2.1 Overview and rationale

This study aims to identify immunoregulatory CDGs by leveraging time-resolved scRNA-seq data within a dynamic modeling framework called PICDGI. Unlike conventional differential expression or pseudotime trajectory methods, PICDGI explicitly models gene-gene interactions as stochastic, time varying processes and infers latent regulatory trajectories using Bayesian inference. This enables the identification of genes that conditionally regulate other genes over time, including those with immunoregulatory effects in the tumor microenvironment [37,38].

The framework consists of four major components; each directly tied to the observed scRNA-seq data:

1. 1. Time-dependent gene expression:

The scRNA-seq data are preprocessed and normalized, dimensionally reduced, and annotated into cell types across distinct cancer stages. We then construct temporal gene expression matrices for each annotated cell type, forming the basis for modeling dynamic gene activity.

1. 2. Cancer originating cell identification:

Cancer originating cells are identified as the most likely cells of origin based on trends in cell population expansion and cancer cell fraction (CCF), expression of cancer-associated programs, and stage-wise persistence. These cells provide the primary context for modeling regulatory evolution and serve as the reference lineage for downstream driver inference.

1. 3. Stochastic modeling of gene-gene interactions:

The temporal expression of each gene is modeled as a nonstationary stochastic process using a time-varying fractional Autoregressive Moving Average model (ARMA) model. Gene-gene interactions are captured through latent variables representing the regulatory influence of one gene on another during progression.

1. 4. Bayesian inference and driver scoring:

Variational Bayesian inference and MCMC sampling are used to approximate the joint posterior distribution of mutation states and gene-gene interaction effects. From this posterior, a driver coefficient (DrCoef) is computed as a squared signal-to-noise ratio, quantifying both the strength and stability of each gene’s inferred regulatory impact on tumor progression. Genes with high DrCoef values are prioritized as candidate functional drivers because they exhibit strong and reliable influence on expression trajectories over time.

By modeling latent regulatory interactions across time and evaluating their differential impact on immune versus tumor compartments, PICDGI provides a principled approach to uncover functionally significant cancer drivers that may evade detection through static or marginal analysis.

Throughout this study, all modeling in PICDGI is based exclusively on scRNA-seq expression data. No genomic mutation calls are used as input. References in the text to “mutation events,” “mutation states,” or “driver genes” correspond to latent regulatory influence variables inferred from transcriptional dynamics, not observed DNA-level alterations. Thus, the Driver Coefficient quantifies functional regulatory impact, not genomic mutation status.

2.2 The PICDGI algorithm

In PICDGI, the term gene mutation state denotes a latent regulatory activity process inferred from expression dynamics. It does not correspond to observed DNA-level mutations, but rather represents a probabilistic variable used to model time-varying gene influence within regulatory networks. The PICDGI algorithm consists of four main steps to model and infer cancer driver-like genes (CDG) from single-cell data using a time-aware, probabilistic framework: (1) identifying cancer originating cells and summarizing gene expression temporal data from reduced scRNA-seq data, (2) modeling gene expression trajectories as nonstationary, time-varying stochastic processes, allowing regulatory influences between genes to change across progression (3) using Variational Bayesian inference combined with MCMC sampling to estimate posterior distributions over latent regulatory influences. and (4) Computing driver coefficients from posterior mean and variance to quantify each gene’s regulatory impact and stability over time, and genes are ranked accordingly as candidate drivers of cancer progression.

2.2.1 PICDGI identifies cancer progenitor cells for discovering cancer driver.

Let the gene expression profileof cell be denoted by , where is the number of genes. For a given gene, let denote its expression levels across cells in a cluster at a given biological stage. The cluster-level mean expression of gene is computed as:

(1)

To model temporal dynamics, we define an ordered set of biological sampling stages. In this study, cancer progression stages are denoted by , such that where each stage corresponds to a clinically or experimentally defined time point (e.g., diagnosis, treatment response, relapse, or early/advanced disease). These biological stages are mapped to ordered model time indices used for dynamic inference.

Given genes, clusters, and time points, we compute the mean for each cluster and each time point . This results in a temporal gene expression dataset of dimension (Fig 1B) enabling joint modeling of gene dynamics across cell populations and disease progression.

Cancer progenitor cells are identified using two criteria: (1) The abundance of cancer originating cells, denoted as , exhibits a consistent stage-dependent trend across progression stages [39,40], satisfying:

(2)

(2) For each cell type , we compute its cancer cell fraction using marker genes. For each cluster , the CCF is defined as:

(3)

where is the number of cells in cluster and is an indicator function equal to 1 if the gene expression profile of cell exceeds a defined threshold for a known cancer marker gene. In this analysis, a cell is considered marker-positive (and thus potentially cancerous) if it shows any non-zero expression of the selected gene (e.g., EPCAM). A progenitor cell type must have higher CCF than all other cell types:

(4)

By jointly applying Eqs (2) and (3), we identify cancer originating cells. Specifically, for each cluster across patients and stages , we calculate , the fraction of that cluster at stage . A valid progenitor population must exhibit consistent stage-dependent trend across stages (Eq. 2) and the highest CCF among clusters (Eq. 3). This classification allows estimation of CCF by counting the proportion of marker-positive cells within each cluster exhibiting tumor-associated expression signatures. The final progenitor cell population is defined as the cluster that (1) shows increasing/decreasing abundance or enrichment across cancer stages and (2) has the highest average CCF among all clusters. This dual criterion ensures that the selected cluster both demonstrates stage-associated expansion during progression and displays strong tumor-like expression, consistent with a likely cancer-originating population. The above described stage-aware aggregation framework is agnostic to cancer type and is applicable to both solid tumors (e.g., LUAD) and hematologic malignancies (e.g., AML), provided that ordered sampling stages are available.

2.2.2 Modeling nonstationary, discrete time-varying genetic events.

We model gene mutations as nonstationary, discrete-time, integer-valued stochastic processes. This modeling follows five key steps, outlined below

Step 1: Modeling gene expression dynamics as stochastic processes using the ARMA model

We treat gene mutations as nonstationary, discrete-time, integer-valued stochastic processes, where event counts fluctuate over time or space [41,42]. In our framework, a gene system consists of different distributions or populations, each represented by a latent variable ]. Their evolution is driven by gene interaction effects (Fig 2A-2C).

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Fig 2. PICDGI framework.

(A) Representation of gene-gene interaction effects (GIE) in cancer progression. Nodes denote genes and edges denote regulatory interactions, with statistical variability in interactions contributing to genetic heterogeneity. Five categories of genes are considered, with their interaction effects differing by type. (B) Illustration of GIE strength: oncogenes (OGs) and tumor suppressor genes (TSGs) are expected to exert stronger effects on network dynamics compared with other gene classes. (C) Computational formulation of PICDGI. The model links observed temporal gene expression data to hidden variables at two levels: (i) local hidden variables (e.g., gene-specific mutations and expression fluctuations) and (ii) global hidden variables capturing the overall GIE structure across the network. (D) Inference procedure. The effect of a gene on driving mutations in other genes is quantified through the highest density interval (HDI) of the posterior distribution over gene expression dynamics, integrating both temporal patterns and estimated gene–gene interactions.

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Following Grenier (1983) [43], we model the nonstationary signal of a single gene distribution at time denoted as using a finite-order, time-varying Autoregressive Moving Average (ARMA) process. We formulate the ARMA model as:

(5)

where is the gene mutation state at time , and represents the innovation (input) or error process, capturing random mutation events that drive changes in gene populations over time. In Eq. (5), the indices and denote the autoregressive and moving-average “lag orders”, respectively. Consequently, and refer to earlier time points of the same gene signal, rather than to different genes. Gene-gene regulatory influences are incorporated later through the global interaction matrix defined in Section 2.2.3. Unlike gene expression, which reflects transcript abundance, models additional stochastic mutation signals beyond past history, allowing the ARMA process to account for the nonstationary nature of mutation dynamics. The coefficients, , and are the autoregressive and moving average coefficients, respectively, which capture the autocorrelation of the output process . The input is assumed to be a zero-mean Gaussian error process [44], correlated over time to allow for a wide range of memory decay properties in the time series.

Step 2: State-space representation

Equation (5) express the system in stacked state-space form, where the concatenated state vector and the innovation process capture the gene expression or mutation dynamics across all stages up to time . We model the system as a linear transformation of innovations:

(6)

Both and are concatenated multivariate vectors, reflecting the simultaneous modeling of interacting gene distributions across time points. The transfer matrix defined as , governs the relationship between the innovations and the system states, encoding both the observability and the controllability of the evolving gene network [32]. The matrices , and represent the ARMA coefficients (See S1 Text).

Step 3: Modeling non-stationarity with fractional gaussian noise

To account for the model’s non-stationarity, the innovation process is modeled as fractional Gaussian noise with a mean representing stationary increments [45]. The increment process is characterized by the Hurst exponent , governing long-range dependence in time series [46]. Following Chiang et al.[47], we define the autocovariance function of the increments as:

(7)

We constrain the variance and the Hurst exponent to to preserve non-stationary properties [48]. For sequence lengths (where =3, as shown in Fig 1B), the autocorrelation function simplifies to: yielding , which parameterizes the noise process using only the Hurst exponent .

Step 4: Covariance matrix for the innovation process

The covariance matrix for the zero-mean Gaussian vector is:

(8)

where is the correlation matrix, defined as a Toeplitz matrix:

(9)

The correlation structure reflects long-range dependencies in the innovation process, governed by the Hurst exponent . Heatmaps of for different values illustrate how persistence increases with (Fig 3). Based on these analyses, the optimal Hurst exponent is chosen as (Fig 3, S2 Text).

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Fig 3. Heatmap visualization of covariance structures across hurst exponents.

Heatmaps of covariance matrices for the innovation (error generating) process illustrating the Influence of the Hurst Exponent on long-range dependence over time. For and, covariance is highly localized along the diagonal, with weak long-range dependence. At , the covariance matrix is more uniform, balancing local and global dependence. As increases to and , covariance spreads further, indicating stronger long-range dependence. The optimal H is the value that minimizes the error between the estimated and observed covariance matrices, ensuring the best alignment with the observed covariance structure.

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Step 5: Covariance matrix for the state process

In this model, the transfer matrix is typically dense, meaning that all entries can potentially be nonzero. This density reflects the complex dependencies between different gene populations, where each gene’s mutation dynamics can be influenced by innovations from multiple other genes. Thus, encodes both direct and indirect interactions between genes. Using Equation 6, we define the covariance matrix for the zero-mean Gaussian-distributed variable as:

(10)

The evolution of the -th gene population, where , follows a Gaussian process defined as:

(11)

where represents the zero mean and is the covariance matrix governing the system’s dynamics.

2.2.3 Modeling gene-gene interaction.

We define a generative model where observed gene expression arises from latent mutation states and global interaction parameters. Tumor cellular complexity emerges from gene interplay, rather than the actual individual genes alone. To model this complexity, we introduce a local hidden variable representing gene mutation states at time and a global hidden variable representing the gene interaction effects at time . The observed time-series gene expression vector, is modeled with additive Gaussian noise , resulting in:

(12)

with . Here, is a nonlinear generative function governed by a probabilistic graphical model , where depends on both the latent mutation state ( and interaction coefficients (). Specifically, is the observed gene expression vector, is the latent gene mutation signal, and is the global interaction matrix with entries modeled as gamma-distributed random variables. The kernel function encodes similarity between gene states and interaction patterns at different times or across cells, enabling a flexible and nonparametric mapping. and correspond to an alternative latent mutation state and interaction matrix. The noise term accounts for biological and technical variation. This model supports highly nonlinear, context-dependent relationships while providing uncertainty quantification. To ensure tractability, we use a variational Bayesian approach to approximate the joint posterior as described in the following section.

Briefly the model includes: (1) observations , time-series gene expression data; (2) global hidden variables , capturing gene interaction effects during cancer progression; and (3) local hidden variables , representing gene mutation states (Fig 2C). Specifically, we define as the set of observed expression vectors, , as the global hidden variables and as the local hidden variables. Applying Bayes’ rule [32], we compute the joint posterior distribution [49] as:

(13)

where is the likelihood, and is the prior distribution. Due to the computational intractability of the joint posterior, an approximation inference approach is used. This formulation enables us to capture how mutations () and gene-gene interactions () jointly shape observed gene expression (), allowing robust inference of context-specific driver gene effects during tumor progression [50].

2.2.4 Bayesian inference in time-varying gene mutation for cancer progression.

The probabilistic formulation in Equations (5) through (13) models latent gene mutation trajectories over the constructed time derived from single-cell data. The observed input corresponds to estimated average gene expression levels for a given gene at time points (Early), 2 (Mid), and 3 (Late). These observed trajectories are used to infer hidden cancer drivers via variational Bayesian inference.

We use variational Bayesian inference to approximate the joint posterior distribution of both local and global hidden variables, thereby making the joint posterior density function computationally tractable. This process consists of two key steps: variational Bayesian inference and the mean field approximation of the variational free energy [51] (S3 Text), which is closely related to maximizing the Evidence Lower Bound (ELBO). We derive an approximate probability density function that captures gene mutation dynamics during cancer progression, while explicitly incorporating the influence of gene-gene interactions as:

(14)

with denotes the expected value of the global hidden variable , and is a normalization constant. The covariance in the approximated distribution captures the gene dynamics and is used to compute the Hurst exponent (Equation 7), which measures long-term memory in the mutation process. Full derivations are provided in S3 Text.

To assess the contribution of gene-gene interactions to PICDGI’s performance, we conducted a comparative evaluation between two models as described in S4 Text. The first model served as a baseline and assumed that gene expression trajectories are mutually independent, thereby excluding any interaction structure. The second, interaction-aware model incorporated a structured gene-gene interaction matrix directly into the posterior formulation. Across simulated datasets designed to mirror the sparse temporal resolution of our LUAD application, the interaction-aware model consistently outperformed the baseline. The independence model, constrained by its inability to represent regulatory coupling among genes, exhibited inflated prediction errors and poorly calibrated posterior estimates. In contrast, the interaction-aware formulation accurately recovered underlying expression dynamics, yielding posterior predictions that aligned closely with the simulated ground truth. This improvement was reflected in both a substantial reduction in mean squared error (MSE) and markedly lower negative log-posterior values. These findings demonstrate that the interaction parameters are identifiable under conditions similar to those of our empirical data and that modeling gene dependencies is essential for generating biologically coherent predictions. Because the driver coefficient in PICDGI is derived directly from the inferred interaction effects, this robustness is particularly important: it ensures that the genes prioritized by PICDGI reflect stable and meaningful regulatory influences rather than artifacts of model misspecification.

2.2.5 Gene driver coefficient calculation for PICDGI.

While variational Bayesian inference (VBI) offers computational efficiency for high-dimensional latent variable models, it is known to potentially underestimate posterior uncertainty due to the mean-field independence assumption. To address this limitation and enhance the accuracy of downstream inference, we adopted a hybrid inference strategy.

In the initial phase, VBI was employed to approximate the joint posterior distribution , allowing efficient estimation of gene mutation dynamics and interaction effects across time-series scRNA-seq data. To improve the precision of the driver gene identification, we then applied Markov Chain Monte Carlo (MCMC) sampling, drawing 2000 samples from the posterior distribution . These samples were used to estimate the driver coefficient (DrCoef) [52]. The 95% highest density interval (HDI) of the posterior was then computed, providing the range of the most probable true gene effects [53]. This step ensures that credible intervals and posterior variances are accurately quantified, thereby improving the robustness of driver gene identification. By combining VBI for initial scalability with MCMC for final inference precision, our hybrid approach effectively balances computational efficiency and statistical reliability [54]. This makes it particularly well-suited for modeling complex gene-gene interactions in large-scale single-cell RNA sequencing (scRNA-seq) datasets.

To compute the 95% HDI, we conditioned on the interval , which contains the most credible values of DrCoef. The driver coefficient is formally defined as:

(15)

where represents the estimated posterior mean of the effect size, and denotes the standard deviation of the posterior samples. This formulation captures both the magnitude and stability of gene effects, facilitating a more reliable identification of key driver genes in complex biological systems. In S5 Text, we illustrate the construction of the driver coefficient using a toy example with four hypothetical genes. For each gene, PICDGI yields a posterior distribution over its regulatory effect size, approximated here by a normal distribution with mean and standard deviation . The supplement S5 Text, S1 Fig shows the posterior densities, with dashed lines indicating the posterior mean and dotted lines indicating zero effect. The S5 Text, S2 Fig in the supplement displays barplots of the corresponding DrCoef values, defined as . Genes with strong, well-constrained effects (large , small ) obtain high DrCoef values, whereas genes with either small effects or high uncertainty receive lower DrCoef values. This schematic demonstrates how posterior mean and variance jointly determine the ranking of genes in PICDGI.

Having illustrated how PICDGI quantifies and ranks gene-level regulatory influence, we also contrast this framework with existing cancer-driver discovery methods to clarify its distinct modeling assumptions and data requirements. Traditional cancer-driver discovery tools such as MutSigCV, OncodriveFM, OncodriveCLUST, DriverNet, DawnRank, and related approaches operate exclusively on bulk sequencing data and rely on mutation recurrence or static network information rather than dynamic, time-resolved single-cell gene expression. Because PICDGI infers regulatory influence from temporal interaction trajectories in scRNA-seq data, these tools are not directly comparable and do not provide a meaningful benchmarking reference. A detailed summary of these methods, their required input data types, and their modeling assumptions is provided in S6 Text.

2.3 Trajectory analysis for identifying key genes in cancer development

Genes with trajectory-dependent expression act as CDGs by influencing progression at different stages. For example, they may promote early proliferation and later facilitate metastasis by altering tumor microenvironment interactions. Such genes regulate pathways like DNA repair and immune evasion in a stage-specific manner. Techniques such as scRNA-seq and time-dependent data analysis reveal their role in cancer transitions [35], supporting both targeted therapy and improved prediction of disease progression [55].

Building on this, we sought to identify genes with trajectory-dependent expression patterns by integrating scRNA-seq datasets across different times from cancer patient. To achieve this, we applied a statistical test commonly used in spatial data analysis [56] to detect genes exhibiting expression variations along developmental time-dependent trajectories throughout cancer progression. Specifically, within Monocle 3, we used the principalGraphTest() function, which utilizes Moran’s I test [57] to detect differentially expressed genes along trajectories. Moran’s I measures spatial autocorrelation by capturing relationships between data points through a nearest neighbor graph [58], making it ideal for large scRNA-seq datasets. The Moran’s I statistic is defined as:

(16)

where is the number of cells, represents gene expression, and are gene expression values for cells and , and is the mean across all cells. The weight matrix is based on a nearest neighbor graph, with diagonal elements set to zero and off-diagonal elements defined as , where is the number of nearest neighbors. is the sum of all values, ensuring proper autocorrelation normalization.

3.1 Identification of epithelial cells as cancer progenitors for PICDGI LUAD analysis

Cell clustering, annotation, and identification of epithelial cells were performed using Seurat R package. PICDGI subsequently uses these epithelial temporal expression profiles as the progenitor population for dynamic modeling of cancer progression.

We analyzed scRNA-seq data from three LUAD patients, each sampled at three distinct stages of cancer progression: Early (normal lung tissue), Mid (primary lung tumor), and Late (metastatic brain tissue), resulting in nine single-cell datasets in total. Following quality control and filtering procedures, we retained 42,996 cells for the Early stage, 45,150 cells from the Mid stage, and 29,061 cells from the Late stage for downstream analysis. Using unsupervised clustering and marker-based cell type annotation with Seurat R package [59], we identified key immune and non-immune cell types, including dendritic cells (DC), mast cells, T cells, B cells, NK cells, fibroblasts, endothelial cells, ependymal cells, oligodendrocytes, and epithelial cells (Fig 4A, S7 Text, S1–S9 Figs).

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Fig 4. Overview of single cells from the lung tissues of three patients.

(A) t-SNE plots showing profiles of single cells from each tissue origin for three patients. In the first row (patient 1), 42,996, 45,150, and 29,061 cells are shown, respectively. In the second row (patient 2), 3,871, 4,362, and 3,301 cells are shown, respectively. In the third row (patient 3), 3,381, 3,766, and 5,731 cells are shown, respectively. Plots are color-coded by major cell lineages and gene expression counts. (B) Fractions of cells originating from tumor versus non-malignant lung tissues across cell types. Tumor-origin cell fractions vary by cell type and LUAD stage across patients, with epithelial cells consistently exhibiting the highest tumor fractions, increasing with LUAD progression.

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To determine candidate cancer progenitor cell types, we tracked changes in cell type abundance and calculated the cancer cell fraction (CCF) across the three stages. Epithelial cells showed consistent expansion in relative proportion from Early, Mid, and Late stages, satisfying the originating criteria defined in Equations (2)-(4). CCF was assessed using EpCAM (CD326), a widely used epithelial tumor-associated marker marker [60,61]. Epithelial cells exhibited the highest CCF values, which increased with disease progression (Fig 4B), supporting their role as LUAD progenitor cells likely harboring driver mutations.

To ensure that epithelial lineage markers were accurately represented in our dataset, we performed an additional ambient RNA-correction step using SoupX prior during progenitor-cell identification [62]. Ambient RNA contamination is common in droplet-based scRNA-seq of solid tumors and can result in misleading detection of epithelial transcripts in non-epithelial lineages. After correction, EpCAM expression was restricted to epithelial clusters, confirming that its presence in immune populations originated from background contamination rather than true biological signal. We further verified that epithelial cells uniquely exhibited a consistent increase in abundance across cancer progression and retained the highest CCF values. Although CCF was computed for all annotated cell types, only epithelial-derived CCF values were used in subsequent analyses. Full details of this validation is provided in S8 Text.

3.2 PICDGI predicts gene expression levels of cells considering gene-gene interactions

Genes encode proteins that regulate essential functions like cell growth [63], and mutations can disrupt protein function and drive cancerous transformations [64]. Specific gene mutations can alter proteins in ways that promote tumorigenesis, making it crucial to understand not only gene expression levels but also the interactions between genes that influence these levels. Thus, modeling gene expression dynamics from scRNA-seq data is essential for identifying cancer driver genes (CDGs) whose effects are mediated through gene-gene interactions.

To achieve this, we applied the PICDGI framework to model gene expression dynamics in individual epithelial cells, driving LUAD progression across the three patients. To evaluate performance, we calculated Pearson’s correlation coefficient () and the coefficient of determination () between observed and predicted gene expression (TGE and PGE), followed by statistical significance testing. Results showed positive Pearson correlation coefficients () with p-values < 0.05, indicating a strong linear relationship between TGE and PGE (Fig 5A-5C). Correlations for each patient at different LUAD stages are shown in Table 1. Fig 5D displays the distribution of values across genes, further validating prediction consistency. The focus on epithelial cells is critical for identifying cancer drivers, as PICDGI relies on predicted gene expression patterns in these cells, where gene interactions influence disease progression.

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Table 1. Pearson’s correlation coefficient () and coefficient of determination ().

https://doi.org/10.1371/journal.pcbi.1014143.t001

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Fig 5. Predicted vs. observed gene expression levels in epithelial cells.

(A-C) Scatterplots illustrating the performance of the PICDGI framework in predicting epithelial cell gene expression across the Early, Mid, and Late stages of LUAD progression for Patients 1, 2, and 3, respectively. Each plot shows the relationship between true gene expression (TGE) and predicted gene expression (PGE), with Pearson’s correlation coefficient (ρ), coefficient of determination (R²), and corresponding p-value computed using a two-sided t-test. (D) Summary of predictive accuracy across stages. Barplots display the mean Pearson correlation coefficients (ρ) ± SEM (Standard Error of the Mean) for the comparison between TGE and PGE at each of the three time points; Early, Mid, Late for each patient. These summary statistics complement the scatterplots by providing an aggregated view of model performance across genes. From top to bottom, the panels correspond to Patient 1, Patient 2, and Patient 3.

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3.3 PICDGI identifies cancer driver genes based on the influence of gene-gene interactions

To enhance PICDGI’s accuracy in identifying cancer driver genes (CDGs), we derived predicted gene expression from the latent hidden variables (gene mutation states and gene-gene interaction matrix). This approach filters noise and captures the underlying gene expression patterns, even in noisy or low-quality scRNA-seq measurements. Using Bayesian analysis, we quantified uncertainty through the 95% HDI of the posterior distribution, reflecting the conditional effect of each gene while accounting for gene interactions driving mutations. These predicted expression values enable the reliable identification of CDGs and help distinguish observed driver mutations from passengers, which have minimal impact on cancer progression.

We ranked the top 30 genes with the highest coefficients for the three patients (Fig 6A, S7 Text,S10A–S11A Figs), finding that 63.33%, 63.33%, and 60% were previously identified as CDGs (Markers, OGs, or TSGs) (S9 Text). The remaining uncharacterized genes may represent potential CDGs for further validation. In particular, genes TP53INP1, CA12, and LCNL1 were predicted as key drivers for cancer progression in patients 1, 2, and 3, respectively. TP53INP1, a tumor suppressor gene, is downregulated in cancers and collaborates with p53 to regulate cell death and migration [65]. CA12, involved in pH regulation, is overexpressed in cancers and may be a novel prognostic marker [50,66]. LCNL1 affects lung cancer susceptibility, particularly in never-smokers, highlighting its potential role in cancer risk [67].

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Fig 6. Cancer driver genes with the highest driver coefficient.

(A) Barplot showing the driver coefficients of epithelial cell genes derived from patient 1 gene expression data using the PICDGI framework. Data are presented as mean + /- SEM (Standard Error of the Mean). Black cross marks indicate genes previously identified as oncogenes (OGs) or tumor suppressor genes (TSGs). (B) Heatmap showing PICDGI-derived DrCoef values for the top 30 epithelial driver genes (selected based on panel A) recalculated independently within each annotated immune cell type from patient 1 single-cell data. DrCoef values in this panel are computed using cell-type specific models, enabling assessment of the regulatory influence of epithelial-identified driver genes across immune compartment. (C) Boxplots comparing transcription factor (TF) expression and TF activity between normal epithelial and cancer cells for two representative TFs showing discordance between differential activity and differential expression. P-values for differential TF activity and expression were calculated using a t-test and Wilcoxon rank-sum test, respectively. Boxplot elements indicate the median (horizontal line), interquartile range (box), and whiskers extending to 1.5 × interquartile range.

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To examine more closely the biological relevance of the driver genes prioritized by PICDGI, we performed cross-patient pathway enrichment analysis on the union of predicted drivers and their inferred modulatory partners. This analysis revealed that PICDGI-identified genes converge on pathways central to LUAD progression, including cell-cycle regulation, metabolic rewiring, autophagy, and microenvironmental remodeling, with distinct yet coherent patterns observed across all three patients. These findings provide an additional layer of validation by demonstrating that the inferred drivers map to biological programs known to intensify during tumor evolution and metastatic expansion. A detailed presentation of these pathway enrichment results, including cancer-focused and Gene Ontology analyses for each patient, is provided in S10 Text.

3.4 PICDGI reveals that top epithelial cancer drivers exhibit strong immunoregulatory influence

The immune system is crucial for detecting and eliminating abnormal cells, including cancer cells. However, tumor progression is frequently associated with the establishment of an immunosuppressive microenvironment that enables immune evasion. In lung cancer, multiple regulatory genes have been implicated in modulating immune signaling and suppressing anti-tumor responses [68,69]. To explore the potential immunomodulatory roles of PICDGI-identified drivers, we examined the 30 highest-ranked epithelial driver genes in each of the three patients (Fig 6B, S7 Text, S10B–S11B Figs). Although these genes were selected based on their high DrCoef values in epithelial cells, we observed that many of them exhibited equal or even higher DrCoef values in immune cell populations, particularly in NK cells.

Importantly, elevated DrCoef in NK cells does not indicate epithelial identity within immune cells. Rather, it reflects strong dynamic regulatory influence within the NK-cell transcriptional network across disease stages. The consistently high DrCoef values observed in NK cells suggest substantial regulatory rewiring in this compartment during tumor progression. Given the known role of NK cells in anti-tumor immunity, this pattern is consistent with tumor-driven modulation of NK-cell function and may reflect mechanisms of immune evasion active in advanced-stage LUAD (Fig 4A).

To ensure methodological consistency, DrCoef values for immune cells were computed using the identical PICDGI pipeline applied to epithelial cells. After identifying the top 30 epithelial candidate driver genes, we evaluated their dynamic activity across major immune populations, including T cells, B cells, dendritic, mast, and NK cells. Although immune cells are not tumor-initiating populations, they are critical components of the tumor microenvironment and engage in continuous crosstalk with cancer cells. Several of the top-ranked genes are known to participate in immune signaling or stress-response pathways, supporting a dual role in tumor progression and immune modulation.

Among the top-ranked genes in each patient, we further assessed transcription factor (TF) activity for five representative genes in both normal and cancer epithelial cells. These included TP53INP1, CCNL2, DCTD, PDCD4-AS1, and GRK6 (patient 1); ALG1, C9orf16, GPX1, CA12, and LINC01620 (patient 2); and NRBF2, C9orf16, SFR1, CA12, and PITPNC1 (patient 3). Differential TF activity between normal and tumor epithelial cells indicates regulatory reprogramming during tumor progression (Fig 6C, S7 Text, S10C–S11C Figs), potentially affecting transcriptional control, downstream target engagement, and cellular proliferation dynamics.

The variability in top-ranked transcriptional regulators across patients likely reflects both biological heterogeneity and technical variability. Biologically, lung cancer exhibits substantial inter-patient heterogeneity in mutational landscape, tumor subtype, and microenvironmental context [70,71]. Technical factors inherent to scRNA-seq, including sampling bias, dropout effects, and batch variation, may also contribute [72]. However, given the reproducible recovery of coherent regulatory programs within each patient and in external validation datasets, biological heterogeneity is likely the dominant contributor to the observed differences [73].

3.5 Comparison of PICDGI and Monocle 3 in identifying cancer progression genes

We compared the genes prioritized by PICDGI with those identified by Moran’s I test implemented in Monocle 3, a tool shown by Cao & Spielmann et al. [58], to identify variable genes in scRNA-seq data. While Moran’s I assesses spatial autocorrelation of gene expression across temporal trajectories [74], PICDGI incorporates dynamic modeling of nonstationary gene interactions to prioritize putative driver genes. Comparing the two approaches allows benchmarking PICDGI against a well-established method for identifying biologically variable genes in scRNA-seq data.

For this comparison, we integrated scRNA-seq data across the three time points per patient, creating a progression LUAD single-cell landscape. Using PCA for Slingshot and UMAP for Monocle3 [18], we inferred cell-type trajectories and performed temporal analysis for clustering and visualization [75] (Fig 7A).

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Fig 7. Comparison of the PICDG framework with the existing Moran’s I test algorithm for predicting driver genes’ inference in immune cells.

The driver genes identified through Moran’s I test display a lower average expression level compared to the expression level of driver genes presented by the PICDGI computational framework. The genes are ranked from the highest to the lowest immune-suppressive role (1 to 10): (A) Single-cell atlas map the trajectory and time values of cells progression; (B) Mast cell; (C) Natural Killer; (D) T cell; (E) B cell; (F) Dendritic cell.

https://doi.org/10.1371/journal.pcbi.1014143.g007

The analysis revealed that the genes identified by the PICDGI framework exhibited higher average expression levels than those identified by Monocle 3 across the three patients thus positioning them as strong candidates for true cancer drivers [35,36] (Fig 7, S7 Text, S12 - S13 Figs). This difference stems from Monocle 3’s non-spatial trajectory inference, which ignores gene-gene interactions [76]. While Monocle3 excels at capturing dynamic expression patterns, PICDGI emphasizes gene interactions during progression, explaining the variation in results.

Although the overlap between the top-ranked genes from PICDGI and Monocle3 is limited, this divergence is expected due to the distinct methodological assumptions of each approach. Monocle3 primarily identifies genes whose expression changes significantly over pseudotime, independent of their regulatory influence on other genes. In contrast, PICDGI ranks genes based on their conditional impact on the expression of other genes, modeled through a time-dependent interaction framework. This leads to the identification of genes with high regulatory importance, even if their individual expression dynamics are not prominent.

From a biological perspective, this difference underscores the complexity of cancer progression. Monocle3 captures responsive genes whose expression reflects temporal transitions or lineage states, while PICDGI is optimized to uncover putative causal regulators; genes that may drive these transitions through network-level influence. For instance, genes with relatively stable expression but central roles in oncogenic signaling may be highlighted by PICDGI but overlooked by Monocle3. In our study, PICDGI successfully identified TP53INP1, CA12, and LCNL1 as high-confidence cancer driver genes for patients 1, 2, and 3 respectively; each exhibiting the highest cancer driver coefficients within their individual profile. These genes are not merely transiently responsive but act as key regulators in tumor development. This demonstrates that, unlike Monocle3, our approach captures essential yet stable drivers of oncogenesis, offering more robust insights into patient-specific cancer mechanisms and paving the way for personalized therapeutic strategies. Therefore, the minimal overlap reflects complementary strengths of the methods in dissecting tumor progression from different angles.

3.6 External validation of PICDGI in an independent pediatric AML cohort

To assess whether PICDGI generalizes beyond lung adenocarcinoma and is not specific to a single tumor type or dataset, we next evaluated the framework in an independent pediatric acute myeloid leukemia (AML) single-cell RNA-seq cohort from Mumme et al.[77], which profiles bone marrow samples at Diagnosis (Dx), End-of-Induction chemotherapy (EOI), and Relapse. This dataset provides a stringent out-of-sample test because it spans longitudinal disease stages, resolves both malignant blasts and microenvironmental compartments, and includes curated AML blast signatures and relapse-associated biological programs.

Using a unified Seurat-based single-cell analysis pipeline and a comprehensive AML blast-centric annotation strategy, we resolved a continuum of leukemic myeloid states encompassing leukemia stem cell (LSC)-like cells, early myeloid progenitors, myeloblasts, cycling myeloid/monocytic/granulocytic populations, mature monocytic and granulocytic lineages, and inflammatory CXCL8 ⁺ states. These populations were defined based on established AML-associated genes including granule and protease markers (MPO, ELANE, AZU1, CTSG, CTSD, PRTN3, LYZ), inflammatory markers (S100A8/A9), transcriptional and developmental regulators (RUNX1, HOXA9), and stem/progenitor markers (CD34, KIT) [78–80]. In parallel, non-malignant immune populations (T, NK, immature B cells) and stromal compartments were cleanly separated using established lineage markers consistent with prior single-cell studies of hematopoitic differenciation and leukemia [81,82]. This standardized annotation enabled robust estimation of malignant cell fractions across cell types and stages.

Across Dx, EOI, and Relapse, myeloid leukemic populations consistently exhibited the highest malignant fractions, with early involvement at diagnosis, persistence following induction chemotherapy, and marked enrichment at relapse (S11 Text, S1 Fig A-C). In contrast, lymphoid and stromal populations remained largely non-malignant or showed only transient malignant signal, consistent with their roles as reactive or bystander compartments rather than leukemia-initiating lineages [80,83]. These longitudinal dynamics satisfy PICDGI’s criteria for inferring a leukemia-originating lineage, namely: early presence, therapy resistance, and relapse enrichment, thereby identifying LSC-like, progenitor, and cycling myeloid populations as the dominant cancer-originating compartment in pediatric AML.

Leveraging these cell-state-resolved malignancy trajectories, PICDGI prioritizes candidate cancer driver genes by integrating longitudinal changes in malignant cell fractions with disease-transition aware driver coefficients (DrCoef). Across both Dx-EOI and Dx-Relapse transitions, the framework robustly recovered known pediatric AML-relevant drivers and facilitators (S11 Text, S2 Fig A-B), most notably PRDM1 (BLIMP1), a tumor suppressor implicated in hematologic malignancies and leukemic differentiation control. In addition, PICDGI consistently prioritized genes involved in cellular stress responses and metabolic adaptation including STIP1, GLO1, ISG15, and CD164 which have been linked to leukemic cell survival, oxidative stress tolerance, immune signaling, and bone-marrow niche interactions, particularly in therapy-resistant AML contexts [84–86].

Beyond these established AML-associated genes, PICDGI nominated coherent sets of candidate drivers involved in RNA processing and splicing, protein homeostasis and proteasomal regulation, mitochondrial and metabolic pathways, and immune modulation. Notably, many of these candidates were consistently upregulated across malignant myeloid populations and disease stages, suggesting roles in leukemic maintenance, adaptation to cytotoxic therapy, or relapse-specific fitness rather than transient or lineage-restricted expression. Together, these results indicate that PICDGI captures both canonical AML driver biology and biologically plausible novel candidates, supporting its utility for systematic driver gene discovery in pediatric AML.

Overall, this external validation demonstrates that PICDGI generalizes across independent pediatric AML cohorts, robustly linking single-cell malignant cell dynamics to biologically meaningful driver gene prioritization. Full details of this external validation, including cell-type annotation, malignancy scoring, and cross-dataset driver inference, are provided in S11 Text.