The basis of easy controllability in Boolean networks

Modular Control of Biological Networks

The concept of control is central to understanding and applications of biological network models. Some of their key structural features relate to control functions, through gene regulation, signaling, or metabolic mechanisms, and computational models need to encode these. Applications of models often focus on model-based control, such as in biomedicine or metabolic engineering. This paper presents an approach to model-based control that exploits two common features of biological networks, namely their modular structure and canalizing features of their regulatory mechanisms. The paper focuses on intracellular regulatory networks, represented by Boolean network models. A main result of this paper is that control strategies can be identified by focusing on one module at a time. This paper also presents a criterion based on canalizing features of the regulatory rules to identify modules that do not contribute to network control and can be excluded. For even moderately sized networks, finding global control inputs is computationally very challenging. The modular approach presented here leads to a highly efficient approach to solving this problem. This approach is applied to a published Boolean network model of blood cancer large granular lymphocyte (T-LGL) leukemia to identify a minimal control set that achieves a desired control objective.

Canalization reduces the nonlinearity of regulation in biological networks

Biological networks, such as gene regulatory networks, possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated into biological networks. A recent meta-analysis of published, expert-curated Boolean biological network models has revealed several such features, often referred to as design principles. Among others, the biological networks are enriched for certain recurring network motifs, the dynamic update rules are more redundant, more biased, and more canalizing than expected, and the dynamics of biological networks are better approximable by linear and lower-order approximations than those of comparable random networks. Since most of these features are interrelated, it is paramount to disentangle cause and effect, that is, to understand which features evolution actively selects for, and thus truly constitute evolutionary design principles. Here, we compare published Boolean biological network models with different ensembles of null models and show that the abundance of canalization in biological networks can almost completely explain their recently postulated high approximability. Moreover, an analysis of random N-K Kauffman models reveals a strong dependence of approximability on the dynamical robustness of a network.

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.

Modularity of biological systems: a link between structure and function

This paper addresses two topics in systems biology, the hypothesis that biological systems are modular and the problem of relating structure and function of biological systems. The focus here is on gene regulatory networks, represented by Boolean network models, a commonly used tool. Most of the research on gene regulatory network modularity has focused on network structure, typically represented through either directed or undirected graphs. But since gene regulation is a highly dynamic process as it determines the function of cells over time, it is natural to consider functional modularity as well. One of the main results is that the structural decomposition of a network into modules induces an analogous decomposition of the dynamic structure, exhibiting a strong relationship between network structure and function. An extensive simulation study provides evidence for the hypothesis that modularity might have evolved to increase phenotypic complexity while maintaining maximal dynamic robustness to external perturbations.

Phenotype Control techniques for Boolean gene regulatory networks

Modeling cell signal transduction pathways via Boolean networks (BNs) has become an established method for analyzing intracellular communications over the last few decades. What's more, BNs provide a course-grained approach, not only to understanding molecular communications, but also for targeting pathway components that alter the long-term outcomes of the system. This has come to be known as phenotype control theory. In this review we study the interplay of various approaches for controlling gene regulatory networks such as: algebraic methods, control kernel, feedback vertex set, and stable motifs. The study will also include comparative discussion between the methods, using an established cancer model of T-Cell Large Granular Lymphocyte Leukemia. Further, we explore possible options for making the control search more efficient using reduction and modularity. Finally, we will include challenges presented such as the complexity and the availability of software for implementing each of these control techniques.

Phenotype control techniques for Boolean gene regulatory networks

Modeling cell signal transduction pathways via Boolean networks (BNs) has become an established method for analyzing intracellular communications over the last few decades. What’s more, BNs provide a course-grained approach, not only to understanding molecular communications, but also for targeting pathway components that alter the long-term outcomes of the system. This has come to be known as phenotype control theory . In this review we study the interplay of various approaches for controlling gene regulatory networks such as: algebraic methods, control kernel, feedback vertex set, and stable motifs. The study will also include comparative discussion between the methods, using an established cancer model of T-Cell Large Granular Lymphocyte (T-LGL) Leukemia. Further, we explore possible options for making the control search more efficient using reduction and modularity. Finally, we will include challenges presented such as the complexity and the availability of software for implementing each of these control techniques.

The nonlinearity of regulation in biological networks

The extent to which the components of a biological system are (non)linearly regulated determines how amenable they are to therapy and control. To better understand this property termed "regulatory nonlinearity", we analyzed a suite of 137 published Boolean network models, containing a variety of complex nonlinear regulatory interactions, using a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation, we used Taylor decomposition to approximate the models with various levels of regulatory nonlinearity. A comparison of the resulting series of approximations of the biological models with appropriate random ensembles revealed that biological regulation tends to be less nonlinear than expected, meaning that higher-order interactions among the regulatory inputs tend to be less pronounced. A further categorical analysis of the biological models revealed that the regulatory nonlinearity of cancer and disease networks could not only be sometimes higher than expected but also be relatively more variable. We show that this variation is caused by differences in the apportioning of information among the various orders of regulatory nonlinearity. Our results suggest that there may have been a weak but discernible selection pressure for biological systems to evolve linear regulation on average, but for certain systems such as cancer, on the other hand, to simultaneously evolve more nonlinear rules.

Temporary and permanent control of partially specified Boolean networks

Boolean networks (BNs) are a well-accepted modelling formalism in computational systems biology. Nevertheless, modellers often cannot identify only a single BN that matches the biological reality. The typical reasons for this is insufficient knowledge or a lack of experimental data. Formally, this uncertainty can be expressed using partially specified Boolean networks (PSBNs), which encode the wide range of network candidates into a single structure. In this paper, we target the control of PSBNs. The goal of BN control is to find perturbations which guarantee stabilisation of the system in the desired state. Specifically, we consider variable perturbations (gene knock-out and over-expression) with three types of application time-window: one-step, temporary, and permanent. While the control of fully specified BNs is a thoroughly explored topic, control of PSBNs introduces additional challenges that we address in this paper. In particular, the unspecified components of the model cause a significant amount of additional state space explosion. To address this issue, we propose a fully symbolic methodology that can represent the numerous system variants in a compact form. In fully specified models, the efficiency of a perturbation is characterised by the count of perturbed variables (the perturbation size). However, in the case of a PSBN, a perturbation might work only for a subset of concrete BN models. To that end, we introduce and quantify perturbation robustness. This metric characterises how efficient the given perturbation is with respect to the model uncertainty. Finally, we evaluate the novel control methods using non-trivial real-world PSBN models. We inspect the method's scalability and efficiency with respect to the size of the state space and the number of unspecified components. We also compare the robustness metrics for all three perturbation types. Our experiments support the hypothesis that one-step perturbations are significantly less robust than temporary and permanent ones.

Influence maximization in Boolean networks

The optimization problem aiming at the identification of minimal sets of nodes able to drive the dynamics of Boolean networks toward desired long-term behaviors is central for some applications, as for example the detection of key therapeutic targets to control pathways in models of biological signaling and regulatory networks. Here, we develop a method to solve such an optimization problem taking inspiration from the well-studied problem of influence maximization for spreading processes in social networks. We validate the method on small gene regulatory networks whose dynamical landscapes are known by means of brute-force analysis. We then systematically study a large collection of gene regulatory networks. We find that for about 65% of the analyzed networks, the minimal driver sets contain less than 20% of their nodes.

Translocating proteins compartment-specifically alter the fate of epithelial-mesenchymal transition in a compartmentalized Boolean network model

Regulation of translocating proteins is crucial in defining cellular behaviour. Epithelial-mesenchymal transition (EMT) is important in cellular processes, such as cancer progression. Several orchestrators of EMT, such as key transcription factors, are known to translocate. We show that translocating proteins become enriched in EMT-signalling. To simulate the compartment-specific functions of translocating proteins we created a compartmentalized Boolean network model. This model successfully reproduced known biological traits of EMT and as a novel feature it also captured organelle-specific functions of proteins. Our results predicted that glycogen synthase kinase-3 beta (GSK3B) compartment-specifically alters the fate of EMT, amongst others the activation of nuclear GSK3B halts transforming growth factor beta-1 (TGFB) induced EMT. Moreover, our results recapitulated that the nuclear activation of glioma associated oncogene transcription factors (GLI) is needed to achieve a complete EMT. Compartmentalized network models will be useful to uncover novel control mechanisms of biological processes. Our algorithmic procedures can be automatically rerun on the https://translocaboole.linkgroup.hu website, which provides a framework for similar future studies.

Discovering sparse control strategies in neural activity

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology. Though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity and could eventually help characterize collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations—ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms—to neural states and their impact on collective neural activity. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, “pivotal” neurons that account for most of the system’s sensitivity, suggesting a sparse mechanism of collective control.

Dynamical Analysis of a Boolean Network Model of the Oncogene Role of lncRNA ANRIL and lncRNA UFC1 in Non-Small Cell Lung Cancer

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