Boolean Model Research Articles

Construction of Discrete Model of Human Pluripotency in Predicting Lineage-Specific Outcomes and Targeted Knockdowns of Essential Genes

A network consisting of 45 core genes was developed for the genes/proteins responsible for loss/gain of function in human pluripotent stem cells. The nodes were included on the basis of literature curation. The initial network topology was further refined by constructing an inferred Boolean model from time-series RNA-seq expression data. The final Boolean network was obtained by integration of the initial topology and the inferred topology into a refined model termed as the integrated model. Expression levels were observed to be bi-modular for most of the genes involved in the mechanism of human pluripotency. Thus, single and combinatorial perturbations/knockdowns were executed using an in silico approach. The model perturbations were validated with literature studies. A number of outcomes are predicted using the knockdowns of the core pluripotency circuit and we are able to establish the minimum requirement for maintenance of pluripotency in human. The network model is able to predict lineage-specific outcomes and targeted knockdowns of essential genes involved in human pluripotency which are challenging to perform due to ethical constraints surrounding human embryonic stem cells.

Modeling the role of microRNA-449a in the regulation of the G2/M cell cycle checkpoint in prostate LNCaP cells under ionizing radiation.

Recent studies showed that induced microRNA-449a (miR-449a) enhances a G2/M cell cycle checkpoint arrest in prostate cancer (LNCaP) and lung adenocarcinoma cell lines. In the case of LNCaP cells, upregulated miR-449a directly downregulates c-Myc that is required to induce the cell cycle regulators Cdc25A and Cdc2/CyclinB whose inactivation blocks G2 to M phase transition. However, the molecular mechanisms involved are yet unclear, although in other prostate cancer cells the interactions among p53, miR-449a and Sirt-1 can affect the induction of the G2/M arrest. In order to clarify these molecular mechanisms, in this work we propose a boolean model of the G2/M checkpoint arrest regulation contemplating the influence of miR-449a. The model shows that the cell fate determination between two cellular phenotypes: G2/M-Arrest for DNA repair and G2/M-induced apoptosis is stochastic and influenced by miR-449a state of activation. The results were compared with experimental data available presenting agreement. We also found that several feedback loops are involved in this cell fate regulation and we indicate, through in silico gain or loss of function perturbations of genes, which of these feedback loops are more efficient to favor a specific phenotype.

Prediction of Mutations to Control Pathways Enabling Tumor Cell Invasion with the CoLoMoTo Interactive Notebook (Tutorial).

Boolean and multi-valued logical formalisms are increasingly used to model complex cellular networks. To ease the development and analysis of logical models, a series of software tools have been proposed, often with specific assets. However, combining these tools typically implies a series of cumbersome software installation and model conversion steps. In this respect, the CoLoMoTo Interactive Notebook provides a joint distribution of several logical modeling software tools, along with an interactive web Python interface easing the chaining of complementary analyses. Our computational workflow combines (1) the importation of a GINsim model and its display, (2) its format conversion using the Java library BioLQM, (3) the formal prediction of mutations using the OCaml software Pint, (4) the model checking using the C++ software NuSMV, (5) quantitative stochastic simulations using the C++ software MaBoSS, and (6) the visualization of results using the Python library matplotlib. To illustrate our approach, we use a recent Boolean model of the signaling network controlling tumor cell invasion and migration. Our model analysis culminates with the prediction of sets of mutations presumably involved in a metastatic phenotype.

Identification of Boolean Network Models From Time Series Data Incorporating Prior Knowledge.

Motivation: Mathematical models take an important place in science and engineering. A model can help scientists to explain dynamic behavior of a system and to understand the functionality of system components. Since length of a time series and number of replicates is limited by the cost of experiments, Boolean networks as a structurally simple and parameter-free logical model for gene regulatory networks have attracted interests of many scientists. In order to fit into the biological contexts and to lower the data requirements, biological prior knowledge is taken into consideration during the inference procedure. In the literature, the existing identification approaches can only deal with a subset of possible types of prior knowledge.Results: We propose a new approach to identify Boolean networks from time series data incorporating prior knowledge, such as partial network structure, canalizing property, positive and negative unateness. Using vector form of Boolean variables and applying a generalized matrix multiplication called the semi-tensor product (STP), each Boolean function can be equivalently converted into a matrix expression. Based on this, the identification problem is reformulated as an integer linear programming problem to reveal the system matrix of Boolean model in a computationally efficient way, whose dynamics are consistent with the important dynamics captured in the data. By using prior knowledge the number of candidate functions can be reduced during the inference. Hence, identification incorporating prior knowledge is especially suitable for the case of small size time series data and data without sufficient stimuli. The proposed approach is illustrated with the help of a biological model of the network of oxidative stress response.Conclusions: The combination of efficient reformulation of the identification problem with the possibility to incorporate various types of prior knowledge enables the application of computational model inference to systems with limited amount of time series data. The general applicability of this methodological approach makes it suitable for a variety of biological systems and of general interest for biological and medical research.

GIS based modeling using Analytic Hierarchy Process (AHP) for optimization of landfill site selection of Rohtak city, Haryana (India)

Landfills are the most common method for the disposal of municipal solid waste the world over, as well as in India due to their low technical and economic requirements. The selection of an appropriate site for the establishment of a landfill is a complex process because it must combine social, environmental and technical parameters. The scientific selection of landfill site is based on several diverse criteria (Land Use and Land Cover, ground water table depth, soil permeability, surface water, roads distance, slop etc) and regulations. The study presents the selection of a site for the establishment of a landfill based on several criteria using geographic information system (GIS) based site suitability modeling and analytical hierarchy process (AHP). Site suitability modeling was implemented using Boolean and Index overlay models. Each criterion and sub criteria was evaluated with the aid of AHP to assign a relative weightage in the index overlay model. Rules and criteria’s set by Central Pollution Control Board (CPCB) and Central Public Health and Environmental Engineering Organisation (CPHEEO) were implemented through Boolean model. The combination of the results of the two models generated a map with several suitable sites. Further selection was done on basis of the size requirement of the site, to handle Municipal solid waste (MSW) for next ten years. Two sites having the maximum suitability and also fulfilling the size requirement were shortlisted. Final selection from the two sites was done by a field survey of the sites. Finally the site B was selected on the basis of field survey which revealed it being better on account of certain factors discussed and social acceptability.

DSGRN: Examining the Dynamics of Families of Logical Models.

We present a computational tool DSGRN for exploring the dynamics of a network by computing summaries of the dynamics of switching models compatible with the network across all parameters. The network can arise directly from a biological problem, or indirectly as the interaction graph of a Boolean model. This tool computes a finite decomposition of parameter space such that for each region, the state transition graph that describes the coarse dynamical behavior of a network is the same. Each of these parameter regions corresponds to a different logical description of the network dynamics. The comparison of dynamics across parameters with experimental data allows the rejection of parameter regimes or entire networks as viable models for representing the underlying regulatory mechanisms. This in turn allows a search through the space of perturbations of a given network for networks that robustly fit the data. These are the first steps toward discovering a network that optimally matches the observed dynamics by searching through the space of networks.

Sharpness of the phase transition and lower bounds for the critical intensity in continuum percolation on $\mathbb{R}^{d}$

Nous considérons le modèle Booléen $Z$ sur $\mathbb{R}^{d}$ avec des grains compacts aléatoires de diamètres bornés, c’est-à-dire $Z:=\bigcup_{i\in\mathbb{N}}(Z_{i}+X_{i})$ où $\{X_{1},X_{2},\dots\}$ est un processus de Poisson d’intensité $t$ et $(Z_{1},Z_{2},\dots)$ est une suite i.i.d. de grains compacts (non nécessairement des boules) de diamètres p.s. bornés par une constante. Nous montrons une décroissance exponentielle dans le régime sous-critique, ce qui veut dire que le volume et le rayon du cluster d’un grain typique dans $Z$ a une queue exponentielle. Pour cela, nous adaptons des résultats de (A new proof of the sharpness of the phase transition for Bernoulli percolation on $\mathbb{Z}^{d}$ (2015) Preprint) et appliquons une nouvelle construction du cluster d’un grain typique avec des arguments issus des processus de branchement. Dans la seconde partie du papier, nous obtenons de nouvelles bornes inférieures pour le modèle booléen avec grains déterministes. Certaines des ces bornes sont rigoureuses, alors que d’autres sont obtenues par simulation. Les bornes obtenues par simulation sont fournies avec des intervalles de confiance et sont beaucoup plus précises que celles obtenues rigoureusement. Elles améliorent les résultats connus (J. Chem. Phys. 137 (2012) 074106) en dimension 6 et plus.

Geometry and Topology of the Boolean Model on a Stationary Point Processes : A Brief Survey

Geometry and Topology of the Boolean Model on a Stationary Point Processes : A Brief Survey

Black-boxing and cause-effect power.

Reductionism assumes that causation in the physical world occurs at the micro level, excluding the emergence of macro-level causation. We challenge this reductionist assumption by employing a principled, well-defined measure of intrinsic cause-effect power–integrated information (Φ), and showing that, according to this measure, it is possible for a macro level to “beat” the micro level. Simple systems were evaluated for Φ across different spatial and temporal scales by systematically considering all possible black boxes. These are macro elements that consist of one or more micro elements over one or more micro updates. Cause-effect power was evaluated based on the inputs and outputs of the black boxes, ignoring the internal micro elements that support their input-output function. We show how black-box elements can have more common inputs and outputs than the corresponding micro elements, revealing the emergence of high-order mechanisms and joint constraints that are not apparent at the micro level. As a consequence, a macro, black-box system can have higher Φ than its micro constituents by having more mechanisms (higher composition) that are more interconnected (higher integration). We also show that, for a given micro system, one can identify local maxima of Φ across several spatiotemporal scales. The framework is demonstrated on a simple biological system, the Boolean network model of the fission-yeast cell-cycle, for which we identify stable local maxima during the course of its simulated biological function. These local maxima correspond to macro levels of organization at which emergent cause-effect properties of physical systems come into focus, and provide a natural vantage point for scientific inquiries.

Network-Based Analysis of Bortezomib Pharmacodynamic Heterogeneity in Multiple Myeloma Cells.

The objective of this study is to evaluate the heterogeneity in pharmacodynamic response in four in vitro multiple myeloma cell lines to treatment with bortezomib, and to assess whether such differences are associated with drug-induced intracellular signaling protein dynamics identified via a logic-based network modeling approach. The in vitro pharmacodynamic-efficacy of bortezomib was evaluated through concentration-effect and cell proliferation dynamical studies in U266, RPMI8226, MM.1S, and NCI-H929 myeloma cell lines. A Boolean logic-based network model incorporating intracellular protein signaling pathways relevant to myeloma cell growth, proliferation, and apoptosis was developed based on information available in the literature and used to identify key proteins regulating bortezomib pharmacodynamics. The time-course of network-identified proteins was measured using the MAGPIX protein assay system. Traditional pharmacodynamic modeling endpoints revealed variable responses of the cell lines to bortezomib treatment, classifying cell lines as more sensitive (MM.1S and NCI-H929) and less sensitive (U266 and RPMI8226). Network centrality and model reduction identified key proteins (e.g., phosphorylated nuclear factor-κB, phosphorylated protein kinase B, phosphorylated mechanistic target of rapamycin, Bcl-2, phosphorylated c-Jun N-terminal kinase, phosphorylated p53, p21, phosphorylated Bcl-2-associated death promoter, caspase 8, and caspase 9) that govern bortezomib pharmacodynamics. The corresponding relative expression (normalized to 0-hour untreated-control cells) of proteins demonstrated a greater magnitude and earlier onset of stimulation/inhibition in cells more sensitive (MM.1S and NCI-H929) to bortezomib-induced cell death at 20 nM, relative to the less sensitive cells (U266 and RPMI8226). Overall, differences in intracellular signaling appear to be associated with bortezomib pharmacodynamic heterogeneity, and key proteins may be potential biomarkers to evaluate bortezomib responses.

Gene regulatory network state estimation from arbitrary correlated measurements

BackgroundAdvancements in gene expression technology allow acquiring cheap and abundant data for analyzing cell behavior. However, these technologies produce noisy, and often correlated, measurements on the transcriptional states of genes. The Boolean network model has been shown to be effective in capturing the complex dynamics of gene regulatory networks (GRNs). It is important in many applications, such as anomaly detection and optimal intervention, to be able to track the evolution of the Boolean states of a gene regulatory network using noisy time-series transcriptional measurements, which may be correlated in time.ResultsWe propose efficient estimators for the Boolean states of GRNs using correlated time-series transcriptional measurements, where the nature of the correlation and of the measurements themselves are entirely arbitrary. More specifically, we propose new algorithms based on a hypothesis tree to compute optimal minimum mean square error (MMSE) filtering and smoothing state estimators for a Partially-Observed Boolean Dynamical System (POBDS) with correlated measurements. The algorithms are exact but may be computationally expensive for large state spaces or long time horizons, in which case a process for pruning the hypothesis tree is employed to obtain an approximation of the optimal MMSE estimators, while keeping computation tractable. Performance is assessed through a comprehensive set of numerical experiments based on the p53-MDM2 negative-feedback loop Boolean regulatory network, where the standard Boolean Kalman Filter (BKF) and Boolean Kalman Smoother (BKS) for uncorrelated measurements are compared to the corresponding new estimators for correlated measurements, called BKF-CORR and BKS-CORR, respectively.

A Boolean Model of Microvascular Rarefaction to Predict Renal Outcomes in Renovascular Disease

Renal microvascular (MV) rarefaction, a hallmark of renovascular disease (RVD), associates with decreased renal vascular endothelial growth factor (VEGF) and progressive renal damage. We designed a novel bioengineered fusion of an elastin‐like polypeptide (ELP) with VEGF, and demonstrated that ELP‐VEGF therapy decreases MV rarefaction, improves renal function, and reduces renal injury in RVD. Renal angioplasty (PTRA) of a stenotic kidney is a frequently used treatment in RVD that often does not ameliorate renal injury. We thus aimed to create a Boolean model of MV rarefaction to predict the renal outcomes of an RVD kidney after ELP‐VEGF therapy following PTRA.We first created a Boolean model with 20 factors known to be involved in MV rarefaction and progression of renal injury in RVD (assuming each to be either totally present/active or totally absent/inactive) to predict the possible pathophysiological states and outcomes after treatments. The model predicts that MV rarefaction and fibrosis remain active following PTRA, driven by a feed‐forward cycle of inflammation and oxidative stress leading to glomerulosclerosis and fibrosis (Figure). When ELP‐VEGF therapy followed PTRA in the simulation, MV rarefaction, glomerulosclerosis, and fibrosis were inactivated. The model predicted that injurious processes driving progressive renal deterioration are decreased only with ELP‐VEGF therapy following PTRA.We next performed in vivo studies. RVD was induced by renal artery stenosis in 12 pigs fed a high‐cholesterol diet. Six weeks later, single‐kidney blood flow (RBF) and filtration (GFR) were quantified in vivo using multi‐detector CT, then pigs were randomized to either PTRA (RVD+PTRA, n=6) or PTRA followed by single intra‐renal injection of ELP‐VEGF (RVD+PTRA+ELP‐VEGF, n=7). Pigs were observed for 4 additional weeks; in vivo CT studies were repeated, then pigs euthanized and ex vivo renal micro‐CT quantification and fibrosis determined. Administration of ELP‐VEGF following PTRA improved RBF, GFR, MV density, and fibrosis more efficiently than PTRA alone.ConclusionThe Boolean model predicted the in vivo/ex vivo data and confirmed pathological mechanisms and the key role of MV damage in renal injury progression. Our results may support the use of Boolean simulations to predict renal outcomes after treatments. Furthermore, this study unravels a simple but useful tool that may help to design, confirm, or deny pre‐clinical studies and predict therapeutic effects.Support or Funding InformationAHA 18490005 (ARC), Intramural Research Support Program (IRSP) grant from UMMC (ARC), and PO1 HL 51971 (WAP)This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Regulation of dual specificity phosphatases in breast cancer during initial treatment with Herceptin: a Boolean model analysis

Background25% of breast cancer patients suffer from aggressive HER2-positive tumours that are characterised by overexpression of the HER2 protein or by its increased tyrosine kinase activity. Herceptin is a major drug used to treat HER2 positive breast cancer. Understanding the molecular events that occur when breast cancer cells are exposed to Herceptin is therefore of significant importance. Dual specificity phosphatases (DUSPs) are central regulators of cell signalling that function downstream of HER2, but their role in the cellular response to Herceptin is mostly unknown. This study aims to model the initial effects of Herceptin exposure on DUSPs in HER2-positive breast cancer cells using Boolean modelling.ResultsWe experimentally measured expression time courses of 21 different DUSPs between 0 and 24 h following Herceptin treatment of human MDA-MB-453 HER2-positive breast cancer cells. We clustered these time courses into patterns of similar dynamics over time. In parallel, we built a series of Boolean models representing the known regulatory mechanisms of DUSPs and then demonstrated that the dynamics predicted by the models is in agreement with the experimental data. Furthermore, we used the models to predict regulatory mechanisms of DUSPs, where these mechanisms were partially known.ConclusionsBoolean modelling is a powerful technique to investigate and understand signalling pathways. We obtained an understanding of different regulatory pathways in breast cancer and new insights on how these signalling pathways are activated. This method can be generalized to other drugs and longer time courses to better understand how resistance to drugs develops in cancer cells over time.

Equivalence of some subcritical properties in continuum percolation

We consider the Boolean model on $\mathbb{R}^{d}$. We prove some equivalences between subcritical percolation properties. Let us introduce some notations to state one of these equivalences. Let $C$ denote the connected component of the origin in the Boolean model. Let $|C|$ denotes its volume. Let $\ell$ denote the maximal length of a chain of random balls from the origin. Under optimal integrability conditions on the radii, we prove that $\mathbb{E}(|C|)$ is finite if and only if there exists $A,B>0$ such that $\mathbb{P}(\ell\ge n)\le Ae^{-Bn}$ for all $n\ge1$.

A physico-genetic module for the polarisation of auxin efflux carriers PIN-FORMED (PIN)

Intracellular polarisation of auxin efflux carriers is crucial for understanding how auxin gradients form in plants. The polarisation dynamics of auxin efflux carriers PIN-FORMED (PIN) depends on both biomechanical forces as well as chemical, molecular and genetic factors. Biomechanical forces have shown to affect the localisation of PIN transporters to the plasma membrane. We propose a physico-genetic module of PIN polarisation that integrates biomechanical, molecular, and cellular processes as well as their non-linear interactions. The module was implemented as a discrete Boolean model and then approximated to a continuous dynamic system, in order to explore the relative contribution of the factors mediating PIN polarisation at the scale of single cell. Our models recovered qualitative behaviours that have been experimentally observed and enable us to predict that, in the context of PIN polarisation, the effects of the mechanical forces can predominate over the activity of molecular factors such as the GTPase ROP6 and the ROP-INTERACTIVE CRIB MOTIF-CONTAINING PROTEIN RIC1.

Percolation results for the continuum random cluster model

Abstract The continuum random cluster model is a Gibbs modification of the standard Boolean model with intensity z > 0 and law of radii Q. The formal unnormalised density is given by q N cc , where q is a fixed parameter and N cc is the number of connected components in the random structure. We prove for a large class of parameters that percolation occurs for large enough z and does not occur for small enough z. We provide an application to the phase transition of the Widom–Rowlinson model with random radii. Our main tools are stochastic domination properties, a detailed study of the interaction of the model, and a Fortuin–Kasteleyn representation.

Concentration inequalities for measures of a Boolean model

We consider a Boolean model $Z$ driven by a Poisson particle process $\eta$ on a metric space $\mathbb{Y}$. We study the random variable $\rho(Z)$, where $\rho$ is a (deterministic) measure on $\mathbb{Y}$. Due to the interaction of overlapping particles, the distribution of $\rho(Z)$ cannot be described explicitly. In this note we derive concentration inequalities for $\rho(Z)$. To this end we first prove two concentration inequalities for functions of a Poisson process on a general phase space.

Non-triviality of the vacancy phase transition for the Boolean model

In the spherical Poisson Boolean model, one takes the union of random balls centred on the points of a Poisson process in Euclidean $d$-space with $d \geq 2$. We prove that whenever the radius distribution has a finite $d$-th moment, there exists a strictly positive value for the intensity such that the vacant region percolates.

Boolean Gossip Networks

This paper proposes and investigates a Boolean gossip model as a simplified but non-trivial probabilistic Boolean network. With positive node interactions, in view of standard theories from Markov chains, we prove that the node states asymptotically converge to an agreement at a binary random variable, whose distribution is characterized for large-scale networks by mean-field approximation. Using combinatorial analysis, we also successfully count the number of communication classes of the positive Boolean network explicitly in terms of the topology of the underlying interaction graph, where remarkably minor variation in local structures can drastically change the number of network communication classes. With general Boolean interaction rules, emergence of absorbing network Boolean dynamics is shown to be determined by the network structure with necessary and sufficient conditions established regarding when the Boolean gossip process defines absorbing Markov chains. Particularly, it is shown that for the majority of the Boolean interaction rules, except for nine out of the total $2^{16}-1$ possible nonempty sets of binary Boolean functions, whether the induced chain is absorbing has nothing to do with the topology of the underlying interaction graph, as long as connectivity is assumed. These results illustrate the possibilities of relating dynamical properties of Boolean networks to graphical properties of the underlying interactions.

A Boolean network model of bacterial quorum-sensing systems

There are several mathematical models to represent gene regulatory networks, one of the simplest is the Boolean network paradigm. In this paper, we reconstruct a regulatory network of bacterial quorum-sensing systems, in particular, we consider Paraburkholderia phytofirmans PsJN which is a plant growth promoting bacteria that produces positive effects in horticultural crops like tomato, potato and grape. To learn the regulatory network from temporal expression pattern of quorum-sensing genes at root plants, we present a methodology that considers the training of perceptrons for each gene and then the integration into one Boolean regulatory network. Using the proposed approach, we were able to infer a regulatory network model whose topology and dynamic exhibited was helpful to gain insight on the quorum-sensing systems regulation mechanism. We compared our results with REVEAL and Best-Fit extension algorithm, showing that the proposed neural network approach obtained a more biologically meaningful network and dynamics, demonstrating the effectiveness of the proposed method.