A Nullclines Approach to the Study of 2D Artificial Network

The system of two the first order ordinary differential equations arising in the gene regulatory networks theory is studied. The structure of attractors for this system is described for three important behavioral cases: activation, inhibition, mixed activation-inhibition. The geometrical approach combined with the vector field analysis allows treating the problem in full generality. A number of propositions are stated and the proof is geometrical, avoiding complex analytic. Although not all the possible cases are considered, the instructions are given what to do in any particular situation.

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Inference of gene regulatory networks based on nonlinear ordinary differential equations

Bioinformatics ◽

10.1093/bioinformatics/btaa032 ◽

2020 ◽

Vol 36 (19) ◽

pp. 4885-4893 ◽

Cited By ~ 2

Author(s):

Baoshan Ma ◽

Mingkun Fang ◽

Xiangtian Jiao

Keyword(s):

Gene Expression ◽

Time Series ◽

Steady State ◽

Differential Equations ◽

Gene Regulatory Networks ◽

Regulatory Networks ◽

Time Series Data ◽

Series Data ◽

State Data ◽

Gene Regulatory

Abstract Motivation Gene regulatory networks (GRNs) capture the regulatory interactions between genes, resulting from the fundamental biological process of transcription and translation. In some cases, the topology of GRNs is not known, and has to be inferred from gene expression data. Most of the existing GRNs reconstruction algorithms are either applied to time-series data or steady-state data. Although time-series data include more information about the system dynamics, steady-state data imply stability of the underlying regulatory networks. Results In this article, we propose a method for inferring GRNs from time-series and steady-state data jointly. We make use of a non-linear ordinary differential equations framework to model dynamic gene regulation and an importance measurement strategy to infer all putative regulatory links efficiently. The proposed method is evaluated extensively on the artificial DREAM4 dataset and two real gene expression datasets of yeast and Escherichia coli. Based on public benchmark datasets, the proposed method outperforms other popular inference algorithms in terms of overall score. By comparing the performance on the datasets with different scales, the results show that our method still keeps good robustness and accuracy at a low computational complexity. Availability and implementation The proposed method is written in the Python language, and is available at: https://github.com/lab319/GRNs_nonlinear_ODEs Supplementary information Supplementary data are available at Bioinformatics online.

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Reverse engineering of gene regulatory networks based on S-systems and Bat algorithm

Journal of Bioinformatics and Computational Biology ◽

10.1142/s0219720016500104 ◽

2016 ◽

Vol 14 (03) ◽

pp. 1650010 ◽

Cited By ~ 6

Author(s):

Sudip Mandal ◽

Abhinandan Khan ◽

Goutam Saha ◽

Rajat Kumar Pal

Keyword(s):

Reverse Engineering ◽

Gene Regulatory Networks ◽

Regulatory Networks ◽

Real Life ◽

Bat Algorithm ◽

Genetic Network ◽

Model Parameters ◽

Mathematical Tool ◽

Gene Regulatory ◽

Artificial Network

The correct inference of gene regulatory networks for the understanding of the intricacies of the complex biological regulations remains an intriguing task for researchers. With the availability of large dimensional microarray data, relationships among thousands of genes can be simultaneously extracted. Among the prevalent models of reverse engineering genetic networks, S-system is considered to be an efficient mathematical tool. In this paper, Bat algorithm, based on the echolocation of bats, has been used to optimize the S-system model parameters. A decoupled S-system has been implemented to reduce the complexity of the algorithm. Initially, the proposed method has been successfully tested on an artificial network with and without the presence of noise. Based on the fact that a real-life genetic network is sparsely connected, a novel Accumulative Cardinality based decoupled S-system has been proposed. The cardinality has been varied from zero up to a maximum value, and this model has been implemented for the reconstruction of the DNA SOS repair network of Escherichia coli. The obtained results have shown significant improvements in the detection of a greater number of true regulations, and in the minimization of false detections compared to other existing methods.

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Modelling Three Dimensional Gene Regulatory Networks

WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL ◽

10.37394/23203.2021.16.67 ◽

2021 ◽

Vol 16 ◽

pp. 755-763

Author(s):

Inna Samuilik ◽

Felix Sadyrbaev

Keyword(s):

Differential Equations ◽

Gene Regulatory Networks ◽

Regulatory Network ◽

Regulatory Networks ◽

Linear Part ◽

Three Dimensional ◽

Special Kind ◽

Sigmoidal Function ◽

Solution Vector ◽

Gene Regulatory

We consider the three-dimensional gene regulatory network (GRN in short). This model consists of ordinary differential equations of a special kind, where the nonlinearity is represented by a sigmoidal function and the linear part is present also. The evolution of GRN is described by the solution vector X(t), depending on time. We describe the changes that system undergoes if the entries of the regulatory matrix are perturbed in some way.

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