DReSS: a method to quantitatively describe the influence of structural perturbations on state spaces of genetic regulatory networks

2020 ◽  
Author(s):  
Ziqiao Yin ◽  
Binghui Guo ◽  
Shuangge Ma ◽  
Yifan Sun ◽  
Zhilong Mi ◽  
...  
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Random Networks ◽  
Graph Distance ◽  
State Spaces ◽  
Biological Regulatory Networks ◽  
Structural Perturbations ◽  
The Relationship ◽  
Index Family

Abstract Structures of genetic regulatory networks are not fixed. These structural perturbations can cause changes to the reachability of systems’ state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system’s state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes.

scholarly journals DReSS: A difference measurement based on reachability between state spaces of Boolean networks

2020 ◽  
Author(s):  
Ziqiao Yin ◽  
Binghui Guo ◽  
Shuangge Steven Ma ◽  
Yifan Sun ◽  
Zhilong Mi ◽  
...  
Keyword(s):  
State Space ◽  
Regulatory Network ◽  
Biological Systems ◽  
Boolean Networks ◽  
Random Networks ◽  
Biological Factors ◽  
Related Factors ◽  
State Spaces ◽  
Structural Perturbations ◽  
Dynamical Features

AbstractResearches on dynamical features of biological systems are mostly based on fixed network structure. However, both biological factors and data factors can cause structural perturbations to biological regulatory networks. There are researches focus on the influence of such structural perturbations to the systems’ dynamical features. Reachability is one of the most important dynamical features, which describe whether a state can automatically evolve into another state. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. DReSS, Difference based on Reachability between State Spaces, is proposed in this research to solve this problem. First, basic properties of DReSS such as non-negativity, symmetry and subadditivity are proved based on the definition. And two more indexes, diagDReSS and iDReSS are proposed based on the definition of DReSS. Second, typical examples like DReSS = 0 or 1 are shown to explain the meaning of DReSS family, and the differences between DReSS and traditional graph distance are shown based on the calculation steps of DReSS. Finally, differences of DReSS distribution between real biological regulatory network and random networks are compared. Multiple interaction positions in real biological regulatory network show significant different DReSS value with those in random networks while none of them show significant different diagDReSS value, which illustrates that the structural perturbations tend to affect reachability inside and between attractor basins rather than to affect attractor set itself.Author summaryBoolean network is a kind of networks which is widely used to model biological regulatory systems. There are structural perturbations in biological systems based on both biological factors and data-related factors. We propose a measurement called DReSS to describe the difference between state spaces of Boolean networks, which can be used to evaluate the influence of specific structural perturbations of a network to its state space quantitively. We can use DReSS to detect the sensitive interactions in a regulatory network, where structural perturbations can influence its state space significantly. We proved properties of DReSS including non-negativity, symmetry and subadditivity, and gave examples to explain the meaning of some special DReSS values. Finally, we present an example of using DReSS to detect sensitive vertexes in yeast cell cycle regulatory network. DReSS can provide a new perspective on how different interactions affect the state space of a specific regulatory network differently.

scholarly journals Informeasure: an R/Bioconductor package to quantify nonlinear dependence between variables in biological networks from an information theory perspective

2021 ◽  
Author(s):  
CHU PAN
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Partial Information ◽  
R Package ◽  
Nonlinear Dependence ◽  
Bioconductor Package ◽  
Information Measures ◽  
Biological Regulatory Networks

Using information measures to infer biological regulatory networks can observe nonlinear relationship between variables, but it is computationally challenging and there is currently no convenient tool available. We here describe an information theory R package named Informeasure that devotes to quantifying nonlinear dependence between variables in biological regulatory networks from an information theory perspective. This package compiles most of the information measures currently available: mutual information, conditional mutual information, interaction information, partial information decomposition and part mutual information. The first estimator is used to infer bivariate networks while the last four estimators are dedicated to analysis of trivariate networks. The base installation of this turn-key package allows users to approach these information measures out of the box. Informeasure is implemented in R program and is available as an R/Bioconductor package at https://bioconductor.org/packages/Informeasure.

Generalized Boolean Networks

2010 ◽  
pp. 429-449 ◽  
Author(s):  
Christian Darabos ◽  
Mario Giacobini ◽  
Marco Tomassini
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Dynamical Behavior ◽  
Real Life ◽  
Network Models ◽  
Cell Types ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Point Of View ◽  
Scale Free

Random Boolean Networks (RBN) have been introduced by Kauffman more than thirty years ago as a highly simplified model of genetic regulatory networks. This extremely simple and abstract model has been studied in detail and has been shown capable of extremely interesting dynamical behavior. First of all, as some parameters are varied such as the network’s connectivity, or the probability of expressing a gene, the RBN can go through a phase transition, going from an ordered regime to a chaotic one. Kauffman’s suggestion is that cell types correspond to attractors in the RBN phase space, and only those attractors that are short and stable under perturbations will be of biological interest. Thus, according to Kauffman, RBN lying at the edge between the ordered phase and the chaotic phase can be seen as abstract models of genetic regulatory networks. The original view of Kauffman, namely that these models may be useful for understanding real-life cell regulatory networks, is still valid, provided that the model is updated to take into account present knowledge about the topology of real gene regulatory networks, and the timing of events, without loosing its attractive simplicity. According to present data, many biological networks, including genetic regulatory networks, seem, in fact, to be of the scale-free type. From the point of view of the timing of events, standard RBN update their state synchronously. This assumption is open to discussion when dealing with biologically plausible networks. In particular, for genetic regulatory networks, this is certainly not the case: genes seem to be expressed in different parts of the network at different times, according to a strict sequence, which depends on the particular network under study. The expression of a gene depends on several transcription factors, the synthesis of which appear to be neither fully synchronous nor instantaneous. Therefore, we have recently proposed a new, more biologically plausible model. It assumes a scale-free topology of the networks and we define a suitable semi-synchronous dynamics that better captures the presence of an activation sequence of genes linked to the topological properties of the network. By simulating statistical ensembles of networks, we discuss the attractors of the dynamics, showing that they are compatible with theoretical biological network models. Moreover, the model demonstrates interesting scaling abilities as the size of the networks is increased.

scholarly journals Dynamical Criticality in Gene Regulatory Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Marco Villani ◽  
Luca La Rocca ◽  
Stuart Alan Kauffman ◽  
Roberto Serra
Keyword(s):  
Regulatory Networks ◽  
Single Gene ◽  
Biological Evolution ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Dynamical Regime ◽  
Random Boolean Networks ◽  
Statistical Framework ◽  
Gene Regulatory ◽  
The Relationship

A well-known hypothesis, with far-reaching implications, is that biological evolution should preferentially lead to states that are dynamically critical. In previous papers, we showed that a well-known model of genetic regulatory networks, namely, that of random Boolean networks, allows one to study in depth the relationship between the dynamical regime of a living being’s gene network and its response to permanent perturbations. In this paper, we analyze a huge set of new experimental data on single gene knockouts in S. cerevisiae, laying down a statistical framework to determine its dynamical regime. We find that the S. cerevisiae network appears to be slightly ordered, but close to the critical region. Since our analysis relies on dichotomizing continuous data, we carefully consider the issue of an optimal threshold choice.

scholarly journals Hierarchical Coordinate Systems for Understanding Complexity and its Evolution, with Applications to Genetic Regulatory Networks

2008 ◽  
Vol 14 (3) ◽  
pp. 299-312 ◽  
Author(s):  
Attila Egri-Nagy ◽  
Chrystopher L. Nehaniv
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Complexity Analysis ◽  
Structural Complexity ◽  
Evolutionary Process ◽  
Genetic Regulatory Networks ◽  
Lac Operon ◽  
Complexity Measures ◽  
Evolution Of Complexity ◽  
Hierarchical Complexity

Beyond complexity measures, sometimes it is worthwhile in addition to investigate how complexity changes structurally, especially in artificial systems where we have complete knowledge about the evolutionary process. Hierarchical decomposition is a useful way of assessing structural complexity changes of organisms modeled as automata, and we show how recently developed computational tools can be used for this purpose, by computing holonomy decompositions and holonomy complexity. To gain insight into the evolution of complexity, we investigate the smoothness of the landscape structure of complexity under minimal transitions. As a proof of concept, we illustrate how the hierarchical complexity analysis reveals symmetries and irreversible structure in biological networks by applying the methods to the lac operon mechanism in the genetic regulatory network of Escherichia coli.

scholarly journals Evolutionary constraints on the complexity of genetic regulatory networks allow predictions of the total number of genetic interactions

2018 ◽  
Author(s):  
Adrian I. Campos-González ◽  
Julio A. Freyre-González
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Clustering Coefficient ◽  
Valuable Insight ◽  
Large Set ◽  
Final Size ◽  
Scale Free ◽  
Daunting Task ◽  
Complete Networks

Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network is currently complete. In this study, we analyzed the distribution of GRN structural properties across a large set of distinct prokaryotic organisms and found a set of constrained characteristics such as network density and number of regulators. Our results allowed us to estimate the number of interactions that complete networks would have, a valuable insight that could aid in the daunting task of network curation, prediction, and validation. Using state-of-the-art statistical approaches, we also provided new evidence to settle a previously stated controversy that raised the possibility of complete biological networks being random. Therefore, attributing the observed scale-free properties to an artifact emerging from the sampling process during network discovery. Furthermore, we identified a set of properties that enabled us to assess the consistency of the connectivity distribution for various GRNs against different alternative statistical distributions. Our results favor the hypothesis that highly connected nodes (hubs) are not a consequence of network incompleteness. Finally, an interaction coverage computed for the GRNs as a proxy for completeness revealed that high-throughput based reconstructions of GRNs could yield biased networks with a low average clustering coefficient, showing that classical targeted discovery of interactions is still needed.

scholarly journals The Age of Analog Networks

AI Magazine ◽  
2008 ◽  
Vol 29 (3) ◽  
pp. 63 ◽  
Author(s):  
Claudio Mattiussi ◽  
Daniel Marbach ◽  
Peter Dürr ◽  
Dario Floreano
Keyword(s):  
Reverse Engineering ◽  
Control Systems ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Metabolic Networks ◽  
Temporal Dynamics ◽  
Genetic Regulatory Networks ◽  
Nonlinear Feedback ◽  
Electronic Circuits ◽  
Genetic Encoding

A large class of systems of biological and technological relevance can be described as analog networks, that is, collections of dynamical devices interconnected by links of varying strength. Some examples of analog networks are genetic regulatory networks, metabolic networks, neural networks, analog electronic circuits, and control systems. Analog networks are typically complex systems which include nonlinear feedback loops and possess temporal dynamics at different time scales. Both the synthesis and reverse engineering of analog networks are recognized as knowledge-intensive activities, for which few systematic techniques exist. In this paper we will discuss the general relevance of the analog network concept and describe an evolutionary approach to the automatic synthesis and the reverse engineering of analog networks. The proposed approach is called analog genetic encoding (AGE) and realizes an implicit genetic encoding of analog networks. AGE permits the evolution of human-competitive solutions to real-world analog network design and identification problems. This is illustrated by some examples of application to the design of electronic circuits, control systems, learning neural architectures, and the reverse engineering of biological networks.

scholarly journals Biological regulatory networks are less nonlinear than expected by chance

2021 ◽  
Author(s):  
Santosh Manicka ◽  
Kathleen Johnson ◽  
David Murrugarra ◽  
Michael Levin
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Boolean Network ◽  
Network Models ◽  
Decomposition Methods ◽  
Boolean Logic ◽  
Nonlinear Interactions ◽  
Biological Regulatory Networks ◽  
Probabilistic Generalization ◽  
Selection For

Nonlinearity is a characteristic of complex biological regulatory networks that has implications ranging from therapy to control. To better understand its nature, we analyzed a suite of published Boolean network models, containing a variety of complex nonlinear interactions, with an approach involving a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation using Taylor-decomposition methods revealed the distinct layers of nonlinearity of the models. A comparison of the resulting series of model approximations with the corresponding sets of randomized ensembles furthermore revealed that the biological networks are relatively more linearly approximable. We hypothesize that this is a result of optimization by natural selection for the purpose of controllability.

scholarly journals Meeting Measurement Precision Requirements for Effective Engineering of Genetic Regulatory Networks

2021 ◽  
Author(s):  
Jacob Beal ◽  
Brian Teague ◽  
John T. Sexton ◽  
Sebastian Castillo-Hair ◽  
Nicholas A. DeLateur ◽  
...  
Keyword(s):  
Flow Cytometry ◽  
Regulatory Networks ◽  
Current Model ◽  
Genetic Regulatory Networks ◽  
Measurement Precision ◽  
Cellular Behavior ◽  
Flow Cytometry Data ◽  
Accuracy Measurement ◽  
The Relationship

Reliable, predictable engineering of cellular behavior is one of the key goals of synthetic biology. As the field matures, biological engineers will become increasingly reliant on computer models that allow for the rapid exploration of design space prior to the more costly construction and characterization of candidate designs. The efficacy of such models, however, depends on the accuracy of their predictions, the precision of the measurements used to parameterize the models, and the tolerance of biological devices for imperfections in modeling and measurement. To better understand this relationship, we have derived an Engineering Error Inequality that provides a quantitative mathematical bound on the relationship between predictability of results, model accuracy, measurement precision, and device characteristics. We apply this relation to estimate measurement precision requirements for engineering genetic regulatory networks given current model and device characteristics, recommending a target standard deviation of 1.5-fold. We then compare these requirements with the results of an interlaboratory study to validate that these requirements can be met via flow cytometry with matched instrument channels and an independent calibrant. Based on these results, we recommend a set of best practices for quality control of flow cytometry data and discuss how these might be extended to other measurement modalities and applied to support further development of genetic regulatory network engineering.

scholarly journals bioLQM: a java library for the manipulation and conversion of Logical Qualitative Models of biological networks

2018 ◽  
Author(s):  
Aurélien Naldi
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Model Simulation ◽  
Biological Regulatory Networks ◽  
Interactive Tools ◽  
Graphical Interfaces ◽  
Qualitative Models ◽  
Import And Export ◽  
Definition Of ◽  
Java Library

AbstractHere we introduce bioLQM, a new Java software toolkit for the conversion, modification, and analysis of Logical Qualitative Models of biological regulatory networks, aiming to foster the development of novel complementary tools by providing core modelling operations. Based on the definition of multi-valued logical models, it implements import and export facilities, notably for the recent SBML-qual exchange format, as well as for formats used by several popular tools, facilitating the design of workflows combining these tools. Model modifications enable the definition of various perturbations, as well as model reduction, easing the analysis of large models. Another modification enables the study of multi-valued models with tools limited to the Boolean case. Finally, bioLQM provides a framework for the development of novel analysis tools. The current version implements the usual updating modes for model simulation (notably synchronous, asynchronous, and random asynchronous), as well as some static analysis features for the identification of attractors. The bioLQM software can be integrated into analysis workflows through command line and scripting interfaces. As a Java library, it further provides core data structures to the GINsim and EpiLog interactive tools, which supply graphical interfaces and additional analysis methods for cellular and multi-cellular qualitative models.

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