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1.
Noncoding RNA Res ; 9(1): 185-193, 2024 Mar.
Artículo en Inglés | MEDLINE | ID: mdl-38125755

RESUMEN

Patients with non-small cell lung cancer (NSCLC) are often treated with chemotherapy. Poor clinical response and the onset of chemoresistance limit the anti-tumor benefits of drugs such as cisplatin. According to recent research, metastasis-associated lung adenocarcinoma transcript 1 (MALAT1) is a long non-coding RNA related to cisplatin resistance in NSCLC. Furthermore, MALAT1 targets microRNA-145-5p (miR-145), which activates Krüppel-like factor 4 (KLF4) in associated cell lines. B lymphoma Mo-MLV insertion region 1 homolog (BMI1), on the other hand, inhibits miR-145 expression, which stimulates Specificity protein 1 (Sp1) to trigger the epithelial-mesenchymal transition (EMT) process in pemetrexed-resistant NSCLC cells. The interplay between these molecules in drug resistance is still unclear. Therefore, we propose a dynamic Boolean network that can encapsulate the complexity of these drug-resistant molecules. Using published clinical data for gain or loss-of-function perturbations, our network demonstrates reasonable agreement with experimental observations. We identify four new positive circuits: miR-145/Sp1/MALAT1, BMI1/miR-145/Myc, KLF4/p53/miR-145, and miR-145/Wip1/p38MAPK/p53. Notably, miR-145 emerges as a central player in these regulatory circuits, underscoring its pivotal role in NSCLC drug resistance. Our circuit perturbation analysis further emphasizes the critical involvement of these new circuits in drug resistance for NSCLC. In conclusion, targeting MALAT1 and BMI1 holds promise for overcoming drug resistance, while activating miR-145 represents a potential strategy to significantly reduce drug resistance in NSCLC.

2.
Noncoding RNA Res ; 8(4): 605-614, 2023 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-37767112

RESUMEN

Long non-coding RNA (lncRNA) distal-less homeobox 6 antisense RNA 1 (DLX6-AS1) is elevated in a variety of cancers, including non-small cell lung cancer (NSCLC) and cervical cancer. Although it was found that the microRNA-16-5p (miR-16), which is known to regulate autophagy and apoptosis, had been downregulated in similar cancers. Recent research has shown that in tumors with similar characteristics, DLX6-AS1 acts as a sponge for miR-16 expression. However, the cell death-related molecular mechanism of the DLX6-AS1/miR-16 axis has yet to be investigated. Therefore, we propose a dynamic Boolean model to investigate gene regulation in cell death processes via the DLX6-AS1/miR-16 axis. We found the finest concordance when we compared our model to many experimental investigations including gain-of-function genes in NSCLC and cervical cancer. A unique positive circuit involving BMI1/ATM/miR-16 is also something we predict. Our results suggest that this circuit is essential for regulating autophagy and apoptosis under stress signals. Thus, our Boolean network enables an evident cell-death process coupled with NSCLC and cervical cancer. Therefore, our results suggest that DLX6-AS1 targeting may boost miR-16 activity and thereby restrict tumor growth in these cancers by triggering autophagy and apoptosis.

3.
Comput Biol Chem ; 106: 107926, 2023 Oct.
Artículo en Inglés | MEDLINE | ID: mdl-37487252

RESUMEN

The ultimate goal of this study is to analyze the gene regulation between FAM111B and p53 in lung adenocarcinoma using Boolean networks. Recent studies have shown that downregulation of FAM111B enhances the G2/M cell cycle checkpoint in the respective cell lines. Upregulation of p53 directly downregulates FAM111B, which is directed to affect cell cycle controllers Cdc25C and Cdk1/CyclinB, thereby controlling G2/M cell cycle arrest. As for apoptosis, down-regulation of FAM111B by p53 directly regulates the BAG3/Bcl-2 axis, which triggers apoptotic cell death. However, the molecular mechanisms involving p53 and FAM111B in G2/M checkpoint regulation are still unknown. Thus, we present a Boolean model of the G2/M checkpoint considering the effect of p53 and FAM111B. Our model indicates that the cell fate between the two cellular phenotypes, arrest, and apoptosis, at the G2/M checkpoint is non-deterministic and is controlled by p53. The model was compared with the experimental data involving gain- or loss-of-function genes and achieved a fair agreement. The model predicts a positive circuit involving p53/FAM111B/BAG3. Our circuit perturbation analysis suggests that this circuit may be essential for controlling cell-fate decisions at the G2/M checkpoint. Our model supports that FAM111B is an engaging target for drug development in lung adenocarcinoma.


Asunto(s)
Adenocarcinoma del Pulmón , Neoplasias Pulmonares , Humanos , Proteína p53 Supresora de Tumor/genética , Adenocarcinoma del Pulmón/genética , Apoptosis/genética , Oncogenes , Neoplasias Pulmonares/genética , Proteínas Adaptadoras Transductoras de Señales , Proteínas Reguladoras de la Apoptosis , Proteínas de Ciclo Celular
4.
Cells ; 12(7)2023 04 04.
Artículo en Inglés | MEDLINE | ID: mdl-37048159

RESUMEN

Cell fate determination is a complex process that is frequently described as cells traveling on rugged pathways, beginning with DNA damage response (DDR). Tumor protein p53 (p53) and phosphatase and tensin homolog (PTEN) are two critical players in this process. Although both of these proteins are known to be key cell fate regulators, the exact mechanism by which they collaborate in the DDR remains unknown. Thus, we propose a dynamic Boolean network. Our model incorporates experimental data obtained from NSCLC cells and is the first of its kind. Our network's wild-type system shows that DDR activates the G2/M checkpoint, and this triggers a cascade of events, involving p53 and PTEN, that ultimately lead to the four potential phenotypes: cell cycle arrest, senescence, autophagy, and apoptosis (quadra-stable dynamics). The network predictions correspond with the gain-and-loss of function investigations in the additional two cell lines (HeLa and MCF-7). Our findings imply that p53 and PTEN act as molecular switches that activate or deactivate specific pathways to govern cell fate decisions. Thus, our network facilitates the direct investigation of quadruplicate cell fate decisions in DDR. Therefore, we concluded that concurrently controlling PTEN and p53 dynamics may be a viable strategy for enhancing clinical outcomes.


Asunto(s)
Daño del ADN , Fosfohidrolasa PTEN , Proteína p53 Supresora de Tumor , Humanos , Apoptosis , Puntos de Control del Ciclo Celular , Células HeLa , Fosfohidrolasa PTEN/genética , Fosfohidrolasa PTEN/metabolismo , Proteína p53 Supresora de Tumor/genética , Proteína p53 Supresora de Tumor/metabolismo
5.
Sci Rep ; 12(1): 18312, 2022 10 31.
Artículo en Inglés | MEDLINE | ID: mdl-36316351

RESUMEN

The lncRNA GAS5 acts as a tumor suppressor and is downregulated in gastric cancer (GC). In contrast, E2F1, an important transcription factor and tumor promoter, directly inhibits miR-34c expression in GC cell lines. Furthermore, in the corresponding GC cell lines, lncRNA GAS5 directly targets E2F1. However, lncRNA GAS5 and miR-34c remain to be studied in conjunction with GC. Here, we present a dynamic Boolean network to classify gene regulation between these two non-coding RNAs (ncRNAs) in GC. This is the first study to show that lncRNA GAS5 can positively regulate miR-34c in GC through a previously unknown molecular pathway coupling lncRNA/miRNA. We compared our network to several in-vivo/in-vitro experiments and obtained an excellent agreement. We revealed that lncRNA GAS5 regulates miR-34c by targeting E2F1. Additionally, we found that lncRNA GAS5, independently of p53, inhibits GC proliferation through the ATM/p38 MAPK signaling pathway. Accordingly, our results support that E2F1 is an engaging target of drug development in tumor growth and aggressive proliferation of GC, and favorable results can be achieved through tumor suppressor lncRNA GAS5/miR-34c axis in GC. Thus, our findings unlock a new avenue for GC treatment in response to DNA damage by these ncRNAs.


Asunto(s)
MicroARNs , ARN Largo no Codificante , Neoplasias Gástricas , Humanos , Línea Celular Tumoral , Proliferación Celular/genética , Daño del ADN/genética , Regulación Neoplásica de la Expresión Génica , MicroARNs/genética , MicroARNs/metabolismo , ARN Largo no Codificante/genética , ARN Largo no Codificante/metabolismo , Neoplasias Gástricas/patología
6.
Biology (Basel) ; 11(4)2022 Mar 22.
Artículo en Inglés | MEDLINE | ID: mdl-35453680

RESUMEN

The long non-coding RNA X inactivate-specific transcript (lncRNA XIST) has been verified as an oncogenic gene in non-small cell lung cancer (NSCLC) whose regulatory role is largely unknown. The important tumor suppressors, microRNAs: miR-449a and miR-16 are regulated by lncRNA XIST in NSCLC, these miRNAs share numerous common targets and experimental evidence suggests that they synergistically regulate the cell-fate regulation of NSCLC. LncRNA XIST is known to sponge miR-449a and miR-34a, however, the regulatory network connecting all these non-coding RNAs is still unknown. Here we propose a Boolean regulatory network for the G1/S cell cycle checkpoint in NSCLC contemplating the involvement of these non-coding RNAs. Model verification was conducted by comparison with experimental knowledge from NSCLC showing good agreement. The results suggest that miR-449a regulates miR-16 and p21 activity by targeting HDAC1, c-Myc, and the lncRNA XIST. Furthermore, our circuit perturbation simulations show that five circuits are involved in cell fate determination between senescence and apoptosis. The model thus allows pinpointing the direct cell fate mechanisms of NSCLC. Therefore, our results support that lncRNA XIST is an attractive target of drug development in tumor growth and aggressive proliferation of NSCLC, and promising results can be achieved through tumor suppressor miRNAs.

7.
Sci Rep ; 12(1): 4911, 2022 03 22.
Artículo en Inglés | MEDLINE | ID: mdl-35318393

RESUMEN

Transfection of tumor suppressor miRNAs such as miR-34a, miR-449a, and miR-16 with DNA damage can regulate apoptosis and senescence in cancer cells. miR-16 has been shown to influence autophagy in cervical cancer. However, the function of miR-34a and miR-449a in autophagy remains unknown. The functional and persistent G1/S checkpoint signaling pathways in HeLa cells via these three miRNAs, either synergistically or separately, remain a mystery. As a result, we present a synthetic Boolean network of the functional G1/S checkpoint regulation, illustrating the regulatory effects of these three miRNAs. To our knowledge, this is the first synthetic Boolean network that demonstrates the advanced role of these miRNAs in cervical cancer signaling pathways reliant on or independent of p53, such as MAPK or AMPK. We compared our estimated probability to the experimental data and found reasonable agreement. Our findings indicate that miR-34a or miR-16 may control senescence, autophagy, apoptosis, and the functional G1/S checkpoint. Additionally, miR-449a can regulate just senescence and apoptosis on an individual basis. MiR-449a can coordinate autophagy in HeLa cells in a synergistic manner with miR-16 and/or miR-34a.


Asunto(s)
MicroARNs , Neoplasias del Cuello Uterino , Apoptosis/genética , Autofagia/genética , Línea Celular Tumoral , Femenino , Regulación Neoplásica de la Expresión Génica , Células HeLa , Humanos , MicroARNs/genética , MicroARNs/metabolismo , Transducción de Señal , Neoplasias del Cuello Uterino/genética
8.
Biomolecules ; 12(3)2022 03 09.
Artículo en Inglés | MEDLINE | ID: mdl-35327612

RESUMEN

Long non-coding RNA (lncRNA) such as ANRIL and UFC1 have been verified as oncogenic genes in non-small cell lung cancer (NSCLC). It is well known that the tumor suppressor microRNA-34a (miR-34a) is downregulated in NSCLC. Furthermore, miR-34a induces senescence and apoptosis in breast, glioma, cervical cancer including NSCLC by targeting Myc. Recent evidence suggests that these two lncRNAs act as a miR-34a sponge in corresponding cancers. However, the biological functions between these two non-coding RNAs (ncRNAs) have not yet been studied in NSCLC. Therefore, we present a Boolean model to analyze the gene regulation between these two ncRNAs in NSCLC. We compared our model to several experimental studies involving gain- or loss-of-function genes in NSCLC cells and achieved an excellent agreement. Additionally, we predict three positive circuits involving miR-34a/E2F1/ANRIL, miR-34a/E2F1/UFC1, and miR-34a/Myc/ANRIL. Our circuit- perturbation analysis shows that these circuits are important for regulating cell-fate decisions such as senescence and apoptosis. Thus, our Boolean network permits an explicit cell-fate mechanism associated with NSCLC. Therefore, our results support that ANRIL and/or UFC1 is an attractive target for drug development in tumor growth and aggressive proliferation of NSCLC, and that a valuable outcome can be achieved through the miRNA-34a/Myc pathway.


Asunto(s)
Carcinoma de Pulmón de Células no Pequeñas , Neoplasias Pulmonares , MicroARNs , ARN Largo no Codificante , Apoptosis/genética , Carcinoma de Pulmón de Células no Pequeñas/genética , Carcinoma de Pulmón de Células no Pequeñas/patología , Línea Celular Tumoral , Proliferación Celular/genética , Regulación Neoplásica de la Expresión Génica , Humanos , Neoplasias Pulmonares/genética , Neoplasias Pulmonares/patología , MicroARNs/genética , MicroARNs/metabolismo , Oncogenes , ARN Largo no Codificante/genética , ARN Largo no Codificante/metabolismo , Enzimas Ubiquitina-Conjugadoras/genética
9.
Genes Cancer ; 7(9-10): 323-339, 2016 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-28050233

RESUMEN

According to the World Health Organization (WHO), Plasmodium falciparum is the deadliest parasite among all species. This parasite possesses the ability to sense molecules, including melatonin (MEL) and cAMP, and modulate its cell cycle accordingly. MEL synchronizes the development of this malaria parasite by activating several cascades, including the generation of the second messenger cAMP. Therefore, we performed RNA sequencing (RNA-Seq) analysis in P. falciparum erythrocytic stages (ring, trophozoite and schizont) treated with MEL and cAMP. To investigate the expression profile of P. falciparum genes regulated by MEL and cAMP, we performed RNA-Seq analysis in three P. falciparum strains (control, 3D7; protein kinase 7 knockout, PfPK7-; and PfPK7 complement, PfPK7C). In the 3D7 strain, 38 genes were differentially expressed upon MEL treatment; however, none of the genes in the trophozoite (T) stage PfPK7- knockout parasites were differentially expressed upon MEL treatment for 5 hours compared to untreated controls, suggesting that PfPK7 may be involved in the signaling leading to differential gene expression. Moreover, we found that MEL modified the mRNA expression of genes encoding membrane proteins, zinc ion-binding proteins and nucleic acid-binding proteins, which might influence numerous functions in the parasite. The RNA-Seq data following treatment with cAMP show that this molecule modulates different genes throughout the intraerythrocytic cycle, namely, 75, 101 and 141 genes, respectively, in the ring (R), T and schizont (S) stages. Our results highlight P. falciparum's perception of the external milieu through the signaling molecules MEL and cAMP, which are able to drive to changes in gene expression in the parasite.

10.
BMC Bioinformatics ; 16 Suppl 19: S9, 2015.
Artículo en Inglés | MEDLINE | ID: mdl-26696568

RESUMEN

BACKGROUND: Complex diseases are characterized as being polygenic and multifactorial, so this poses a challenge regarding the search for genes related to them. With the advent of high-throughput technologies for genome sequencing, gene expression measurements (transcriptome), and protein-protein interactions, complex diseases have been sistematically investigated. Particularly, Protein-Protein Interaction (PPI) networks have been used to prioritize genes related to complex diseases according to its topological features. However, PPI networks are affected by ascertainment bias, in which more studied proteins tend to have more connections, degrading the results quality. Additionally, methods using only PPI networks can provide only static and non-specific results, since the topologies of these networks are not specific of a given disease. RESULTS: The goal of this work is to develop a methodology that integrates PPI networks with disease specific data sources, such as GWAS and gene expression, to find genes more specific of a given complex disease. After the integration of PPI networks and gene expression data, the resulting network is used to connect genes related to the disease through the shortest paths that have the greatest concordance between their gene expressions. Both case and control expression data are used separately and, at the end, the most altered genes between the two conditions are selected. To evaluate the method, schizophrenia was adopted as case study. CONCLUSION: Results show that the proposed method successfully retrieves differentially coexpressed genes in two conditions, while avoiding the bias from literature. Moreover we were able to achieve a greater concordance in the selection of important genes from different microarray studies of the same disease and to produce a more specific gene set related to the studied disease.


Asunto(s)
Biología Computacional/métodos , Enfermedad/genética , Mapas de Interacción de Proteínas , Algoritmos , Bases de Datos de Proteínas , Genes , Humanos , Reproducibilidad de los Resultados
11.
Gene ; 541(2): 129-37, 2014 May 15.
Artículo en Inglés | MEDLINE | ID: mdl-24631265

RESUMEN

Inference of gene regulatory networks (GRNs) is one of the most challenging research problems of Systems Biology. In this investigation, a new GRNs inference methodology, called Entropic Biological Score (EBS), which linearly combines the mean conditional entropy (MCE) from expression levels and a Biological Score (BS), obtained by integrating different biological data sources, is proposed. The EBS is validated with the Cell Cycle related functional annotation information, available from Munich Information Center for Protein Sequences (MIPS), and compared with some existing methods like MRNET, ARACNE, CLR and MCE for GRNs inference. For real networks, the performance of EBS, which uses the concept of integrating different data sources, is found to be superior to the aforementioned inference methods. The best results for EBS are obtained by considering the weights w1=0.2 and w2=0.8 for MCE and BS values, respectively, where approximately 40% of the inferred connections are found to be correct and significantly better than related methods. The results also indicate that expression profile is able to recover some true connections, that are not present in biological annotations, thus leading to the possibility of discovering new relations between its genes.


Asunto(s)
Ciclo Celular/genética , Biología Computacional/métodos , Redes Reguladoras de Genes , Entropía , Expresión Génica , Modelos Teóricos , Fenotipo , Mapeo de Interacción de Proteínas
12.
Artículo en Inglés | MEDLINE | ID: mdl-23702542

RESUMEN

Models of gene regulatory networks (GRN) have been proposed along with algorithms for inferring their structure. By structure, we mean the relationships among the genes of the biological system under study. Despite the large number of genes found in the genome of an organism, it is believed that a small set of genes is responsible for maintaining a specific core regulatory mechanism (small subnetworks). We propose an algorithm for inference of subnetworks of genes from a small initial set of genes called seed and time series gene expression data. The algorithm has two main steps: First, it grows the seed of genes by adding genes to it, and second, it searches for subnetworks that can be biologically meaningful. The seed growing step is treated as a feature selection problem and we used a thresholded Boolean network with a perturbation model to design the criterion function that is used to select the features (genes). Given that the reverse engineering of GRN is a problem that does not necessarily have one unique solution, the proposed algorithm has as output a set of networks instead of one single network. The algorithm also analyzes the dynamics of the networks which can be time-consuming. Nevertheless, the algorithm is suitable when the number of genes is small. The results showed that the algorithm is capable of recovering an acceptable rate of gene interactions and to generate regulatory hypotheses that can be explored in the wet lab.


Asunto(s)
Algoritmos , Biología Computacional/métodos , Redes Reguladoras de Genes , Modelos Genéticos , Ciclo Celular/genética , Genes Fúngicos , Ingeniería Genética , Modelos Estadísticos , Saccharomyces cerevisiae/genética , Proteínas de Saccharomyces cerevisiae/genética
13.
BMC Genomics ; 13 Suppl 6: S7, 2012.
Artículo en Inglés | MEDLINE | ID: mdl-23134775

RESUMEN

BACKGROUND: A current challenge in gene annotation is to define the gene function in the context of the network of relationships instead of using single genes. The inference of gene networks (GNs) has emerged as an approach to better understand the biology of the system and to study how several components of this network interact with each other and keep their functions stable. However, in general there is no sufficient data to accurately recover the GNs from their expression levels leading to the curse of dimensionality, in which the number of variables is higher than samples. One way to mitigate this problem is to integrate biological data instead of using only the expression profiles in the inference process. Nowadays, the use of several biological information in inference methods had a significant increase in order to better recover the connections between genes and reduce the false positives. What makes this strategy so interesting is the possibility of confirming the known connections through the included biological data, and the possibility of discovering new relationships between genes when observed the expression data. Although several works in data integration have increased the performance of the network inference methods, the real contribution of adding each type of biological information in the obtained improvement is not clear. METHODS: We propose a methodology to include biological information into an inference algorithm in order to assess its prediction gain by using biological information and expression profile together. We also evaluated and compared the gain of adding four types of biological information: (a) protein-protein interaction, (b) Rosetta stone fusion proteins, (c) KEGG and (d) KEGG+GO. RESULTS AND CONCLUSIONS: This work presents a first comparison of the gain in the use of prior biological information in the inference of GNs by considering the eukaryote (P. falciparum) organism. Our results indicates that information based on direct interaction can produce a higher improvement in the gain than data about a less specific relationship as GO or KEGG. Also, as expected, the results show that the use of biological information is a very important approach for the improvement of the inference. We also compared the gain in the inference of the global network and only the hubs. The results indicates that the use of biological information can improve the identification of the most connected proteins.


Asunto(s)
Redes Reguladoras de Genes , Algoritmos , Bases de Datos Genéticas , Genoma , Plasmodium falciparum/genética , Mapas de Interacción de Proteínas , Proteínas/metabolismo
14.
BMC Proc ; 5 Suppl 2: S5, 2011 May 28.
Artículo en Inglés | MEDLINE | ID: mdl-21554763

RESUMEN

BACKGROUND: A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it. RESULTS: We applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered. CONCLUSIONS: The algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.

15.
Bioinformatics ; 20(8): 1241-7, 2004 May 22.
Artículo en Inglés | MEDLINE | ID: mdl-14871865

RESUMEN

MOTIVATION: A number of models have been proposed for genetic regulatory networks. In principle, a network may contain any number of genes, so long as data are available to make inferences about their relationships. Nevertheless, there are two important reasons why the size of a constructed network should be limited. Computationally and mathematically, it is more feasible to model and simulate a network with a small number of genes. In addition, it is more likely that a small set of genes maintains a specific core regulatory mechanism. RESULTS: Subnetworks are constructed in the context of a directed graph by beginning with a seed consisting of one or more genes believed to participate in a viable subnetwork. Functionalities and regulatory relationships among seed genes may be partially known or they may simply be of interest. Given the seed, we iteratively adjoin new genes in a manner that enhances subnetwork autonomy. The algorithm is applied using both the coefficient of determination and the Boolean-function influence among genes, and it is illustrated using a glioma gene-expression dataset. AVAILABILITY: Software for the seed-growing algorithm will be available at the website for Probabilistic Boolean Networks: http://www2.mdanderson.org/app/ilya/PBN/PBN.htm


Asunto(s)
Algoritmos , Perfilación de la Expresión Génica/métodos , Regulación de la Expresión Génica/fisiología , Glioma/genética , Melanoma/genética , Modelos Genéticos , Transducción de Señal/genética , Animales , Simulación por Computador , Evolución Molecular , Variación Genética , Humanos , Modelos Estadísticos , Transcripción Genética/genética
16.
Comp Funct Genomics ; 4(6): 601-8, 2003.
Artículo en Inglés | MEDLINE | ID: mdl-18629023

RESUMEN

Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes.

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