scholarly journals Minimum complexity drives regulatory logic in Boolean models of living systems

2021 ◽  
Author(s):  
Ajay Subbaroyan ◽  
Olivier C. Martin ◽  
Areejit Samal
Keyword(s):  
Biological Networks ◽  
Boolean Functions ◽  
Regulatory Networks ◽  
Statistical Physics ◽  
Boolean Networks ◽  
Average Sensitivity ◽  
Boolean Models ◽  
Complexity Measures ◽  
Random Boolean Networks ◽  
Update Rules

The properties of random Boolean networks as models of gene regulation have been investigated extensively by the statistical physics community. In the past two decades, there has been a dramatic increase in the reconstruction and analysis of Boolean models of biological networks. In such models, neither network topology nor Boolean functions (or logical update rules) should be expected to be random. In this contribution, we focus on biologically meaningful types of Boolean functions, and perform a systematic study of their preponderance in gene regulatory networks. By applying the k[P] classification based on number of inputs k and bias P of functions, we find that most Boolean functions astonishingly have odd bias in a reference biological dataset of 2687 functions compiled from published models. Subsequently, we are able to explain this observation along with the enrichment of read-once functions (RoFs) and its subset, nested canalyzing functions (NCFs), in the reference dataset in terms of two complexity measures: Boolean complexity based on string lengths in formal logic which is yet unexplored in the biological context, and the average sensitivity. Minimizing the Boolean complexity naturally sifts out a subset of odd-biased Boolean functions which happen to be the RoFs. Finally, we provide an analytical proof that NCFs minimize not only the Boolean complexity, but also the average sensitivity in their k[P] set.

scholarly journals Degeneracy measures in biologically plausible random Boolean networks

2021 ◽  
Author(s):  
Basak Kocaoglu ◽  
William Alexander
Keyword(s):  
Gene Regulatory Networks ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Biological Systems ◽  
Boolean Networks ◽  
Data Sets ◽  
Random Boolean Networks ◽  
Weighted Networks ◽  
Underlying Network ◽  
Gene Regulatory

Degeneracy, the ability of structurally different elements to perform similar functions, is a property of many biological systems. Systems exhibiting a high degree of degeneracy continue to exhibit the same macroscopic behavior following a lesion even though the underlying network dynamics are significantly different. Degeneracy thus suggests how biological systems can thrive despite changes to internal and external demands. Although degeneracy is a feature of network topologies and seems to be implicated in a wide variety of biological processes, research on degeneracy in biological networks is mostly limited to weighted networks (e.g., neural networks). To date, there has been no extensive investigation of information theoretic measures of degeneracy in other types of biological networks. In this paper, we apply existing approaches for quantifying degeneracy to random Boolean networks used for modeling biological gene regulatory networks. Using random Boolean networks with randomly generated rulesets to generate synthetic gene expression data sets, we systematically investigate the effect of network lesions on measures of degeneracy. Our results are comparable to measures of degeneracy using weighted networks, and this suggests that degeneracy measures may be a useful tool for investigating gene regulatory networks.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

2019 ◽  
Vol 19 (6) ◽  
pp. 413-425 ◽  
Author(s):  
Athanasios Alexiou ◽  
Stylianos Chatzichronis ◽  
Asma Perveen ◽  
Abdul Hafeez ◽  
Ghulam Md. Ashraf
Keyword(s):  
Protein Interactions ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Review Paper ◽  
Boolean Networks ◽  
Diagnostic Tools ◽  
Complex Nature ◽  
Cellular Interactions ◽  
Protein Protein Interactions ◽  
Deterministic Models

Background:Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.Objective:Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.Methods:Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.Results:GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.Conclusion:In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.

scholarly journals Adaptive Local Information Transfer in Random Boolean Networks

2017 ◽  
Vol 23 (1) ◽  
pp. 105-118 ◽  
Author(s):  
Taichi Haruna
Keyword(s):  
Information Processing ◽  
Information Transfer ◽  
Regulatory Networks ◽  
Mean Field Theory ◽  
Mean Field ◽  
Boolean Networks ◽  
Local Information ◽  
System Level ◽  
Adjustment Process ◽  
Random Boolean Networks

Living systems such as gene regulatory networks and neuronal networks have been supposed to work close to dynamical criticality, where their information-processing ability is optimal at the whole-system level. We investigate how this global information-processing optimality is related to the local information transfer at each individual-unit level. In particular, we introduce an internal adjustment process of the local information transfer and examine whether the former can emerge from the latter. We propose an adaptive random Boolean network model in which each unit rewires its incoming arcs from other units to balance stability of its information processing based on the measurement of the local information transfer pattern. First, we show numerically that random Boolean networks can self-organize toward near dynamical criticality in our model. Second, the proposed model is analyzed by a mean-field theory. We recognize that the rewiring rule has a bootstrapping feature. The stationary indegree distribution is calculated semi-analytically and is shown to be close to dynamical criticality in a broad range of model parameter values.

CHAOTIC MEAN FIELD DYNAMICS OF A BOOLEAN NETWORK WITH RANDOM CONNECTIVITY

2007 ◽  
Vol 18 (09) ◽  
pp. 1459-1473 ◽  
Author(s):  
MALIACKAL POULO JOY ◽  
DONALD E. INGBER ◽  
SUI HUANG
Keyword(s):  
Regulatory Networks ◽  
Boolean Network ◽  
Mean Field ◽  
Period Doubling ◽  
Structural Heterogeneity ◽  
Boolean Networks ◽  
Analytical Treatment ◽  
Random Boolean Networks ◽  
The Mean ◽  
Parameter Values

Random Boolean networks have been used as simple models of gene regulatory networks, enabling the study of the dynamic behavior of complex biological systems. However, analytical treatment has been difficult because of the structural heterogeneity and the vast state space of these networks. Here we used mean field approximations to analyze the dynamics of a class of Boolean networks in which nodes have random degree (connectivity) distributions, characterized by the mean degree k and variance D. To achieve this we generalized the simple cellular automata rule 126 and used it as the Boolean function for all nodes. The equation for the evolution of the density of the network state is presented as a one-dimensional map for various input degree distributions, with k and D as the control parameters. The mean field dynamics is compared with the data obtained from the simulations of the Boolean network. Bifurcation diagrams and Lyapunov exponents for different parameter values were computed for the map, showing period doubling route to chaos with increasing k. Onset of chaos was delayed (occurred at higher k) with the increase in variance D of the connectivity. Thus, the network tends to be less chaotic when the heterogeneity, as measured by the variance of connectivity, was higher.

The Robustness and Mutual Information Entropy of Random Modular Boolean Networks

2014 ◽  
Vol 989-994 ◽  
pp. 4417-4420 ◽  
Author(s):  
Nan Zhao ◽  
Bing Hui Guo ◽  
Fan Chao Meng
Keyword(s):  
Mutual Information ◽  
Regulatory Networks ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Information Propagation ◽  
Entropy Analysis ◽  
Random Boolean Networks ◽  
Basic Model ◽  
Different Types

Random Boolean networks have been proposed as a basic model of genetic regulatory networks for more than four decades. Attractors have been considered as the best way to represent the long-term behaviors of random Boolean networks. Most studies on attractors are made with random topologies. However, the real regulatory networks have been found to be modular or more complex topologies. In this work, we extend classical robustness and entropy analysis of random Boolean networks to random modular Boolean networks. We firstly focus on the robustness of the attractor to perturbations with different parameters. Then, we investigate and calculate how the amount of information propagated between the nodes when on an attractor, as quantified by the average pairwise mutual information. The results can be used to study the capability of genetic information propagation of different types of genetic regulatory networks.

scholarly journals Modular Random Boolean Networks

2011 ◽  
Vol 17 (4) ◽  
pp. 331-351 ◽  
Author(s):  
Rodrigo Poblanno-Balp ◽  
Carlos Gershenson
Keyword(s):  
Chaotic Dynamics ◽  
Regulatory Networks ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Random Boolean Networks ◽  
Analytical Results ◽  
Statistical Experiments

Random Boolean networks (RBNs) have been a popular model of genetic regulatory networks for more than four decades. However, most RBN studies have been made with random topologies, while real regulatory networks have been found to be modular. In this work, we extend classical RBNs to define modular RBNs. Statistical experiments and analytical results show that modularity has a strong effect on the properties of RBNs. In particular, modular RBNs have more attractors, and are closer to criticality when chaotic dynamics would be expected, than classical RBNs.

scholarly journals Flexibility of Boolean Network Reservoir Computers in Approximating Arbitrary Recursive and Non-Recursive Binary Filters

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 954
Author(s):  
Moriah Echlin ◽  
Boris Aguilar ◽  
Max Notarangelo ◽  
David Gibbs ◽  
Ilya Shmulevich
Keyword(s):  
Boolean Functions ◽  
Boolean Networks ◽  
Average Sensitivity ◽  
Approximation Accuracy ◽  
Balance System ◽  
Binary Signal ◽  
And Function ◽  
Binary Functions ◽  
And Training ◽  
Effective Approximation

Reservoir computers (RCs) are biology-inspired computational frameworks for signal processing that are typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and identifying the factors that determine the effective approximation of Boolean functions applied in a sliding-window fashion over a binary signal, both non-recursively and recursively. We train and test BN RCs of different sizes, signal connectivity, and in-degree to approximate three-bit, five-bit, and three-bit recursive binary functions, respectively. We analyze how BN RC parameters and function average sensitivity, which is a measure of function smoothness, affect approximation accuracy as well as the spread of accuracies for a single reservoir. We found that approximation accuracy and reservoir flexibility are highly dependent on RC parameters. Overall, our results indicate that not all reservoirs are equally flexible, and RC instantiation and training can be more efficient if this is taken into account. The optimum range of RC parameters opens up an angle of exploration for understanding how biological systems might be tuned to balance system restraints with processing capacity.

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.

The impact of sources and sinks on the dynamics of homogeneous and heterogeneous boolean networks

2021 ◽  
Author(s):  
Luca Agostini
Keyword(s):  
Regulatory Networks ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
The Other ◽  
Structural Elements ◽  
Sources And Sinks ◽  
Random Boolean Networks ◽  
Dynamical Behaviors ◽  
Other Hand ◽  
The Impact

Random Boolean networks, originally introduced as simplified models for the genetic regulatory networks, are abstract models widely applied for the study of the dynamical behaviors of self-organizing complex systems. In these networks, connectivity and the bias of the Boolean functions are the most important factors that can determine the behavioral regime of the systems. On the other hand, it has been found that topology and some structural elements of the networks such as the reciprocity, self-loops and source nodes, can have relevant effects on the dynamical properties of critical Boolean networks. In this paper, we study the impact of source and sink nodes on the dynamics of homogeneous and heterogeneous Boolean networks. Our research shows that an increase of the source nodes causes an exponentially growing of the different behaviors that the system can exhibit regardless of the network topology, while the amount of order seems to undergo modifications depending on the topology of the system. Indeed, with the increase of the source nodes the orderliness of the heterogeneous networks also increases, whereas it diminishes in the homogeneous ones. On the other hand, although the sink nodes seem not to have effects on the dynamic of the homogeneous networks, for the heterogeneous ones we have found that an increase of the sinks gives rise to an increasing of the order, although the different potential behaviors of the system remains approximately the same.

Sign in / Sign up

Export Citation Format

Share Document