 MTAB-2805 mESCs dataset. Genes meeting the criteria of an adjusted P -value ≤ 358 0.05 and |log2FC| ≥ 1 were designated as DEGs. Second, gene set enrichment 359 analysis of the DEGs revealed significant enrichment of Cdc20, Fzr1, Cdk1, and Ccnb1 360 in both the cell cycle pathway and the progesterone -mediated oocyte maturation 361 pathway. The critical role of these pathways in cell cycle regulation provided a strong 362 rationale for their selection for further investigation. 363 SPAE accurately detects Nutlin-induced G1 arrest in TP53 wild-type cancer cells 364 To validate SPAE’s efficacy in cell cycle prediction, we analyzed a dataset of cancer 365 cells treated with nutlin and DMSO. Nutlin, an antagonist of the MDM2-p53 pathway 366 [36], is known to induce cell cycle arrest [37]. Nutlin promotes the stability and activity 367 of p53 by inhibiting the interaction between MDM2 and p53, thereby inducing G1 368 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint phase arrest, particularly in TP53 wild-type (WT) cells. As a key tumor suppressor 369 protein, p53 initiates cell cycle checkpoints, especially the G1/S checkpoint, in response 370 to cellular stress, preventing damaged cells from entering the S phase. Therefore, it is 371 expected that Nutlin treatment in TP53 WT cells will significantly increase the 372 proportion of G1 phase cells and reduce the number of cells in the S and G2/M phases. 373 We utilized two groups of data: one group consisted of cells treated with DMSO (the 374 control group), and the other group comprised the same type of cells treated with nutlin 375 [25]. The experimental samples comprised 7 TP53 wild-type (WT). As shown in 376 Figure 6A, SPAE’s predictions revealed a significant rise in G1 phase cells in TP53 377 WT samples treated with nutlin, compared to the control group. Further analysis 378 specifically targeting TP53 WT cell lines reinforced this finding, showing a significant 379 increase in the proportion of G1 phase cells, indicating that Nutlin induced G1 phase 380 arrest in these cells (Figure 6B). Additionally, we identified DEGs for each cell cycle 381 stage using D ESeq2 ( Figure 6C), revealing multiple pathways related to cell cycle 382 regulation, particularly the regulation pathway of the G2/M checkpoint. In Nutlin -383 treated TP53 WT cells, the G2/M checkpoint process ranks third among the DEGs. 384 These findings not only confirm the high accuracy of SPAE in predicting cell cycle 385 stages but also demonstrate its effectiveness in detecting G1 arrest induced by Nutlin 386 in TP53 WT cells. 387 388 SPAE disentangles cell cycle effects from intrinsic cell states 389 In cellular biology, removing cell cycle effects is critical for accurately identifying cell 390 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint types and understanding cellular differentiation [38]. Cells in different stages of the cell 391 cycle often exhibit large differences in gene expression, which can obscure true 392 biological signals and hinder functional analysis [39]. In this study, we evaluated the 393 performance of SPAE in removing cell cycle effects across three datasets: mouse 394 embryonic stem cells (mESCs), human myoblasts (hMyo), and breast cancer cells. The 395 mESCs dataset includes data from four different withdrawal intervals of leukemia 396 inhibitory factor (LIF) at 0, 2, 4, and 7 days. The hMyo dataset comprises scRNA-seq 397 data from human myoblasts collected at various time points, namely 0, 24, 48, and 72 398 hours. The breast cancer dataset encompasses cell types with CSL gene knockout 399 (CSLKO1 and CSLKO2) and wild-type controls (WT1 and WT2). To comprehensively 400 assess SPAE’s performance in removing cell cycle effects, we compared it with four 401 other methods: Cyclum, CCPE, ccRemover, and Seurat. We performed dimensionality 402 reduction analyses using UMAP [40] on both raw data and the output of each method 403 after cell cycle correction. The data were visualized with UMAP plots labeled by cell 404 cycle stages (upper panels in Figure 7A-C) and by cell types, states or time points 405 (lower panels in Figure 7A -C). The distribution of cells across different cell cycle 406 stages was examined to evaluate the effectiveness of each method in mitigating cell 407 cycle-driven clustering. Before the removal of the cell cycle effect, the distribution of 408 cells in all three datasets was predominantly influenced by their cell cycle phases, 409 obscuring the differences between cell types and hindering the clear separation of 410 similar cell populations. However, after applying SPAE, cells of the same type, state or 411 time point were more accurately clustered together, no longer being dispersed based on 412 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint their cell cycle stages (Figure 7A-C). Specifically, in mouse embryonic stem cells, the 413 raw data can distinguish cells from four different withdrawal intervals of leukemia 414 inhibitory factor (LIF) at undifferentiated, 2, 4, and 7 days (Figure 7A). However, at 415 each interval, cells in the three cell cycle stages are not well mixed, indicating that cell 416 state classification is influenced by cell cycle effects. For instance, most ES7d cells are 417 in the G1 phase. After applying SPAE to remove cell cycle effects, the distribution of 418 cells across the three cell cycle stages in ES7d becomes more uniform. In contrast, 419 CCPE effectively mixed cells from different cell cycle stages but failed to distinguish 420 the four LIF withdrawal intervals. ccRemover distinguished the four intervals but did 421 not evenly mix the three cell cycle stages, indicating residual cell cycle influence. 422 Cyclum neither distinguished the LIF withdrawal intervals nor evenly mixed the three 423 cell cycle stages. Seurat was able to distinguish between different LIF discontinuation 424 intervals to some extent but failed to effectively and evenly mix cells in the three cell 425 cycle stages (Figure 7A). Similar trends were observed in the hMyo dataset (Figure 426 7B) and the breast cancer dataset (Figure 7C). SPAE consistently outperformed other 427 methods, effectively mixing cells across different cell cycle phases while maintaining 428 distinctions between different time points, cell states, or cell types. This improved 429 clustering suggests that SPAE successfully removed confounding cell cycle effects, 430 allowing the data to reflect true biological differences. In contrast, other methods, 431 including Cyclum, CCPE, Seurat, and ccRemover, did not achieve comparable results. 432 Even after applying these methods, cell cycle -driven clustering remained evident 433 (Figure 7A-C). SPAE ranked highest in both mixing cells from different cell cycle 434 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint phases and maintaining clear separation of cells collected from different time points or 435 biological states. These findings highlight SPAE’s robustness in removing cell cycle 436 effects, making it a valuable tool for accurately analyzing single -cell transcriptomic 437 data and uncovering true cellular identities. 438 439 Prediction of cell cycle transitions in breast cancer treatment using SPAE 440 Cell cycle dysregulation manifests as changes in the distribution of cells across various 441 stages and alterations in the expression of cell cycle regulatory genes [41]. To assess 442 SPAE’s effectiveness and discern changes in single-cell data, we analyzed scRNA-seq 443 tumor data from 176,644 cells. These were divided into three treatment groups: 444 endocrine therapy alone (letrozole plus placebo), intermittent high -dose combination 445 therapy (letrozole plus ribociclib [600 mg/day, 3 weeks on/off]), and continuous low -446 dose combination therapy (letrozole plus ribociclib [400 mg/day]) [26]. Patients 447 underwent six cycles of treatment, with biopsies collected at baseline (day 0), the start 448 of treatment (day 14), and at the end of treatment (around day 180 at surgery). SPAE 449 was employed to predict transitions in the cancer cell cycle. Additionally, a cyclic 450 generalized additive model was used to describe the dynamics of gene expression at 451 various cell cycle stages. The SPAE-inferred cell cycle stages were used to color cells 452 (Figure 8A). Reconstructing the cell cycle based on scRNA -seq data ( Figure 8A), 453 SPAE recovered the expected cell cycle stages, including the G1 checkpoint transition, 454 where cyclin D initially rises, followed by CDK6 expression. Additionally, we observed 455 a decrease in RB1 expression (a key G1 checkpoint protein) and an increase in E2F3, a 456 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint proliferation gene. Moreover, based on SPAE-inferred cell cycle staging, we calculated 457 the proportion of mitotic (S/G2 phase) cancer cells in each patient’s biopsy (Figure 8B). 458 During combination therapy, an increase in the proportion of mitotic and proliferating 459 (S/G2 phase) cancer cells was observed in each patient. Persistent tumors exhibited an 460 increased frequency of proliferating cells, especially those undergoing high -dose 461 combination therapy. In contrast, patients receiving only endocrine therapy showed 462 fewer proliferating cells. These results suggest that in surviving subclonal populations, 463 the ribociclib-enhanced G1/S checkpoint can be effectively bypassed. Subsequently, 464 applying the cyclic generalized additive model revealed fluctuations in ESR1 and FOS 465 gene expression throughout the cell cycle. By applying this approach to cells sampled 466 at different time points and patients undergoing different treatments, we differentiated 467 whether treatment altered expression at specific cell cycle stages, or if gene expression 468 was independent of cell cycle dysregulation. ESR1 showed consistent expression levels 469 throughout the cell cycle ( Figure 8C). However, a decline in ESR1 expression over 470 time, coupled with an increase in FOS expression, was observed across the entire cohort 471 receiving combination therapy (Figure 8C). Additionally, during combination therapy, 472 a reduction in CDK inhibitor 2A (CDKN2A encoding p14 and p16) and an increase in 473 CDK6 expression from G1 to S/G2 phase were observed ( Figure 8C). In summary, 474 SPAE accurately estimates cancer cell cycle transitions and can be used to explore the 475 phenotypic evolution of cancer cells under endocrine therapy and CDK4/6 inhibitor 476 treatment, as well as the relationship of these phenotypic changes to genomic variations. 477 This information helps to reveal resistance mechanisms in early estrogen receptor -478 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint positive breast cancer and identify potential therapeutic targets. 479 480 SPAE identifies key transcription factors driving cell cycle transitions 481 The SPAE also enables us to identify potential transcription factors (TFs) responsible 482 for the dynamics of gene expression along the cell cycle process. Transcription factors 483 bind to specific DNA sequences (binding motifs) and activate the transcription of their 484 target genes. They encode cellular programs for many functions required by the cell. 485 We used SCENIC [42] to infer TF activity during the cell cycle . SCENIC is a method 486 that computes gene regulatory networks in single -cell transcriptomic data through co -487 expression and motif analysis. Based on the cell cycle predicted by SPAE, we analyzed 488 transcription factors using the mESCs Quartz -Seq dataset and the hESCs scRNA -seq 489 dataset, with motif analysis predictions. In the mESCs Quartz-Seq dataset, observed TF 490 activities suggested that the E2f family appears to be a group of key regulators, known 491 to act at the onset of the cell cycle, especially during the G1/S transition [43, 44]. E2f1 492 and E2f2 peaked between the G1 and S phases, potentially activating genes required 493 for the transition [45] (Supplementary Figure S 9A). Specificity factor 1 (Sp1) and 494 nuclear respiratory factor 1 (Nrf1) were both active in early G1 (Supplementary 495 Figure S 9B). For factors emerging from the hESCs scRNA -seq dataset, MYB is 496 involved in the G2/M transition, functioning during the G2/M transition[46]. Kruppel-497 Like Factor 6 (KLF6), a transcription factor active in the G1 phase, can induce cell 498 cycle arrest and reduce the rate of cell proliferation [47]. These results reveal the 499 dynamic changes in transcription factor activity across different cell cycle stages, 500 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint further supporting the critical role of transcription factors in regulating the cell cycle 501 process. The observed TF activity patterns reflect the specific needs of cells at each 502 stage for transcriptional regulation and offer a new perspective for understanding the 503 cell cycle regulation of stem cells. These findings reinforce the central role of 504 transcription factors in cell fate decisions and could provide potential targets for the 505 treatment of cell cycle-related diseases. 506 507

508 In this work, we present SPAE, a computational framework that integrates a sinusoidal 509 autoencoder with piecewise linear regression to decouple cell cycle dynamics from cell 510 states. By utilizing an alternating optimization strategy, SPAE simultaneously learns 511 continuous pseudotime and discrete cell clusters. While we employed a Gaussian 512 Mixture Model (GMM) [48] to map pseudotime to discrete cell cycle phases (G1, S, 513 G2/M), we acknowledge that standard GMMs may not fully capture the cyclic 514 continuity and non -Gaussian patterns of biological processes. Nevertheless, this 515 approach provides a practical approximation for delineating clinical stages from 516 continuous trajectories. 517 Comprehensive benchmarking against established methods (including CCPE, 518 Cyclum, CYCLOPS, Seurat and Monocle ) across diverse scRNA -seq datasets 519 demonstrated SPAE’s superior performance. Unlike linear models (e.g., CCPE) that 520 struggle with complex nonlinear topologies, SPAE’s piecewise architecture effectively 521 characterizes multi -stage transitions and nonlinear gene expression patterns. 522 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint Consequently, SPAE exhibited greater accuracy and robustness in pseudotime 523 inference, stability against data sparsity (dropout) and subsampling, and the 524 identification of key cell cycle -related transcription factors. Critically, SPAE proved 525 effective in removing cell cycle confounding effects, thereby revealing true cell type 526 identities that were otherwise obscured. Biological validation on Nutlin-treated cancer 527 cells further confirmed SPAE’s sensitivity in detecting specific G1 arrest and predicting 528 therapy-resistant states, highlighting its translational potential. 529 Despite these advancements, limitations remain. Currently, SPAE lacks explicit 530 modeling for complex technical variations, such as batch effects or tissue -specific 531 biases, which may constrain its application in large -scale integrative studies. Future 532 work will focus on incorporating mechanisms, such as adversarial domain adaptation, 533 to mitigate these confounding factors and extend SPAE to complex disease models. In 534 conclusion, SPAE provides a robust and flexible tool for dissecting the interplay 535 between cell cycle dynamics and cell fate, offering new insights into biological 536 heterogeneity and potential therapeutic targets. 537 538 Code availability 539 SPAE developed for this study is implemented in Python 3.9 and is available for 540 download on GitHub (https://github.com/YaJahn/SPAE). The code has also been 541 submitted to BioCode at the National Genomics Data Center (NGDC), China National 542 Center for Bioinformation (CNCB) (BioCode: BT008079), which is publicly accessible 543 at https://ngdc.cncb.ac.cn/biocode/tool/ BT008079. 544 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint CRediT author statement 545 Jiahao Yi: Methodology, Software, Formal analysis, Investigation, Writing – original 546 draft. Jiajia Liu: Methodology, Software, Formal analysis. Peng Guo: Writing – 547 original draft. Yuan-Nong Ye: Conceptualization, Supervision, Writing – review & 548 editing. Xiaobo Zhou: Conceptualization, Supervision, Writing – review & editing. 549 All authors read and approved the final manuscript. 550 551 Competing interests 552 The authors declare no competing interests. 553 554

555 This work was supported by the National Institutes of Health [ R01LM014156, 556 R01GM153822 and R01CA241930 to X.Z .], the National Science Foundation 557 [2217515, 2326879 to X.Z.] and the National Natural Science Foundation of China 558 [32160151 to Y .N.Y .]. 559 560 Supplementary material 561 Supplementary material is available at Genomics, Proteomics & Bioinformatics online. 562 563 ORCID 564 0009-0006-0791-6005 (Jiahao Yi) 565 0000-0002-0038-9592 (Jiajia Liu) 566 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 0009-0008-8981-3310 (Peng Guo) 567 0000-0002-2029-4558 (Yuan-nong Ye) 568 0000-0001-7191-6495 (Xiaobo Zhou) 569 570

571 1. Chang X, Zheng Y, Xu K. Single-Cell RNA Sequencing: Technological Progress and Biomedical 572 Application in Cancer Research, Mol Biotechnol 2023; 66:1497-1519. 573 2. Jovic D, Liang X, Zeng H et al. Single -cell RNA sequencing technologies and applications: A 574 brief overview, Clin Transl Med 2022;12:e694. 575 3. Wen L, Tang F. Recent advances in single -cell sequencing technologies, Precis Clin Med 576 2022;5:pbac002. 577 4. Papalexi E, Satija R. Single -cell RNA sequencing to explore immune cell heterogeneity, Nat 578 Rev Immunol 2018;18:35-45. 579 5. Scialdone A, Natarajan KN, Saraiva LR et al. Computational assignment of cell -cycle stage 580 from single-cell transcriptome data, Methods 2015;85:54-61. 581 6. Buettner F, Natarajan KN, Casale FP et al. Computational analysis of cell-to-cell heterogeneity 582 in single -cell RNA -sequencing data reveals hidden subpopulations of cells, Nat Biotechnol 583 2015;33:155-160. 584 7. Trapnell C, Cacchiarelli D, Grimsby J et al. The dynamics and regulators of cell fate decisions 585 are revealed by pseudotemporal ordering of single cells, Nat Biotechnol 2014;32:381 -386. 586 8. Matthews HK, Bertoli C, de Bruin RAM. Cell cycle control in cancer, Nat Rev Mol Cell Biol 587 2022;23:74-88. 588 9. Bertoli C, Skotheim JM, de Bruin RA. Control of cell cycle transcription during G1 and S phases, 589 Nat Rev Mol Cell Biol 2013;14:518-528. 590 10. Dang F, Nie L, Wei W. Ubiquitin signaling in cell cycle control and tumorigenesis, Cell Death 591 Differ 2021;28:427-438. 592 11. Malumbres M, Barbacid M. Cell cycle, CDKs and cancer: a changing paradigm, Nat Rev Cancer 593 2009;9:153-166. 594 12. Mahdessian D, Cesnik AJ, Gnann C et al. Spatiotemporal dissection of the cell cycle with 595 single-cell proteogenomics, Nature 2021;590:649-654. 596 13. Lee RD, Munro SA, Knutson TP et al. Single -cell analysis identifies dynamic gene expression 597 networks that govern B cell development and transformation, Nat Commun 2021;12:6843. 598 14. Narotamo H, Fernandes MS, Moreira AM et al. A machine learning approach for single cell 599 interphase cell cycle staging, Sci Rep 2021;11:19278. 600 15. Chen G, Ning B, Shi T. Single -Cell RNA-Seq Technologies and Related Computational Data 601 Analysis, Front Genet 2019;10:317. 602 16. Liu J, Fan Z, Zhao W et al. Machine Intelligence in Single -Cell Data Analysis: Advances and 603 New Challenges, Front Genet 2021;12:655536. 604 17. Butler A, Hoffman P, Smibert P et al. Integrating single -cell transcriptomic data across 605 different conditions, technologies, and species, Nat Biotechnol 2018;36:411-420. 606 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 18. Liu Z, Lou H, Xie K et al. Reconstructing cell cycle pseudo time -series via single -cell 607 transcriptome data, Nat Commun 2017;8:22. 608 19. Liu J, Yang M, Zhao W et al. CCPE: cell cycle pseudotime estimation for single cell RNA -seq 609 data, Nucleic Acids Res 2022;50:704-716. 610 20. Liang S, Wang F, Han J et al. Latent periodic process inference from single-cell RNA-seq data, 611 Nat Commun 2020;11:1441. 612 21. Anafi RC, Francey LJ, Hogenesch JB et al. CYCLOPS reveals human transcriptional rhythms in 613 health and disease, Proc Natl Acad Sci U S A 2017;114:5312-5317. 614 22. Sasagawa Y, Nikaido I, Hayashi T et al. Quartz-Seq: a highly reproducible and sensitive single-615 cell RNA sequencing method, reveals non -genetic gene-expression heterogeneity, Genome Biol 616 2013;14:R31. 617 23. Leng N, Chu LF, Barry C et al. Oscope identifies oscillatory genes in unsynchronized single -618 cell RNA-seq experiments, Nat Methods 2015;12:947-950. 619 24. van Dijk D, Sharma R, Nainys J et al. Recovering Gene Interactions from Single-Cell Data Using 620 Data Diffusion, Cell 2018;174:716-729.e727. 621 25. McFarland JM, Paolella BR, Warren A et al. Multiplexed single -cell transcriptional response 622 profiling to define cancer vulnerabilities and therapeutic mechanism of action, Nat Commun 623 2020;11:4296. 624 26. Griffiths JI, Chen J, Cosgrove PA et al. Serial single-cell genomics reveals convergent subclonal 625 evolution of resistance as early -stage breast cancer patients progress on endocrine plus CDK4/6 626 therapy, Nat Cancer 2021;2:658-671. 627 27. Klein AM, Mazutis L, Akartuna I et al. Droplet barcoding for single-cell transcriptomics applied 628 to embryonic stem cells, Cell 2015;161:1187-1201. 629 28. Braune EB, Tsoi YL, Phoon YP et al. Loss of CSL Unlocks a Hypoxic Response and Enhanced 630 Tumor Growth Potential in Breast Cancer Cells, Stem Cell Reports 2016;6:643-651. 631 29. McZgee VE, Carleton WT. Piecewise Regression, Journal of the American Statistical 632 Association 1970;65:1109-1124. 633 30. Spearman C. The proof and measurement of association between two things. By C. Spearman, 634 1904, Am J Psychol 1987;100:441-471. 635 31. Roy A, Veroli MV, Prasad S et al. Protein Kinase D2 Modulates Cell Cycle By Stabilizing Aurora 636 A Kinase at Centrosomes, Mol Cancer Res 2018;16:1785-1797. 637 32. Wang S, Cao K, Liao Y et al. CDCA2 protects against oxidative stress by promoting BRCA1 -638 NRF2 signaling in hepatocellular carcinoma, Oncogene 2021;40:4368-4383. 639 33. Guo X, Wang Z, Zhang J et al. Upregulated KPNA2 promotes hepatocellular carcinoma 640 progression and indicates prognostic significance across human cancer types, Acta Biochim 641 Biophys Sin (Shanghai) 2019;51:285-292. 642 34. Love MI, Huber W, Anders S. Moderated estimation of fold change and dispersion for RNA -643 seq data with DESeq2, Genome Biol 2014;15:550. 644 35. Kuleshov MV, Jones MR, Rouillard AD et al. Enrichr: a comprehensive gene set enrichment 645 analysis web server 2016 update, Nucleic Acids Res 2016;44:W90-97. 646 36. Shangary S, Wang S. Small-molecule inhibitors of the MDM2-p53 protein-protein interaction 647 to reactivate p53 function: a novel approach for cancer therapy, Annu Rev Pharmacol Toxicol 648 2009;49:223-241. 649 37. Arya AK, El-Fert A, Devling T et al. Nutlin-3, the small-molecule inhibitor of MDM2, promotes 650 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint senescence and radiosensitises laryngeal carcinoma cells harbouring wild -type p53, Br J Cancer 651 2010;103:186-195. 652 38. Barron M, Li J. Identifying and removing the cell -cycle effect from single -cell RNA -653 Sequencing data, Sci Rep 2016;6:33892. 654 39. Liu L, Michowski W, Kolodziejczyk A et al. The cell cycle in stem cell proliferation, pluripotency 655 and differentiation, Nat Cell Biol 2019;21:1060-1067. 656 40. McInnes L, Healy J, Melville JJapa. Umap: Uniform manifold approximation and projection for 657 dimension reduction 2018. 658 41. Pramparo T, Lombardo MV, Campbell K et al. Cell cycle networks link gene expression 659 dysregulation, mutation, and brain maldevelopment in autistic toddlers, Mol Syst Biol 2015;11:841. 660 42. Aibar S, Gonzalez-Blas CB, Moerman T et al. SCENIC: single-cell regulatory network inference 661 and clustering, Nat Methods 2017;14:1083-1086. 662 43. Tsai SY, Opavsky R, Sharma N et al. Mouse development with a single E2F activator, Nature 663 2008;454:1137-1141. 664 44. Gaubatz S, Lindeman GJ, Ishida S et al. E2F4 and E2F5 play an essential role in pocket protein-665 mediated G1 control, Mol Cell 2000;6:729-735. 666 45. Timmers C, Sharma N, Opavsky R et al. E2f1, E2f2, and E2f3 control E2F target expression and 667 cellular proliferation via a p53-dependent negative feedback loop, Mol Cell Biol 2007;27:65-78. 668 46. Nakata Y, Shetzline S, Sakashita C et al. c -Myb contributes to G2/M cell cycle transition in 669 human hematopoietic cells by direct regulation of cyclin B1 expression, Mol Cell Biol 670 2007;27:2048-2058. 671 47. Trucco LD, Andreoli V, Nunez NG et al. Kruppel -like factor 6 interferes with cellular 672 transformation induced by the H-ras oncogene, FASEB J 2014;28:5262-5276. 673 48. Wan C, Chang W, Zhang Y et al. LTMG: a novel statistical modeling of transcriptional 674 expression states in single-cell RNA-Seq data, Nucleic Acids Res 2019;47:e111. 675 676 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 677 Figure 1. Overview of the SPAE framework. 678 SPAE primarily consists of two components: a nonlinear component and a piecewise 679 linear component. The nonlinear component is employed for the estimation of cell cycle 680 pseudotime, while the piecewise linear component is dedicated to predicting various 681 cell types. Six downstream analyses and applications of SPAE have been employed to 682 evaluate its performance. 683 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 684 Figure 2. Cell cycle pseudotime analysis of mESCs Quartz-Seq data. 685 (A) Boxplots show the distribution of cell cycle pseudotimes inferred by five different 686

(SPAE, Cyclum, CYCLOPS, reCAT, and Monocle). The boxplots are colored 687 according to the three stages of the cell cycle (G1, S, G2/M). (B) Correlation between 688 the expression of three cell cycle marker genes ( Aurka, Cdca2, Kpna2) and the cell 689 cycle pseudotime estimated by SPAE. The top-left corner of each plot is marked with 690 the correlation coefficient (R) and P-value, demonstrating a strong correlation between 691 expression levels and pseudotime. (C) A heatmap displays several G2/M phase marker 692 genes correlated with cell cycle pseudotime inferred by SPAE. Each column represents 693 a cell. The color changes in the heatmap represent variations in gene expression levels, 694 ranging from low (blue) to high (red). 695 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 696 Figure 3. Inferring cell cycle stages from real datasets. 697 (A) Radar chart showing seven multi -class classification metrics (Fscore, Recall, 698 Precision, Accuracy, NMI, ARI, RI) used to evaluate the cell cycle classification 699 accuracy of SPAE, CCPE, cyclone, Seurat, reCAT, Cyclum, and CYCLOPS on H1 700 hESCs data. (B) Radar chart displaying the same seven multi -class classification 701 metrics for assessing the performance of SPAE and the six benchmark methods on E -702 MTAB-2805 mESCs data. (C) Robustness analysis under gene subsampling. The 703 boxplots illustrate the Accuracy, Adjusted Rand Index (ARI), and Normalized Mutual 704 Information (NMI) of SPAE, CYCLOPS, and Cyclum on datasets with varying 705 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint numbers of genes (ranging from 50 to 600). (D) Robustness analysis under cell 706 subsampling. The boxplots illustrate the performance of SPAE, CYCLOPS, and 707 Cyclum in terms of Accuracy, ARI, and NMI metrics on datasets with varying cell 708 counts (ranging from 10 to 100). 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 724 Figure 4. Robustness of SPAE in handling dropout events in the E -MTAB-2805 725 mESCs dataset. 726 Evaluation of the impact of different dropout rates (ranging from 0% to 70%) on the 727 performance of SPAE, Cyclum, and CYCLOPS. The comparison utilizes seven multi-728 class classification metrics: RI, ARI, NMI, Accuracy, Precision, Recall, and Fscore. 729 730 731 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 732 Figure 5. Differential gene expression analysis of E-MTAB-2805 mESCs Data. 733 (A) Comparison of biological pathway enrichment. The left panel (red) shows the top 734 ten biological processes enriched in DEGs identified by SPAE -inferred stages, 735 including relevant terms like cell cycle, oocyte meiosis, and the p53 signaling pathway. 736 The right panel (blue) shows processes associated with DEGs identified by Cyclum, 737 which include unrelated pathways such as T-cell receptor signaling and non-small cell 738 lung cancer. (B) Expression dynamics of G2/M phase marker genes. Scatter plots 739 showing the expression variation of Cdc20, Fzr1, Cdk1, and Ccnb1 along the cell cycle 740 pseudotime inferred by SPAE. Each point represents a single cell, and the red curve 741 indicates the smoothed gene expression trend along the inferred pseudotime. 742 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 743 Figure 6. Validation of SPAE predictions using scRNA-seq datasets of cells treated 744 with cell cycle perturbants. 745 (A) UMAP visualization of 7 cancer cell lines treated with DMSO (control) or Nutlin. 746 Cells are colored according to cell cycle phases (G1, S, G2/M) inferred by SPAE. (B) 747 Quantitative analysis of G1 arrest. Bar chart showing the proportion of cells in different 748 cell cycle stages for TP53 wild-type (WT) cell lines in DMSO versus Nutlin treatment 749 groups. SPAE accurately detects the accumulation of cells in the G1 phase upon Nutlin 750 treatment. (C) Functional enrichment analysis. Bar charts showing the top enriched 751 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint biological processes for Differentially Expressed Genes (DEGs) in the DMSO group 752 (top) and the Nutlin group (bottom), highlighting pathways related to cell cycle 753 regulation and p53 signaling. 754 755 756 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 757 Figure 7. Comparison of different methods for removing cell cycle effects. 758 (A) UMAP of mouse ES cells before and after removing cell cycle effects by SPAE, 759 Cyclum, CCPE, ccRemover, Seurat . (B) UMAP of human myoblast cells before and 760 after removing cell cycle effects by SPAE, Cyclum, CCPE, ccRemover, Seurat . (C) 761 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint UMAP of breast cancer cells before and after removing cell cycle effects by SPAE, 762 Cyclum, CCPE, ccRemover, Seurat . Raw represents data before cell cycle effect 763 removal. Upper panel is labeled by cell cycle stages and lower panel is labeled by cell 764 types, states or time points. 765 766 767 768 769 770 771 772 773 774 775 776 777 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint 778 Figure 8. Analysis of cell cycle dysregulation based on SPAE. 779 (A) Cell cycle phases colored based on predictions by SPAE, depicting expression 780 changes of cell cycle regulatory genes CDK6, Cyclin D, RB1, and E2F3 using a cyclic 781 generalized additive model. The distance from the point to the origin indicates the 782 expression of the cell at that phase. (B) Changes in the proportion of cells at different 783 stages of the cell cycle (S/G2 phase) in patient tumor samples treated with Letrozole 784 alone, intermittent high -dose Ribociclib, and continuous low -dose Ribociclib, as 785 inferred by SPAE. Blue represents patients sensitive to treatment, and red represents 786 patients resistant to treatment, with changes in cell proportions over time. (C) Changes 787 in the expression of ESR1, CDK6, CDKN2A, and FOS before, during, and after the cell 788 cycle and treatment (columns). Colored lines show the expected gene expression in 789 cells throughout the cell cycle before (blue), during (orange), and after (red) treatment. 790 The distance from the center of the circle indicates gene expression at a particular point 791 in the cell cycle. 792 Table 1. Cell-cycle scRNA-seq datasets. 793 Table 2. scRNA-seq datasets of cell cycle effect removal 794 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint Supplementary Figure Legends 795 Supplementary Figure S1. Performance of CYCLOPS on pseudotime inference. 796 (A) Scatter plots showing the Pearson correlation between gene expression and 797 pseudotime for the top six genes identified by CYCLOPS. (B) Pearson correlation 798 between gene expression and pseudotime for known cell cycle markers Aurka, Cdca2, 799 and Kpna2 as inferred by CYCLOPS. 800 801 Supplementary Figure S2. Performance of Cyclum on pseudotime inference. 802 (A) Scatter plots showing the Pearson correlation between gene expression and 803 pseudotime for the top six genes identified by Cyclum. (B) Pearson correlation between 804 gene expression and pseudotime for known cell cycle markers Aurka, Cdca2, and 805 Kpna2 as inferred by Cyclum. 806 807 Supplementary Figure S3. Performance of reCAT on pseudotime inference. (A) 808 Scatter plots showing the Pearson correlation between gene expression and pseudotime 809 for the top six genes identified by reCAT. (B) Pearson correlation between gene 810 expression and pseudotime for known cell cycle markers Aurka, Cdca2, and Kpna2 as 811 inferred by reCAT. 812 813 Supplementary Figure S4. Performance of Monocle on pseudotime inference. (A) 814 Scatter plots showing the Pearson correlation between gene expression and pseudotime 815 for the top six genes identified by Monocle. (B) Pearson correlation between gene 816 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint expression and pseudotime for known cell cycle markers Aurka, Cdca2, and Kpna2 as 817 inferred by Monocle. 818 819 Supplementary Figure S5. Benchmarking classification metrics on mESCs 820 Quartz-Seq data. 821 Radar chart displaying seven multi -class classification metrics (Fscore, Recall, 822 Precision, Accuracy, NMI, ARI, RI) evaluated on the mESCs Quartz-Seq dataset. The 823 performance of SPAE is compared against Cyclum, CYCLOPS, Seurat, Cyclone, and 824 reCAT. 825 826 Supplementary Figure S6. Robustness analysis under gene subsampling. 827 Boxplots of Fscore, Precision, Recall, and RI metrics indicating the performance of 828 SPAE, CYCLOPS, and Cyclum on subsampled datasets with varying numbers of genes 829 (ranging from 50 to 600). 830 831 Supplementary Figure S7. Robustness analysis under cell subsampling. 832 Boxplots of Fscore, Precision, Recall, and RI metrics indicating the performance of 833 SPAE, CYCLOPS, and Cyclum on subsampled datasets with varying numbers of cells 834 (ranging from 10 to 100). 835 836 Supplementary Figure S8. Functional enrichment analysis of benchmark methods. 837 Bar charts showing the top ten enriched biological processes associated with 838 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint Differentially Expressed Genes (DEGs) identified by cell cycle stages inferred through 839 (A) Seurat, (B) reCAT, (C) Cyclone, and (D) CYCLOPS. 840 841 Supplementary Figure S9. SPAE predictions of core transcription factor activity. 842 Heatmaps visualizing the motif activity of transcription factors during the cell cycle. 843 (A) Transcription factor activity in the mESCs Quartz -Seq dataset. (B) Transcription 844 factor activity in the H1 hESCs scRNA -seq dataset. The color gradient represents the 845 variation in activity levels, ranging from low (blue) to high (red). 846 847 Supplementary Notes 848 Supplementary Note 1: Piecewise linear regression model formulation. 849 Supplementary Note 2: Optimization of the autoencoder-based piecewise model. 850 Supplementary Table S1. Summary of computational methods for single -cell cell 851 cycle analysis compared in this study. 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint Table 1. Cell-cycle scRNA-seq datasets. 870 Dataset Tissue Cell cycle stage labeled Total cell count G0/G1 S G2/M Gene count mESCs Quartz - Seq mESC Yes 35 20 7 8 33,412 H1 hESCs scRNA-seq hESC Yes 247 91 80 76 19,084 E-MTAB-2805 mESCs mESC Yes 279 95 88 96 38,293 Nutlin-treated Multiple Cancer Cell Lines Cancer cell line No 3,097 ( nutlin-treated group) and 2,381 (control group) 32,738 FELINE Breast Cancer Single - Cell Genomics Breast Tumor No 46,986 (letrozole alone) 27,790 (high dose ribociclib) 34,543 (low dose ribociclib) 21,279 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint Table 2. scRNA-seq datasets of cell cycle effect removal 892 Dataset Tissue Cell type Total cell count Gene count Mouse ES cells Mouse embryonic stem cellss 4 2717 24,046 hMyo Differentiating myoblasts (0 h, 24 h, 48 h, 72 h) 4 372 47,192 Breast cancer Human Breast Cancer (MDA- MB-231) 4 376 16,383 893 .CC-BY 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is The copyright holder for this preprintthis version posted March 8, 2026. ; https://doi.org/10.64898/2026.03.05.709782doi: bioRxiv preprint