Boolean Model Research Articles

Partial-order Boolean games: informational independence in a logic-based model of strategic interaction

As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a game. More precisely, dependency graphs play two roles. First, when we say that variable x depends on variable y, then we mean that when a strategy assigns a value to variable x, it can be informed by the value that has been assigned to y. Second, and as a consequence of the first property, they capture a richer and more plausible model of concurrency than the simultaneous-action model implicit in conventional Boolean games. Dependency graphs implicitly define a partial ordering of the run-time events in a game: if x is dependent on y, then the assignment of a value to y must precede the assignment of a value to x; if x and y are independent, however, then we can say nothing about the ordering of assignments to these variables—the assignments may occur concurrently. We refer to Boolean games with dependency graphs as partial-order Boolean games. After motivating and presenting the partial-order Boolean games model, we explore its properties. We show that while some problems associated with our new games have the same complexity as in conventional Boolean games, for others the complexity blows up dramatically. We also show that the concurrency in partial-order Boolean games can be modelled using a closure-operator semantics, and conclude by considering the relationship of our model to Independence-Friendly (IF) logic.

Invariance Under Quasi-isometries of Subcritical and Supercritical Behavior in the Boolean Model of Percolation

In this work we study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. In other words, we prove that if the Poisson Boolean model of percolation is subcritical or supercritical (or exhibits phase transition) in a metric space M which is mm-quasi-isometric to a metric space N, then these phases also exist for the Poisson Boolean model of percolation in N. Then we apply these results to understand the phenomenon of phase transition in a large family of metric spaces. Indeed, we study the Poisson Boolean model of percolation in the context of Riemannian manifolds, in a large family of nilpotent Lie groups and in Cayley graphs. Also, we prove the existence of a subcritical phase in Gromov spaces with bounded growth at some scale.

Deriving Boolean structures from distributional vectors

Corpus-based distributional semantic models capture degrees of semantic relatedness among the words of very large vocabularies, but have problems with logical phenomena such as entailment, that are instead elegantly handled by model-theoretic approaches, which, in turn, do not scale up. We combine the advantages of the two views by inducing a mapping from distributional vectors of words (or sentences) into a Boolean structure of the kind in which natural language terms are assumed to denote. We evaluate this Boolean Distributional Semantic Model (BDSM) on recognizing entailment between words and sentences. The method achieves results comparable to a state-of-the-art SVM, degrades more gracefully when less training data are available and displays interesting qualitative properties.

New scaling relation for information transfer in biological networks.

We quantify characteristics of the informational architecture of two representative biological networks: the Boolean network model for the cell-cycle regulatory network of the fission yeast Schizosaccharomyces pombe (Davidich et al. 2008 PLoS ONE 3, e1672 (doi:10.1371/journal.pone.0001672)) and that of the budding yeast Saccharomyces cerevisiae (Li et al. 2004 Proc. Natl Acad. Sci. USA 101, 4781-4786 (doi:10.1073/pnas.0305937101)). We compare our results for these biological networks with the same analysis performed on ensembles of two different types of random networks: Erdös-Rényi and scale-free. We show that both biological networks share features in common that are not shared by either random network ensemble. In particular, the biological networks in our study process more information than the random networks on average. Both biological networks also exhibit a scaling relation in information transferred between nodes that distinguishes them from random, where the biological networks stand out as distinct even when compared with random networks that share important topological properties, such as degree distribution, with the biological network. We show that the most biologically distinct regime of this scaling relation is associated with a subset of control nodes that regulate the dynamics and function of each respective biological network. Information processing in biological networks is therefore interpreted as an emergent property of topology (causal structure) and dynamics (function). Our results demonstrate quantitatively how the informational architecture of biologically evolved networks can distinguish them from other classes of network architecture that do not share the same informational properties.

Combinatorial interventions inhibit TGFβ-driven epithelial-to-mesenchymal transition and support hybrid cellular phenotypes.

Epithelial-to-mesenchymal transition (EMT) is a developmental process hijacked by cancer cells to leave the primary tumor site, invade surrounding tissue and establish distant metastases. A hallmark of EMT is the loss of E-cadherin expression, and one major signal for the induction of EMT is transforming growth factor beta (TGFβ), which is dysregulated in up to 40% of hepatocellular carcinoma (HCC). We aim to identify network perturbations that suppress TGFβ-driven EMT, with the goal of suppressing invasive properties of cancer cells. We use a systems-level Boolean dynamic model of EMT to systematically screen individual and combination perturbations (inhibition or constitutive activation of up to four nodes). We use a recently developed network control approach to understand the mechanism through which the combinatorial interventions suppress EMT. We test the results of our in silico analysis using siRNA. Our model predicts that targeting key elements of feedback loops in combination with the SMAD complex is more effective than suppressing the SMAD complex alone. We demonstrate experimentally that expression of a majority of these elements is enriched in mesenchymal relative to epithelial phenotype HCC cell lines. An siRNA screen of the predicted combinations confirms that many targeting strategies suppress TGFβ-driven EMT measured by E-cadherin expression and cell migration. Our analysis reveals that some perturbations give rise to hybrid states intermediate to the epithelial and mesenchymal states. Our results indicate that EMT is driven by an interconnected signaling network and many apparently successful single interventions may lead to steady states that are in-between epithelial and mesenchymal states. As these putative hybrid or partial EMT states may retain invasive properties, our results suggest that combinatorial therapies are necessary to fully suppress invasive properties of tumor cells.

Integrated network model provides new insights into castration-resistant prostate cancer.

Castration-resistant prostate cancer (CRPC) is the main challenge for prostate cancer treatment. Recent studies have indicated that extending the treatments to simultaneously targeting different pathways could provide better approaches. To better understand the regulatory functions of different pathways, a system-wide study of CRPC regulation is necessary. For this purpose, we constructed a comprehensive CRPC regulatory network by integrating multiple pathways such as the MEK/ERK and the PI3K/AKT pathways. We studied the feedback loops of this network and found that AKT was involved in all detected negative feedback loops. We translated the network into a predictive Boolean model and analyzed the stable states and the control effects of genes using novel methods. We found that the stable states naturally divide into two obvious groups characterizing PC3 and DU145 cells respectively. Stable state analysis further revealed that several critical genes, such as PTEN, AKT, RAF, and CDKN2A, had distinct expression behaviors in different clusters. Our model predicted the control effects of many genes. We used several public datasets as well as FHL2 overexpression to verify our finding. The results of this study can help in identifying potential therapeutic targets, especially simultaneous targets of multiple pathways, for CRPC.

Boolean modeling identifies Greatwall/MASTL as an important regulator in the AURKA network of neuroblastoma

Aurora Kinase A (AURKA) is often overexpressed in neuroblastoma (NB) with poor outcome. The causes of AURKA overexpression in NB are unknown. Here, we describe a gene regulatory network consisting of core regulators of AURKA protein expression and activation during mitosis to identify potential causes. This network was transformed to a dynamic Boolean model. Simulated activation of the serine/threonine protein kinase Greatwall (GWL, encoded by MASTL) that attenuates the pivotal AURKA inhibitor PP2A, predicted stabilization of AURKA. Consistent with this notion, gene set enrichment analysis showed enrichment of mitotic spindle assembly genes and MYCN target genes in NB with high GWL/MASTL expression. In line with the prediction of GWL/MASTL enhancing AURKA, elevated expression of GWL/MASTL was associated with NB risk factors and poor survival of patients. These results establish Boolean network modeling of oncogenic pathways in NB as a useful means for guided discovery in this enigmatic cancer.

Abstract B2-28: The development of an individualized Boolean network model for targeted anticancer therapy of glioblastoma

Abstract Understanding the complexity of a cancer signaling network contributed to the discovery of potential targets for therapeutic intervention. Mathematical and computational models have been developed and investigated to predict the molecular dynamics during cancer development and drug treatment. Recent studies analyzing large-scale patient data, however, showed that genetic alterations are dramatically different among patients even for the same type of cancer, and that different therapeutic strategies should be employed for the patients. To resolve this problem using Boolean network modeling and analysis, we have integrated genome-wide data of glioblastoma patients from TCGA database and constructed an individualized network model for each patient. We defined three attractor states that represent different cell fates: proliferation, cell cycle arrest, and apoptosis. We then applied the information of patient-specific genetic alterations to the Boolean model by adjusting the interaction weights of the mutated molecules, and investigated the change of attractors for each patient. Finally, we have investigated the targeted therapy for each patient by performing perturbation analysis of the individualized network model to find the optimal drug combination. Together, our study provides a new insight into the impact of genetic alterations on the drug responses and the patient-specific therapeutic strategies. Acknowledgements: This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea Government, the Ministry of Science, ICT & Future Planning (2014R1A2A1A10052404, 2013M3A9A7046303, and 2010-0017662) and by the KUSTAR-KAIST Institute, Korea, under the R&D program supervised by the KAIST. Citation Format: Hwang-Yeol Lee, Kwang-Hyun Cho. The development of an individualized Boolean network model for targeted anticancer therapy of glioblastoma. [abstract]. In: Proceedings of the AACR Special Conference on Computational and Systems Biology of Cancer; Feb 8-11 2015; San Francisco, CA. Philadelphia (PA): AACR; Cancer Res 2015;75(22 Suppl 2):Abstract nr B2-28.

Abstract B2-27: Systems biological identification of optimal drug targets for combination therapy of non-small cell lung cancer

Abstract Non-small cell lung cancer (NSCLC) is the major subtype of lung cancer, accounting for about 85% of all lung patients. Recently, molecularly targeted inhibitors of receptor tyrosine kinase (RTK) such as epidermal growth factor receptor (EGFR) and fibroblast growth factor receptor (FGFR) signalling pathways have been highlighted as promising anti-tumor drugs because of the prevalence of genetic alterations within EGFR and FGFR signalling pathways in NSCLC patients. However, their functional effects have been reported as varying over a wide range depending on the patient-specific mutational conditions. To understand the underlying mechanism of the heterogeneous responses to EGFR and FGFR inhibitors and to find the optimal strategy for combination therapy, we have developed an integrative Boolean network model of EGFR, FGFR and DNA damage signalling pathways by integrating previous experimental evidences from the literature. Systematic perturbation analysis revealed that the multiple feedback regulations embedded in the signalling pathways play important roles in determining the responses to EGFR and FGFR inhibitors. We further analyzed the mechanism for the heterogeneous responses of cells to the EGFR and FGFR inhibitors under various mutational conditions and identified key genetic alterations that can lead to undesirable responses. Finally, extensive combinatorial perturbation analysis and subsequent comparison of the attractor profiles in the presence and absence of targeted inhibitors identified novel candidate drug targets for combinatorial therapy. Our analysis provides a new insight into the underlying mechanism of the heterogeneous cellular responses to EGFR and FGFR inhibitors and the optimal combinatorial treatment strategies. Acknowledgements: This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea Government, the Ministry of Science, ICT & Future Planning (2014R1A2A1A10052404, 2013M3A9A7046303, and 2010-0017662) and by a grant of the Korean Health Technology R&D Project, Ministry of Health & Welfare, Republic of Korea. (HI13C2162). Citation Format: Jonghoon Lee, Kwang-Hyun Cho. Systems biological identification of optimal drug targets for combination therapy of non-small cell lung cancer. [abstract]. In: Proceedings of the AACR Special Conference on Computational and Systems Biology of Cancer; Feb 8-11 2015; San Francisco, CA. Philadelphia (PA): AACR; Cancer Res 2015;75(22 Suppl 2):Abstract nr B2-27.

Abstract B1-16: Attractor analysis of p53 gene network in colon cancer

Abstract Colon cancer is a heterogeneous and complex disease. Mutation of the p53 gene is most commonly observed in many people with colon cancer [1-2]. In this regard, to understand how the p53 network controls cell fate, it is important not only to identify the network components and their molecular interactions but also to study essential network properties at the system level [3]. However, the molecular mechanisms remain largely unexplored. Here, we used Boolean network modeling and attractor landscape analysis to analyze the state transition dynamics of a simplified p53 network. We first constructed a simplified Boolean network model with multiple feedback loops through p53 for analyzing the p53 network. After building the simplified p53 regulatory network, we modeled the network dynamics using a Boolean network with a set of state transition logics defined on the basis of biological evidence. Attractor landscape analysis of dynamics and its regulation can identify potential therapeutic strategies for treating cancer. Citation Format: Man-Sun Kim, Jeong-Rae Kim. Attractor analysis of p53 gene network in colon cancer. [abstract]. In: Proceedings of the AACR Special Conference on Computational and Systems Biology of Cancer; Feb 8-11 2015; San Francisco, CA. Philadelphia (PA): AACR; Cancer Res 2015;75(22 Suppl 2):Abstract nr B1-16.

Synchronization of Asynchronous Switched Boolean Network.

In this paper, the complete synchronizations for asynchronous switched Boolean network with free Boolean sequence controllers and close-loop controllers are studied. First, the basic asynchronous switched Boolean network model is provided. With the method of semi-tensor product, the Boolean dynamics is translated into linear representation. Second, necessary and sufficient conditions for ASBN synchronization with free Boolean sequence control and close-loop control are derived, respectively. Third, some illustrative examples are provided to show the efficiency of the proposed methods.

Eric Harris Davidson: A systems biologist who studied how genomes function.

The phrase “force of nature” has popped up repeatedly in social media responses to the announcement of Eric Davidson’s death on September 1, 2015. This sobriquet reflects his huge influence on the fields of developmental biology and evolution. His career began about the time Watson and Crick published the structure of DNA, and his contributions continued into the genomic era in which we are now immersed. But his stature wasn’t due to this timing. As Pasteur once said: “Dans les champs de l’observation le hasard ne favorise que les esprits prepares.” (“In the fields of observation chance favors only the prepared mind”). Perhaps Eric’s strong focus on the function of the genome and his great intellect also contributed to this influence. His unwavering focus on how the genome does its job must also play a role. Furthermore, he clearly took genuine delight in confronting complex biological problems, and he erected broad views of the process of nature. This point is documented in his dedication to the third edition of Gene Activity in Early Development, where he credits his father with teaching him about organizing complex perceptions. Eric Davidson was born on April 13, 1937 in New York City, New York. He is the son of Morris and Anne Davidson. His father was a renowned abstract painter of the mid-20th century who maintained a school of painting near Provincetown on Cape Cod, Massachussetts. Eric attended the University of Pennsylvania as an undergraduate, and earned a Ph.D. from Rockefeller University (then Institute). He continued at Rockefeller as a post-doc, and then as assistant professor until 1971. He then moved to the California Institute of Technology, where he remained for the remainder of his career.

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation.

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.

Stochastic Geometry: Boolean model and random geometric graphs

This paper collects the four contributions which were presented during the session devoted to Stochastic Geometry at the journees MAS 2014 . It is focused in particular on several questions related to the transmission of information in a general sense in different random media. The underlying models include the Boolean model, simplicial complexes or geometric random graphs induced by a point process.

The Expanded p53 Interactome as a Predictive Model for Cancer Therapy

The tumor suppressor gene TP53 is implicated in the majority of all human cancers, thus pivotal to genomic integrity. There are more than 72,000 scientific publications describing p53’s function, yet, due to the complexity of its interactions we are still far from fully elucidating p53’s role in tumorigenesis. Computational methodologies are novel tools to depict and dissect complex disease networks. The Boolean PKT206 p53 – DNA damage model has previously demonstrated good predictive capability for p53 wild-type and null tumors in various in silico knockouts. Here, we have expanded PKT206 to generate a more clinically robust representation of p53 dynamics. The new PMH260 model incorporates 260 nodes representing genes, with 980 interactions between them representing inhibitions and activations. Additional biological outputs, including angiogenesis, cell cycle arrest and DNA repair were also amalgamated into the model. Three in silico knockouts of highly connected nodes (p53, MDM2 and FGF2) were generated and logical steady state analysis and dependency relationships applied. 71 % of predictions were considered true from superimposition of human osteosarcoma and HCT116 microarray profiles. In silico knockout analysis revealed 98 potential novel predictions, of which 13 were validated by literature; 83 % of them were overlapping with PKT206. Thus the expanded Boolean PMH260 model offers a promising platform for clinical potential in targeted cancer therapeutics.

Fanconi anemia cells with unrepaired DNA damage activate components of the checkpoint recovery process.

BackgroundThe FA/BRCA pathway repairs DNA interstrand crosslinks. Mutations in this pathway cause Fanconi anemia (FA), a chromosome instability syndrome with bone marrow failure and cancer predisposition. Upon DNA damage, normal and FA cells inhibit the cell cycle progression, until the G2/M checkpoint is turned off by the checkpoint recovery, which becomes activated when the DNA damage has been repaired. Interestingly, highly damaged FA cells seem to override the G2/M checkpoint. In this study we explored with a Boolean network model and key experiments whether checkpoint recovery activation occurs in FA cells with extensive unrepaired DNA damage.MethodsWe performed synchronous/asynchronous simulations of the FA/BRCA pathway Boolean network model. FA-A and normal lymphoblastoid cell lines were used to study checkpoint and checkpoint recovery activation after DNA damage induction. The experimental approach included flow cytometry cell cycle analysis, cell division tracking, chromosome aberration analysis and gene expression analysis through qRT-PCR and western blot.ResultsComputational simulations suggested that in FA mutants checkpoint recovery activity inhibits the checkpoint components despite unrepaired DNA damage, a behavior that we did not observed in wild-type simulations. This result implies that FA cells would eventually reenter the cell cycle after a DNA damage induced G2/M checkpoint arrest, but before the damage has been fixed. We observed that FA-A cells activate the G2/M checkpoint and arrest in G2 phase, but eventually reach mitosis and divide with unrepaired DNA damage, thus resolving the initial checkpoint arrest. Based on our model result we look for ectopic activity of checkpoint recovery components. We found that checkpoint recovery components, such as PLK1, are expressed to a similar extent as normal undamaged cells do, even though FA-A cells harbor highly damaged DNA.ConclusionsOur results show that FA cells, despite extensive DNA damage, do not loss the capacity to express the transcriptional and protein components of checkpoint recovery that might eventually allow their division with unrepaired DNA damage. This might allow cell survival but increases the genomic instability inherent to FA individuals and promotes cancer.

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle.

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.

Dynamic boolean model for the bone marrow intercelular regulation in acute lymphoblastic leukemia

Dynamic boolean model for the bone marrow intercelular regulation in acute lymphoblastic leukemia

Modelling mesoporous alumina microstructure with 3D random models of platelets.

This work focuses on a mesoporous material made up of nanometric alumina 'platelets' of unknown shape. We develope a 3D random microstructure to model the porous material, based on 2D transmission electron microscopy (TEM) images, without prior knowledge on the spatial distribution of alumina inside the material. The TEM images, acquired on samples with thickness 300 nm, a scale much larger than the platelets's size, are too blurry and noisy to allow one to distinguish platelets or platelets aggregates individually. In a first step, the TEM images correlation function and integral range are estimated. The presence of long-range fluctuations, due to the TEM inhomogeneous detection, is detected and corrected by filtering. The corrected correlation function is used as a morphological descriptor for the model. After testing a Boolean model of platelets, a two-scale model of microstructure is introduced to replicate the statistical dispersion of platelets observed on TEM images. Accordingly, a set of two-scale Boolean models with varying physically admissible platelets shapes is proposed. Upon optimization, the model takes into account the dispersion of platelets in the microstructure as observed on TEM images. Comparing it to X-ray diffraction and nitrogen porosimetry data, the model is found to be in good agreement with the material in terms of specific surface area.

Stokes Flow Through a Boolean Model of Spheres: Representative Volume Element

The Stokes flow is numerically computed in porous media based on 3D Boolean random sets of spheres. Two configurations are investigated in which the fluid flows inside the spheres or in the complementary set of the spheres. Full-field computations are carried out using the Fourier method of Wiegmann (2007). The latter is applied to large system sizes representative of the microstructure. The overall permeability of the two models as well as the representative volume element are estimated as a function of the pore volume fraction. We give numerical estimates for the asymptotic behavior of the permeability in the dilute limit for the solid phase, and close to the percolation threshold of the pores. FFT maps of the velocity field are presented, for increasing values of the pore volume fraction. The patterns of the local velocity field is analyzed using various morphological criteria. The tortuosity of the streamlines is found to be much higher than the geometrical tortuosity, for both models. The histograms of the velocity field are computed at increasing pore volume fraction. The covariance of orientation is used to characterize the spatial correlation of the velocity field.