Boolean networks provide robust, explainable, and predictive models of cellular dynamics, especially for cellular differentiation and fate decision processes. Yet, the construction of such models is extremely challenging, as it requires integrating prior knowledge with experimental observation of the transcriptome, potentially relating thousands of genes. We present a general methodology for integrating transcriptome data and prior knowledge on the underlying gene regulatory network in order to generate automatically ensembles of Boolean networks able to reproduce the modeled qualitative behavior. Our methodology builds on the software BoNesis, which implements the automatic construction of Boolean networks from a specification of their expected structural and dynamical properties. We show how to transform transcriptome data into such a qualitative specification, and then how to exploit the generated ensembles of Boolean networks for identifying families of candidate models, and for predicting robust cellular reprogramming targets. We illustrate the scalability and versatility of our overall approach with two applications: the modeling of hematopoiesis from single-cell RNA-Seq data, and modeling the differentiation of bone marrow stromal cells into adipocytes and osteoblasts from bulk RNA-seq time series data. For this latter case, we took advantage of ensemble modeling to predict combinations of reprogramming factors for trans-differentiation that are robust to model uncertainties due to variations in experimental replicates and choice of binarization method. Moreover, we performed an in silico assessment of the fidelity and efficiency of the reprogramming and conducted preliminary experimental validation.

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.

In recent years, great efforts have been made to analyze biological systems to understand the long-run behaviors. As a well-established formalism for modelling real-life biological systems, Boolean networks (BNs) allow their representation and analysis using formal reasoning and tools. Most biological systems are robust—they can withstand the loss of links and cope with external environmental perturbations. Hence, the BNs used to model such systems are necessarily large and dense, and yet modular. However, existing analysis methods only work well on networks of moderate size. Thus, there is a great need for efficient methods that can handle large-scale BNs and for doing so it is inevitable to exploit both the structural and dynamic properties of the networks. In this paper, we propose a method towards the optimal decomposition of BNs to balance the relation between the structure and dynamics of a network. We show that our method can greatly improve the existing decomposition-based attractor detection by analyzing a number of large real-life biological networks.

SUMMARY:Direct cell reprogramming, also called transdifferentiation, has great potential for tissue engineering and regenerative medicine. Boolean networks, a popular modelling framework for gene regulatory networks, make it possible to identify intervention targets for direct cell reprogramming with computational methods. In this work, we present our software, CABEAN, for the control of asynchronous Boolean networks. CABEAN identifies efficacious nodes, whose perturbations can drive the dynamics of a network from a source attractor (the initial cell type) to a target attractor (the desired cell type). CABEAN provides several control methods integrating practical constraints. Thus, it has the ability to provide a rich set of control sets, such that biologists can select suitable ones for validation based on specific experimental settings.AVAILABILITY AND IMPLEMENTATION:The executable binary and the user guide of the software are publicly available at https://satoss.uni.lu/software/CABEAN/.

We present a new version of the software, Cabean, integrating six source-target control methods and three target control methods for the reprogramming of asynchronous Boolean networks. The source-target control methods compute the minimal one-step and sequential control strategies that can guide the dynamics of a Boolean network from a source attractor to the desired target attractor with instantaneous, temporary, or permanent perturbations. The target control methods further identify efficacious interventions that can drive the network from any initial state to the desired target attractor with these three types of perturbations. These control methods have been applied to various real-life biological networks to demonstrate their efficacy and efficiency.

Direct cell reprogramming makes it feasible to reprogram abundant somatic cells into desired cells. It has great potential for regenerative medicine and tissue engineering. In this work, we study the control of biological networks, modelled as Boolean networks, to identify control paths driving the dynamics of the network from a source attractor (undesired cells) to the target attractor (desired cells). Instead of achieving control in one step, we develop attractor-based sequential temporary and permanent control methods (AST and ASP) to identify a sequence of interventions that can alter the dynamics in a stepwise manner. To improve their feasibility, both AST and ASP only use biologically observable attractors as intermediates. They can find the shortest sequential paths and guarantee 100% reachability of the target attractor. We apply the two methods to several real-life biological networks and compare their performance with the attractor-based sequential instantaneous control (ASI). The results demonstrate that AST and ASP have the ability to identify a richer set of control paths with fewer perturbations than ASI, which will greatly facilitate practical applications.

We study the target control problem of asynchronous Boolean networks, to identify a set of nodes, the perturbation of which can drive the dynamics of the network from any initial state to the desired steady state (or attractor). We are particularly interested in temporary perturbations, which are applied for sufficient time and then released to retrieve the original dynamics. Temporary perturbations have the apparent advantage of averting unforeseen consequences, which might be induced by permanent perturbations. Despite the infamous state-space explosion problem, in this work, we develop an efficient method to compute the temporary target control for a given target attractor of a Boolean network. We apply our method to a number of real-life biological networks and compare its performance with the stable motif-based control method to demonstrate its efficacy and efficiency.

We address the sequential reprogramming of gene regulatory networks modelled as Boolean networks. We develop an attractor-based sequential reprogramming method to compute all sequential reprogramming paths from a source attractor to a target attractor, where only attractors of the network are used as intermediates. Our method is more practical than existing reprogramming methods as it incorporates several practical constraints: (1) only biologically observable states, viz. attractors, can act as intermediates; (2) certain attractors, such as apoptosis, can be avoided as intermediates; (3) certain nodes can be avoided to perturb as they may be essential for cell survival or difficult to perturb with biomolecular techniques; and (4) given a threshold k, all sequential reprogramming paths with no more than k perturbations are computed. We compare our method with the minimal one-step reprogramming and the minimal sequential reprogramming on a variety of biological networks. The results show that our method can greatly reduce the number of perturbations compared to the one-step reprogramming, while having comparable results with the minimal sequential reprogramming. Moreover, our implementation is scalable for networks of more than 60 nodes.

A salient objective of studying gene regulatory networks (GRNs) is to identify potential target genes whose perturbations would lead to effective treatment of diseases. In this paper, we develop two control methods for GRNs in the context of asynchronous Boolean networks. Our methods compute a minimal subset of nodes of a given Boolean network, such that temporary or permanent perturbations of these nodes drive the network from an initial state to a target steady state. The main advantages of our methods include: (1) temporary and permanent perturbations can be feasibly conducted with techniques for genetic modifications in biological experiments; and (2) the minimality of the identified control sets can reduce the cost of experiments to a great extent. We apply our methods to several real-life biological networks in silico to show their efficiency in terms of computation time and their efficacy with respect to the number of nodes to be perturbed.

We summarise our recent research results on developing efficient and scalable control methods for gene regulatory networks modelled as asynchronous Boolean networks. Our methods compute a minimal subset of nodes of a given Boolean network, such that (different types of) perturbations of these nodes, in one step or a sequence of steps, can drive the network (from an initial state) to a target steady state.

Cellular reprogramming, a technique that opens huge opportunities in modern and regenerative medicine, heavily relies on identifying key genes to perturb. Most of the existing computational methods for controlling which attractor (steady state) the cell will reach focus on finding mutations to apply to the initial state. However, it has been shown, and is proved in this article, that waiting between perturbations so that the update dynamics of the system prepares the ground, allows for new reprogramming strategies. To identify such sequential perturbations, we consider a qualitative model of regulatory networks, and rely on Binary Decision Diagrams to model their dynamics and the putative perturbations. Our method establishes a set identification of sequential perturbations, whether permanent (mutations) or only temporary, to achieve the existential or inevitable reachability of an arbitrary state of the system. We apply an implementation for temporary perturbations on models from the literature, illustrating that we are able to derive sequential perturbations to achieve trans-differentiation.

The full-fledging of Chinese national emissions trading system (ETS) still depends on the experiences of its pilot projects. This paper accesses the interdependence between ETSs from a complexity perspective in order to identify which one is with the most important relevance in terms of the entropy-based correlation. Firstly, the complexity of pilots is measured with multi-scale fuzzy entropy. Entropy-based correlations, the correlations of entropy series, are then used to describe dynamic behavior of the pilots. Finally, the role of pilots is studied by norms and eigenvalue variations. Multi-scale fuzzy entropy analysis finds that all pilots have small entropy values, thus indicating a low complexity. Entropy-based correlations show a dominant positive and centered correlations between the pilots. However, the correlations are strong (the absolute value >0.5) within a week while weak (the absolute value <0.5) for time scales larger than one month. Beijing pilot presents the greatest norm in general and has the biggest variations of the eigenvalues. It is thus regarded as the one that is most relevant to others among China's regional carbon markets. The research suggests that more importance should be paid to the core pilot when constructing the national carbon market.

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.

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be perturbed in a single-step to drive its dynamics from an initial state to a target steady state (or attractor), which we call the source-target control of Boolean networks. Due to the phenomenon of state-space explosion, a simple global approach that performs computations on the entire network may not scale well for large networks. We believe that efficient algorithms for such networks must exploit the structure of the networks together with their dynamics. Taking this view, we derive a decomposition-based solution to the minimal source-target control problem which can be significantly faster than the existing approaches on large networks. We then show that the solution can be further optimized if we take into account appropriate information about the source state. We apply our solutions to both real-life biological networks and randomly generated networks, demonstrating the efficiency and efficacy of our approach.

Given a Boolean network BN and a subset A of attractors of BN, we study the problem of identifying a minimal subset C of vertices of BN, such that the dynamics of BN can reach from a state s in any attractor As in A to any attractor At in A by controlling or toggling a subset of vertices in C in a single time step. We describe a method based on the decomposition of the network structure into strongly connected components called blocks. The control subset can be locally computed for each such block and the results then merged to derive the global control subset C. This potentially improves the efficiency for many real-life networks that are large but modular and well-structured. We are currently in the process of implementing our method in software.

Carbon markets provide a market-based way to reduce climate pollution. Subject to general market regulations, the major existing emission trading markets present complex characteristics. This paper analyzes the complexity of carbon market by using the multi-scale entropy. Pilot carbon markets in China are taken as the example. Moving average is adopted to extract the scales due to the short length of the data set. Results show a low-level complexity inferring that China's pilot carbon markets are quite immature in lack of market efficiency. However, the complexity varies in different time scales. China's carbon markets (except for the Chongqing pilot) are more complex in the short period than in the long term. Furthermore, complexity level in most pilot markets increases as the markets developed, showing an improvement in market efficiency. All these results demonstrate that an effective carbon market is required for the full function of emission trading.

Boolean networks (BNs), introduced by Kauffman [3], is a popular and well-established framework for modelling gene regulatory networks and their associated signalling pathways. The main advantage of this framework is that it is relatively simple and yet able to capture the important dynamical properties of the system under study, thus facilitating the modelling and analysis of large biological networks as a whole.

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be controlled to drive its dynamics from an initial steady state (or attractor) to a target steady state. Due to the phenomenon of state-space explosion, a simple global approach that performs computations on the entire network, may not scale well for large networks. We believe that efficient algorithms for such networks must exploit the structure of the networks together with their dynamics. Taking such an approach, we derive a decomposition-based solution to the minimal control problem which can be significantly faster than the existing approaches on large networks. We apply our solution to both real-life biological networks and randomly generated networks, demonstrating promising results.

How to achieve accurately and automatically inject anesthetics is a great challenge both in clinic and neural engineering. Employing the computer to simulate the anesthesia process and control performance are valuable for the design of actual control system.The virtual patient library was established to test the ability of the control system,which responds to differences between patients.And Renyi permutation entropy as the depth of anesthesia monitoring index is proposed,according to the changes of Renyi permutation entropy,the control of propofol input speed is changed.For individualized model of patient,the identification is done, and the model predictive controller is designed and used to control the patient based on identification model.The performance of the control system is analyzed by four indexes: error, median performance error, median absolute performance error, wobble.The simulation results show that the system can well track the desired Renyi permutation entropy and maintain the desired depth of anesthesia.