Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we quantify the dynamical impact of a node as the probability of damage spreading after switching the node's state. We find that the leading eigenvector of the adjacency matrix is a good predictor of dynamical impact in the case of long-term spreading. This so-called eigenvector centrality is also a good proxy measure of the influence a node's initial state has on the attractor the system eventually arrives at. Quality of prediction is further improved when eigenvector centrality is based on the weighted matrix of activities rather than the unweighted adjacency matrix. Simulations are performed with ensembles of random Boolean networks and a Boolean model of signaling in fibroblasts. The findings are supported by analytic arguments from a linear approximation of damage spreading.
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 ne…
The study of control mechanisms of biological systems allows for interesting applications in bioengineering and medicine, for instance in cell reprogramming or drug target identification. A control strategy often consists of a set of interventions that, by fixing the values of some components, ensure that the long term dynamics of the controlled system is in a desired state. A common approach to control in the Boolean framework consists in checking how the fixed values propagate through the network, to establish whether the effect of percolating the interventions is sufficient to induce the ta…
This Thesis presents research at the boundary between Statistical Physics and Biology. First, we have devised a class of Boolean constraint satisfaction problems (CSP) whose solutions describe the feasible operational states of a chemical reaction network. After developing statistical mechanics techniques to generate solutions and studying the properties of the solution space for both ensembles and individual instances of random reaction networks, we have applied this framework to the metabolic network of the bacterium E.Coli. Results highlight, on one hand, a complex organization of operation…
Recent progress in experimental techniques has enabled us to quantitatively study stochastic and flexible behavior of biological systems. For example, gene regulatory networks perform stochastic information processing and their functionalities have been extensively studied. In gene regulatory networks, there are specific subgraphs called network motifs that occur at frequencies much higher than those found in randomized networks. Further understanding of the designing principle of such networks is highly desirable. In a different context, information thermodynamics has been developed as a theo…
Motivation: 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 signal…
In this paper, we address the formal characterization of targets triggering cellular trans-differentiation in the scope of Boolean networks with asynchronous dynamics. Given two fixed points of a Boolean network, we are interested in all the combinations of mutations which allow to switch from one fixed point to the other, either possibly, or inevitably. In the case of existential reachability, we prove that the set of nodes to (permanently) flip are only and necessarily in certain connected components of the interaction graph. In the case of inevitable reachability, we provide an algorithm to…
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 e…
Relating biomarkers and phenotypes using dynamical trap spaces
Faculty of Informatics, Masaryk University（马萨里克大学信息学院）；Department of Physics, Pennsylvania State University（宾夕法尼亚州立大学物理系）；Biological Sciences Division, Pacific Northwest National Laboratory（太平洋西北国家实验室生物科学部）；Faculty of Computer Science and Engineering, Ho Chi Minh City University of Technology (HCMUT)（胡志明市理工大学计算机科学与工程学院）
LRI, CNRS, U. Paris-Sud U. Paris-Saclay（巴黎-萨克雷大学南巴黎校区法国国家科学研究中心计算机研究所）；LaBRI, CNRS, U. Bordeaux Bordeaux INP（波尔多大学波尔多国立理工学院法国国家科学研究中心计算机与自动化研究所）；Institut Curie, INSERM U. PSL, Mines ParisTech（巴黎文理研究大学法国国家健康与医学研究院巴黎高等矿业学院居里研究所）
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability…
Recent developments in Omics-technologies revolutionized the investigation of biology by producing molecular data in multiple dimensions and scale. This breakthrough in biology raises the crucial issue of their interpretation based on modelling. In this undertaking, network provides a suitable framework for modelling the interactions between molecules. Basically a Biological network is composed of nodes referring to the components such as genes or proteins, and the edges/arcs formalizing interactions between them. The evolution of the interactions is then modelled by the definition of a dynami…
The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modelling, e.g., in systems biology. Yet there are currently very few tools available that are able to compute and visualise not only attractors but also their basins. In the realm of asynchronous, non-deterministic modeling not only is the repertoire of software even more limited, but also the formal notions for basins of attraction are often lacking. In this setting, the difficulty both for theory and computation arises from the fact that states may be ele- ments of s…
