
==== Front
NPJ Syst Biol Appl
NPJ Syst Biol Appl
NPJ Systems Biology and Applications
2056-7189
Nature Publishing Group UK London

39223160
422
10.1038/s41540-024-00422-9
Article
A Boolean model explains phenotypic plasticity changes underlying hepatic cancer stem cells emergence
http://orcid.org/0000-0001-7273-516X
Hernández-Magaña Alexis 12
Bensussen Antonio 3
http://orcid.org/0000-0003-2931-0531
Martínez-García Juan Carlos 3
http://orcid.org/0000-0002-7938-6473
Álvarez-Buylla Elena R. eabuylla@gmail.com

12
1 grid.9486.3 0000 0001 2159 0001 Instituto de Ecología, Universidad Nacional Autónoma de México, Ciudad de México, México
2 https://ror.org/01tmp8f25 grid.9486.3 0000 0001 2159 0001 Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, Ciudad de México, México
3 grid.512574.0 Departamento de Control Automático, Cinvestav-IPN, Ciudad de México, México
2 9 2024
2 9 2024
2024
10 9913 2 2024
8 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
In several carcinomas, including hepatocellular carcinoma, it has been demonstrated that cancer stem cells (CSCs) have enhanced invasiveness and therapy resistance compared to differentiated cancer cells. Mathematical-computational tools could be valuable for integrating experimental results and understanding the phenotypic plasticity mechanisms for CSCs emergence. Based on the literature review, we constructed a Boolean model that recovers eight stable states (attractors) corresponding to the gene expression profile of hepatocytes and mesenchymal cells in senescent, quiescent, proliferative, and stem-like states. The epigenetic landscape associated with the regulatory network was analyzed. We observed that the loss of p53, p16, RB, or the constitutive activation of β-catenin and YAP1 increases the robustness of the proliferative stem-like phenotypes. Additionally, we found that p53 inactivation facilitates the transition of proliferative hepatocytes into stem-like mesenchymal phenotype. Thus, phenotypic plasticity may be altered, and stem-like phenotypes related to CSCs may be easier to attain following the mutation acquisition.

Subject terms

Regulatory networks
Cancer
Patrones genéricos y sistémicos de la diferenciación y la proliferación en los nichos de células troncales: Raíz de Arabidopsis thaliana como sistema de estudio teórico-experimental (PAPIIT IN211721).Patrones genéricos y sistémicos de la diferenciación y la proliferación en los nichos de células troncales: Raíz de Arabidopsis thaliana como sistema de estudio teórico-experimental (PAPIIT IN211721). PROYECTO CONACYT/PRONACES 194186: Biología matemática y computacional de sistemas médicos: modulación preventiva de la emergencia y progresión de enfermedades crónico-degenerativas.issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Hepatocellular carcinoma (HCC) is the most common subtype of liver cancer1. In 2020, 905,700 new cases were counted, and 830,200 patients died from this illness globally2. The most common etiologic origin of HCC is viral hepatitis. However, the incidence of HCC related to obesity, type 2 diabetes mellitus, and nonalcoholic fatty liver disease (NAFLD) has increased in recent years1,3. Remarkably, it is projected that liver cancer mortality may increase by more than 56% by 20402.

Notably, cancer mortality is associated with critical processes such as drug resistance, tumor recurrence, and metastasis, which significantly rely on phenotypic plasticity4–6. Thus, understanding the mechanisms involved in phenotypic plasticity regulation may be essential to improving HCC treatments and prevention strategies. In particular, phenotypic plasticity can be studied using concepts and tools from dynamical systems theory.

In multicellular organisms, multiple cell phenotypes (e.g., cell types) emerge from the same genome, and a specific gene expression profile characterizes each one7. From a systems biology perspective, these stable gene expression profiles are called attractors and arise from gene regulatory networks (GRNs)8,9. In this context, the conceptual model of the epigenetic landscape proposed by Waddington to illustrate cell differentiation can be formalized using GRN dynamical models, for instance, Boolean models grounded on experimental data10,11. Thus, each GRN has a specific associated epigenetic landscape, where each attractor is a valley, and a phenotypic transition can be represented as the jump from one valley to another8.

During development and tissue repair, phenotypic plasticity is driven by environmental cues12 and gene expression noise coupled with constraints from a wild-type GRN8. However, in the case of cancer cells, it has been shown experimentally that phenotypic plasticity can be altered by genetic factors, e.g., gene mutations13–15. It has been proposed that mutations could change the epigenetic landscape topography and, therefore, the transition probabilities among attractors of a GRN9,11,16. However, the interaction between non-genetic mechanisms and genetic factors controlling cancer cell plasticity is still not comprehensively understood. Analyzing cancer cell plasticity regulation could be essential to prevent critical phenotypic changes, for example, epithelial-mesenchymal transition (EMT).

Specifically, EMT is a process by which epithelial cells lose polarity and cell-cell adhesion while gaining mesenchymal characteristics such as migratory capacity17. These changes are associated with the downregulation of epithelial markers such as E-cadherin and miR200 microRNA family and the upregulation of mesenchymal markers such as SNAI1 (Snail), SNAI2 (Slug), TWIST, and ZEB17,18. EMT is involved in embryonic development, wound healing, and cancer-related processes such as metastasis19–21 and acquiring stem-like features, i.e., cancer stem cells (CSCs) emergence6,22,23.

Notably, senescence, proliferation, and inflammation regulators such as p53, p21, β-catenin, YAP1, NF-κB, and IL-6 have also been associated with EMT and stemness24–34. However, despite having a vast amount of experimental information, it is still necessary to search for tools that allow data integration to characterize the complex GRNs underlying the cell behavior. In this sense, previous dynamic models of GRN have been used to provide a mechanistic understanding of cell differentiation and morphogenetic processes during normal and altered development35–38. In the same way, a previous GRN Boolean model has been proposed to understand the EMT dynamics39. This generic EMT model recovered three attractors corresponding to the gene expression profiles in epithelial, senescent epithelial, and stem-like mesenchymal cells. It was observed constitutive activation of NF-κB decreased the frequency of the epithelial phenotype and increased the frequency of the stem-like mesenchymal phenotype relative to the wild-type model39, in agreement with the role of NF-κB as an inducer of EMT31.

Here, we aimed to understand the specific regulatory processes by which CSCs are generated in HCC context. To this end, we integrated experimental evidence to propose a dynamic model of hepatocyte EMT (hEMT). In methodological terms, we extended a generic EMT model39 by incorporating regulatory modules described in normal hepatocytes and stem cells. Our resulting Boolean model recovers 8 attractors associated with the hepatocyte and mesenchymal phenotypes: senescent hepatocytes, senescent mesenchymal cells, quiescent hepatocytes, quiescent mesenchymal cells, proliferative hepatocytes, proliferative mesenchymal cells, proliferative stem-like hepatocytes, and proliferative stem-like mesenchymal cells. Furthermore, analysis of the epigenetic landscape derived from our model shows that the loss of tumor suppressor genes such as p53, p16, p21, and RB, as well as the constitutive activation of β-catenin and YAP1, may change cell plasticity and facilitate the CSCs emergence. Thus, these results provide a mechanism to understand CSCs emergence in the specific context of HCC.

Results

Hepatocytes have genetic markers that influence EMT

In order to analyzing dynamical properties of EMT in HCC context, we first searched for genetic markers and molecular features that distinguish hepatocytes from other epithelial cells. We then incorporated such interactions to a previously published and validated model of EMT proposed by Méndez-López et al.39. In this model we added specific transcription factors (TFs) that have been described in hepatocyte differentiation such as HNF4A, HNF1A, FOXA2, and HNF6. These genetic markers belong to a cross-regulatory network that controls the development and adult function of the liver40,41. Particularly, it has been reported that HNF4 and HNF1A are negative regulators of Snail and Slug42. Moreover, we incorporated TFs and interactions that are related to stemness and endodermal differentiation. In this sense, we added to the network OCT4, SOX2, NANOG and KLF4 because they are central regulators for the induction and maintenance of stem cells43–45. It is noteworthy to mention that such TFs are involved in the emergence of a small stem-like cell population present in injured liver of mice46.

Other genetic markers that have been incorporated to the network are GATA6, SOX9, β-catenin, YAP1 as well as miR-200a,b,c, and miR34a. Concerning each marker, GATA6 is essential for visceral endoderm differentiation and embryonic development of the liver47,48. SOX9 expression has been associated with proliferation and stem cell features in HCC49. SOX9 is expressed in liver stem/progenitor cells but not in hepatocytes50,51. Wnt/β-catenin signaling pathway plays a pivotal role in liver development and regeneration52. In particular, β-catenin regulates EMT in HCC cells through double-negative feedback with HNF4A53. Regarding YAP1, it forms a circuit with SNAI1 and HNF4A54, to regulate EMT55, proliferation, and differentiation in HCC cells56. The miR-200 family (miR-200a,b,c) and miR-34a are involved in EMT57, reprogramming58, and differentiation59. MiR-34a plays a role in EMT60. SNAI1 and HNF4A regulate the expression of the miR-200 family and miR-34a. Grounded on experimental evidence of a total number of 240 papers (Supplementary data 1), we were able to postulate a regulatory network of 45 nodes that represents hEMT in the context of HCC (Fig. 1). We use all the information presented in this network to build a Boolean model of 45 logic rules, available in Supplementary Information.Fig. 1 Full gene regulatory network of hEMT.

In this figure, we show the complete hEMT network. The square-shaped nodes are TFs, and the circular nodes are other biological molecules. Interactions ending in T-bar are inhibitions and those ending in an arrow are activations. In this figure, violet, orange, and pink are exclusive markers of hepatocytes, mesenchymal cells, and stem cells, respectively. On the other hand, green, blue, yellow, and red are used to represent nodes of intracellular processes such as cell cycle, senescence, epigenetic silencing, and inflammation. See Supplementary data 1 (Supplementary data 1) to obtain more details about all biological interactions described here.

hEMT regulatory network is a source of phenotypic diversity

The network presented above, includes much of the complexity associated with hEMT. However, we seek to understand what is the effect of mutations observed in cancer cells on hEMT. For this reason, we decided to find the necessary and sufficient nodes to control the global dynamics of the GRN. To do this, we proceed to compact the network model using the algorithm proposed by Véliz-Cuba61. Such procedure uses discrete math operations to simplify linear interactions, conserving all non-linear motifs that contribute to the system dynamics, like positive and negative feedback loops (see Methods). Using this algorithm, we obtained a reduced network of 23 nodes (Fig. 2). In the same way, we validated our reduction by using the GINsim software62. All Boolean logic rules of this reduced network are presented in Supplementary Information.Fig. 2 Reduced network of hEMT.

In this figure, we show the reduced hEMT GRN. Square-shape nodes are TFs, circular nodes are other biological molecules, interactions ending in T-bars are inhibitions, interactions ending in arrows are activations, and dual interactions ending in V-inverted shape. See Supplementary Information (Supplementary Information) to obtain more details about the reduction outcomes.

After reduction, we needed to know whether the simplified model of the hEMT network had preserved the essential dynamic information of the full model of GRN. To this end, we identified the attractors of both Boolean models using the BoolNet R package. In particular, for the simulation of the GRN full model, 5,000,000 configurations of the network as initial conditions were randomly selected, and it was found that the model converges to only eight attractors that correspond to the following phenotypes: Senescent hepatocytes (SH), senescent mesenchymal cells (SM), quiescent hepatocytes (QH), quiescent mesenchymal cells (QM), proliferative hepatocytes (PH), proliferative mesenchymal cells (PM), proliferative stem-like hepatocytes (PSH), and proliferative stem-like mesenchymal cells (PMS) (Fig. 3a).Fig. 3 Phenotypic diversity of hEMT.

Both models generate eight attractors: senescent hepatocytes (SH), senescent mesenchymal cells (SM), quiescent hepatocytes (QH), quiescent mesenchymal cells (QM), proliferative hepatocytes (PH), proliferative mesenchymal cells (PM), proliferative stem-like hepatocytes (PSH), and proliferative stem-like mesenchymal cells (PMS). a Extended model provides more details about the genetic profile of each phenotype, while b reduced model maintains the essence of each phenotype. The frequencies of each phenotypic attractor are given by the size of their basins of attraction. Extended model (c) and reduced model (d) present similar characteristics at a qualitative level. Thus, we concluded that reduction maintains enough information of the extended model.

The mesenchymal phenotype was identified by the activation of SNAI1, SNAI2, TWIST1, ZEB1, FOXC217,63. The activation of HNF4A, HNF1A, HNF6, and FOXA2 correspond to the hepatocyte phenotype40,64. In the same way, the senescent phenotype was identified by the activation of p53, p16, p21 and RB65,66; proliferation was identified by E2F1 activation, cyclin D, and RB inactivation67,68; quiescence was identified by RB and p21 activation, as well as by the absence of proliferation markers like E2F1, cyclin D, and the absence of senescence markers such as p53 and p1669. Finally, the stem-like phenotype was associated with the activation of OCT4, SOX2, and NANOG45,70.

As expected, the reduced model presented equivalent attractors (Fig. 3b), which indicates that the set of nodes of this model is sufficient to describe the network dynamics. Subsequently, we compared the size of the basin of attraction (i.e., the number of network states converging to a given attractor) for each phenotype. This was done for both the full model (Fig. 3c) and the reduced model (Fig. 3d). We observed that such results are qualitatively congruent with each other. Remarkably, PMS and PSH present stem-like features given by the activity of NANOG, OCT4, and SOX2 (Fig. 3a, b), which suggests that such phenotypes have self-renewal properties. Moreover, the size of the basin of attraction of PMS and PSH indicates that such phenotypes may be less frequent than others (Fig. 3c, d), which is congruent with the low prevalence of stem cells in nature71. Collectively, these results indicate that the reduced model captures the essential dynamical properties of the extended model. Therefore, it could be used to assess the effect of mutations on hEMT plasticity.

Phenotypes produced by hEMT GRN are robust and physiologically feasible

The results presented above show that hEMT GRN reproduces a set of well-defined hepatic phenotypes. In a physiological context, phenotypes persist despite gene expression noise and slight molecular changes produced by stimuli, such as thermal changes, and osmotic pressure variations72. In other words, phenotypes are robust. For this reason, we determined whether these phenotypes (i.e., attractors) produced by the hEMT model could persist in the presence of perturbations. To do this, we tested the robustness of the GRN in the presence of fluctuations in the output of logical rules. Specifically, Boolean simulations were started with each state of the network. Using a particular state, the successor state was obtained by applying stochastic noise to the logical rules of the nodes (i.e., the normal output of logical rules was changed with a given probability, η = 0.01). Subsequently, it was determined whether the successor state belonged to the same basin of attraction, or whether the system transited to a different basin of attraction39,73. It was repeated 1000 times for each network state. Finally, the number of times each basin of attraction was reached was divided by the total number of initial configurations of the corresponding basin of attraction (see Methods section “Robustness of the Boolean model”). As a result of this procedure, we determine the probabilities that an hEMT-produced phenotype remains fixed or changes towards other phenotypes randomly (Fig. 4a). Numerically, we found the probabilities that the phenotypes are maintained in the face of fluctuations are higher than 0.9, which indicates that such phenotypes are robust and, therefore, physiologically feasible (Fig. 4b).Fig. 4 Evaluation of physiological feasibility of hEMT network.

Reduced model of hEMT proved to be stable against stochastic noise, η=0.01. a Diagram that illustrates the procedure that was used to test the robustness of the GRN. In this stochastic process, we calculate the probabilities that one phenotype transitions to another in an indeterminate time (represented with arrows). The probability that a phenotype will be maintained over time (blue arrows) is a measure of the robustness and stability of the phenotype in the face of normal physiological changes. b This matrix of Markov shows all probabilities represented in the last panel, where blue cells are the probabilities to conserve each phenotype over time. These results show that the GRN of hEMT is robust against stochastic perturbations, which indicates that hEMT phenotypes are physiologically feasible.

Experimental observations on hEMT are mechanistically explained by the GRN

After determining the feasibility of the minimal hEMT model under stochastic fluctuations, we test its effectiveness as a predictive tool. To this end, we simulate a series of loss-or-gain-of-function mutations on a particular set of genes like SNAI1, SNAI2, HNF1A, and HNF4A as well as oncogenes as YAP1 and β-catenin. In the same way, we studied the effects of targeting tumor suppressors such as p53, p21, p16, and RB (Fig. 5a and Supplementary Information). To simulate the gain of the function, we set the value of the target node as one. Similarly, to simulate the loss of function, we set the value of the target node to zero for all time steps of simulation (see Methods). Next, we identified the attractors and basin sizes of each mutated network. Finally, we analyze the impact (∆Si) that each mutation has on the WT attractor landscape by subtracting the value of each wild-type basin (SWT) from the value of the mutated basin (Si), that is: ∆Si=Si−SWT (Fig. 5b).Fig. 5 Visualizing the effect of mutations on hEMT attractor landscape.

This figure shows the outcomes of exploring the effect of different reported mutations on hEMT behavior. a Graphical representation of the basin of attraction size under different mutations. Here is shown that mutations like KO HNF4A abrogate hepatocyte phenotype, contributing to increased mesenchymal phenotypes. b Heat map showing the net effect of mutations on hEMT. The blue color indicates the decreases that an attraction basin presents with respect to the WT value. The red color shows the gain with respect to the reference value of the wild type. This heatmap shows that knockouts in HNF4A and HNF1A enhance mesenchymal phenotypes, as well as overexpression of SNAI1 and SNAI2. On the other hand, knockouts in p53 and p16 downregulate senescent phenotypes and increase quiescent and proliferative phenotypes. Therefore, these results reveal non-trivial details about functional changes in hEMT GRN produced by mutations.

As a result of these assays, the model was able to qualitatively reproduce several experimental observations, such as either the inhibition of HNF4A and HNF1A or the overexpression of SNAI1 and SNAI2 increase the mesenchymal phenotype (Fig. 5b and Table 1). The opposite occurs when HNF4A and HNF1A are overexpressed, increasing the hepatocyte phenotype (Fig. 4d and Table 1). In the same direction, inhibition of p53, p16, and p21 reduces senescent phenotypes (Fig. 5b and Table 1), while the opposite occurs when p53 and p16 are overexpressed (Fig. 5b and Table 1). Interestingly, the model showed that BMI1 has an important role in the appearance of CSCs (Fig. 5b and Table 1). On the other hand, the model shows that overexpression of HNF6 reduces the appearance of cells with a mesenchymal phenotype (Fig. 5b and Table 1).Table 1 Validation of the hEMT model

Mutationa	Predictionb	Experimental outcomes	References	
KO HNF4A	This condition increases mesenchymal cells.	HNF4A silencing increased migratory capacity and the expression of mesenchymal markers.	100	
KO HNF1A	This condition increases mesenchymal cells.	This increases the cell’s migratory capacity and the expression of mesenchymal markers.	100	
KO SNAI1	This condition reduces mesenchymal cells.	SNAI1 silencing decreased migratory capacity and the expression of mesenchymal markers.	30,101	
KO p53	This condition reduces senescence.	p53 deletion reduces senescence.	65,102,103	
KO p16	This condition reduces senescence.	p16 deletion reduces senescence.	104	
KO p21	It reduces senescence and increases proliferation.	p21 deletion reduces senescence and increases proliferation.	105,106	
KO RB	This condition increases proliferation.	RB deletion increases proliferation.	105,107,108	
OE HNF4A	This condition reduces mesenchymal cells.	HNF4A overexpression increases epithelial morphology and reduces motility as well as invasive capacity.	30,100	
OE SNAI1	This condition increases mesenchymal cells.	SNAI1 overexpression increases mesenchymal phenotype.	30,101,109	
OE SNAI2	This condition increases mesenchymal cells.	SNAI2 overexpression increases mesenchymal phenotype.	42,110	
OE β-catenin	This condition increases proliferation.	β-catenin activation promotes proliferation.	111,112.	
OE YAP1	This condition increases stem-like phenotype.	YAP1 activation increases stem-like phenotype.	113	
OE p53	This condition increases senescence.	p53 activation promotes senescence.	114	
OE p16	This condition increases senescence.	p16 overexpression promotes senescence.	104	
KO BMI1	This condition reduces stem-like phenotype.	Knockdown of BMI1 eliminated CSCs.	115	
OE BMI1	This condition increases stem-like phenotype.	BMI1 overexpression promotes cancer stem-like cells.	115	
OE HNF6	This condition reduces mesenchymal phenotype.	HNF6 increases epithelial phenotype and inhibits mesenchymal phenotype.	116	
OE TGF-β	This condition increases mesenchymal stem-like phenotype.	TGFβ induces mesenchymal stem cell differentiation.	22,117	
OE NF-κB	This condition increases stem-like phenotype.	NF-κB activation increases CSC differentiation.	32,118	
OE OCT4	This condition increases stem-like phenotype.	OCT4 overexpression maintains CSCs.	119	
OE SOX2	This condition increases stem-like phenotype.	SOX2 overexpression increases CSCs.	120	
OE Cyclin-D	This condition increases stem-like phenotype.	Cyclin D1 controls cancer stem cells self-renewal and proliferation.	121	
OE EZH2	This condition increases stem-like phenotype.	Overexpression of EZH2 promotes CSCs.	122	
OE OCT4, OE NANOG	This condition increases stem-like phenotype.	OCT4 and NANOG overexpression promotes the emergence of CSCs in HCC.	123	
aKO means ‘knockout’ and OE is ‘overexpression’.

bAll predictions were taken from Fig. 5b.

Furthermore, the model is capable of reproducing observations such as that the overexpression of OCT4 alone and in conjunction with NANOG is capable of enhancing the differentiation of cancer cells with a stem-like phenotype (Fig. 5b and Table 1). Likewise, the model shows that high levels of SOX2, EZH2, NF-kB, Cyclin D, and EZH2 directly influence the emergence of stem-like phenotypes of cancer cells (Fig. 5b and Table 1). Interestingly, our model predicts that the presence of TGF-β will increase cancer mesenchymal stem-like cells, which effectively occurs (Fig. 5b and Table 1). In addition, the model showed that proliferation can be triggered when p21, p16, p53, and RB are inhibited or when YAP1 and β-catenin are overexpressed (Fig. 5b and Table 1). Finally, the model also showed that the constitutive activation of YAP1 increases the stem-like phenotype (Fig. 5b and Table 1). Collectively, these results validate our qualitative model as a predictive tool.

Hepatocytes and other epithelial cells may be similarly transformed into CSCs

The analysis of mutations on hEMT GRN showed that there are genes capable of biasing the process towards proliferative phenotypes, including the PMS phenotype (Fig. 6a, b). Consequently, we decided to investigate the effect on the robustness of attractors (phenotypes) produced by the loss of function of the tumor suppressors p53, p21, p21, and RB, as well as the overexpression of YAP1 and β-catenin oncogenes (see Methods). We observed that all simulated mutations enhance proliferative phenotypes, including PMS (Fig. 6c). Conversely, senescent phenotypes were predominantly affected by p53 inactivation (Fig. 6d). The decreased robustness of the senescent phenotypes by the p53 mutation may explain the senescence escape experimentally observed13. Interestingly, mutations on tumor suppressors as well as oncogenes favor the appearance of proliferative stem-like phenotypes (Fig. 6d). We hypothesize that this augment in stem-like phenotypes corresponds to the appearance of CSCs, represented by PMS and PSH phenotypes.Fig. 6 Somatic mutations increase CSCs in HCC.

This figure shows the effect of loss of function of tumor suppressors like p53, p16, RB, and p21, as well as aberrant activation of oncogenes such as β-catenin and YAP1 on the size of attraction basins and attractors robustness (i.e., the probability of staying in the same basin of attraction despite stochastic perturbations). a Changes in the size of the attraction basins of the proliferative phenotypes due to somatic mutations. b Changes in the size of the attraction basins of the senescent phenotypes. c Changes in the probability of maintaining the phenotype in the presence of different somatic mutations. d Changes in the probability of maintaining the senescent phenotypes due to somatic mutations. e Comparison of the effect of somatic mutations on basins of attraction, HCC vs. other cancers.

It is not clear whether this property is exclusive to hepatocytes or not. To explore this issue, we compared the impact of each mutation (∆Si) on the WT attractor landscape of the hEMT model against Méndez-López et al.39 observations in the generic EMT model (Fig. 6e). Qualitatively, the behavior of hepatocytes was similar to other epithelial cells. However, it is notable that hepatocytes were less sensitive to SNAI2 mutations. In fact, SNAI2 did not induce severe alterations in senescent phenotypes from the hEMT model compared to other epithelial cells (Fig. 6e). Furthermore, we noted that KO p53 strongly reduced senescent phenotypes in the liver compared to other epithelial cells (Fig. 6e). Collectively, these results suggest that there might be a common mechanism in the appearance of CSCs in epithelial cells. However, CSC emergence may be affected by the phenotype-specific regulators of each cell type.

Mutations in oncogenes and tumor suppressor genes affect EMT plasticity and generate CSCs

Next, we determine what the most likely phenotypic transitions are. To investigate this point, we use the mean first passage time (MFPT), which is a metric to determine how difficult it is for a GRN to take the first step in a differentiation trajectory towards another phenotype. In general, the MFPT is used to calculate the net transition rate, which determines how easy it is to move from one state to another (see Methods). As a result of this procedure, we observed no transitions from senescent phenotypes to proliferative or quiescent phenotypes in the WT model (Fig. 7a), which confirms the stability of the senescent phenotypes suggested by the size of the attraction basins (Fig. 3c, d). We also noted that transitions towards proliferative and stem-like phenotypes are relatively low (Fig. 7a). In the WT model, the attractors associated with the quiescent and senescent phenotypes are the most stable.Fig. 7 Differentiation pathways of hEMT.

This figure shows the different pathways and cell fates that a hepatocyte can acquire when hEMT is activated. a Map of the different differentiation pathways that the phenotypes can follow. The numbers in blue correspond to the transition indices calculated for the wild-type hepatocyte, the thickness of the arrows is proportional to the numerical value of the index. b Visualization of the effect of somatic mutations on differentiation pathways in hEMT. In particular, this figure shows the effect of inhibiting tumor suppressors such as p53, p21, p16, and RB, as well as overexpressing oncogenes such as YAP1 and β-catenin, along with immune response genes such as NF-κB and TGF-β.

Finally, we examined how mutations could affect the probabilities of transition from hepatocyte into mesenchymal phenotypes. Specifically, we focused on three phenotypic transitions: proliferative hepatocytes into proliferative mesenchymal phenotype, hepatocytes into stem-like mesenchymal phenotype, and stem-like hepatocytes into stem-like mesenchymal phenotype. To do this, we simulated common alterations in HCC and other cancers like loss-of-function mutations of RB, p21, p16, and p53 and constitutive activation of β-catenin, YAP1, NF-kB, and TGF-β. As a result of these simulations, we found that aberrant activation of β-catenin, YAP1, NF-kB, and TGF-β increased the index of net transition of proliferative hepatocytes to proliferative mesenchymal cells (Fig. 7b), in concordance with previous experimental observations18,31,34. On the other hand, the loss-of-function of tumor suppressor genes like p16, p21, and p53 also increased this transition (Fig. 7b), in agreement with in vitro assays24,27,74. All simulated alterations promoted the transition from hepatocytes with stem-like features to mesenchymal stem-like phenotype. However, only p53 loss-of-function mutation and constitutive activation of NF-κB and TGF-β favored the transition of proliferative hepatocytes to proliferative mesenchymal stem-like phenotype (Fig. 7b). Thus, these mutations may be essential to increase the prevalence of CSCs.

Discussion

Hepatocellular carcinoma (HCC) is a type of cancer with a high mortality rate, and increasing the expression of CSCs markers is associated with a poor prognosis75. This suggests that CSCs emergence could be associated with HCC mortality. Recent evidence has shown that CSCs are a heterogeneous group of cells since there may be stem-like phenotypes with different levels of expression of epithelial and mesenchymal markers76. In this regard, it has been reported that proliferative CSCs displaying an abundance of mesenchymal markers can initiate tumors, resist chemotherapy, and trigger metastasis76. In contrast, proliferative CSCs with a predominance of epithelial markers lose their ability to initiate metastasis76. Thus, understanding the mechanisms underlying the CSCs emergence and phenotypic heterogeneity is essential. It is known that CSCs can be originated from EMT6,22,77, although the detailed mechanism remains to be elucidated.

Although other dynamical models of EMT39,78–83 have been proposed and have provided important insights about EMT regulation, these do not include hepatocyte- and stemness-specific molecular regulators that could be crucial to examine the relationship between EMT and the CSCs emergence in the liver. In the present work, we built a dynamical GRN model, including TFs controlling the epithelial phenotype in hepatocytes (e.g., HNF4A, HNF1A, FOXA2, HNF6) and stemness (e.g., OCT4, SOX2, NANOG, KLF4), to explain the phenotypic transitions in the liver. Our Boolean model was supported by 240 experimental reports (Supplementary Data 1), and despite the fact that our model is qualitative in its computational implementation, it was able to explain several experimental observations of hEMT (Fig. 5b and Table 1). In this sense, our model predicted the existence of eight attractors (Fig. 3a, b) from hEMT GRN, which correspond to the following cell phenotypes: senescent hepatocytes (SH), proliferative hepatocytes (PH), quiescent hepatocytes (QH), proliferative stem-like hepatocytes (PSH), senescent mesenchymal cells (SM), proliferative mesenchymal cells (PM), quiescent mesenchymal cells (QM) and proliferative stem-like mesenchymal cells (PMS).

We suggest that PMS and PSH represent normal stem-like cells arising from WT GRN, and we hypothesize that PMS and PSH may convert into CSCs following the acquisition of mutations on the GRN. Thus, on mutated GRN, PMS may represent mesenchymal CSCs, and PSH may correspond to epithelial CSCs since both cells are NANOG + OCT4 + SOX2+ with mesenchymal and epithelial markers, respectively (Fig. 3a, b). Thus, these results show that our qualitative model may be a satisfactory predictive tool, capable of tracking the emergence of CSCs.

In this sense, our model showed that stem-like cells are formed naturally as a result of hEMT dynamics. However, these phenotypes have low relative stability (Figs. 3c, d and 7a), which could mean that stem-like cells tend to differentiate, and it is unlikely to attain these phenotypes, according to experimental observations84–86. Nevertheless, somatic mutations, such as inactivation of tumor suppressor genes like p53 and aberrant expression of oncogenes like YAP1, may significantly increase the prevalence of CSCs (Figs. 5 and 6). Our simulations show that mutations can modify the epigenetic landscape topography and, consequently, the cell plasticity (Figs. 5b and 7b). For example, the loss of function of p53 simultaneously decreases the robustness of senescence (Fig. 6b, d), increases the robustness of proliferative and stem-like phenotypes (Fig. 6a, c), and also increases the transition of proliferative hepatocytes into mesenchymal stem-like cells (Fig. 7b), in this way, promoting the CSCs emergence.

In general, our model shows that somatic mutations affect the relative stability of attractors. Nonetheless, the intracellular network still maintains its multistability (i.e., multiple stable phenotypes arise from a GRN) (Fig. 5a), suggesting that mutated cells could still attain multiple cell fates. This might explain the phenotypic heterogeneity of tumor cells14. Interestingly, we observed the loss of function of tumor suppressor genes (e.g., RB, p16, p53) and activation of YAP1 promote the transition from epithelial stem-like phenotype to mesenchymal stem-like phenotype (Fig. 7b), which has been reported to enable metastasis6,76,87,88.

On the other hand, it is interesting to determine whether this mechanism to generate CSCs could be universal for all types of epithelial cancers, or whether it is a specific mechanism for HCC. Regarding this point, our results suggest that this mechanism may be common for all epithelial cancers at the qualitative level. However, each epithelial cell type may present its particularities (Fig. 6e). For instance, our results show that suppression of p53 is especially important in the HCC context (Fig. 6e), which may explain why p53 deletions drastically increase HCC mortality89.

Finally, in the research of The Cancer Genome Atlas and other massive sequencing studies of tumors extracted from HCC patients, the main genetic alterations that these tumors present are observed90,91. However, these studies do not delve into the molecular mechanisms that these mutations trigger to generate tumors per se90,91. Consequently, they cannot explain the appearance of this type of carcinoma in patients who do not present the main somatic mutations that have been registered90,91. In this sense, we observe that different mutations can produce qualitatively similar alterations in epigenetic landscape and cell plasticity (Figs. 5, 6, and 7b). Thus, our work provides valuable insights into molecular mechanisms that somatic mutations, such as p53 loss or YAP1 activation, perturb to generate hepatocellular carcinoma.

Although our model includes regulators of various cellular processes (e.g., proliferation, senescence, EMT, inflammation, stemness) and recapitulates the effect of single mutations, further analysis is necessary to understand the impact of multiple mutations on cell plasticity, which is more realistic in the cancer context. Also, we only simulated mutations available in the reduced model. On the other hand, it could be important to determine perturbations generating hybrid epithelial-mesenchymal phenotypes, which have been demonstrated to play a critical role in acquiring the stem-like phenotype and metastasis92,93.

In summary, we show that normal or altered phenotypic plasticity can be generated by an underlying multistable GRN. We suggest that tracking cell plasticity changes against perturbations on hEMT GRN might be valuable for proposing or testing novel therapeutic strategies against HCC.

Our study strongly supports that stem-like phenotypes in the liver are generated from an underlying GRN, and in a non-cancer context, these phenotypes are unlikely to be attained. However, mutations in tumor suppressor genes, such as p53, and aberrant expression of oncogenes, such as YAP1, may generate phenotypic plasticity changes and facilitate the transition into the proliferation and stem-like phenotypes, which, consequently, could favor the CSCs emergence. Finally, the CSC generation mechanism may be common to other epithelial cancers at a qualitative level.

Methods

Construction of the network

To build the model proposed here, we modified the qualitative extended Boolean model of EMT proposed by Méndez-López et al.39. We replaced the generic epithelial markers (ESE-1, ESE-2, ESE-3) with specific markers of liver cells (HNF4A, HNF1A, HNF6, FOXA2, miR-34a, miR-200a,b and miR-200c), and also added stemness regulators (OCT4, SOX2, NANOG, SOX9, GATA6). We also incorporated the YAP1 and β-catenin, two critical regulators in HCC. We consulted 240 experimental references to obtain details about regulatory connections between nodes. Furthermore, we manually select relevant and documented interactions to construct our gene regulatory network of hepatocytes (Fig. 1).

Derivation of the Boolean model

Each molecular component represented as network nodes or Boolean variables may have two categorical states: “activated” or “inactivated”. Numerically, such states can be represented by the elements of the set {0,1} as follows: 0 for “inactivated” and 1 for “activated”. The transition of state for all network nodes is a logical function f that depends on the previous state of other nodes, that is:1 xi(t+1)=fi(x1t,x2(t),…xk(t))

Where xi(t+1) is the current state of the node i at time t+1, fi is the logic function that controls state transition depending on the previous state of nodes x1t,x2(t),…xk(t). Importantly, each logic function was constructed using logic operators {AND, NOT, OR}, depending on the context of biological interactions of each molecular node of the network. For instance, to express situations in which two or more biological regulators must interact to induce the expression or activation of some downstream molecule, the “AND” operator will be used. Likewise, when two or more biological regulators can optionally activate a downstream molecule, we use the “OR” operator to express such a condition. Finally, in cases where the presence of a biological regulator inhibits a downstream molecule, we use the “NOT” operator to indicate that the presence of the regulator inhibits this target molecule94,95. For more information on logical rules derivation, see Supplementary Information.

Model assumptions

Our model is based on general assumptions of Boolean models11:The state of each node(variable) can be represented only by two values: 0 (OFF) or 1 (ON) (i.e., there are no intermediate levels of activation). This is a strong assumption, especially in the case of p53 and NF-κB, which show different activation levels96–98.

The regulation of each node can be represented using a combination of logical operators: AND, OR, NOT. Kinetic parameters are not necessary to characterize the system at a qualitative level.

The system dynamics occur in discrete time intervals.

In particular, we also assumed that transcriptional and post-transcriptional regulation occur in similar time intervals (see Supplementary data 1 for details).

Computational implementation

We use the R-package BoolNet99 to calculate the attractors for both models, the GRN reduced one and the GRN original one. In both cases, we used the synchronous and asynchronous update schemes to verify the robustness of attractors with respect to the update strategy. The synchronous update scheme assumes that all components are updated at the same time, while the asynchronous assumes only a random component is updated at each time step95. Specifically, a sampling strategy was used, in which, 5,000,000 random initial states were tested with the synchronous scheme. On the other hand, with the asynchronous scheme, 500,000 random initial states were evaluated. The same attractors were recovered regardless of the update scheme (Supplementary Information). Finally, to simulate the effect of mutations in the system, only the synchronous scheme was used. Using this R-package, we also obtained the basins of attraction for each attractor (i.e., the set of network states that converge on a specific attractor) and the size of these basins (i.e., the number of network configurations that converge on a particular attractor). The sizes of basins of attraction were indicated as a percentage of the state space.

Reduction of the network

The complexity of the network was reduced without losing its essential biological information using the following algorithm61: For each node removed (yj) with an associated function fyj such that fyj does not depend on yj: (1) If z, with an associated function fz, was a vertex governed by yj, then the function fzy1,...,yj,...,yk was replaced by fzy1,...,fyj,...,yk. (2) Then, fz was simplified using Boolean algebra to remove non-functional variables. (3) If the node x regulates the node yj and yj regulates the node z, that is: x→yj and yj→ z, we placed: x→z. Finally, we verify the reduction of the model using the GINsim software62. For details, see Supplementary Information.

Validation

To validate the model, loss, and gain-of-function mutations were simulated, and verifying that the behavior of the model corresponded to the experimental qualitative observations. All gain-of-function mutations were implemented by setting to one the value of each mutated node. Similarly, for all loss-of-function mutations, the value of mutated nodes was fixed at zero.

Robustness of the Boolean model

To test the robustness of the network against stochastic perturbations, we first solved the Boolean model of the network (i.e., the attractors and their basins of attraction were recovered). After that, we pick each state of the model and set it as the initial configuration of the network. At each time step of the simulation, stochastic noise was applied to the Boolean functions given by the following equation:2 xit+1=fit,ifP=1−η1−fit,ifP=η

The probability (P) that each logical rule obeyed its normal behavior, or changed the output value, was calculated. In all cases, the noise level for the logical rules was set as η=0.01. Subsequently, the basin of attraction to which the successor state belonged was identified. It was determined whether or not the system had transited to another basin of attraction. Each event was counted, and this procedure was repeated 1000 times for each state network. Finally, the number of times each basin of attraction was reached was divided by the total number of initial configurations of each basin. The diagonal of the Markov matrix that we obtain indicates the probability of staying in the same basin of attraction73. The probability close to 1 indicates that the model is robust. This procedure was used to measure the robustness of the attractors in the WT and “mutated” models. It was implemented with the R-script previously published by ref. 39.

Stability of the network

We tested the relative stability of each fixed point by calculating the mean first passage time (MFPT), that is the number of average steps required to transit from an attractor i to an attractor j for the first time. The value of the MFPT is proportional to the barrier or difficulty to transit between two given attractors, which means this metric quantifies the barrier to transition among phenotypes. We calculated the MFPT from the transition probability matrix following the procedure and R-scripts described by39.

Based on MFPT, the network transition index between two attractors (dij) was calculated as follows:3 dij=1MFPTi,j−1MFPTj,i

Where dij > 0 implies that attractor i is more stable than attractor j.

Supplementary information

Supplementary Information

Supplementary data 1

Supplementary information

The online version contains supplementary material available at 10.1038/s41540-024-00422-9.

Acknowledgements

Elena R. Álvarez-Buylla and Juan Carlos Martínez-García acknowledge the support from UNAM-DGAPA PAPIIT IN211721 “Patrones genéricos y sistémicos de la diferenciación y la proliferación en los nichos de células troncales: Raíz de Arabidopsis thaliana como sistema de estudio teórico-experimental” and CONACYT-FORDECYT-PRONACES 194186/2020 “Biología matemática y computacional de sistemas médicos: modulación preventiva de la emergencia y progresión de enfermedades crónico-degenerativas.”, respectively. A.H.M. thank CONAHCYT for his doctoral fellowship. A.B. thank CONACYT and Cinvestav-IPN for their designation as “Investigador por México” and for the research support, respectively.

Author contributions

All authors participated in draft redaction, conceptualization, and discussion of data. A.H.M. constructed the model, searched for experimental data, performed simulations, and interpreted the data. A.B. drew graphics, and prepared and interpreted the data. E.R.A.B. and J.C.M.G. conceptualized, supervised, and provided resources.

Data availability

The experimental data that sustains the GRN and their references are available in additional text file 1 (see Supplementary data 1). The complete unreduced GRN model is available in additional text file 2 (see Supplementary Information). The reduction data, along with the reduced GRN model, are available in additional text file 3 (see Supplementary Information). The network attractors with their corresponding basin of attraction obtained by the loss and gain-of-function simulations are available in additional text file 4 (see Supplementary Information).

Code availability

The scripts used in this work are freely available at: https://github.com/AlexisHdez999/epigeneticLandscapeAnalysis.

Competing interests

The authors declare no competing interests.

Ethics approval and consent to participate

Not applicable.

Consent for publication

All authors agree to publish the manuscript.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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