scholarly journals ROBUSTNESS OF TRANSCRIPTIONAL REGULATION IN YEAST-LIKE MODEL BOOLEAN NETWORKS

2010 ◽  
Vol 20 (03) ◽  
pp. 929-935 ◽  
Author(s):  
MURAT TUĞRUL ◽  
ALKAN KABAKÇIOĞLU
Keyword(s):  
Transcriptional Regulation ◽  
Boolean Functions ◽  
Boolean Network ◽  
Regulation Of Gene Expression ◽  
Boolean Networks ◽  
Transcription Level ◽  
Yeast Saccharomyces Cerevisiae ◽  
Boolean Network Model ◽  
Global Topology ◽  
Model Networks

We investigate the dynamical properties of the transcriptional regulation of gene expression in the yeast Saccharomyces Cerevisiae within the framework of a synchronously and deterministically updated Boolean network model. With a dynamically determinant subnetwork, we explore the robustness of transcriptional regulation as a function of the type of Boolean functions used in the model that mimic the influence of regulating agents on the transcription level of a gene. We compare the results obtained for the actual yeast network with those from two different model networks, one with similar in-degree distribution as the yeast and otherwise random, and another due to Balcan et al., where the global topology of the yeast network is reproduced faithfully. We, surprisingly, find that the first set of model networks better reproduce the results found with the actual yeast network, even though the Balcan et al. model networks are structurally more similar to that of yeast.

scholarly journals On the Lyapunov Exponent of Monotone Boolean Networks †

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1035
Author(s):  
Ilya Shmulevich
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Boolean Functions ◽  
Boolean Network ◽  
Discrete Dynamical Systems ◽  
Boolean Networks ◽  
Asymptotic Formulas ◽  
Small Perturbations ◽  
Monotone Boolean Functions ◽  
Almost All

Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd.

scholarly journals An extended gene protein/products boolean network model including post-transcriptional regulation

2014 ◽  
Vol 11 (S1) ◽  
Author(s):  
Alfredo Benso ◽  
Stefano Di Carlo ◽  
Gianfranco Politano ◽  
Alessandro Savino ◽  
Alessandro Vasciaveo
Keyword(s):  
Transcriptional Regulation ◽  
Network Model ◽  
Boolean Network ◽  
Boolean Network Model ◽  
Post Transcriptional Regulation

INFERENCE OF GENE REGULATORY NETWORKS USING BOOLEAN-NETWORK INFERENCE METHODS

2009 ◽  
Vol 07 (06) ◽  
pp. 1013-1029 ◽  
Author(s):  
GRAHAM J. HICKMAN ◽  
T. CHARLIE HODGMAN
Keyword(s):  
Regulatory Networks ◽  
Boolean Network ◽  
Network Inference ◽  
Genetic Network ◽  
Boolean Networks ◽  
Genetic Networks ◽  
Related Data ◽  
Boolean Network Model ◽  
Gene Regulatory ◽  
Inference Methods

The modeling of genetic networks especially from microarray and related data has become an important aspect of the biosciences. This review takes a fresh look at a specific family of models used for constructing genetic networks, the so-called Boolean networks. The review outlines the various different types of Boolean network developed to date, from the original Random Boolean Network to the current Probabilistic Boolean Network. In addition, some of the different inference methods available to infer these genetic networks are also examined. Where possible, particular attention is paid to input requirements as well as the efficiency, advantages and drawbacks of each method. Though the Boolean network model is one of many models available for network inference today, it is well established and remains a topic of considerable interest in the field of genetic network inference. Hybrids of Boolean networks with other approaches may well be the way forward in inferring the most informative networks.

Estimation of delays in generalized asynchronous Boolean networks

2016 ◽  
Vol 12 (10) ◽  
pp. 3098-3110 ◽  
Author(s):  
Haimabati Das ◽  
Ritwik Kumar Layek
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Network Model ◽  
Boolean Network ◽  
Equation Model ◽  
Boolean Networks ◽  
Temporal Behavior ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Boolean Network Model

The generalized asynchronous Boolean network model proposed in this paper can reliably mimic the temporal behavior of the Ordinary Differential Equation model without compromising the flexibility of the Boolean network model.

ASYNCHRONOUS RANDOM BOOLEAN NETWORK MODEL WITH VARIABLE NUMBER OF PARENTS BASED ON ELEMENTARY CELLULAR AUTOMATA RULE 126

2006 ◽  
Vol 20 (08) ◽  
pp. 897-923 ◽  
Author(s):  
MIHAELA T. MATACHE
Keyword(s):  
Cellular Automata ◽  
Network Model ◽  
Boolean Network ◽  
Random Variable ◽  
Variable Number ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Elementary Cellular Automata ◽  
Boolean Network Model ◽  
Point Analysis

A Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which can vary from one node to another, is considered. This is a generalization of previous results obtained for a constant number of parent nodes, by Matache and Heidel in "Asynchronous Random Boolean Network Model Based on Elementary Cellular Automata Rule 126", Phys. Rev. E71, 026 232, 2005. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. The Boolean rule is a generalization of rule 126 of elementary cellular automata, and is assumed to be the same for all the nodes. We provide a model for the probability of finding a node in state 1 at a time t for the class of generalized asynchronous random Boolean networks (GARBN) in which a random number of nodes can be updated at each time point. We generate consecutive states of the network for both the real system and the models under the various schemes, and use simulation algorithms to show that the results match well. We use the model to study the dynamics of the system through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the GARBN's dynamics range from order to chaos, depending on the type of random variable generating the asynchrony and the parameter combinations.

scholarly journals Random Networks with Quantum Boolean Functions

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 792 ◽  
Author(s):  
Mario Franco ◽  
Octavio Zapata ◽  
David A. Rosenblueth ◽  
Carlos Gershenson
Keyword(s):  
Boolean Functions ◽  
Boolean Network ◽  
Complex Dynamics ◽  
Boolean Networks ◽  
Stable Complex ◽  
Complex Dynamic ◽  
Random Boolean Networks ◽  
Quantum Simulator ◽  
Novel Model ◽  
Unstable Dynamics

We propose quantum Boolean networks, which can be classified as deterministic reversible asynchronous Boolean networks. This model is based on the previously developed concept of quantum Boolean functions. A quantum Boolean network is a Boolean network where the functions associated with the nodes are quantum Boolean functions. We study some properties of this novel model and, using a quantum simulator, we study how the dynamics change in function of connectivity of the network and the set of operators we allow. For some configurations, this model resembles the behavior of reversible Boolean networks, while for other configurations a more complex dynamic can emerge. For example, cycles larger than 2N were observed. Additionally, using a scheme akin to one used previously with random Boolean networks, we computed the average entropy and complexity of the networks. As opposed to classic random Boolean networks, where “complex” dynamics are restricted mainly to a connectivity close to a phase transition, quantum Boolean networks can exhibit stable, complex, and unstable dynamics independently of their connectivity.

scholarly journals A Note on the Observability of Temporal Boolean Control Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenping Shi ◽  
Bo Wu ◽  
Jing Han
Keyword(s):  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Control Networks ◽  
Linear Dynamic Systems ◽  
Regulatory Interactions ◽  
Boolean Control Network ◽  
Boolean Network Model ◽  
Necessary And Sufficient ◽  
Product Of Matrices

Temporal Boolean network is a generalization of the Boolean network model that takes into account the time series nature of the data and tries to incorporate into the model the possible existence of delayed regulatory interactions among genes. This paper investigates the observability problem of temporal Boolean control networks. Using the semi tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems with time delays. Then, necessary and sufficient conditions on the observability via two kinds of inputs are obtained. An example is given to illustrate the effectiveness of the obtained results.

scholarly journals Delay Partial Synchronization of Mutual Delay Coupled Boolean Networks

2020 ◽  
Vol 53 (5-6) ◽  
pp. 870-875 ◽  
Author(s):  
Qiang Wei ◽  
Cheng-jun Xie ◽  
Xu-ri Kou ◽  
Wei Shen
Keyword(s):  
Theoretical Analysis ◽  
Network Model ◽  
Upper Bound ◽  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Partial Synchronization ◽  
Synchronization Time ◽  
Boolean Network Model ◽  
Necessary And Sufficient

This paper studies the delay partial synchronization for mutual delay-coupled Boolean networks. First, the mutual delay-coupled Boolean network model is presented. Second, some necessary and sufficient conditions are derived to ensure the delay partial synchronization of the mutual delay-coupled Boolean networks. The upper bound of synchronization time is obtained. Finally, an example is provided to illustrate the efficiency of the theoretical analysis.

scholarly journals Synchronization of mutual time-varying delay-coupled temporal Boolean networks

2020 ◽  
Vol 53 (7-8) ◽  
pp. 1504-1511
Author(s):  
Qiang Wei ◽  
Cheng-jun Xie
Keyword(s):  
Theoretical Analysis ◽  
Upper Bound ◽  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Time Varying ◽  
Time Varying Delay ◽  
Boolean Network Model ◽  
Necessary And Sufficient ◽  
Varying Delay

This paper presents mutual time-varying delay-coupled temporal Boolean network model and investigates synchronization issue for mutual time-varying delay-coupled temporal Boolean networks. The necessary and sufficient conditions for the synchronization are given, and the check criterion of the upper bound is presented. An example is given to illustrate the correctness of the theoretical analysis.

scholarly journals Construction Method of Probabilistic Boolean Networks Based on Imperfect Information

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 268
Author(s):  
Katsuaki Umiji ◽  
Koichi Kobayashi ◽  
Yuh Yamashita
Keyword(s):  
Gene Regulatory Networks ◽  
Boolean Functions ◽  
Regulatory Networks ◽  
Imperfect Information ◽  
Boolean Network ◽  
Construction Method ◽  
Boolean Networks ◽  
Probabilistic Boolean Network ◽  
Gene Regulatory ◽  
Selection Probabilities

A probabilistic Boolean network (PBN) is well known as one of the mathematical models of gene regulatory networks. In a Boolean network, expression of a gene is approximated by a binary value, and its time evolution is expressed by Boolean functions. In a PBN, a Boolean function is probabilistically chosen from candidates of Boolean functions. One of the authors has proposed a method to construct a PBN from imperfect information. However, there is a weakness that the number of candidates of Boolean functions may be redundant. In this paper, this construction method is improved to efficiently utilize given information. To derive Boolean functions and those selection probabilities, the linear programming problem is solved. Here, we introduce the objective function to reduce the number of candidates. The proposed method is demonstrated by a numerical example.

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