scholarly journals Existence of physical measures in some excitation–inhibition networks*

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 889-915
Author(s):  
Matteo Tanzi ◽  
Lai-Sang Young
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Biological Networks ◽  
Large Time ◽  
Biological Systems ◽  
Network Dynamics ◽  
Network Models ◽  
The Other ◽  
Rigorous Analysis ◽  
Physical Measures

Abstract In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but can be arbitrarily large. They are inspired by real biological networks, and possess features that are idealizations of those in biological systems. Individual components of the network are represented by simple, much studied dynamical systems. Complex dynamical patterns on the network level emerge as a result of the coupling among its constituent subsystems. Appealing to existing techniques in (nonuniform) hyperbolic theory, we study their Lyapunov exponents and entropy, and prove that large time network dynamics are governed by physical measures with the SRB property.

scholarly journals Robustness and lethality in multilayer biological molecular networks

2019 ◽  
Author(s):  
Xueming Liu ◽  
Enrico Maiorino ◽  
Arda Halu ◽  
Joseph Loscalzo ◽  
Jianxi Gao ◽  
...  
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Metabolic Diseases ◽  
Biological Systems ◽  
Interaction Network ◽  
Network Models ◽  
Global Network ◽  
Molecular Networks ◽  
Cancer Genes ◽  
Gene Regulatory

AbstractRobustness is a prominent feature of most biological systems. In a cell, the structure of the interactions between genes, proteins, and metabolites has a crucial role in maintaining the cell’s functionality and viability in presence of external perturbations and noise. Despite advances in characterizing the robustness of biological systems, most of the current efforts have been focused on studying homogeneous molecular networks in isolation, such as protein-protein or gene regulatory networks, neglecting the interactions among different molecular substrates. Here we propose a comprehensive framework for understanding how the interactions between genes, proteins and metabolites contribute to the determinants of robustness in a heterogeneous biological network. We integrate heterogeneous sources of data to construct a multilayer interaction network composed of a gene regulatory layer, and protein-protein interaction layer and a metabolic layer. We design a simulated perturbation process to characterize the contribution of each gene to the overall system’s robustness, defined as its influence over the global network. We find that highly influential genes are enriched in essential and cancer genes, confirming the central role of these genes in critical cellular processes. Further, we determine that the metabolic layer is more vulnerable to perturbations involving genes associated to metabolic diseases. By comparing the robustness of the network to multiple randomized network models, we find that the real network is comparably or more robust than expected in the random realizations. Finally, we analytically derive the expected robustness of multilayer biological networks starting from the degree distributions within or between layers. These results provide new insights into the non-trivial dynamics occurring in the cell after a genetic perturbation is applied, confirming the importance of including the coupling between different layers of interaction in models of complex biological systems.

scholarly journals Dynamic characteristics rather than static hubs are important in biological networks

2020 ◽  
Author(s):  
Silke D. Kühlwein ◽  
Nensi Ikonomi ◽  
Julian D. Schwab ◽  
Johann M. Kraus ◽  
K. Lenhard Rudolph ◽  
...  
Keyword(s):  
Protein Interactions ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Network Dynamics ◽  
Network Models ◽  
Interaction Graphs ◽  
New Class ◽  
Set Up ◽  
Simple Features

AbstractBiological processes are rarely a consequence of single protein interactions but rather of complex regulatory networks. However, interaction graphs cannot adequately capture temporal changes. Among models that investigate dynamics, Boolean network models can approximate simple features of interaction graphs integrating also dynamics. Nevertheless, dynamic analyses are time-consuming and with growing number of nodes may become infeasible. Therefore, we set up a method to identify minimal sets of nodes able to determine network dynamics. This approach is able to depict dynamics without calculating exhaustively the complete network dynamics. Applying it to a variety of biological networks, we identified small sets of nodes sufficient to determine the dynamic behavior of the whole system. Further characterization of these sets showed that the majority of dynamic decision-makers were not static hubs. Our work suggests a paradigm shift unraveling a new class of nodes different from static hubs and able to determine network dynamics.

scholarly journals Convergence of a Belief Propagation Algorithm for Biological Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Sang-Mok Choo ◽  
Young-Hee Kim
Keyword(s):  
Experimental Data ◽  
Biological Networks ◽  
Belief Propagation ◽  
Iterative Scheme ◽  
Biological Systems ◽  
Network Models ◽  
Stochastic Approach ◽  
Factor Graph ◽  
Process Step ◽  
Whole Process

Constructing network models of biological systems is important for effective understanding and control of the biological systems. For the construction of biological networks, a stochastic approach for link weights has been recently developed by using experimental data and belief propagation on a factor graph. The link weights were variable nodes of the factor graph and determined from their marginal probability mass functions which were approximated by using an iterative scheme. However, there is no convergence analysis of the iterative scheme. In this paper, at first, we present a detailed explanation of the complicated multistep process step by step with a network of small size and artificial experimental data, and then we show a sufficient condition for the convergence of the iterative scheme. Numerical examples are given to illustrate the whole process and to verify our result.

scholarly journals The basis of easy controllability in Boolean networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Enrico Borriello ◽  
Bryan C. Daniels
Keyword(s):  
Biological Networks ◽  
Biological Network ◽  
Biological Systems ◽  
Network Models ◽  
Theoretical Explanation ◽  
Boolean Networks ◽  
Effective Control ◽  
External Control ◽  
Final State ◽  
Numerical Evidence

AbstractEffective 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 networks may be typically easy to control even when the number of interacting components is large. We provide a theoretical explanation of the scaling by separating controlling nodes into three types: those that act as inputs, those that distinguish among attractors, and any remaining nodes. We further identify characteristics of dynamics that can invalidate this scaling, and speculate about how this relates more broadly to non-biological systems.

scholarly journals A computational framework for finding parameter sets associated with chaotic dynamics

2021 ◽  
pp. 1-11
Author(s):  
S. Koshy-Chenthittayil ◽  
E. Dimitrova ◽  
E.W. Jenkins ◽  
B.C. Dean
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Computational Framework ◽  
Independent Variables ◽  
Systems Model ◽  
Small Support

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software’s optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.

scholarly journals Modeling Network Dynamics

2020 ◽  
pp. 145-171
Keyword(s):  
Communication Networks ◽  
Random Network ◽  
Network Dynamics ◽  
Network Models ◽  
Random Networks ◽  
Social Phenomena ◽  
Disease Propagation ◽  
The Social ◽  
Wide Range ◽  
Model Dynamics

Social relationships and the social networks over these relationships do not occur arbitrarily. However, the random networks dealt with in this chapter are important tools for modeling the networks of these systems. The authors use random networks to understand and to model dynamics regarding the whole social structure. Random network models became the topic of several studies independently from social network analysis in the 1950s. These models were used in the analysis of a wide range of social and non-social phenomena, from electrical and communication networks to the speed and manner of disease propagation. This chapter explores the modeling network dynamics of random networks.

scholarly journals AIS-BN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks

2000 ◽  
Vol 13 ◽  
pp. 155-188 ◽  
Author(s):  
J. Cheng ◽  
M. J. Druzdzel
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Importance Sampling ◽  
Network Models ◽  
Evidential Reasoning ◽  
The Other ◽  
Sampling Algorithm ◽  
Importance Function ◽  
Sampling Algorithms ◽  
Bayesian Network Models

Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in finite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from different stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, likelihood weighting (Fung & Chang, 1989; Shachter & Peot, 1989) and self-importance sampling (Shachter & Peot, 1989). We used in our tests three large real Bayesian network models available to the scientific community: the CPCS network (Pradhan et al., 1994), the PathFinder network (Heckerman, Horvitz, & Nathwani, 1990), and the ANDES network (Conati, Gertner, VanLehn, & Druzdzel, 1997), with evidence as unlikely as 10^-41. While the AIS-BN algorithm always performed better than the other two algorithms, in the majority of the test cases it achieved orders of magnitude improvement in precision of the results. Improvement in speed given a desired precision is even more dramatic, although we are unable to report numerical results here, as the other algorithms almost never achieved the precision reached even by the first few iterations of the AIS-BN algorithm.

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