Data-driven universal insights into tumorigenesis via hallmark networks

Abstract

Cancers are complex diseases characterized by dynamic perturbations of regulatory networks across multiple hierarchical levels, which cannot be fully captured by alterations in a small number of genes. To this end, based on the concept of Hallmarks of Cancer, a whole genomic data-driven approach is proposed to capture the dynamic variation from normal to cancerous cells. This framework focuses on the characteristic functional modules of cancer via hallmarks of cancer by constructing a coarse-grained gene regulatory network of hallmarks. Through this framework, with stochastic differential equations, macroscopic dynamic changes in tumorigenesis are simulated and further explored. The analysis results reveal that network topology undergoes significant reconfiguration before shifts in hallmark levels, serving as an early indicator of malignancy. A pan-cancer examination across 15 cancer types uncovers universal patterns, for example, the “Tissue Invasion and Metastasis” hallmark exhibits the most significant difference between normal and cancer states, while “Reprogramming Energy Metabolism” shows the least pronounced differences. These findings reinforce the systemic nature of cancer evolution, highlighting the potential of network-based systems biology methods for understanding critical transitions in tumorigenesis.

Introduction

Cancers are complex and dynamic diseases characterized by uncontrollable cell proliferation, genomic instability, and disruption of normal regulatory mechanisms, among others^1–3. They evolve from normal tissues through dysregulation of complex interactions among heterogeneous cellular populations, dysregulated molecular networks, and adaptive evolutionary processes^3–5. Consequently, cancer can be viewed as a systemic pathology. Conventional reductionist approaches, which focus on individual genetic alterations, fail to capture key emergent properties arising from the collective activity of interconnected functional modules⁶.

Complex systems theory offers a framework to address these challenges. Biological systems are generally governed by complex regulatory networks whose evolution is driven by nonlinear interactions^7–9. According to foundational theories of complex systems^10–12, these networks exhibit emergent properties, including robustness, adaptability, low dimensionality, and self-organization. In most cases, they are robust to perturbations of single genes, yet disordered collective perturbations can trigger irreversible transitions. These behaviors cannot be explained by analyzing individual alterations in isolation. Moreover, the low-dimensional hypothesis posits that a complex system’s high-dimensional dynamics can often be captured by a reduced low-dimension system, which is called the coarse-grained system. By aggregating microscopic components (e.g., individual genes) into macroscopic, functionally related units (e.g., gene sets), one can preserve essential network organization while revealing collective modes of behavior¹³. This macroscopic perspective is valuable because systems that differ substantially at the microscopic individual gene level frequently display universal patterns at the level of macroscopic functional modules^14–16. Therefore, it is essential to explore the similarities among different cancers from a complex-systems perspective.

From the perspective of cancer as a complex system, it is reasonable to aggregate individual genes into functional modules and thereby construct an interaction network of these aggregated gene sets. This so-called “coarse-graining” methodology has been shown to be effective in capturing the essential features of a complex system at the macroscopic level in statistical physics and complex network^17–19. In the context of cancer evolution driven by complex gene regulation network, the concept “Hallmarks of Cancer”^1,2,20 provides a reasonable and operationally tractable coarse-graining methodology that delineates the recurring functional capabilities of tumors during malignant development at the macroscopic level. Proposed by Hanahan and Weinberg in 2000 and expanded in 2011 and 2022, this framework organizes traits such as “self-sufficiency in growth signals” “insensitivity to anti-growth signals” “reprogramming energy metabolism” and “evading immune destruction” together with enabling conditions including “tumor-promoting inflammation” and “genome instability and mutation”^1,2,20. Because hallmarks are functional abstractions, they can be operationalized as gene sets which can in turn be viewed as coarse-grained nodes in an interaction network^3,21,22. Building on this idea, one can construct the “hallmark network” in which each hallmark serves as a node and the edges encode their regulatory interdependencies at the macroscopic level. Recent spatial transcriptomics supports the concept that tissues are compartmentalized into interdependent ecological niches that drive tumor progression^23–25. These findings at the cellular scale also underscore the reasonableness of a macroscopic hallmark architecture at the intracellular scale that such a network can capture cancer phenotypic complexity arising from network-level interactions during carcinogenesis^26,27.

In this study, we first construct the hallmark network. The regulatory interactions between hallmarks (gene sets) are computed by mapping hallmarks to gene sets via Gene Ontology (GO) terms and the publicly available GRAND database²⁸ of gene regulatory networks in normal and malignant cells. Next, a macroscopic stochastic dynamical model is developed to simulate the evolution of hallmark dynamics during the transition from normal to malignant phenotypes. By employing this model across 15 cancer types and computational methods, such as the Dynamic Network Biomarker (DNB) theory²⁹, the pan-cancer dynamic patterns of critical transitions are identified. Our findings show that the hallmark level of the hallmark “Tissue Invasion and Metastasis” exhibits the greatest difference between normal and tumor tissues, while “Reprogramming Energy Metabolism” demonstrates a conserved regulatory pattern during tumorigenesis. The phenomena are also observed across 15 cancer types, indicating a universal pattern of tumorigenesis from the hallmark perspective. In addition, the network reconfiguration, characterized by dynamic network biomarkers, consistently precedes significant shifts in hallmark level across all 15 cancer types. These insights enhance our understanding of cancer as a complex adaptive system and provide a framework for anticipating critical transitions in tumor progression.

Results

The hallmark network and the mathematical model for its evolution dynamics

Cancer evolution arises from the dysregulation of interconnected molecular networks, necessitating a systemic perspective to unravel its dynamics. The core framework of this study is the coarse-graining of the complex gene regulatory network into a dynamic network composed of the ten canonical hallmarks of cancer (a full list is provided in Fig. 1). These hallmarks, such as “Evading Apoptosis” and “Tissue Invasion and Metastasis”, represent the core functional capabilities that tumors acquire during their development. Inspired by the low-rank hypothesis of complex systems²¹, simplifying the high-dimensional cellular state space into a low-dimensional network of these key functional modules is a reasonable approach. Based on this principle, we established a research framework for the dynamic evolution of the hallmark network, designed to capture the transition from normal to malignant states and to understand the common principles of cancer development from a macroscopic perspective (Fig. 2).

Fig. 1. The ten hallmarks of cancer.

(H1) Evading Apoptosis, (H2) Evading Immune Destruction, (H3) Genome Instability and Mutation, (H4) Insensitivity to Anti-Growth Signals, (H5) Limitless Replicative Potential, (H6) Reprogramming Energy Metabolism, (H7) Self-Sufficiency in Growth Signals, (H8) Sustained Angiogenesis, (H9) Tissue Invasion and Metastasis, and (H10) Tumor-Promoting Inflammation.

Fig. 2. The workflow diagram of this study.

a The construction of hallmark networks. Upon integrating gene expression data and their regulatory interactions, the interaction network of hallmarks is constructed by coarse-graining of gene regulatory networks. Dynamic equations are established based on the hallmark network to simulate the evolution of hallmark network from normal to cancerous states. Then, pan-cancer analysis across 15 cancer types is conducted to explore commonalities and differences in the evolutionary trajectories during tumorigenesis. b Dynamical equations for simulating state transitions between normal and cancerous phenotypes. c Tipping point detection using DNB theory to identify the critical transition points of network configuration. d Pan-cancer analysis of evolutionary trajectories across 15 cancer types. e Different dynamic patterns of hallmarks' evolutionary trajectories from normal to cancerous states. f Visualization of the temporal evolution of the hallmark network.

To simulate the hallmark dynamics, we established a set of stochastic differential equations that incorporate Ornstein-Uhlenbeck noise. This approach is based on a general framework for modeling gene regulatory network dynamics³⁰. The model utilizes a time-dependent regulatory network to simulate the system’s evolution from an initial stationary state defined by normal tissue data to a final stationary state defined by cancer data. This dynamic transition enables the quantification of three distinct phases in carcinogenesis. These include an initial stationary phase mimicking a healthy homeostatic state, a critical transition marked by network reconfiguration, and the final cancerous state (Fig. 2e). The detailed mathematical formulation of our model is described in the Methods Section.

Differential dynamics of hallmarks during tumorigenesis

To elucidate the tumorigenesis dynamics at the scale of hallmark network, 10,000 trajectories of the hallmark network’s evolution are simulated through the stochastic model (6) and (7) based on the data of gastric adenocarcinoma as a representative example. To simulate the processes from normal to cancer states, in the simulation, three time intervals are divided to mimic the normal state (from t = 0 to t = 30), the intermediate transition phase (from t = 30 to t = 70) and the cancer state (from t = 70 to t = 100). The system reaches a new stationary state after t = 100 (Fig. 3, also see Methods for simulation details). All the hallmark levels of cancer states are higher than those in the normal states (Fig. 3a) while the dynamics of other gene sets may decrease during the processes of tumorigenesis (Supplementary Fig. 2). The probability distributions of the hallmark levels are also extracted for the comparison of the hallmark levels between normal and cancer states (Fig. 3b). Through the Mann–Whitney U tests, it is obvious that the levels of all 10 hallmarks are significantly higher in the cancerous state than those in the normal state (Fig. 3c; all p < 0.001).

Fig. 3. Hallmark dynamics of gastric adenocarcinoma tumorigenesis.

a Stochastic trajectories (10,000 simulations) of the 10 hallmark levels during the transition from normal to cancerous states, each simulated over 100 time points. During the simulation, time points t=0-30 represent the normal network phase, t = 30–70 is the transition phase, and t = 70–100 represents the cancer network phase. b Probability distributions of hallmark levels at the healthy stationary state (at t = 10) and the cancerous stationary state (at t = 100). c Boxplots comparing the hallmark levels between the normal (blue) and cancerous (red) states. Asterisks indicate the level of statistical significance as determined by a Mann–Whitney U test (***p < 0.001). d The JS divergence for the ten hallmarks between the normal and cancerous state distributions. The JS divergence ranges from 0 to 1, where a value of 0 indicates that the distributions for the normal and cancer states are identical, while a value of 1 represents maximal divergence.

To further quantify the differences in hallmark levels between two states, the Jensen-Shannon (JS) divergence is employed (Fig. 3d). The JS divergence is a metric that quantifies the dissimilarity between two probability distributions, with a value ranging from 0 to 1, where values close to 0 indicate insignificant differences in the distributions of hallmark levels between the normal and cancer states, while values close to 1 represent larger divergence. The detailed mathematical formulation is described in the Methods Section.

Accordingly, the analysis based on JS divergence reveals significant heterogeneity in the dynamics of different hallmarks during tumorigenesis. The results show that “Tissue Invasion and Metastasis” exhibits the most significant difference in hallmark level between the normal and cancerous states, with a JS divergence value of 0.692 (Fig. 3d). In contrast, “Reprogramming Energy Metabolism” shows the minimal difference, with a JS divergence of only 0.385 (Fig. 3d). This heterogeneity in hallmark dynamics aligns with their distinct contributions to tumorigenesis, reflecting both shared and cancer-specific mechanisms^1,2. Specifically, “Tissue Invasion and Metastasis” demonstrates the greatest separation between the normal and cancer groups. This hallmark is linked to key processes that include wound healing, negative regulation of cell adhesion, epithelial-to-mesenchymal transition (EMT), and cell migration^31–33. Conversely, hallmarks such as “Reprogramming Energy Metabolism” display smaller differences in their hallmark levels. “Reprogramming Energy Metabolism” is a central hallmark of cancer. However, the metabolic adaptations, such as glycolysis, i.e., the Warburg effect, are also activated in normal cells under hypoxic or stressed conditions^34–36, and therefore it is reasonable that the differences in the metabolic hallmark are less significant.

Additional hallmarks, including “Evading Apoptosis” and “Self-Sufficiency in Growth Signals”, also show notable changes. For example, evading cell death often involves suppressing pro-apoptotic signals and overactivating anti-apoptotic genes³⁷. This allows cancer cells to survive under conditions that would normally trigger apoptosis. Similarly, the heightened divergence in “Self-Sufficiency in Growth Signals” reflects how persistent activation of growth factor pathways can circumvent homeostatic constraints on cell proliferation³⁸. In contrast, “Limitless Replicative Potential” and “Genome Instability and Mutation” show smaller differences. This may be due to their partial overlap with normal proliferative mechanisms or their emergence at later stages of tumorigenesis^39,40.

These results suggest that tumor progression relies on hallmarks that disrupt early cell survival, such as “Evading Apoptosis” and “Self-Sufficiency in Growth Signals”. It also depends on traits that enable advanced dissemination, like “Tissue Invasion and Metastasis”. Meanwhile, hallmarks with smaller distributional shifts, such as “Reprogramming Energy Metabolism”, may still play an essential role but follow regulatory pathways shared with normal proliferative processes.

Notably, our computational model is built upon real-world data from the GRAND datasets²⁸. The simulated results are therefore a consequence of data-driven observations. From a macroscopic view, our analysis of gastric adenocarcinoma reveals that “Tissue Invasion and Metastasis” is central to malignant progression. In contrast, certain metabolic and replicative processes partially overlap with normal cell physiology. Such nuanced insights into hallmark-specific dynamics can foster a better understanding of how cancers emerge and evolve.

Early network reconfiguration precedes the significant changes in hallmark levels

Our stochastic dynamical model (SDEs) generated complete time-series trajectories of the hallmark network’s evolution. A key scientific question is how to objectively identify the tipping point heralding the malignant transition from this dynamic data. While traditional biomarkers (i.e., the levels of individual molecules) may not change significantly near a tipping point, Dynamic Network Biomarker (DNB) theory posits that the structural reconfiguration of the network is a more sensitive early-warning signal^29,41. Therefore, the DNB theory is employed to detect early-warning signals in our simulation data. This theory states that as a biological system approaches a critical transition, a subset of key molecules (the DNB module) begins to exhibit significantly enhanced fluctuations and increased correlations^29,41–44. Among the various DNB indices available, we selected the direct interaction network-based divergence (DIND) score, as it effectively captures the topological reorganization of the network, thereby revealing the initiation of network rewiring during the pre-disease phase⁴¹.

To construct the sample sets for DIND analysis, we first generated 50 independent “virtual patient” samples from the 10,000 raw simulation trajectories via a process of resampling and aggregation. Specifically, each virtual patient sample was composed of 1,000 randomly selected trajectories, representing a single individual with cellular heterogeneity. Based on the time-series data of these 50 virtual patients, we then calculated the global DIND score and the local DIND scores for each node, with the detailed computational procedure described in the Methods Section.

To visualize the dynamic evolution of the hallmark network, we selected 10 representative time points from the 10,000 simulation trajectories (Fig. 4a). In these plots, the size of each node represents the variance of its corresponding hallmark level (a larger variance corresponds to a larger node), and the color represents its mean value. The thickness of the edges between nodes represents the strength of their interaction (a greater regulatory strength corresponds to a thicker edge). During the evolution, the network structure underwent a significant reconfiguration near the tipping point. For instance, at time point t = 41, we observed that the variance (node size) of several nodes (e.g., H4, H7, and H9) significantly increased, while some key regulatory relationships (e.g., the edge between H4 and H7) were also significantly enhanced. This increase in network instability marks the system’s transition from the normal stationary state to a critical state. Subsequently, after t = 71, the network structure tended towards a new, stable pattern, indicating that the system had entered the cancerous stationary state.

Fig. 4. Dynamic evolution of the hallmark network and DIND scores.

a Snapshots of the hallmark network at 10 representative time points during the simulated transition from normal to cancerous states. In these plots, the color of each node represents its mean hallmark level, the size of the node is proportional to its variance, and the thickness of the edges represents the interaction strength. b Dynamic evolution of the DIND score over time. The bold black line represents the global DIND score, which is calculated as the average of all local scores. The ten colored lines represent the local DIND scores for each of the ten individual hallmarks. Red dots mark the tipping points where the DIND score reaches its peak, with the primary peak occurring at t₁ = 37.

This visual result is highly consistent with the DIND score (Fig. 4b). The DIND score exhibited a sharp and significant peak at a time point just before t = 41, heralding the system’s imminent entry into the critical state. Furthermore, the DIND score rose sharply again before t = 71, indicating that the system was approaching the cancerous stationary state.

To further validate the early-warning role of network reconfiguration, we quantified the time difference (Δt = t₂ − t₁) between the onset of network reconfiguration, t₁, and the significant shift in hallmark levels, t₂. Here, t₁ is defined as the first peak in the DIND score, representing the start of network reconfiguration, while t₂ is defined as the moment a hallmark’s level first exceeds a critical threshold set at 1.2 times its normal stationary state level, representing an overt phenotypic shift (Fig. 5a). The analysis clearly shows that network reconfiguration universally precedes the overt shift in hallmark levels. For the “Tissue Invasion and Metastasis” hallmark, which showed the most significant divergence, network reconfiguration occurred approximately three time units earlier than the change in its hallmark level, on average. We performed a one-sample Wilcoxon signed-rank test on the Δt distribution for each hallmark (derived from the 50 “virtual patient” samples) to test if the median was significantly greater than zero. The results showed that the lead time for all 10 hallmarks was highly statistically significant (Fig. 5b, all p < 0.001). Since the structure of the hallmark network reflects the complex inter-relationships among functional modules, this phenomenon indicates that the structure of network is more sensitive to malignant transition than changes in the quantitative level of each hallmark.

Fig. 5. Network reconfiguration precedes significant shifts in hallmark levels.

a Comparison of the average trajectory, individual trajectory distribution, and DNB score for a representative hallmark. The solid blue line represents the hallmark level trajectory for a single, independent “virtual patient” sample. The surrounding pink shaded area illustrates the distribution of the 1000 raw trajectories that were aggregated to compose this “virtual patient'', reflecting the cellular heterogeneity within the sample. The red curve is the DNB score, which quantifies the degree of network reconfiguration. The time point t₁ is defined as the first peak in the DNB score, marking the onset of network reconfiguration. The time point t₂ is defined as the moment the average hallmark level for this virtual patient first exceeds a critical threshold, set at 1.2 times the normal stationary state level. b Boxplots showing the distribution of the time difference (Δt = t₂ − t₁) for each hallmark across 50 independent “virtual patient” samples. A non-parametric one-sample Wilcoxon signed-rank test was performed for each hallmark’s Δt distribution to test if the median was significantly greater than zero. The asterisks indicate the level of statistical significance (***: p < 0.001), confirming that for all hallmarks, network reconfiguration significantly precedes the overt shift in their levels.

The early remodeling of network interactions supports the hypothesis that changes in regulatory connectivity serve as a precursor to overt phenotypic shifts in tumorigenesis. Such early network reconfiguration potentially provides valuable novel therapeutic strategies, such as targeting regulatory hubs before malignant phenotypes emerge, for early intervention in the processes of tumorigenesis.

Pan-cancer hallmark network dynamics reveal sequential progression patterns

After detailing the dynamic evolution of the hallmark network using gastric adenocarcinoma as an example, we extended this analytical framework to our full cohort of 15 cancer types. As shown in the Supplementary Information (Supplementary Figs. 3–9), each cancer type exhibited core dynamic features similar to those observed in STAD.

To further explore the universal principles underlying these dynamics, we then performed a pan-cancer analysis. This analysis comprised a cohort of 15 cancer types from the GRAND database, including Stomach Adenocarcinoma (STAD), Kidney Renal Papillary Cell Carcinoma (KIRP), Kidney Renal Clear Cell Carcinoma (KIRC), Lung Adenocarcinoma (LUAD), Lung Squamous Cell Carcinoma (LUSC), Pheochromocytoma and Paraganglioma (PCPG), Cutaneous Melanoma (SKCM), Thyroid Cancer (THCA), Uveal Melanoma (UVM), Acute Myeloid Leukemia (LAML), Adrenocortical Carcinoma (ACC), Low-Grade Glioma (LGG), Esophageal Cancer (ESCA), Head and Neck Cancer (HNSC), and Kidney Chromophobe (KICH).

For each cancer type, the divergence in hallmark levels between normal and cancerous states was quantified using JS divergence (Fig. 6a). The results revealed a highly consistent pattern across all 15 cancers. “Tissue Invasion and Metastasis” consistently exhibited the largest difference, followed by “Evading Apoptosis” and “Self-Sufficiency in Growth Signals”. In contrast, “Reprogramming Energy Metabolism”, “Limitless Replicative Potential”, and “Genome Instability and Mutation” generally displayed smaller differences. Notably, the “Tissue Invasion and Metastasis” (H9) and “Reprogramming Energy Metabolism” (H6) hallmarks represent the most and least pronounced differences, respectively, across all cancer types examined in this study.

Fig. 6. Analysis of commonalities and temporal patterns across 15 cancer types.

a Each row represents a cancer type, and each column represents a rank from 1 to 10. For each cancer type, the ten hallmarks are ranked based on the JS divergence of their hallmark level distributions between the normal and cancerous states. A lower rank (e.g., column 1) indicates a larger divergence. b Each row represents a cancer type, and each column represents a rank from 1 to 10. For each cancer type, the ten hallmarks are ranked based on their early-warning lead time (Δt = t₂ − t₁). A lower rank indicates a larger lead time (i.e., a larger Δt value). c The bars show the average rank of each hallmark across 15 cancer types, where a lower rank indicates a larger JS divergence between normal and cancerous states. A Friedman test confirmed that this ranking pattern is highly statistically significant (p < 2.55 × 10⁻²³). d The bars show the average rank of the lead time (Δt = t₂ − t₁) for each hallmark across 15 cancer types, where a lower rank indicates an earlier warning signal. A Friedman test confirmed that this ranking pattern is also highly statistically significant (p < 1.08 × 10⁻¹⁹). e Hierarchical clustering of hallmark levels in normal and cancerous states.

This observation suggests that despite the divergent genetic differences among various cancers^45–49, common dynamic patterns are present. This underscores the significant and unified role of considering hallmarks as integrated gene sets in tumorigenesis and tumor evolution. Consequently, future research should move beyond analyzing differential expression at the level of individual genes and instead explore the collective impact of synergistically functioning gene groups on tumor evolution. Investigating strategies to target these functional groups may hold substantial potential for advancing future cancer therapies.

The conserved ordering of hallmark activation across cancer types suggests evolutionary constraints on tumor progression pathways, where hallmarks provide a broad perspective for identifying common patterns across cancer types. The substantial alteration in the hallmark level of “Tissue Invasion and Metastasis” indicates its central role in cancer cell invasion and metastasis.

In addition, we investigated the time difference between the onset of network reconfiguration, as assessed by the DIND score, and the point when hallmark levels exceeded the normal threshold (Fig. 6b). In most cancers, we observed that network reorganization consistently preceded overt changes in hallmark levels. This temporal precedence was evident for key hallmarks, including “Self-Sufficiency in Growth Signals”, “Reprogramming Energy Metabolism”, and “Insensitivity to Antigrowth Signals”. Such a lead time indicates that alterations in inter-hallmark regulatory interactions occur before quantitative changes in individual hallmark levels. It therefore serves as a more sensitive early indicator of malignant transition.

Figure 6a and b visually present the ranking patterns of the hallmarks based on two different metrics across the 15 cancer types. To statistically assess whether these observed patterns are consistent across the cancer cohort, we performed a Friedman test on each of the two rank matrices. The test results for both ranking patterns were highly statistically significant. To further visualize the overall ranking trend for each hallmark, we calculated and plotted their average ranks, as shown in Fig. 6c and d. In Fig. 6c, the bar height represents the average rank of JS divergence for each hallmark (Friedman test, p < 2.55 × 10⁻²³), clearly showing that “Tissue Invasion and Metastasis” is the top-ranked hallmark on average. Similarly, in Fig. 6d, the bar height represents the average rank of the early-warning lead time (Friedman test, p < 1.08 × 10⁻¹⁹), again confirming the early-warning role of network reconfiguration.

To further quantify minor distinctions in hallmark dynamics among cancer types, a hierarchical clustering analysis is applied (Fig. 6e). One major cluster includes STAD, KIRP, KIRC, LUAD, and THCA. These cancers commonly exhibit “insensitivity to antigrowth signals” and “self-sufficiency in growth”, often driven by “TP53” and “RB1” inactivation and TGF-β suppression. They sustain proliferation through autocrine/paracrine growth factors (e.g., EGF, FGF) and receptor alterations (EGFR, HER2), which activate the PI3K/AKT/mTOR and MAPK/ERK pathways. In contrast, some cancer-specific patterns were also evident. LUAD frequently harbors “EGFR/KRAS” mutations affecting these same pathways. LUSC, however, is often driven by smoking-related “CDKN2A” mutations that disrupt cell cycle regulation and apoptosis⁵⁰. Moreover, “CEP55” co-expresses with cell cycle and DNA replication genes in LUAD but not in LUSC⁵¹. These differences underscore the influence of tissue origin, cell type, and microenvironmental adaptation on hallmark network dynamics.

Discussion

Cancer evolution is a multiscale process encompassing both molecular alterations and emergent system-level properties. This study developed a data-driven, macroscopic stochastic network framework to elucidate cancer progression at the systems level. The most important finding is that the reorganization of the inter-hallmark regulatory network precedes the quantitative increases in individual hallmark levels. In other words, changes in the network structure are detected before the hallmark nodes exhibit overt abnormal levels, suggesting that the alteration of regulatory connectivity is an early indicator of the malignant transition.

The pan-cancer analysis conducted across 15 cancer types from the GRAND database reveals a consistent pattern among the ten hallmarks. “Tissue Invasion and Metastasis” consistently shows the largest divergence between normal and cancerous states. In contrast, hallmarks such as “Reprogramming Energy Metabolism,” “Limitless Replicative Potential,” and “Genome Instability and Mutation” display smaller differences. These distinct behaviors have strong biological underpinnings. The significant divergence in “Tissue Invasion and Metastasis” reflects its central role in processes unique to malignancy, such as epithelial-to-mesenchymal transition (EMT), sustained ECM degradation, and alterations in cell adhesion that enable cancer cells to breach tissue barriers^{31–33,52,53}. In normal tissues, cell adhesion and extracellular matrix integrity uphold tissue structure; however, cancer cells must overcome these constraints by downregulating epithelial adhesion molecules (e.g., E-cadherin) while upregulating mesenchymal markers (e.g., N-cadherin, vimentin)^31,32. These unique adaptations account for the significant divergence observed. Similarly, the pronounced differences in “Evading Apoptosis” and “Self-Sufficiency in Growth Signals” are consistent with the suppression of pro-apoptotic pathways (e.g., via p53) and the aberrant activation of growth factor signaling (e.g., EGFR) in cancer^37,38.

Conversely, the smaller divergence in “Reprogramming Energy Metabolism” can be attributed to its overlap with normal physiological processes. For instance, the Warburg effect is also observed in embryonic and immune cells^36,54, and normal cells under hypoxia can activate similar metabolic adaptations through HIFs^54–56. This shared regulatory mechanism of metabolic plasticity explains its more conserved pattern^35,54. The smaller differences in “Limitless Replicative Potential” and “Genome Instability and Mutation” may indicate that these processes are shared with other proliferating cells or are late-stage events^39,40.

To provide a global perspective on the evolutionary dynamics of tumorigenesis, we constructed a potential landscape of the system based on landscape and flux theory^57,58. As shown in Fig. 7a, the landscape clearly identifies two distinct low-potential basins. These basins correspond to the stable attractors of the normal and cancerous states, respectively, which validates that our model successfully simulates these two different biological stationary states. We also observed that the potential basin corresponding to the normal state is deeper than that of the cancer state, indicating that the normal state is a more stable and robust attractor. The valley connecting these two basins reveals the most probable transition path for the system’s evolution (Fig. 7b). To investigate how individual hallmarks evolve along this trajectory, we decomposed the states along the path. Figure 7c illustrates the changes in the hallmark levels of each of the ten individual hallmarks as the system moves from the normal to the cancerous state along this most probable path. Consistent with our previous observations, the hallmarks “Tissue Invasion and Metastasis”, “Evading Apoptosis”, and “Self-Sufficiency in Growth Signals” exhibit the most pronounced increases in their hallmark levels along this transition path, confirming their central role in driving the malignant transformation.

Fig. 7. The potential energy landscape reveals the transition path of tumorigenesis.

a A three-dimensional view of the potential landscape, showing two basins of attraction corresponding to the normal and cancerous states. b A contour plot of the landscape, with the most probable transition path from the normal (P₁) to the cancer (P₅) state indicated by the white line. Five representative state points are uniformly selected and labeled along this path (P1 to P5), where P1 is near the normal stationary state and P5 is near the cancer stationary state. c In the state space defined by the first two principal components (PC1 and PC2), we selected the 10% of samples with the closest Euclidean distance to each representative state point (P1–P5) on the shortest path to form its “neighborhood set.” For each neighborhood set, we then calculated the distribution of the respective hallmark levels. In the plot, the x-axis from P1 to P5 represents the system’s progression from a quasi-normal to a quasi-cancerous state, and the y-axis represents the hallmark level. The data points show the statistical distribution for each neighborhood set at each stage: the red marker represents the median (second quartile) of the hallmark levels in the corresponding set, while the upper and lower limits of the blue error bars correspond to the first and third quartiles, respectively, visually representing the interquartile range (the central 50% of the data) at that stage.

These findings collectively demonstrate that network-level changes precede phenotypic shifts, suggesting a hierarchical control mechanism in tumor evolution. The results emphasize that alterations in the interactions among hallmarks occur at an early stage of tumorigenesis, potentially offering novel opportunities for early diagnosis and intervention. The pan-cancer analysis confirms that hallmarks such as “Tissue Invasion and Metastasis”, “Evading Apoptosis”, and “Self-Sufficiency in Growth Signals” drive malignant progression. The underlying network-level changes may therefore serve as universal precursors to overt phenotypic shifts in diverse cancer types.

Methods

Data sources

The Gene Regulatory Networks (GRNs) used in this study were sourced from the public database GRAND²⁸. GRAND is a database of computationally-inferred gene regulatory network models, specifically designed for comparative analysis across different biological states. This comprehensive resource contains over 12,000 genome-scale GRNs, covering 36 normal human tissues and 28 cancer types. These networks are inferred by a suite of computational tools (the Network Zoo suite, e.g., PANDA, PUMA, etc)^59,60 that process gene expression profiles from large public consortia, including TCGA, GEO, and GTEx.

To ensure the comparability of data from these different sources, the database construction involved a standardized preprocessing of its source data. The expression profiles from GTEx (normal tissues) and TCGA/GEO (cancer tissues) were normalized using a group-wise strategy based on qsmooth⁶¹. This procedure effectively corrects for technical biases between the platforms, ensuring the validity of comparative analyses between different biological states.

Selection of paired normal and cancer datasets

The GRAND database offers a diverse collection of gene regulatory networks. These networks are constructed with various computational tools to model different regulatory mechanisms. For instance, PANDA models interactions between TFs and their target genes, while PUMA models regulation by miRNAs and LIONESS builds single-sample GRNs. To ensure methodological consistency and comparability for this study, our analysis focused on a specific subset of these networks.

The selection was based on three criteria. First, to maintain a uniform inference methodology, the analysis was restricted to Aggregate TF (Transcription Factor) Networks constructed using the PANDA algorithm. Second, to enable direct comparison between normal and cancerous states, we selected only cancer types (from TCGA) that had a corresponding normal tissue network (from GTEx). Finally, a completeness check was performed to ensure the availability of normal tissue gene expression profiles, which are required for model initialization.

This systematic filtering process resulted in a final cohort of 15 cancer types, comprising 14 solid tumors and one hematological tumor (see Supplementary Table S1 for a full list). The samples for these cancer networks are predominantly from primary, untreated tumors. Each paired dataset used for this study is composed of three components, i.e., the cancer aggregate TF regulatory network from TCGA, the normal tissue aggregate TF regulatory network from GTEx, and the normal tissue gene expression profiles for model initialization.

Hallmark gene set construction

The gene sets for the 10 hallmarks of cancer used in this study were curated through a transparent and reproducible workflow. The process begins by strictly adopting the mapping list of hallmarks of cancer to GO terms as published by Plaisier et al.⁶². We then systematically checked the status of each GO ID against the current GO database (as of July 2025). Two GO IDs that were officially marked as obsolete were removed, and the entire process was documented in Supplementary Table S2. Subsequently, we used the official AmiGo tool⁶³ to retrieve the corresponding gene sets for this GO ID list and intersected them with the genes present in our selected GRAND network datasets to form the final hallmark gene sets.

These gene sets were then used to create sub-networks for analysis. Specifically, from the paired normal and cancer regulatory matrices, we retained only the rows and columns corresponding to genes belonging to at least one hallmark gene set, thereby constructing a sub-network that contains only hallmark-related genes.

Dynamical model of hallmark network evolution

To study the systems-level dynamics of tumorigenesis, we developed a model based on stochastic differential equations. We consider a system with M = 10 hallmark nodes, denoted as H_i for i = 1, 2, …, M. The state of the system at any time t is described by a vector x(t) = (x₁(t), x₂(t), …, x_M(t)), where x_i represents the overall hallmark level of node H_i. The model is based on two static, data-driven baseline matrices, V_n and V_c, which represent the regulatory networks of the normal and cancer states, respectively. These matrices are constructed from the hallmark-only sub-networks described in the previous section. Specifically, the element V_ij in either matrix quantifies the influence of hallmark j on hallmark i. It is calculated by summing all regulatory edge weights between their respective gene sets (G_i and G_j) within these sub-networks. The calculation is formulated as

$$V_{ij}=\sum _{g_a\in G_i}\sum _{g_b\in G_j}{w}_{g_b\to g_a},$$ 1

where $w_{g_b\to g_a}$ is the regulatory weight of a gene g_b on a gene g_a. This calculation is performed independently on the normal and cancer sub-networks to yield the constant matrices V_n = [V_ij,n] and V_c = [V_ij,c].

To simulate the transition from the normal to the cancer state, we defined a time-dependent interaction matrix V(t) that interpolates between V_n and V_c. The transition is a complex process with inherent uncertainty in its trajectory. To model this and ensure the robustness of our findings, we employed an ensemble modeling approach where the time-dependent matrix V(t) was defined as

$$V\left(t\right)=V_n+(V_c-V_n)\times f\left(t\right).$$ 2

For each independent simulation run, the transition function f(t) was chosen at random with equal probability from a set of four functions representing different plausible dynamics including linear, sigmoidal and exponential forms. Specifically, f(t) was randomly selected from the following candidates $\frac{t}{T}$, $\frac{1}{2}\left(1+\tanh \left(5\left(\frac{t}{T}-\frac{1}{2}\right)\right)\right)$, $\frac{e^{at/T}-1}{e^a-1}$ and 1 − e^−at/T, where T is the total simulation time and a = 3 is a rate parameter. This ensemble approach allows us to identify robust dynamic features that are not dependent on a specific assumption about the transition’s shape.

Having defined the network structure, we now describe the dynamics of the hallmark levels. The total regulatory input to node i, denoted by w_i, is calculated as the scaled sum of the hallmark levels from all nodes in the network. A scaling factor is introduced to reflect the large number of underlying gene-gene interactions and facilitate numerical computation. The regulatory input is defined as

$$w_i(\mathbf{x},t)=\sum _{j=1}^M\alpha V_{ij}\left(t\right)x_j,$$ 3

where α = 10⁻⁴ is a scaling constant on the order of the inverse of the total number of genes. This input is then transformed by a non-linear activation function F(w_i) given by

$$F\left(w_i\right(\mathbf{x},t\left)\right)=\rho +(1-\rho )\frac{\sqrt{w_i(\mathbf{x},t)}}{\theta \left(t\right)},$$ 4

where ρ = 0.1 is a basal production rate. The term θ(t) is a time-dependent parameter that modulates the activation response and is defined as

$$\theta \left(t\right)=\frac{1}{M}\sum _{i=1}^M\sum _{j=1}^M{V}_{ij}\left(t\right).$$ 5

The full stochastic dynamics of each hallmark level are described by a system of stochastic differential equations that balances the production term with a stochastic degradation term. The dynamics follow

$$\frac{d{x}_i}{dt}={\lambda }_{i}F\left(w_i\right(\mathbf{x},t\left)\right)-e^{{\eta }_i\left(t\right)-\frac{{\sigma }^2}{2}}{x}_i,$$ 6

where λ_i = 3.8 is the maximum production rate. The stochastic component η_i(t) is an Ornstein-Uhlenbeck process governed by the equation

$$d{\eta }_i\left(t\right)=-\frac{1}{\tau }{\eta }_i\left(t\right)dt+\sqrt{\frac{2}{\tau }}\sigma d{W}_i\left(t\right),$$ 7

where W_i(t) is a standard Wiener process, σ = 0.1 is the noise intensity, and τ = 1.0 is the correlation time. The process η_i satisfies

$$E\left[{\eta }_i\right(t\left)\right]=0,E\left[{\eta }_i\right(t_1\left){\eta }_i\right(t_2\left)\right]={\sigma }^2{e}^{-\mid t_1-t_2\mid /\tau }.$$ 8

To study the evolution of the hallmark network, we generated 10,000 stochastic trajectories for each cancer type, with each trajectory simulated over 100 virtual time units. In the simulation, the period from t = 0 to t = 30 represents the normal network phase, from t = 70 to t = 100 the cancer network phase, and from t = 30 to t = 70 the intermediate transition phase. We confirmed that the system generally reached a new stationary state after t = 100. The initial condition for each simulation, x_i(0), was set to the stable stationary state of the normal system. This stationary state was obtained by numerically solving the model equations with the interaction matrix fixed at V(t) = V_n for the normal state. The initial condition is taken as average expression level of the genes in hallmark i based on the normal tissue data, as given by

$${\overline{x}}_i=\frac{1}{N_i}\sum _{k=1}^{N_i}{g}_{ik},$$ 9

where ${\overline{x}}_i$ is the stationary-state value for hallmark i, N_i is the number of genes in its corresponding gene set G_i, and g_ik is the expression level of the k-th gene in that set.

The stochastic differential equation system was solved numerically. The stochastic part was discretized using an Euler–Maruyama scheme, given by

$${\eta }_i^{t+1}={\eta }_i^t-\frac{1}{\tau }{\eta }_i^t\mathrm{\Delta }t+\sqrt{\frac{2}{\tau }}\sigma \sqrt{\mathrm{\Delta }t}{Z}_i^{t+1},$$ 10

with $Z_i^{t+1}~\mathcal{N}(0,1)$. To improve stability when solving for x_i, the main equation was updated using an implicit difference method as follows

$$x_i^{n+1}=\frac{\mathrm{\Delta }t{\lambda }_{i}F\left(w_i\right({\mathbf{x}}^n,t^n\left)\right)+x_i^n}{1+\mathrm{\Delta }t{e}^{{\eta }_i^n-\frac{{\sigma }^2}{2}}}.$$ 11

All model variables and parameters are summarized in Table 1.

Table 1.

Summary of model variables and parameters

Symbol	Explanation
xi	The level of hallmark Hi
wi(x, t)	Total regulatory input to node Hi
Vij(t)	Time-dependent regulatory strength from node Hj to Hi
F(wi)	Non-linear regulatory activation function
λi	Maximum production rate for node Hi (Value: 3.8)
ρ	Basal production rate (Value: 0.1)
θ(t)	Time-dependent normalization constant
ηi(t)	Ornstein-Uhlenbeck noise process
σ	Noise intensity (Value: 0.1)
τ	Noise correlation time (Value: 1.0)
α	Scaling constant for regulatory input (Value: 10−4)

Quantification of distributional divergence

To quantitatively compare the distributions of hallmark levels between the normal and cancer states and to ensure that these comparisons were valid across different hallmarks, we employed a computational pipeline with a consistent processing step. The input data for this analysis consists of the hallmark levels for each hallmark, generated from 10,000 simulations at the healthy stationary state (t = 1) and the cancerous stationary state (t = 100).

First, for our simulation data, it was necessary to estimate their continuous probability density functions (PDFs). We used Kernel Density Estimation (KDE) for this task. To eliminate any methodological bias that could be introduced by using different smoothing parameters, we adopted a rigorous common bandwidth selection strategy. Specifically, we first pooled all sample data from all hallmarks in both the normal and cancer states into a single aggregate dataset. Based on this pooled data, we then calculated a single optimal common bandwidth h_common using Silverman’s rule of thumb for a Gaussian kernel. This common bandwidth was subsequently used to perform KDE for each of the original normal and cancer datasets for every hallmark. For a given sample of N data points {x₁, x₂, …, x_N}, the probability density P(x) at any point x is estimated by the sum of Gaussian kernels as

$$P\left(x\right)=\frac{1}{Nh}\sum _{i=1}^N\frac{1}{\sqrt{2\pi }}\exp \left(-\frac{{(x-x_i)}^2}{2h^2}\right),$$ 12

where h is the common bandwidth h_common. This procedure ensures that all PDFs used for comparison, denoted as P(x) and Q(x), were generated under identical smoothing conditions.

After obtaining these consistently generated PDFs, we utilized the JS divergence to quantify the dissimilarity between them. While the Kullback-Leibler (KL) divergence is a fundamental information-theoretic measure, its asymmetry and unbounded nature limit its use for direct comparison. The JS divergence is a symmetrized and bounded (ranging from 0 to 1) version of the KL divergence, making it a more robust and intuitive metric for dissimilarity. A value of 0 indicates that the hallmark level distributions for the normal and cancer states are identical, while a value of 1 represents maximal divergence between the two states. It was computed as:

$$D_{JS}(P\mid \mid Q)=\frac{1}{2}{D}_{KL}(P\mid \mid M)+\frac{1}{2}{D}_{KL}(Q\mid \mid M),$$ 13

where $M=\frac{1}{2}(P+Q)$ is the average of the two distributions. The KL divergence, D_KL(P∣∣Q), for continuous distributions is defined as:

$$D_{KL}(P\mid \mid Q)={\int }_{-\infty }^{\infty }P\left(x\right)\log \left(\frac{P\left(x\right)}{Q\left(x\right)}\right)dx.$$ 14

Early-warning signal analysis

This study employed the DIND method from DNB theory to identify critical transition points during tumorigenesis⁴¹. The approach detects tipping points by quantifying network state changes between adjacent time points.

To construct the sample sets for DIND analysis, we first generated 50 independent “virtual patient” samples from the 10,000 simulated trajectories through random sampling and aggregation. Specifically, each virtual patient sample was created by randomly selecting and aggregating 1000 trajectories at each time point. At each time point t, the state vectors of these 50 virtual patient samples formed the ’case’ sample set, S_t. The ’reference’ sample set, S_r, was composed of the state vectors of the same 50 virtual patients from the single preceding time point, t − 1.

Following the DIND procedure⁴¹, for each hallmark’s local network, we fitted a multivariate normal distribution to the reference set (S_r) and the case set (S_t), yielding a reference distribution ${\mathcal{N}}_r({\mu }_r,{\mathrm{\Sigma }}_r)$ and a case distribution ${\mathcal{N}}_t({\mu }_t,{\mathrm{\Sigma }}_t)$, respectively. The divergence between these two distributions is quantified by the symmetric KL divergence. The local DIND score $D_i^t$ for each node i is defined as

$$D_i^t=\frac{1}{2}\left(D({\mathcal{N}}_r\mid \mid {\mathcal{N}}_t)+D({\mathcal{N}}_t\mid \mid {\mathcal{N}}_r)\right).$$ 15

The one-way KL divergence is computed as

$$D({\mathcal{N}}_r\mid \mid {\mathcal{N}}_t)=\frac{1}{2}\left[tr\left({\mathrm{\Sigma }}_t^{-1}{\mathrm{\Sigma }}_r\right)+{({\mu }_t-{\mu }_r)}^T{\mathrm{\Sigma }}_t^{-1}({\mu }_t-{\mu }_r)-d+ln\frac{\det {\mathrm{\Sigma }}_t}{\det {\mathrm{\Sigma }}_r}\right],$$ 16

where μ and Σ are the mean vectors and covariance matrices of the distributions, and d is their dimensionality. The global DIND score ${\overline{D}}^t$ at time t is calculated as the average of all M local DIND scores

$${\overline{D}}^t=\frac{1}{M}\sum _{i=1}^M{D}_i^t.$$ 17

A sharp increase in the ${\overline{D}}^t$ score, which reflects a significant short-term change in the hallmark network state, is interpreted as an early-warning signal of an impending critical transition.

Construction of the potential energy landscape

To visualize the dynamic transition of tumorigenesis in a low-dimensional space and identify its most probable evolutionary trajectory, we constructed a potential energy landscape of the system. The input for this analysis was the time-series data from the full ensemble of simulated trajectories generated by our stochastic dynamical model. Specifically, the input is a data matrix $X\in {\mathbb{R}}^{N\times M}$, where M = 10 is the number of features (hallmarks), and N is the total number of data points (10,000 trajectories × 100 time points).

The landscape was constructed as follows. First, the high-dimensional state data was projected into a lower-dimensional space using Principal Component Analysis (PCA). The data matrix was centered ($X_{centered}=X-\overline{X}$), its covariance matrix was computed ($\mathrm{\Sigma }=\frac{1}{N-1}{X}_{centered}^T{X}_{centered}$), and then subjected to eigendecomposition (ΣV = VΛ). The centered data was subsequently projected onto the two-dimensional plane defined by the first two principal components (the first two columns of V, denoted V₂), resulting in the dimensionally-reduced data Z = X_centeredV₂.

Next, we employed KDE to estimate the probability density function P(x, y) of the projected points. For a set of N two-dimensional data points (x_i, y_i), the density at a point (x, y) is computed using a sum of Gaussian kernels

$$P(x,y)=\frac{1}{N}\sum _{i=1}^N\frac{1}{\sqrt{2\pi }h}\exp \left(-\frac{{(x-x_i)}^2+{(y-y_i)}^2}{2h^2}\right),$$ 18

with h being the bandwidth parameter, set to 0.5 in this study.

The potential energy U(x, y) of the system is defined as the negative logarithm of the estimated density

$$U(x,y)=-ln\left(P\right(x,y\left)\right).$$ 19

In this landscape, regions with low potential values (basins) correspond to stable system states such as the normal and cancer states. The valley that connects these basins represents the most probable transition path for the system state to evolve from one to the other.

Statistical analysis

Multiple non-parametric statistical tests are employed in this study to assess the significance of our findings, with a uniform significance threshold of P < 0.05. To compare the distributions of hallmark levels between the normal and cancerous states for each hallmark (as shown in Fig. 3c), a Mann-Whitney U test was used. This test assesses whether two independent samples are drawn from the same underlying population. For this analysis, the null hypothesis (H₀) was that there is no difference between the distributions of hallmark levels in the normal and cancer groups for a given hallmark. For the analysis of the time difference (Δt) between network reconfiguration and the shift in hallmark levels (as shown in Fig. 5a), a one-sample Wilcoxon signed-rank test was performed. This test is used to determine if the median of a single sample group is significantly different from a specified value (in this case, zero). The null hypothesis (H₀) was that the median of the Δt distribution is equal to zero. The consistency of hallmark rankings across the 15 cancer types (as shown in Fig. 6a and b) was evaluated using the Friedman test. This test is designed to detect differences in treatments (the 10 hallmarks) across multiple matched blocks (the 15 cancer types) for ranked data. The null hypothesis (H₀) was that the average ranks of all hallmarks are identical, implying no consistent ranking pattern across the cancers.

Author contributions

Conceptualization: C. Zhuge, Y. Han, D. Xu; Data curation: Y. Wu, Y. Hou, J. Wang; Computational resources: D. Xu, Y. Li, C. Zhuge; Investigation: J. Wang, Y. Wu, C. Zhuge; Project administration: C. Zhuge; Supervision: D. Xu, Y. Han, C. Zhuge; Writing – original draft: J. Wang, Y. Wu, C. Zhuge; Writing – review and editing: D. Xu, C. Zhuge, Y. Li, Y. Han, J. Wang, Y. Wang, Y. Hou.

Data availability

The datasets used in the present study are all publicly available. The primary data used in this study are available in the GRAND database (https://grand.networkmedicine.org). All the genes in the hallmark-of-cancer related GO terms were downloaded from Gene Ontology (https://geneontology.org). The list of cancer names selected for this study in the GRAND database is in Supplementary Table S1 (Supplementary Information). Detailed information on the GO term names corresponding to hallmarks and their GO term IDs is provided in Supplementary Table S2 (Supplementary Information). Final hallmark gene sets are provided in Supplementary Data 1. Source data for the figures presented in the main text are available in Supplementary Data 2.

Code availability

Analysis pipelines and simulation codes are maintained at https://github.com/zhuge-c/Hallmark_dynamics.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41540-025-00602-1.