LogicGep: Boolean networks inference using symbolic regression from time-series transcriptomic profiling data.

Reconstructing the topology of gene regulatory network from gene expression data has been extensively studied. With the abundance functional transcriptomic data available, it is now feasible to systematically decipher regulatory interaction dynamics in a logic form such as a Boolean network (BN) framework, which qualitatively indicates how multiple regulators aggregated to affect a common target gene. However, inferring both the network topology and gene interaction dynamics simultaneously is still a challenging problem since gene expression data are typically noisy and data discretization is prone to information loss. We propose a new method for BN inference from time-series transcriptional profiles, called LogicGep. LogicGep formulates the identification of Boolean functions as a symbolic regression problem that learns the Boolean function expression and solve it efficiently through multi-objective optimization using an improved gene expression programming algorithm. To avoid overly emphasizing dynamic characteristics at the expense of topology structure ones, as traditional methods often do, a set of promising Boolean formulas for each target gene is evolved firstly, and a feed-forward neural network trained with continuous expression data is subsequently employed to pick out the final solution. We validated the efficacy of LogicGep using multiple datasets including both synthetic and real-world experimental data. The results elucidate that LogicGep adeptly infers accurate BN models, outperforming other representative BN inference algorithms in both network topology reconstruction and the identification of Boolean functions. Moreover, the execution of LogicGep is hundreds of times faster than other methods, especially in the case of large network inference.

Canalizing kernel for cell fate determination.

The tendency for cell fate to be robust to most perturbations, yet sensitive to certain perturbations raises intriguing questions about the existence of a key path within the underlying molecular network that critically determines distinct cell fates. Reprogramming and trans-differentiation clearly show examples of cell fate change by regulating only a few or even a single molecular switch. However, it is still unknown how to identify such a switch, called a master regulator, and how cell fate is determined by its regulation. Here, we present CAESAR, a computational framework that can systematically identify master regulators and unravel the resulting canalizing kernel, a key substructure of interconnected feedbacks that is critical for cell fate determination. We demonstrate that CAESAR can successfully predict reprogramming factors for de-differentiation into mouse embryonic stem cells and trans-differentiation of hematopoietic stem cells, while unveiling the underlying essential mechanism through the canalizing kernel. CAESAR provides a system-level understanding of how complex molecular networks determine cell fates.

Reconstruction of gene regulatory networks for Caenorhabditis elegans using tree-shaped gene expression data.

Constructing gene regulatory networks is a widely adopted approach for investigating gene regulation, offering diverse applications in biology and medicine. A great deal of research focuses on using time series data or single-cell RNA-sequencing data to infer gene regulatory networks. However, such gene expression data lack either cellular or temporal information. Fortunately, the advent of time-lapse confocal laser microscopy enables biologists to obtain tree-shaped gene expression data of Caenorhabditis elegans, achieving both cellular and temporal resolution. Although such tree-shaped data provide abundant knowledge, they pose challenges like non-pairwise time series, laying the inaccuracy of downstream analysis. To address this issue, a comprehensive framework for data integration and a novel Bayesian approach based on Boolean network with time delay are proposed. The pre-screening process and Markov Chain Monte Carlo algorithm are applied to obtain the parameter estimates. Simulation studies show that our method outperforms existing Boolean network inference algorithms. Leveraging the proposed approach, gene regulatory networks for five subtrees are reconstructed based on the real tree-shaped datatsets of Caenorhabditis elegans, where some gene regulatory relationships confirmed in previous genetic studies are recovered. Also, heterogeneity of regulatory relationships in different cell lineage subtrees is detected. Furthermore, the exploration of potential gene regulatory relationships that bear importance in human diseases is undertaken. All source code is available at the GitHub repository https://github.com/edawu11/BBTD.git.

The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling.

The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization-the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular.

Analysis of the Main Checkpoints of the JNK-MAPK Pathway in HTLV-1-Associated Leukemia/Lymphoma via Boolean Network Simulation.

The c-Jun N-terminal kinase (JNK) pathway is a signal transduction pathway that plays a critical role in cell growth and survival. Its dysregulation is related to various cancers, including adult T-cell leukemia/lymphoma (ATLL), an aggressive peripheral T-cell malignancy caused by human T-cell lymphotropic virus type 1 (HTLV-1) infection. There is currently no vaccine or definitive treatment for ATLL. This research aimed to identify the JNK-MAPK pathway checkpoints to identify possible therapeutic targets using Boolean network analysis. First, the genes involved in the JNK pathway and their interactions were identified and mapped. Next, a Boolean network analysis was performed using the R programming language, which suggested protein kinase B (AKT) and MAP kinase phosphatase (MKP) for further evaluation. Finally, to confirm the effect of these two genes, a clinical study was conducted among ATLL patients and healthy individuals. The quantitative real time polymerase chain reaction (qRT‒PCR) results revealed a statistically significant decrease in the expression of AKT and MKP in ATLL patients compared to normal controls. This highlights the potential role of these two genes as potential therapeutic targets in ATLL.

Reducing Boolean networks with backward equivalence.

BACKGROUND: Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis. RESULTS: We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance. CONCLUSIONS: BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

A common molecular logic determines embryonic stem cell self-renewal and reprogramming.

During differentiation and reprogramming, new cell identities are generated by reconfiguration of gene regulatory networks. Here, we combined automated formal reasoning with experimentation to expose the logic of network activation during induction of naïve pluripotency. We find that a Boolean network architecture defined for maintenance of naïve state embryonic stem cells (ESC) also explains transcription factor behaviour and potency during resetting from primed pluripotency. Computationally identified gene activation trajectories were experimentally substantiated at single-cell resolution by RT-qPCR Contingency of factor availability explains the counterintuitive observation that Klf2, which is dispensable for ESC maintenance, is required during resetting. We tested 124 predictions formulated by the dynamic network, finding a predictive accuracy of 77.4%. Finally, we show that this network explains and predicts experimental observations of somatic cell reprogramming. We conclude that a common deterministic program of gene regulation is sufficient to govern maintenance and induction of naïve pluripotency. The tools exemplified here could be broadly applied to delineate dynamic networks underlying cell fate transitions.

Multi-scale model of lumen formation via inverse membrane blebbing mechanism during sprouting angiogenesis process.

Cancer is one of the leading causes of mortality and morbidity among people worldwide. Cancer appears as solid tumors in many cases. Angiogenesis is the growth of blood vessels from the existing vasculature and is one of the imperative processes in tumor growth. Another vital phenomenon for formation and functionality of this vasculature network is lumen formation. The results of recent studies indicate the importance of blood pressure in this mechanism. Computational modeling can study these processes in different scales. Hence, wide varieties of these models have been proposed during recent years. In this research, a multi-scale model is developed for the angiogenesis process. In the extracellular scale, the growth factor concentration is calculated via the reaction diffusion equation. At the cellular scale, growth, migration, and the adhesion of endothelial cells are modeled by the Potts cellular model. At the intra-cellular scale by considering biochemical signals, a Boolean network model describes migration, division, or apoptosis of endothelial cells. A stochastic model developed for lumen formation via inverse membrane blebbing mechanism. A CFD simulation was also used to investigate the role of pulsated blood pressure in the inverse membrane blebbing mechanism. The lumen formation model shows stochastic behavior in blebs expansion and lumen expansion. Comparing the stochastic model's results with the CFD simulation also shows the vital role of pressure pulse and the topology of the blebs in bleb retraction.

Temporal, Structural, and Functional Heterogeneities Extend Criticality and Antifragility in Random Boolean Networks.

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality-a balance between change and stability, order and chaos-is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks-a general model of discrete dynamical systems-we show that heterogeneity-in time, structure, and function-can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.

Mathematical model of the cell signaling pathway based on the extended Boolean network model with a stochastic process.

BACKGROUND: In cell signaling pathways, proteins interact with each other to determine cell fate in response to either cell-extrinsic (micro-environmental) or intrinsic cues. One of the well-studied pathways, the mitogen-activated protein kinase (MAPK) signaling pathway, regulates cell processes such as differentiation, proliferation, apoptosis, and survival in response to various micro-environmental stimuli in eukaryotes. Upon micro-environmental stimulus, receptors on the cell membrane become activated. Activated receptors initiate a cascade of protein activation in the MAPK pathway. This activation involves protein binding, creating scaffold proteins, which are known to facilitate effective MAPK signaling transduction. RESULTS: This paper presents a novel mathematical model of a cell signaling pathway coordinated by protein scaffolding. The model is based on the extended Boolean network approach with stochastic processes. Protein production or decay in a cell was modeled considering the stochastic process, whereas the protein-protein interactions were modeled based on the extended Boolean network approach. Our model fills a gap in the binary set applied to previous models. The model simultaneously considers the stochastic process directly. Using the model, we simulated a simplified mitogen-activated protein kinase (MAPK) signaling pathway upon stimulation of both a single receptor at the initial time and multiple receptors at several time points. Our simulations showed that the signal is amplified as it travels down to the pathway from the receptor, generating substantially amplified downstream ERK activity. The noise generated by the stochastic process of protein self-activity in the model was also amplified as the signaling propagated through the pathway. CONCLUSIONS: The signaling transduction in a simplified MAPK signaling pathway could be explained by a mathematical model based on the extended Boolean network model with a stochastic process. The model simulations demonstrated signaling amplifications when it travels downstream, which was already observed in experimental settings. We also highlight the importance of stochastic activity in regulating protein inactivation.

From data to QSP models: a pipeline for using Boolean networks for hypothesis inference and dynamic model building.

Quantitative Systems Pharmacology (QSP) models capture the physiological underpinnings driving the response to a drug and express those in a semi-mechanistic way, often involving ordinary differential equations (ODEs). The process of developing a QSP model generally starts with the definition of a set of reasonable hypotheses that would support a mechanistic interpretation of the expected response which are used to form a network of interacting elements. This is a hypothesis-driven and knowledge-driven approach, relying on prior information about the structure of the network. However, with recent advances in our ability to generate large datasets rapidly, often in a hypothesis-neutral manner, the opportunity emerges to explore data-driven approaches to establish the network topologies and models in a robust, repeatable manner. In this paper, we explore the possibility of developing complex network representations of physiological responses to pharmaceuticals using a logic-based analysis of available data and then convert the logic relations to dynamic ODE-based models. We discuss an integrated pipeline for converting data to QSP models. This pipeline includes using k-means clustering to binarize continuous data, inferring likely network relationships using a Best-Fit Extension method to create a Boolean network, and finally converting the Boolean network to a continuous ODE model. We utilized an existing QSP model for the dual-affinity re-targeting antibody flotetuzumab to demonstrate the robustness of the process. Key output variables from the QSP model were used to generate a continuous data set for use in the pipeline. This dataset was used to reconstruct a possible model. This reconstruction had no false-positive relationships, and the output of each of the species was similar to that of the original QSP model. This demonstrates the ability to accurately infer relationships in a hypothesis-neutral manner without prior knowledge of a system using this pipeline.

Describing and Controlling Multivariate Nonlinear Dynamics: A Boolean Network Approach.

We introduce a discrete-time dynamical system method, the Boolean network method, that may be useful for modeling, studying, and controlling nonlinear dynamics in multivariate systems, particularly when binary time-series are available. We introduce the method in three steps: inference of the temporal relations as Boolean functions, extraction of attractors and assignment of desirability based on domain knowledge, and design of network control to direct a psychological system toward a desired attractor. To demonstrate how the Boolean network can describe and prescribe control for emotion regulation dynamics, we applied this method to data from a study of how children use bidding to an adult and/or distraction to regulate their anger during a frustrating task (N = 120, T = 480 seconds). Network control strategies were designed to move the child into attractors where anger is OFF. The sample shows heterogeneous emotion regulation dynamics across children in 22 distinct Boolean networks, and heterogeneous control strategies regarding which behavior to perturb and how to perturb it. The Boolean network method provides a novel method to describe nonlinear dynamics in multivariate psychological systems and is a method with potential to eventually inform the design of interventions that can guide those systems toward desired goals.

Cell phenotypes as macrostates of the GRN dynamics.

The two most fundamental processes describing change in biology, development, and evolution, occur over drastically different timescales. Development involves temporal sequences of cell states controlled by hierarchies of regulatory structures. It occurs over the lifetime of a single individual and is associated with gene expression level change of a given genotype. Evolution, by contrast, entails genotypic change through mutation, the acquisition/loss of genes and changes in the network topology of interactions among genes. It involves the emergence of new, environmentally selected phenotypes over the lifetimes of many individuals. We start by reviewing the most limiting aspects of the theoretical modeling of gene regulatory networks (GRNs) which prevent the study of both timescales in a common, mathematical language. We then consider the simple framework of Boolean network models of GRNs and point out its inadequacy to include evolutionary processes. As opposed to one-to-one maps to specific attractors, we adopt a many-to-one map which makes each phenotype correspond to multiple attractors. This definition no longer requires a fixed size for the genotype and opens the possibility for modeling the phenotypic change of a genotype, which is itself changing over evolutionary timescales. At the same time, we show that this generalized framework does not interfere with established numerical techniques for the identification of the kernel of controlling nodes responsible for cell differentiation through external signals.

Automated inference of gene regulatory networks using explicit regulatory modules.

Gene regulatory networks are a popular tool for modelling important biological phenomena, such as cell differentiation or oncogenesis. Efficient identification of the causal connections between genes, their products and regulating transcription factors, is key to understanding how defects in their function may trigger diseases. Modelling approaches should keep up with the ever more detailed descriptions of the biological phenomena at play, as provided by new experimental findings and technical improvements. In recent years, we have seen great improvements in mapping of specific binding sites of many transcription factors to distinct regulatory regions. Recent gene regulatory network models use binding measurements; but usually only to define gene-to-gene interactions, ignoring regulatory module structure. Moreover, current huge amount of transcriptomic data, and exploration of all possible cis-regulatory arrangements which can lead to the same transcriptomic response, makes manual model building both tedious and time-consuming. In our paper, we propose a method to specify possible regulatory connections in a given Boolean network, based on transcription factor binding evidence. This is implemented by an algorithm which expands a regular Boolean network model into a "cis-regulatory" Boolean network model. This expanded model explicitly defines regulatory regions as additional nodes in the network, and adds new, valuable biological insights to the system dynamics. The expanded model can automatically be compared with expression data. And, for each node, a regulatory function, consistent with the experimental data, can be found. The resulting models are usually more constrained (by biologically-motivated metadata), and can then be inspected in in silico simulations. The fully automated method for model identification has been implemented in Python, and the expansion algorithm in R. The method resorts to the Z3 Satisfiability Modulo Theories (SMT) solver, and is similar to the RE:IN application (Yordanov et al., 2016). It is available on https://github.com/regulomics/expansion-network.

Reconstructing blood stem cell regulatory network models from single-cell molecular profiles.

Adult blood contains a mixture of mature cell types, each with specialized functions. Single hematopoietic stem cells (HSCs) have been functionally shown to generate all mature cell types for the lifetime of the organism. Differentiation of HSCs toward alternative lineages must be balanced at the population level by the fate decisions made by individual cells. Transcription factors play a key role in regulating these decisions and operate within organized regulatory programs that can be modeled as transcriptional regulatory networks. As dysregulation of single HSC fate decisions is linked to fatal malignancies such as leukemia, it is important to understand how these decisions are controlled on a cell-by-cell basis. Here we developed and applied a network inference method, exploiting the ability to infer dynamic information from single-cell snapshot expression data based on expression profiles of 48 genes in 2,167 blood stem and progenitor cells. This approach allowed us to infer transcriptional regulatory network models that recapitulated differentiation of HSCs into progenitor cell types, focusing on trajectories toward megakaryocyte-erythrocyte progenitors and lymphoid-primed multipotent progenitors. By comparing these two models, we identified and subsequently experimentally validated a difference in the regulation of nuclear factor, erythroid 2 (Nfe2) and core-binding factor, runt domain, alpha subunit 2, translocated to, 3 homolog (Cbfa2t3h) by the transcription factor Gata2. Our approach confirms known aspects of hematopoiesis, provides hypotheses about regulation of HSC differentiation, and is widely applicable to other hierarchical biological systems to uncover regulatory relationships.

MiRNA therapeutics based on logic circuits of biological pathways.

BACKGROUND: In silico experiments, with the aid of computer simulation, speed up the process of in vitro or in vivo experiments. Cancer therapy design is often based on signalling pathway. MicroRNAs (miRNA) are small non-coding RNA molecules. In several kinds of diseases, including cancer, hepatitis and cardiovascular diseases, they are often deregulated, acting as oncogenes or tumor suppressors. miRNA therapeutics is based on two main kinds of molecules injection: miRNA mimics, which consists of injection of molecules that mimic the targeted miRNA, and antagomiR, which consists of injection of molecules inhibiting the targeted miRNA. Nowadays, the research is focused on miRNA therapeutics. This paper addresses cancer related signalling pathways to investigate miRNA therapeutics. RESULTS: In order to prove our approach, we present two different case studies: non-small cell lung cancer and melanoma. KEGG signalling pathways are modelled by a digital circuit. A logic value of 1 is linked to the expression of the corresponding gene. A logic value of 0 is linked to the absence (not expressed) gene. All possible relationships provided by a signalling pathway are modelled by logic gates. Mutations, derived according to the literature, are introduced and modelled as well. The modelling approach and analysis are widely discussed within the paper. MiRNA therapeutics is investigated by the digital circuit analysis. The most effective miRNA and combination of miRNAs, in terms of reduction of pathogenic conditions, are obtained. A discussion of obtained results in comparison with literature data is provided. Results are confirmed by existing data. CONCLUSIONS: The proposed study is based on drug discovery and miRNA therapeutics and uses a digital circuit simulation of a cancer pathway. Using this simulation, the most effective combination of drugs and miRNAs for mutated cancer therapy design are obtained and these results were validated by the literature. The proposed modelling and analysis approach can be applied to each human disease, starting from the corresponding signalling pathway.

Comparison of Combinatorial Signatures of Global Network Dynamics Generated by Two Classes of ODE Models.

Modeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameterization. Discrete time Boolean networks and related continuous time switching systems provide a computationally accessible way to translate the structure of the network to predictions about the dynamics. Recent work has shown that the parameterized dynamics of switching systems can be captured by a combinatorial object, called a Dynamic Signatures Generated by Regulatory Networks (DSGRN) database, that consists of a parameter graph characterizing a finite parameter space decomposition, whose nodes are assigned a Morse graph that captures global dynamics for all corresponding parameters. We show that for a given network there is a way to associate the same type of object by considering a continuous time ODE system with a continuous right-hand side, which we call an L-system. The main goal of this paper is to compare the two DSGRN databases for the same network. Since the L-systems can be thought of as perturbations (not necessarily small) of the switching systems, our results address the correspondence between global parameterized dynamics of switching systems and their perturbations. We show that, at corresponding parameters, there is an order preserving map from the Morse graph of the switching system to that of the L-system that is surjective on the set of attractors and bijective on the set of fixed-point attractors. We provide important examples showing why this correspondence cannot be strengthened.

Discriminate the response of Acute Myeloid Leukemia patients to treatment by using proteomics data and Answer Set Programming.

BACKGROUND: During the last years, several approaches were applied on biomedical data to detect disease specific proteins and genes in order to better target drugs. It was shown that statistical and machine learning based methods use mainly clinical data and improve later their results by adding omics data. This work proposes a new method to discriminate the response of Acute Myeloid Leukemia (AML) patients to treatment. The proposed approach uses proteomics data and prior regulatory knowledge in the form of networks to predict cancer treatment outcomes by finding out the different Boolean networks specific to each type of response to drugs. To show its effectiveness we evaluate our method on a dataset from the DREAM 9 challenge. RESULTS: The results are encouraging and demonstrate the benefit of our approach to distinguish patient groups with different response to treatment. In particular each treatment response group is characterized by a predictive model in the form of a signaling Boolean network. This model describes regulatory mechanisms which are specific to each response group. The proteins in this model were selected from the complete dataset by imposing optimization constraints that maximize the difference in the logical response of the Boolean network associated to each group of patients given the omic dataset. This mechanistic and predictive model also allow us to classify new patients data into the two different patient response groups. CONCLUSIONS: We propose a new method to detect the most relevant proteins for understanding different patient responses upon treatments in order to better target drugs using a Prior Knowledge Network and proteomics data. The results are interesting and show the effectiveness of our method.

A circuit-preserving mapping from multilevel to Boolean dynamics.

Many discrete models of biological networks rely exclusively on Boolean variables and many tools and theorems are available for analysis of strictly Boolean models. However, multilevel variables are often required to account for threshold effects, in which knowledge of the Boolean case does not generalise straightforwardly. This motivated the development of conversion methods for multilevel to Boolean models. In particular, Van Ham's method has been shown to yield a one-to-one, neighbour and regulation preserving dynamics, making it the de facto standard approach to the problem. However, Van Ham's method has several drawbacks: most notably, it introduces vast regions of "non-admissible" states that have no counterpart in the multilevel, original model. This raises special difficulties for the analysis of interaction between variables and circuit functionality, which is believed to be central to the understanding of dynamic properties of logical models. Here, we propose a new multilevel to Boolean conversion method, with software implementation. Contrary to Van Ham's, our method doesn't yield a one-to-one transposition of multilevel trajectories; however, it maps each and every Boolean state to a specific multilevel state, thus getting rid of the non-admissible regions and, at the expense of (apparently) more complicated, "parallel" trajectories. One of the prominent features of our method is that it preserves dynamics and interaction of variables in a certain manner. As a demonstration of the usability of our method, we apply it to construct a new Boolean counter-example to the well-known conjecture that a local negative circuit is necessary to generate sustained oscillations. This result illustrates the general relevance of our method for the study of multilevel logical models.

Boolean network modeling in systems pharmacology.

Quantitative systems pharmacology (QSP) is an emerging discipline that aims to discover how drugs modulate the dynamics of biological components in molecular and cellular networks and the impact of those perturbations on human pathophysiology. The integration of systems-based experimental and computational approaches is required to facilitate the advancement of this field. QSP models typically consist of a series of ordinary differential equations (ODE). However, this mathematical framework requires extensive knowledge of parameters pertaining to biological processes, which is often unavailable. An alternative framework that does not require knowledge of system-specific parameters, such as Boolean network modeling, could serve as an initial foundation prior to the development of an ODE-based model. Boolean network models have been shown to efficiently describe, in a qualitative manner, the complex behavior of signal transduction and gene/protein regulatory processes. In addition to providing a starting point prior to quantitative modeling, Boolean network models can also be utilized to discover novel therapeutic targets and combinatorial treatment strategies. Identifying drug targets using a network-based approach could supplement current drug discovery methodologies and help to fill the innovation gap across the pharmaceutical industry. In this review, we discuss the process of developing Boolean network models and the various analyses that can be performed to identify novel drug targets and combinatorial approaches. An example for each of these analyses is provided using a previously developed Boolean network of signaling pathways in multiple myeloma. Selected examples of Boolean network models of human (patho-)physiological systems are also reviewed in brief.