Molecular network control through boolean canalization

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.

Boolean model of the gene regulatory network of Pseudomonas aeruginosa CCBH4851

Introduction

Pseudomonas aeruginosa infections are one of the leading causes of death in immunocompromised patients with cystic fibrosis, diabetes, and lung diseases such as pneumonia and bronchiectasis. Furthermore, P. aeruginosa is one of the main multidrug-resistant bacteria responsible for nosocomial infections worldwide, including the multidrug-resistant CCBH4851 strain isolated in Brazil.

Methods

One way to analyze their dynamic cellular behavior is through computational modeling of the gene regulatory network, which represents interactions between regulatory genes and their targets. For this purpose, Boolean models are important predictive tools to analyze these interactions. They are one of the most commonly used methods for studying complex dynamic behavior in biological systems.

Results and discussion

Therefore, this research consists of building a Boolean model of the gene regulatory network of P. aeruginosa CCBH4851 using data from RNA-seq experiments. Next, the basins of attraction are estimated, as these regions and the transitions between them can help identify the attractors, representing long-term behavior in the Boolean model. The essential genes of the basins were associated with the phenotypes of the bacteria for two conditions: biofilm formation and polymyxin B treatment. Overall, the Boolean model and the analysis method proposed in this work can identify promising control actions and indicate potential therapeutic targets, which can help pinpoint new drugs and intervention strategies.

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.

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.

Capturing dynamic relevance in Boolean networks using graph theoretical measures

Motivation

Interaction graphs are able to describe regulatory dependencies between compounds without capturing dynamics. In contrast, mathematical models that are based on interaction graphs allow to investigate the dynamics of biological systems. However, since dynamic complexity of these models grows exponentially with their size, exhaustive analyses of the dynamics and consequently screening all possible interventions eventually becomes infeasible. Thus, we designed an approach to identify dynamically relevant compounds based on the static network topology.

Results

Here, we present a method only based on static properties to identify dynamically influencing nodes. Coupling vertex betweenness and determinative power, we could capture relevant nodes for changing dynamics with an accuracy of 75% in a set of 35 published logical models. Further analyses of the selected compounds’ connectivity unravelled a new class of not highly connected nodes with high impact on the networks’ dynamics, which we call gatekeepers. We validated our method’s working concept on logical models, which can be readily scaled up to complex interaction networks, where dynamic analyses are not even feasible.

Availability and implementation

Code is freely available at https://github.com/sysbio-bioinf/BNStatic.

Supplementary information

Supplementary data are available at Bioinformatics online.

Mathematical modeling of the Candida albicans yeast to hyphal transition reveals novel control strategies

Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating multiple environmental factors and regulatory mechanisms. We validate the model by a systematic comparison to prior experiments, which led to agreement in 17 out of 22 cases. The discrepancies motivate alternative hypotheses that are testable by follow-up experiments. Analysis of this model revealed two time-constrained windows of opportunity that must be met for the complete transition from the yeast to hyphal phenotype, as well as control strategies that can robustly prevent this transition. We experimentally validate two of these control predictions in C. albicans strains lacking the transcription factor UME6 and the histone deacetylase HDA1, respectively. This model will serve as a strong base from which to develop a systems biology understanding of C. albicans morphogenesis.

Evolution of Cellular Differentiation: From Hypotheses to Models

Cellular differentiation is one of the hallmarks of complex multicellularity, allowing individual organisms to capitalize on among-cell functional diversity. The evolution of multicellularity is a major evolutionary transition that allowed for the increase of organismal complexity in multiple lineages, a process that relies on the functional integration of cell-types within an individual. Multiple hypotheses have been proposed to explain the origins of cellular differentiation, but we lack a general understanding of what makes one cell-type distinct from others, and how such differentiation arises. Here, we describe how the use of Boolean networks (BNs) can aid in placing empirical findings into a coherent conceptual framework, and we emphasize some of the standing problems when interpreting data and model behaviors.

A Near-Optimal Control Method for Stochastic Boolean Networks

One of the ultimate goals in systems biology is to develop control strategies to find efficient medical treatments. One step towards this goal is to develop methods for changing the state of a cell into a desirable state. We propose an efficient method that determines combinations of network perturbations to direct the system towards a predefined state. The method requires a set of control actions such as the silencing of a gene or the disruption of the interaction between two genes. An optimal control policy defined as the best intervention at each state of the system can be obtained using existing methods. However, these algorithms are computationally prohibitive for models with tens of nodes. Our method generates control actions that approximates the optimal control policy with high probability with a computational efficiency that does not depend on the size of the state space. Our C++ code is available at https://github.com/boaguilar/SDDScontrol.

Control of Intracellular Molecular Networks Using Algebraic Methods

Many problems in biology and medicine have a control component. Often, the goal might be to modify intracellular networks, such as gene regulatory networks or signaling networks, in order for cells to achieve a certain phenotype, what happens in cancer. If the network is represented by a mathematical model for which mathematical control approaches are available, such as systems of ordinary differential equations, then this problem might be solved systematically. Such approaches are available for some other model types, such as Boolean networks, where structure-based approaches have been developed, as well as stable motif techniques. However, increasingly many published discrete models are mixed-state or multistate, that is, some or all variables have more than two states, and thus the development of control strategies for multistate networks is needed. This paper presents a control approach broadly applicable to general multistate models based on encoding them as polynomial dynamical systems over a finite algebraic state set, and using computational algebra for finding appropriate intervention strategies. To demonstrate the feasibility and applicability of this method, we apply it to a recently developed multistate intracellular model of E2F-mediated bladder cancerous growth and to a model linking intracellular iron metabolism and oncogenic pathways. The control strategies identified for these published models are novel in some cases and represent new hypotheses, or are supported by the literature in others as potential drug targets. Our Macaulay2 scripts to find control strategies are publicly available through GitHub at https://github.com/luissv7/multistatepdscontrol.

Edgetic perturbations to eliminate fixed-point attractors in Boolean regulatory networks

The dynamics of complex biological networks may be modeled in a Boolean framework, where the state of each system component is either abundant (ON) or scarce/absent (OFF), and each component's dynamic trajectory is determined by a logical update rule involving the state(s) of its regulator(s). It is possible to encode the update rules in the topology of the so-called expanded graph, analysis of which reveals the long-term behavior, or attractors, of the network. Here, we develop an algorithm to perturb the expanded graph (or, equivalently, the logical update rules) to eliminate stable motifs: subgraphs that cause a subset of components to stabilize to one state. Depending on the topology of the expanded graph, these perturbations lead to the modification or loss of the corresponding attractor. While most perturbations of biological regulatory networks in the literature involve the knockout (fixing to OFF) or constitutive activation (fixing to ON) of one or more nodes, we here consider edgetic perturbations, where a node's update rule is modified such that one or more of its regulators is viewed as ON or OFF regardless of its actual state. We apply the methodology to two biological networks. In a network representing T-LGL leukemia, we identify edgetic perturbations that eliminate the cancerous attractor, leaving only the healthy attractor representing cell death. In a network representing drought-induced closure of plant stomata, we identify edgetic perturbations that modify the single attractor such that stomata, instead of being fixed in the closed state, oscillates between the open and closed states.

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.

Target Control in Logical Models Using the Domain of Influence of Nodes

Dynamical models of biomolecular networks are successfully used to understand the mechanisms underlying complex diseases and to design therapeutic strategies. Network control and its special case of target control, is a promising avenue toward developing disease therapies. In target control it is assumed that a small subset of nodes is most relevant to the system's state and the goal is to drive the target nodes into their desired states. An example of target control would be driving a cell to commit to apoptosis (programmed cell death). From the experimental perspective, gene knockout, pharmacological inhibition of proteins, and providing sustained external signals are among practical intervention techniques. We identify methodologies to use the stabilizing effect of sustained interventions for target control in Boolean network models of biomolecular networks. Specifically, we define the domain of influence (DOI) of a node (in a certain state) to be the nodes (and their corresponding states) that will be ultimately stabilized by the sustained state of this node regardless of the initial state of the system. We also define the related concept of the logical domain of influence (LDOI) of a node, and develop an algorithm for its identification using an auxiliary network that incorporates the regulatory logic. This way a solution to the target control problem is a set of nodes whose DOI can cover the desired target node states. We perform greedy randomized adaptive search in node state space to find such solutions. We apply our strategy to in silico biological network models of real systems to demonstrate its effectiveness.

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.

Structure-based control of complex networks with nonlinear dynamics

What can we learn about controlling a system solely from its underlying network structure? Here we adapt a recently developed framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system toward any of its natural long-term dynamic behaviors, regardless of the specific functional forms and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of structural controllability in control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case but not in specific model instances.

Estimating Propensity Parameters Using Google PageRank and Genetic Algorithms

Stochastic Boolean networks, or more generally, stochastic discrete networks, are an important class of computational models for molecular interaction networks. The stochasticity stems from the updating schedule. Standard updating schedules include the synchronous update, where all the nodes are updated at the same time, and the asynchronous update where a random node is updated at each time step. The former produces a deterministic dynamics while the latter a stochastic dynamics. A more general stochastic setting considers propensity parameters for updating each node. Stochastic Discrete Dynamical Systems (SDDS) are a modeling framework that considers two propensity parameters for updating each node and uses one when the update has a positive impact on the variable, that is, when the update causes the variable to increase its value, and uses the other when the update has a negative impact, that is, when the update causes it to decrease its value. This framework offers additional features for simulations but also adds a complexity in parameter estimation of the propensities. This paper presents a method for estimating the propensity parameters for SDDS. The method is based on adding noise to the system using the Google PageRank approach to make the system ergodic and thus guaranteeing the existence of a stationary distribution. Then with the use of a genetic algorithm, the propensity parameters are estimated. Approximation techniques that make the search algorithms efficient are also presented and Matlab/Octave code to test the algorithms are available at http://www.ms.uky.edu/~dmu228/GeneticAlg/Code.html.

Identification of control targets in Boolean molecular network models via computational algebra

BACKGROUND

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system.

RESULTS

This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg .

CONCLUSIONS

This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.