Convergence of a Belief Propagation Algorithm for Biological Networks

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.

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Robustness and lethality in multilayer biological molecular networks

10.1101/818963 ◽

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.

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Creating, generating and comparing random network models with Network Randomizer

F1000Research ◽

10.12688/f1000research.9203.1 ◽

2016 ◽

Vol 5 ◽

pp. 2524 ◽

Cited By ~ 8

Author(s):

Gabriele Tosadori ◽

Ivan Bestvina ◽

Fausto Spoto ◽

Carlo Laudanna ◽

Giovanni Scardoni

Keyword(s):

Experimental Data ◽

High Throughput ◽

Biological Networks ◽

Random Network ◽

Network Models ◽

Information Network ◽

Statistical Tool ◽

New Techniques ◽

High Throughput Data ◽

Randomized Networks

Biological networks are becoming a fundamental tool for the investigation of high-throughput data in several fields of biology and biotechnology. With the increasing amount of information, network-based models are gaining more and more interest and new techniques are required in order to mine the information and to validate the results. We have developed an app for the Cytoscape platform which allows the creation of randomized networks and the randomization of existing, real networks. Since there is a lack of tools for generating and randomizing networks, our app helps researchers to exploit different, well known random network models which could be used as a benchmark for validating real datasets. We also propose a novel methodology for creating random weighted networks starting from experimental data. Finally the app provides a statistical tool which compares real versus random attributes, in order to validate all the numerical findings. In summary, our app aims at creating a standardised methodology for the validation of the results in the context of the Cytoscape platform.

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The basis of easy controllability in Boolean networks

Nature Communications ◽

10.1038/s41467-021-25533-3 ◽

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.

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Existence of physical measures in some excitation–inhibition networks*

Nonlinearity ◽

10.1088/1361-6544/ac3eb6 ◽

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.

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ClusterSLAM: A SLAM backend for simultaneous rigid body clustering and motion estimation

Computational Visual Media ◽

10.1007/s41095-020-0195-3 ◽

2021 ◽

Author(s):

Jiahui Huang ◽

Sheng Yang ◽

Zishuo Zhao ◽

Yu-Kun Lai ◽

Shi-Min Hu

Keyword(s):

Motion Estimation ◽

Rigid Body ◽

Iterative Scheme ◽

Dynamic Environments ◽

Rigid Bodies ◽

Factor Graph ◽

Agglomerative Clustering ◽

Multiple Objects ◽

Graph Optimization ◽

Dynamic Objects

AbstractWe present a practical backend for stereo visual SLAM which can simultaneously discover individual rigid bodies and compute their motions in dynamic environments. While recent factor graph based state optimization algorithms have shown their ability to robustly solve SLAM problems by treating dynamic objects as outliers, their dynamic motions are rarely considered. In this paper, we exploit the consensus of 3D motions for landmarks extracted from the same rigid body for clustering, and to identify static and dynamic objects in a unified manner. Specifically, our algorithm builds a noise-aware motion affinity matrix from landmarks, and uses agglomerative clustering to distinguish rigid bodies. Using decoupled factor graph optimization to revise their shapes and trajectories, we obtain an iterative scheme to update both cluster assignments and motion estimation reciprocally. Evaluations on both synthetic scenes and KITTI demonstrate the capability of our approach, and further experiments considering online efficiency also show the effectiveness of our method for simultaneously tracking ego-motion and multiple objects.

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BioNetLink - An Architecture for Working with Network Data

Journal of Integrative Bioinformatics ◽

10.1515/jib-2014-241 ◽

2014 ◽

Vol 11 (2) ◽

pp. 68-79

Author(s):

Matthias Klapperstück ◽

Falk Schreiber

Keyword(s):

Experimental Data ◽

Biological Networks ◽

Regulatory Networks ◽

Large Data ◽

Biological Data ◽

Network Data ◽

Data Sets ◽

Dynamic Views ◽

Gene Regulatory ◽

Multiple Network

Summary The visualization of biological data gained increasing importance in the last years. There is a large number of methods and software tools available that visualize biological data including the combination of measured experimental data and biological networks. With growing size of networks their handling and exploration becomes a challenging task for the user. In addition, scientists also have an interest in not just investigating a single kind of network, but on the combination of different types of networks, such as metabolic, gene regulatory and protein interaction networks. Therefore, fast access, abstract and dynamic views, and intuitive exploratory methods should be provided to search and extract information from the networks. This paper will introduce a conceptual framework for handling and combining multiple network sources that enables abstract viewing and exploration of large data sets including additional experimental data. It will introduce a three-tier structure that links network data to multiple network views, discuss a proof of concept implementation, and shows a specific visualization method for combining metabolic and gene regulatory networks in an example.

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Making high-dimensional molecular distribution functions tractable through Belief Propagation on Factor Graphs

10.1101/2021.06.28.450193 ◽

2021 ◽

Author(s):

Zachary Smith ◽

Pratyush Tiwary

Keyword(s):

Belief Propagation ◽

Conformational Dynamics ◽

Joint Probability ◽

Md Simulations ◽

Distribution Functions ◽

Factor Graph ◽

High Dimensional ◽

Enhanced Sampling ◽

Small Peptides ◽

Approximate Probability

Molecular dynamics (MD) simulations provide a wealth of high-dimensional data at all-atom and femtosecond resolution but deciphering mechanistic information from this data is an ongoing challenge in physical chemistry and biophysics. Theoretically speaking, joint probabilities of the equilibrium distribution contain all thermodynamic information, but they prove increasingly difficult to compute and interpret as the dimensionality increases. Here, inspired by tools in probabilistic graphical modeling, we develop a factor graph trained through belief propagation that helps factorize the joint probability into an approximate tractable form that can be easily visualized and used. We validate the study through the analysis of the conformational dynamics of two small peptides with 5 and 9 residues. Our validations include testing the conditional dependency predictions through an intervention scheme inspired by Judea Pearl. Secondly we directly use the belief propagation based approximate probability distribution as a high-dimensional static bias for enhanced sampling, where we achieve spontaneous back-and-forth motion between metastable states that is up to 350 times faster than unbiased MD. We believe this work opens up useful ways to thinking about and dealing with high-dimensional molecular simulations.

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Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

10.36227/techrxiv.14781489.v1 ◽

2021 ◽

Author(s):

Dino Zivojevic ◽

Muhamed Delalic ◽

Darijo Raca ◽

Dejan Vukobratovic ◽

Mirsad Cosovic

Keyword(s):

Least Squares ◽

Large Scale ◽

Belief Propagation ◽

Weighted Least Squares ◽

Measurement Data ◽

Integrated Approach ◽

Factor Graph ◽

State Variables ◽

Large Scale Systems ◽

Distributed Approach

The purpose of a state estimation (SE) algorithm is to estimate the values of the state variables considering the available set of measurements. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (\ie subsystems) and distributing the computation across clusters, solves the constraints of centralised based approach. In such scenarios, using distributed SE methods brings numerous advantages over the centralised ones. In this paper, we propose a novel distributed approach to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed algorithm is based on the factor graph operating without a central coordinator, where subsystems exchange only ``beliefs", thus preserving privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solution upon arrival of a new information to the subsystem. Finally, the proposed algorithm provides results that reach accuracy of the centralised WLS solution in a few iterations, and outperforms vanilla GBP algorithm with respect to its convergence properties.

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