Discovery of a kernel for controlling biomolecular regulatory networks

Network community detection via neural embeddings

Recent advances in machine learning research have produced powerful neural graph embedding methods, which learn useful, low-dimensional vector representations of network data. These neural methods for graph embedding excel in graph machine learning tasks and are now widely adopted. However, how and why these methods work-particularly how network structure gets encoded in the embedding-remain largely unexplained. Here, we show that node2vec-shallow, linear neural network-encodes communities into separable clusters better than random partitioning down to the information-theoretic detectability limit for the stochastic block models. We show that this is due to the equivalence between the embedding learned by node2vec and the spectral embedding via the eigenvectors of the symmetric normalized Laplacian matrix. Numerical simulations demonstrate that node2vec is capable of learning communities on sparse graphs generated by the stochastic blockmodel, as well as on sparse degree-heterogeneous networks. Our results highlight the features of graph neural networks that enable them to separate communities in the embedding space.

Network dynamics-based subtyping of Alzheimer's disease with microglial genetic risk factors

BACKGROUND

The potential of microglia as a target for Alzheimer's disease (AD) treatment is promising, yet the clinical and pathological diversity within microglia, driven by genetic factors, poses a significant challenge. Subtyping AD is imperative to enable precise and effective treatment strategies. However, existing subtyping methods fail to comprehensively address the intricate complexities of AD pathogenesis, particularly concerning genetic risk factors. To address this gap, we have employed systems biology approaches for AD subtyping and identified potential therapeutic targets.

METHODS

We constructed patient-specific microglial molecular regulatory network models by utilizing existing literature and single-cell RNA sequencing data. The combination of large-scale computer simulations and dynamic network analysis enabled us to subtype AD patients according to their distinct molecular regulatory mechanisms. For each identified subtype, we suggested optimal targets for effective AD treatment.

RESULTS

To investigate heterogeneity in AD and identify potential therapeutic targets, we constructed a microglia molecular regulatory network model. The network model incorporated 20 known risk factors and crucial signaling pathways associated with microglial functionality, such as inflammation, anti-inflammation, phagocytosis, and autophagy. Probabilistic simulations with patient-specific genomic data and subsequent dynamics analysis revealed nine distinct AD subtypes characterized by core feedback mechanisms involving SPI1, CASS4, and MEF2C. Moreover, we identified PICALM, MEF2C, and LAT2 as common therapeutic targets among several subtypes. Furthermore, we clarified the reasons for the previous contradictory experimental results that suggested both the activation and inhibition of AKT or INPP5D could activate AD through dynamic analysis. This highlights the multifaceted nature of microglial network regulation.

CONCLUSIONS

These results offer a means to classify AD patients by their genetic risk factors, clarify inconsistent experimental findings, and advance the development of treatments tailored to individual genotypes for AD.

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.

Decoding the principle of cell-fate determination for its reverse control

Understanding and manipulating cell fate determination is pivotal in biology. Cell fate is determined by intricate and nonlinear interactions among molecules, making mathematical model-based quantitative analysis indispensable for its elucidation. Nevertheless, obtaining the essential dynamic experimental data for model development has been a significant obstacle. However, recent advancements in large-scale omics data technology are providing the necessary foundation for developing such models. Based on accumulated experimental evidence, we can postulate that cell fate is governed by a limited number of core regulatory circuits. Following this concept, we present a conceptual control framework that leverages single-cell RNA-seq data for dynamic molecular regulatory network modeling, aiming to identify and manipulate core regulatory circuits and their master regulators to drive desired cellular state transitions. We illustrate the proposed framework by applying it to the reversion of lung cancer cell states, although it is more broadly applicable to understanding and controlling a wide range of cell-fate determination processes.

A review on gene regulatory network reconstruction algorithms based on single cell RNA sequencing

BACKGROUND

Understanding gene regulatory networks (GRNs) is essential for unraveling the molecular mechanisms governing cellular behavior. With the advent of high-throughput transcriptome measurement technology, researchers have aimed to reverse engineer the biological systems, extracting gene regulatory rules from their outputs, which represented by gene expression data. Bulk RNA sequencing, a widely used method for measuring gene expression, has been employed for GRN reconstruction. However, it falls short in capturing dynamic changes in gene expression at the level of individual cells since it averages gene expression across mixed cell populations.

OBJECTIVE

In this review, we provide an overview of 15 GRN reconstruction tools and discuss their respective strengths and limitations, particularly in the context of single cell RNA sequencing (scRNA-seq).

METHODS

Recent advancements in scRNA-seq break new ground of GRN reconstruction. They offer snapshots of the individual cell transcriptomes and capturing dynamic changes. We emphasize how these technological breakthroughs have enhanced GRN reconstruction.

CONCLUSION

GRN reconstructors can be classified based on their requirement for cellular trajectory, which represents a dynamical cellular process including differentiation, aging, or disease progression. Benchmarking studies support the superiority of GRN reconstructors that do not require trajectory analysis in identifying regulator-target relationships. However, methods equipped with trajectory analysis demonstrate better performance in identifying key regulatory factors. In conclusion, researchers should select a suitable GRN reconstructor based on their specific research objectives.

Normalizing Input-Output Relationships of Cancer Networks for Reversion Therapy

Accumulated genetic alterations in cancer cells distort cellular stimulus-response (or input-output) relationships, resulting in uncontrolled proliferation. However, the complex molecular interaction network within a cell implicates a possibility of restoring such distorted input-output relationships by rewiring the signal flow through controlling hidden molecular switches. Here, a system framework of analyzing cellular input-output relationships in consideration of various genetic alterations and identifying possible molecular switches that can normalize the distorted relationships based on Boolean network modeling and dynamics analysis is presented. Such reversion is demonstrated by the analysis of a number of cancer molecular networks together with a focused case study on bladder cancer with in vitro experiments and patient survival data analysis. The origin of reversibility from an evolutionary point of view based on the redundancy and robustness intrinsically embedded in complex molecular regulatory networks is further discussed.

Critical transition and reversion of tumorigenesis

Cancer is caused by the accumulation of genetic alterations and therefore has been historically considered to be irreversible. Intriguingly, several studies have reported that cancer cells can be reversed to be normal cells under certain circumstances. Despite these experimental observations, conceptual and theoretical frameworks that explain these phenomena and enable their exploration in a systematic way are lacking. In this review, we provide an overview of cancer reversion studies and describe recent advancements in systems biological approaches based on attractor landscape analysis. We suggest that the critical transition in tumorigenesis is an important clue for achieving cancer reversion. During tumorigenesis, a critical transition may occur at a tipping point, where cells undergo abrupt changes and reach a new equilibrium state that is determined by complex intracellular regulatory events. We introduce a conceptual framework based on attractor landscapes through which we can investigate the critical transition in tumorigenesis and induce its reversion by combining intracellular molecular perturbation and extracellular signaling controls. Finally, we present a cancer reversion therapy approach that may be a paradigm-changing alternative to current cancer cell-killing therapies.

Emergent Criticality in Coupled Boolean Networks

Early embryonic development involves forming all specialized cells from a fluid-like mass of identical stem cells. The differentiation process consists of a series of symmetry-breaking events, starting from a high-symmetry state (stem cells) to a low-symmetry state (specialized cells). This scenario closely resembles phase transitions in statistical mechanics. To theoretically study this hypothesis, we model embryonic stem cell (ESC) populations through a coupled Boolean network (BN) model. The interaction is applied using a multilayer Ising model that considers paracrine and autocrine signaling, along with external interventions. It is demonstrated that cell-to-cell variability can be interpreted as a mixture of steady-state probability distributions. Simulations have revealed that such models can undergo a series of first- and second-order phase transitions as a function of the system parameters that describe gene expression noise and interaction strengths. These phase transitions result in spontaneous symmetry-breaking events that generate new types of cells characterized by various steady-state distributions. Coupled BNs have also been shown to self-organize in states that allow spontaneous cell differentiation.

Global stabilizing control of large-scale biomolecular regulatory networks

MOTIVATION

Cellular behavior is determined by complex non-linear interactions between numerous intracellular molecules that are often represented by Boolean network models. To achieve a desired cellular behavior with minimal intervention, we need to identify optimal control targets that can drive heterogeneous cellular states to the desired phenotypic cellular state with minimal node intervention. Previous attempts to realize such global stabilization were based solely on either network structure information or simple linear dynamics. Other attempts based on non-linear dynamics are not scalable.

RESULTS

Here, we investigate the underlying relationship between structurally identified control targets and optimal global stabilizing control targets based on non-linear dynamics. We discovered that optimal global stabilizing control targets can be identified by analyzing the dynamics between structurally identified control targets. Utilizing these findings, we developed a scalable global stabilizing control framework using both structural and dynamic information. Our framework narrows down the search space based on strongly connected components and feedback vertex sets then identifies global stabilizing control targets based on the canalization of Boolean network dynamics. We find that the proposed global stabilizing control is superior with respect to the number of control target nodes, scalability, and computational complexity.

AVAILABILITY AND IMPLEMENTATION

We provide a GitHub repository that contains the DCGS framework written in Python as well as biological random Boolean network datasets (https://github.com/sugyun/DCGS).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Target Control of Asynchronous Boolean Networks

We study the target control of asynchronous Boolean networks, to identify interventions that can drive the dynamics of a given Boolean network from any initial state to the desired target attractor. Based on the application time, the control can be realised with three types of perturbations, including instantaneous, temporary and permanent perturbations. We develop efficient methods to compute the target control for a given target attractor with these three types of perturbations. We compare our methods with the stable motif-based control method on a variety of real-life biological networks to evaluate their performance. We show that our methods scale well for large Boolean networks and they are able to identify a rich set of solutions with a small number of perturbations.

Daphnia as a Sentinel Species for Environmental Health Protection: A Perspective on Biomonitoring and Bioremediation of Chemical Pollution

Despite available technology and the knowledge that chemical pollution damages human and ecosystem health, chemical pollution remains rampant, ineffectively monitored, rarely prevented, and only occasionally mitigated. We present a framework that helps address current major challenges in the monitoring and assessment of chemical pollution by broadening the use of the sentinel species Daphnia as a diagnostic agent of water pollution. And where prevention has failed, we propose the application of Daphnia as a bioremediation agent to help reduce hazards from chemical mixtures in the environment. By applying "omics" technologies to Daphnia exposed to real-world ambient chemical mixtures, we show improvements at detecting bioactive components of chemical mixtures, determining the potential effects of untested chemicals within mixtures, and identifying targets of toxicity. We also show that using Daphnia strains that naturally adapted to chemical pollution as removal agents of ambient chemical mixtures can sustainably improve environmental health protection. Expanding the use of Daphnia beyond its current applications in regulatory toxicology has the potential to improve both the assessment and the remediation of environmental pollution.

Network Dynamics Caused by Genomic Alteration Determine the Therapeutic Response to FGFR Inhibitors for Lung Cancer

Recently, FGFR inhibitors have been highlighted as promising targeted drugs due to the high prevalence of FGFR1 amplification in cancer patients. Although various potential biomarkers for FGFR inhibitors have been suggested, their functional effects have been shown to be limited due to the complexity of the cancer signaling network and the heterogenous genomic conditions of patients. To overcome such limitations, we have reconstructed a lung cancer network model by integrating a cell line genomic database and analyzing the model in order to understand the underlying mechanism of heterogeneous drug responses. Here, we identify novel genomic context-specific candidates that can increase the efficacy of FGFR inhibitors. Furthermore, we suggest optimal targets that can induce more effective therapeutic responses than that of FGFR inhibitors in each of the FGFR-resistant lung cancer cells through computational simulations at a system level. Our findings provide new insights into the regulatory mechanism of differential responses to FGFR inhibitors for optimal therapeutic strategies in lung cancer.

Systemic approaches using single cell transcriptome reveal that C/EBPγ regulates autophagy under amino acid starved condition

Autophagy, a catabolic process to remove unnecessary or dysfunctional organelles, is triggered by various signals including nutrient starvation. Depending on the types of the nutrient deficiency, diverse sensing mechanisms and signaling pathways orchestrate for transcriptional and epigenetic regulation of autophagy. However, our knowledge about nutrient type-specific transcriptional regulation during autophagy is limited. To understand nutrient type-dependent transcriptional mechanisms during autophagy, we performed single cell RNA sequencing (scRNAseq) in the mouse embryonic fibroblasts (MEFs) with or without glucose starvation (GS) as well as amino acid starvation (AAS). Trajectory analysis using scRNAseq identified sequential induction of potential transcriptional regulators for each condition. Gene regulatory rules inferred using TENET newly identified CCAAT/enhancer binding protein γ (C/EBPγ) as a regulator of autophagy in AAS, but not GS, condition, and knockdown experiment confirmed the TENET result. Cell biological and biochemical studies validated that activating transcription factor 4 (ATF4) is responsible for conferring specificity to C/EBPγ for the activation of autophagy genes under AAS, but not under GS condition. Together, our data identified C/EBPγ as a previously unidentified key regulator under AAS-induced autophagy.

Identification of dynamic driver sets controlling phenotypical landscapes

Controlling phenotypical landscapes is of vital interest to modern biology. This task becomes highly demanding because cellular decisions involve complex networks engaging in crosstalk interactions. Previous work on control theory indicates that small sets of compounds can control single phenotypes. However, a dynamic approach is missing to determine the drivers of the whole network dynamics. By analyzing 35 biologically motivated Boolean networks, we developed a method to identify small sets of compounds sufficient to decide on the entire phenotypical landscape. These compounds do not strictly prefer highly related compounds and show a smaller impact on the stability of the attractor landscape. The dynamic driver sets include many intervention targets and cellular reprogramming drivers in human networks. Finally, by using a new comprehensive model of colorectal cancer, we provide a complete workflow on how to implement our approach to shift from in silico to in vitro guided experiments.

Network Analysis Identifies Regulators of Basal-Like Breast Cancer Reprogramming and Endocrine Therapy Vulnerability

Basal-like breast cancer is the most aggressive breast cancer subtype with the worst prognosis. Despite its high recurrence rate, chemotherapy is the only treatment for basal-like breast cancer, which lacks expression of hormone receptors. In contrast, luminal A tumors express ERα and can undergo endocrine therapy for treatment. Previous studies have tried to develop effective treatments for basal-like patients using various therapeutics but failed due to the complex and dynamic nature of the disease. In this study, we performed a transcriptomic analysis of patients with breast cancer to construct a simplified but essential molecular regulatory network model. Network control analysis identified potential targets and elucidated the underlying mechanisms of reprogramming basal-like cancer cells into luminal A cells. Inhibition of BCL11A and HDAC1/2 effectively drove basal-like cells to transition to luminal A cells and increased ERα expression, leading to increased tamoxifen sensitivity. High expression of BCL11A and HDAC1/2 correlated with poor prognosis in patients with breast cancer. These findings identify mechanisms regulating breast cancer phenotypes and suggest the potential to reprogram basal-like breast cancer cells to enhance their targetability. SIGNIFICANCE: A network model enables investigation of mechanisms regulating the basal-to-luminal transition in breast cancer, identifying BCL11A and HDAC1/2 as optimal targets that can induce basal-like breast cancer reprogramming and endocrine therapy sensitivity.

Optimising Boolean Synthetic Regulatory Networks to Control Cell States

Controlling the dynamics of gene regulatory networks is a challenging problem. In recent years, a number of control methods have been proposed, but most of these approaches do not address the problem of how they could be implemented in practice. In this paper, we consider the idea of using a synthetic regulatory network as a closed-loop controller that can control and respond to the dynamics of a cell's native regulatory network in situ. We explore this idea using a computational model in which both native and synthetic regulatory networks are represented by Boolean networks. We then use an evolutionary algorithm to optimise both the structure and parameters of the synthetic Boolean network. To test this approach, we look at whether controllers can be optimised to target specific steady states in five different Boolean regulatory circuit models. Our results show that in most cases the controllers are able to drive the dynamics of the target system to a specified steady state, often using few interventions, and further experiments using random Boolean networks show that the approach scales well to larger controlled networks.

The basis of easy controllability in Boolean networks

Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the effectiveness of external control in selecting a desired final state when that state is among the original attractors of the dynamics. Analyzing 49 existing biological network models, we find strong numerical evidence that the average number of nodes that must be forced scales logarithmically with the number of original attractors. This suggests that biological networks may be typically easy to control even when the number of interacting components is large. We provide a theoretical explanation of the scaling by separating controlling nodes into three types: those that act as inputs, those that distinguish among attractors, and any remaining nodes. We further identify characteristics of dynamics that can invalidate this scaling, and speculate about how this relates more broadly to non-biological systems.

Boolean networks allow a simplified representation of interactions. Here, the authors systematically analyze regulation in dozens of biological Boolean networks, finding mathematical regularities that suggest biological systems could be controlled through a relatively small number of components.

Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks

We present new applications of parity inversion and time reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal construction efficiently reveal discrete analogs of stable and unstable manifolds. We demonstrate their predictive power by studying decision-making in systems biology and statistical physics models. These applications underpin a novel attractor identification algorithm implemented for Boolean networks under stochastic dynamics. Its speed enables resolving a long-standing open question of how attractor count in critical random Boolean networks scales with network size and whether the scaling matches biological observations. Via 80-fold improvement in probed network size (N = 16,384), we find the unexpectedly low scaling exponent of 0.12 ± 0.05, approximately one-tenth the analytical upper bound. We demonstrate a general principle: A system's relationship to its time reversal and state-space inversion constrains its repertoire of emergent behaviors.

Informational architecture across non-living and living collectives

Collective behavior is widely regarded as a hallmark property of living and intelligent systems. Yet, many examples are known of simple physical systems that are not alive, which nonetheless display collective behavior too, prompting simple physical models to often be adopted to explain living collective behaviors. To understand collective behavior as it occurs in living examples, it is important to determine whether or not there exist fundamental differences in how non-living and living systems act collectively, as well as the limits of the intuition that can be built from simpler, physical examples in explaining biological phenomenon. Here, we propose a framework for comparing non-living and living collectives as a continuum based on their information architecture: that is, how information is stored and processed across different degrees of freedom. We review diverse examples of collective phenomena, characterized from an information-theoretic perspective, and offer views on future directions for quantifying living collective behaviors based on their informational structure.

TENET: gene network reconstruction using transfer entropy reveals key regulatory factors from single cell transcriptomic data

Accurate prediction of gene regulatory rules is important towards understanding of cellular processes. Existing computational algorithms devised for bulk transcriptomics typically require a large number of time points to infer gene regulatory networks (GRNs), are applicable for a small number of genes and fail to detect potential causal relationships effectively. Here, we propose a novel approach 'TENET' to reconstruct GRNs from single cell RNA sequencing (scRNAseq) datasets. Employing transfer entropy (TE) to measure the amount of causal relationships between genes, TENET predicts large-scale gene regulatory cascades/relationships from scRNAseq data. TENET showed better performance than other GRN reconstructors, in identifying key regulators from public datasets. Specifically from scRNAseq, TENET identified key transcriptional factors in embryonic stem cells (ESCs) and during direct cardiomyocytes reprogramming, where other predictors failed. We further demonstrate that known target genes have significantly higher TE values, and TENET predicted higher TE genes were more influenced by the perturbation of their regulator. Using TENET, we identified and validated that Nme2 is a culture condition specific stem cell factor. These results indicate that TENET is uniquely capable of identifying key regulators from scRNAseq data.

Realizing Cancer Precision Medicine by Integrating Systems Biology and Nanomaterial Engineering

Many clinical trials for cancer precision medicine have yielded unsatisfactory results due to challenges such as drug resistance and low efficacy. Drug resistance is often caused by the complex compensatory regulation within the biomolecular network in a cancer cell. Recently, systems biological studies have modeled and simulated such complex networks to unravel the hidden mechanisms of drug resistance and identify promising new drug targets or combinatorial or sequential treatments for overcoming resistance to anticancer drugs. However, many of the identified targets or treatments present major difficulties for drug development and clinical application. Nanocarriers represent a path forward for developing therapies with these "undruggable" targets or those that require precise combinatorial or sequential application, for which conventional drug delivery mechanisms are unsuitable. Conversely, a challenge in nanomedicine has been low efficacy due to heterogeneity of cancers in patients. This problem can also be resolved through systems biological approaches by identifying personalized targets for individual patients or promoting the drug responses. Therefore, integration of systems biology and nanomaterial engineering will enable the clinical application of cancer precision medicine to overcome both drug resistance of conventional treatments and low efficacy of nanomedicine due to patient heterogeneity.

Feedback analysis identifies a combination target for overcoming adaptive resistance to targeted cancer therapy

Targeted drugs aim to treat cancer by directly inhibiting oncogene activity or oncogenic pathways, but drug resistance frequently emerges. Due to the intricate dynamics of cancer signaling networks, which contain complex feedback regulations, cancer cells can rewire these networks to adapt to and counter the cytotoxic effects of a drug, thereby limiting the efficacy of targeted therapies. To identify a combinatorial drug target that can overcome such a limitation, we developed a Boolean network simulation and analysis framework and applied this approach to a large-scale signaling network of colorectal cancer with integrated genomic information. We discovered Src as a critical combination drug target that can overcome the adaptive resistance to the targeted inhibition of mitogen-activated protein kinase pathway by blocking the essential feedback regulation responsible for resistance. The proposed framework is generic and can be widely used to identify drug targets that can overcome adaptive resistance to targeted therapies.

Reconciling periodic rhythms of large-scale biological networks by optimal control

Periodic rhythms are ubiquitous phenomena that illuminate the underlying mechanism of cyclic activities in biological systems, which can be represented by cyclic attractors of the related biological network. Disorders of periodic rhythms are detrimental to the natural behaviours of living organisms. Previous studies have shown that the state transition from one to another attractor can be accomplished by regulating external signals. However, most of these studies until now have mainly focused on point attractors while ignoring cyclic ones. The aim of this study is to investigate an approach for reconciling abnormal periodic rhythms, such as diminished circadian amplitude and phase delay, to the regular rhythms of complex biological networks. For this purpose, we formulate and solve a mixed-integer nonlinear dynamic optimization problem simultaneously to identify regulation variables and to determine optimal control strategies for state transition and adjustment of periodic rhythms. Numerical experiments are implemented in three examples including a chaotic system, a mammalian circadian rhythm system and a gastric cancer gene regulatory network. The results show that regulating a small number of biochemical molecules in the network is sufficient to successfully drive the system to the target cyclic attractor by implementing an optimal control strategy.

Signal flow control of complex signaling networks

Complex disease such as cancer is often caused by genetic mutations that eventually alter the signal flow in the intra-cellular signaling network and result in different cell fate. Therefore, it is crucial to identify control targets that can most effectively block such unwanted signal flow. For this purpose, systems biological analysis provides a useful framework, but mathematical modeling of complicated signaling networks requires massive time-series measurements of signaling protein activity levels for accurate estimation of kinetic parameter values or regulatory logics. Here, we present a novel method, called SFC (Signal Flow Control), for identifying control targets without the information of kinetic parameter values or regulatory logics. Our method requires only the structural information of a signaling network and is based on the topological estimation of signal flow through the network. SFC will be particularly useful for a large-scale signaling network to which parameter estimation or inference of regulatory logics is no longer applicable in practice. The identified control targets have significant implication in drug development as they can be putative drug targets.

Minimal intervening control of biomolecular networks leading to a desired cellular state

A cell phenotype can be represented by an attractor state of the underlying molecular regulatory network, to which other network states eventually converge. Here, the set of states converging to each attractor is called its basin of attraction. A central question is how to drive a particular cell state toward a desired attractor with minimal interventions on the network system. We develop a general control framework of complex Boolean networks to provide an answer to this question by identifying control targets on which one-time temporary perturbation can induce a state transition to the boundary of a desired attractor basin. Examples are shown to illustrate the proposed control framework which is also applicable to other types of complex Boolean networks.

Controlling large Boolean networks with single-step perturbations

Motivation

The control of Boolean networks has traditionally focussed on strategies where the perturbations are applied to the nodes of the network for an extended period of time. In this work, we study if and how a Boolean network can be controlled by perturbing a minimal set of nodes for a single-step and letting the system evolve afterwards according to its original dynamics. More precisely, given a Boolean network (BN), we compute a minimal subset Cmin of the nodes such that BN can be driven from any initial state in an attractor to another ‘desired’ attractor by perturbing some or all of the nodes of Cmin for a single-step. Such kind of control is attractive for biological systems because they are less time consuming than the traditional strategies for control while also being financially more viable. However, due to the phenomenon of state-space explosion, computing such a minimal subset is computationally inefficient and an approach that deals with the entire network in one-go, does not scale well for large networks.

Results

We develop a ‘divide-and-conquer’ approach by decomposing the network into smaller partitions, computing the minimal control on the projection of the attractors to these partitions and then composing the results to obtain Cmin for the whole network. We implement our method and test it on various real-life biological networks to demonstrate its applicability and efficiency.

Supplementary information

Supplementary data are available at Bioinformatics online.

Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology

Nowadays, networks are pervasively used as examples of models suitable to mathematically represent and visualize the complexity of systems associated with many diseases, including cancer. In the cancer context, the concept of network entropy has guided many studies focused on comparing equilibrium to disequilibrium (i.e., perturbed) conditions. Since these conditions reflect both structural and dynamic properties of network interaction maps, the derived topological characterizations offer precious support to conduct cancer inference. Recent innovative directions have emerged in network medicine addressing especially experimental omics approaches integrated with a variety of other data, from molecular to clinical and also electronic records, bioimaging etc. This work considers a few theoretically relevant concepts likely to impact the future of applications in personalized/precision/translational oncology. The focus goes to specific properties of networks that are still not commonly utilized or studied in the oncological domain, and they are: controllability, synchronization and symmetry. The examples here provided take inspiration from the consideration of metastatic processes, especially their progression through stages and their hallmark characteristics. Casting these processes into computational frameworks and identifying network states with specific modular configurations may be extremely useful to interpret or even understand dysregulation patterns underlying cancer, and associated events (onset, progression) and disease phenotypes.

Identification of regulatory variables for state transition of biological networks

Attractors represent steady states of biological networks. Recent studies have shown that regulatory variables can be used to steer a network state transition from an undesired attractor, such as a cancerous state, to a desired healthy one. Therefore, it is important to identify the regulatory variables and determine their time-dependent profile for state transition of a given network. However, this is a challenging task since regulatory variables have to be identified among numerous candidates in a large-scale biological network. In this study, we developed a new method for identifying regulatory variables in large-scale biological networks for the purpose of state transition. As a result, a set of optimal regulatory variables can be determined based on formulating and solving a mixed-integer nonlinear dynamic optimization problem. A relaxation scheme is used to overcome the difficulties in solving this complex problem containing a large number of binary variables. The solution to this problem simultaneously identifies the optimal regulatory variables, provides strength of regulatory interactions, and obtains the minimal control time to realize the required state transition. In addition, by adjusting the objective function, various combinations of the strength of regulatory interactions and the transition time can be achieved according to the requirement for disease therapy. Results of three case studies (a myeloid differentiation regulatory network, a cancer gene regulatory network, and a T-LGL signaling network) demonstrate the efficacy of the proposed approach. Therefore, this study establishes an appropriate framework for identifying the regulatory variables for state transition of complex biological networks.

A Boolean network control algorithm guided by forward dynamic programming

Control problem in a biological system is the problem of finding an interventional policy for changing the state of the biological system from an undesirable state, e.g. disease, into a desirable healthy state. Boolean networks are utilized as a mathematical model for gene regulatory networks. This paper provides an algorithm to solve the control problem in Boolean networks. The proposed algorithm is implemented and applied on two biological systems: T-cell receptor network and Drosophila melanogaster network. Results show that the proposed algorithm works faster in solving the control problem over these networks, while having similar accuracy, in comparison to previous exact methods. Source code and a simple web service of the proposed algorithm is available at http://goliaei.ir/net-control/www/.

Systems analysis identifies potential target genes to overcome cetuximab resistance in colorectal cancer cells

Cetuximab (CTX), a monoclonal antibody against epidermal growth factor receptor, is being widely used for colorectal cancer (CRC) with wild-type (WT) KRAS. However, its responsiveness is still very limited and WT KRAS is not enough to indicate such responsiveness. Here, by analyzing the gene expression data of CRC patients treated with CTX monotherapy, we have identified DUSP4, ETV5, GNB5, NT5E, and PHLDA1 as potential targets to overcome CTX resistance. We found that knockdown of any of these five genes can increase CTX sensitivity in KRAS WT cells. Interestingly, we further found that GNB5 knockdown can increase CTX sensitivity even for KRAS mutant cells. We unraveled that GNB5 overexpression contributes to CTX resistance by modulating the Akt signaling pathway from experiments and mathematical simulation. Overall, these results indicate that GNB5 might be a promising target for combination therapy with CTX irrespective of KRAS mutation.

The Hidden Control Architecture of Complex Brain Networks

The brain controls various cognitive functions in a robust and efficient way. What is the control architecture of brain networks that enables such robust and optimal control? Is this brain control architecture distinct from that of other complex networks? Here, we developed a framework to delineate a control architecture of a complex network that is compatible with the behavior of the network and applied the framework to structural brain networks and other complex networks. As a result, we revealed that the brain networks have a distributed and overlapping control architecture governed by a small number of control nodes, which may be responsible for the robust and efficient brain functions. Moreover, our artificial network evolution analysis showed that the distributed and overlapping control architecture of the brain network emerges when it evolves toward increasing both robustness and efficiency.

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We develop a framework to delineate the control architecture of brain networks

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The control architecture of brain networks is compared with other complex networks

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Brain networks have a distributed and overlapping control architecture

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Robust and efficient brain functions might be rooted in its control architecture

Evolution of control with learning classifier systems

In this paper we describe the application of a learning classifier system (LCS) variant known as the eXtended classifier system (XCS) to evolve a set of 'control rules' for a number of Boolean network instances. We show that (1) it is possible to take the system to an attractor, from any given state, by applying a set of 'control rules' consisting of ternary conditions strings (i.e. each condition component in the rule has three possible states; 0, 1 or #) with associated bit-flip actions, and (2) that it is possible to discover such rules using an evolutionary approach via the application of a learning classifier system. The proposed approach builds on learning (reinforcement learning) and discovery (a genetic algorithm) and therefore the series of interventions for controlling the network are determined but are not fixed. System control rules evolve in such a way that they mirror both the structure and dynamics of the system, without having 'direct' access to either.

Determining Relative Dynamic Stability of Cell States Using Boolean Network Model

Cell state transition is at the core of biological processes in metazoan, which includes cell differentiation, epithelial-to-mesenchymal transition (EMT) and cell reprogramming. In these cases, it is important to understand the molecular mechanism of cellular stability and how the transitions happen between different cell states, which is controlled by a gene regulatory network (GRN) hard-wired in the genome. Here we use Boolean modeling of GRN to study the cell state transition of EMT and systematically compare four available methods to calculate the cellular stability of three cell states in EMT in both normal and genetically mutated cases. The results produced from four methods generally agree but do not totally agree with each other. We show that distribution of one-degree neighborhood of cell states, which are the nearest states by Hamming distance, causes the difference among the methods. From that, we propose a new method based on one-degree neighborhood, which is the simplest one and agrees with other methods to estimate the cellular stability in all scenarios of our EMT model. This new method will help the researchers in the field of cell differentiation and cell reprogramming to calculate cellular stability using Boolean model, and then rationally design their experimental protocols to manipulate the cell state transition.

Global Stabilization of Boolean Networks to Control the Heterogeneity of Cellular Responses

Boolean networks (BNs) have been widely used as a useful model for molecular regulatory networks in systems biology. In the state space of BNs, attractors represent particular cell phenotypes. For targeted therapy of cancer, there is a pressing need to control the heterogeneity of cellular responses to the targeted drug by reducing the number of attractors associated with the ill phenotypes of cancer cells. Here, we present a novel control scheme for global stabilization of BNs to a unique fixed point. Using a sufficient condition of global stabilization with respect to the adjacency matrix, we can determine a set of constant controls so that the controlled BN is steered toward an unspecified fixed point which can then be further transformed to a desired attractor by subsequent control. Our method is efficient in that it has polynomial complexity with respect to the number of state variables, while having exponential complexity with respect to in-degree of BNs. To demonstrate the applicability of the proposed control scheme, we conduct simulation studies using a regulation influence network describing the metastatic process of cells and the Mitogen-activated protein kinase (MAPK) signaling network that is crucial in cancer cell fate determination.

Attractor landscape analysis of the cardiac signaling network reveals mechanism-based therapeutic strategies for heart failure

Apoptosis and hypertrophy of cardiomyocytes are the primary causes of heart failure (HF), a global leading cause of death, and are regulated through the complicated intracellular signaling network, limiting the development of effective treatments due to its complexity. To identify effective therapeutic strategies for HF at a system level, we develop a large-scale comprehensive mathematical model of the cardiac signaling network by integrating all available experimental evidence. Attractor landscape analysis of the network model identifies distinct sets of control nodes that effectively suppress apoptosis and hypertrophy of cardiomyocytes under ischemic or pressure overload-induced HF, the two major types of HF. Intriguingly, our system-level analysis suggests that intervention of these control nodes may increase the efficacy of clinical drugs for HF and, of most importance, different combinations of control nodes are suggested as potentially effective candidate drug targets depending on the types of HF. Our study provides a systematic way of developing mechanism-based therapeutic strategies for HF.

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.

We challenge the reductionist assumption by studying causal properties of physical systems across different spatiotemporal scales. The result is that–contrary to reductionist views–causal power can emerge at macro scales. Rather than relying on the traditional notion of coarse-grains (averages), we introduce the notion of functional black boxes that are defined based on their input-output relationship. Using a sequence of examples, our work demonstrates that black boxes are particularly well suited to capture the heterogeneous and specialized nature of components in biological systems. While the emergence of coarse-grained systems relies on increased specificity, black-boxing reveals the importance of structure and integration. Our framework is mathematically rigorous and fully general, hence applicable across many disciplines; it is particularly useful in objectively identifying informative perspectives on complex systems in the physical sciences.

The phenotype control kernel of a biomolecular regulatory network

Background

Controlling complex molecular regulatory networks is getting a growing attention as it can provide a systematic way of driving any cellular state to a desired cell phenotypic state. A number of recent studies suggested various control methods, but there is still deficiency in finding out practically useful control targets that ensure convergence of any initial network state to one of attractor states corresponding to a desired cell phenotype.

Results

To find out practically useful control targets, we introduce a new concept of phenotype control kernel (PCK) for a Boolean network, defined as the collection of all minimal sets of control nodes having their fixed state values that can generate all possible control sets which eventually drive any initial state to one of attractor states corresponding to a particular cell phenotype of interest. We also present a detailed method with which we can identify PCK in a systematic way based on the layered network and converging tree of a given network. We identify all candidates for control nodes from the layered network and then hierarchically search for all possible minimal sets by using the converging tree. We show the usefulness of PCK by applying it to cell proliferation and apoptosis signaling networks and comparing the results with other control methods. PCK is the unique control method for Boolean network models that can be used to identify all possible minimal sets of control nodes. Interestingly, many of the minimal sets have only one or two control nodes.

Conclusions

Based on the new concept of PCK, we can identify all possible minimal sets of control nodes that can drive any molecular network state to one of multiple attractor states representing a same desired cell phenotype.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0576-8) contains supplementary material, which is available to authorized users.

Attractor controllability of Boolean networks by flipping a subset of their nodes

The controllability analysis of Boolean networks (BNs), as models of biomolecular regulatory networks, has drawn the attention of researchers in recent years. In this paper, we aim at governing the steady-state behavior of BNs using an intervention method which can easily be applied to most real system, which can be modeled as BNs, particularly to biomolecular regulatory networks. To this end, we introduce the concept of attractor controllability of a BN by flipping a subset of its nodes, as the possibility of making a BN converge from any of its attractors to any other one, by one-time flipping members of a subset of BN nodes. Our approach is based on the algebraic state-space representation of BNs using semi-tensor product of matrices. After introducing some new matrix tools, we use them to derive necessary and sufficient conditions for the attractor controllability of BNs. A forward search algorithm is then suggested to identify the minimal perturbation set for attractor controllability of a BN. Next, a lower bound is derived for the cardinality of this set. Two new indices are also proposed for quantifying the attractor controllability of a BN and the influence of each network variable on the attractor controllability of the network and the relationship between them is revealed. Finally, we confirm the efficiency of the proposed approach by applying it to the BN models of some real biomolecular networks.

Topological estimation of signal flow in complex signaling networks

In a cell, any information about extra- or intra-cellular changes is transferred and processed through a signaling network and dysregulation of signal flow often leads to disease such as cancer. So, understanding of signal flow in the signaling network is critical to identify drug targets. Owing to the development of high-throughput measurement technologies, the structure of a signaling network is becoming more available, but detailed kinetic parameter information about molecular interactions is still very limited. A question then arises as to whether we can estimate the signal flow based only on the structure information of a signaling network. To answer this question, we develop a novel algorithm that can estimate the signal flow using only the topological information and apply it to predict the direction of activity change in various signaling networks. Interestingly, we find that the average accuracy of the estimation algorithm is about 60–80% even though we only use the topological information. We also find that this predictive power gets collapsed if we randomly alter the network topology, showing the importance of network topology. Our study provides a basis for utilizing the topological information of signaling networks in precision medicine or drug target discovery.

How causal analysis can reveal autonomy in models of biological systems

Standard techniques for studying biological systems largely focus on their dynamical or, more recently, their informational properties, usually taking either a reductionist or holistic perspective. Yet, studying only individual system elements or the dynamics of the system as a whole disregards the organizational structure of the system-whether there are subsets of elements with joint causes or effects, and whether the system is strongly integrated or composed of several loosely interacting components. Integrated information theory offers a theoretical framework to (1) investigate the compositional cause-effect structure of a system and to (2) identify causal borders of highly integrated elements comprising local maxima of intrinsic cause-effect power. Here we apply this comprehensive causal analysis to a Boolean network model of the fission yeast (Schizosaccharomyces pombe) cell cycle. We demonstrate that this biological model features a non-trivial causal architecture, whose discovery may provide insights about the real cell cycle that could not be gained from holistic or reductionist approaches. We also show how some specific properties of this underlying causal architecture relate to the biological notion of autonomy. Ultimately, we suggest that analysing the causal organization of a system, including key features like intrinsic control and stable causal borders, should prove relevant for distinguishing life from non-life, and thus could also illuminate the origin of life problem.This article is part of the themed issue 'Reconceptualizing the origins of life'.

Differential Tissue-specific and Pathway-specific Anti-obesity Effects of Green Tea and Taeumjowitang, a Traditional Korean Medicine, in Mice

Background

Traditional medicines have been leveraged for the treatment and prevention of obesity, one of the fastest growing diseases in the world. However, the exact mechanisms underlying the effects of traditional medicine on obesity are not yet fully understood.

Methods

We produced the transcriptomes of epididymal white adipose tissue (eWAT), liver, muscle, and hypothalamus harvested from mice fed a normal diet, high-fat-diet alone, high-fat-diet together with green tea, or a high-fat-diet together with Taeumjowitang, a traditional Korean medicine.

Results

We found tissue-specific gene expression patterns as follows: (i) the eWAT transcriptome was more significantly altered by Taeumjowitang than by green tea, (ii) the liver transcriptome was similarly altered by Taeumjowitang and green tea, and (iii) both the muscle and hypothalamus transcriptomes were more significantly altered by green tea than Taeumjowitang. We then applied integrated network analyses, which revealed that functional networks associated with lymphocyte activation were more effectively regulated by Taeumjowitang than by green tea in the eWAT. In contrast, green tea was a more effective regulator of functional networks associated with glucose metabolic processes in the eWAT.

Conclusions

Taeumjowitang and green tea have a differential tissue-specific and pathway-specific therapeutic effect on obesity.

Quantitative evaluation and reversion analysis of the attractor landscapes of an intracellular regulatory network for colorectal cancer

BACKGROUND

Cancer reversion, converting the phenotypes of a cancer cell into those of a normal cell, has been sporadically observed throughout history. However, no systematic analysis has been attempted so far.

RESULTS

To investigate this from a systems biological perspective, we have constructed a logical network model of colorectal tumorigenesis by integrating key regulatory molecules and their interactions from previous experimental data. We identified molecular targets that can reverse cancerous cellular states to a normal state by systematically perturbing each molecular activity in the network and evaluating the resulting changes of the attractor landscape with respect to uncontrolled proliferation, EMT, and stemness. Intriguingly, many of the identified targets were well in accord with previous studies. We further revealed that the identified targets constitute stable network motifs that contribute to enhancing the robustness of attractors in cancerous cellular states against diverse regulatory signals.

CONCLUSIONS

The proposed framework for systems analysis is applicable to the study of tumorigenesis and reversion of other types of cancer.

Attractor landscape analysis of colorectal tumorigenesis and its reversion

Background

Colorectal cancer arises from the accumulation of genetic mutations that induce dysfunction of intracellular signaling. However, the underlying mechanism of colorectal tumorigenesis driven by genetic mutations remains yet to be elucidated.

Results

To investigate colorectal tumorigenesis at a system-level, we have reconstructed a large-scale Boolean network model of the human signaling network by integrating previous experimental results on canonical signaling pathways related to proliferation, metastasis, and apoptosis. Throughout an extensive simulation analysis of the attractor landscape of the signaling network model, we found that the attractor landscape changes its shape by expanding the basin of attractors for abnormal proliferation and metastasis along with the accumulation of driver mutations. A further hypothetical study shows that restoration of a normal phenotype might be possible by reversely controlling the attractor landscape. Interestingly, the targets of approved anti-cancer drugs were highly enriched in the identified molecular targets for the reverse control.

Conclusions

Our results show that the dynamical analysis of a signaling network based on attractor landscape is useful in acquiring a system-level understanding of tumorigenesis and developing a new therapeutic strategy.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0341-9) contains supplementary material, which is available to authorized users.

The hidden simplicity of biology

Life is so remarkable, and so unlike any other physical system, that it is tempting to attribute special factors to it. Physics is founded on the assumption that universal laws and principles underlie all natural phenomena, but is it far from clear that there are 'laws of life' with serious descriptive or predictive power analogous to the laws of physics. Nor is there (yet) a 'theoretical biology' in the same sense as theoretical physics. Part of the obstacle in developing a universal theory of biological organization concerns the daunting complexity of living organisms. However, many attempts have been made to glimpse simplicity lurking within this complexity, and to capture this simplicity mathematically. In this paper we review a promising new line of inquiry to bring coherence and order to the realm of biology by focusing on 'information' as a unifying concept.

Controllability and stability analysis of large transcriptomic dynamic systems for host response to influenza infection in human

Background

Gene regulatory networks are complex dynamic systems and the reverse-engineering of such networks from high-dimensional time course transcriptomic data have attracted researchers from various fields. It is also interesting and important to study the behavior of the reconstructed networks on the basis of dynamic models and the biological mechanisms. We focus on the gene regulatory networks reconstructed using the ordinary differential equation (ODE) modelling approach and investigate the properties of these networks.

Results

Controllability and stability analyses are conducted for the reconstructed gene response networks of 17 influenza infected subjects based on ODE models. Symptomatic subjects tend to have larger numbers of driver nodes, higher proportions of critical links and lower proportions of redundant links than asymptomatic subjects. We also show that the degree distribution, rather than the structure of networks, plays an important role in controlling the network in response to influenza infection. In addition, we find that the stability of high-dimensional networks is very sensitive to randomness in the reconstructed systems brought by errors in measurements and parameter estimation.

Conclusions

The gene response networks of asymptomatic subjects are easier to be controlled than those of symptomatic subjects. This may indicate that the regulatory systems of asymptomatic subjects are easier to recover from disease stimulations, so these subjects are less likely to develop symptoms. Our results also suggest that stability constraint should be considered in the modelling of high-dimensional networks and the estimation of network parameters.

The reverse control of irreversible biological processes

Most biological processes have been considered to be irreversible for a long time, but some recent studies have shown the possibility of their reversion at a cellular level. How can we then understand the reversion of such biological processes? We introduce a unified conceptual framework based on the attractor landscape, a molecular phase portrait describing the dynamics of a molecular regulatory network, and the phenotype landscape, a map of phenotypes determined by the steady states of particular output molecules in the attractor landscape. In this framework, irreversible processes involve reshaping of the phenotype landscape, and the landscape reshaping causes the irreversibility of processes. We suggest reverse control by network rewiring which changes network dynamics with constant perturbation, resulting in the restoration of the original phenotype landscape. The proposed framework provides a conceptual basis for the reverse control of irreversible biological processes through network rewiring. WIREs Syst Biol Med 2016, 8:366–377. doi: 10.1002/wsbm.1346

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