scholarly journals Nonlinear delay differential equations and their application to modeling biological network motifs

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
David S. Glass ◽  
Xiaofan Jin ◽  
Ingmar H. Riedel-Kruse
Keyword(s):  
Differential Equation ◽  
Biological Networks ◽  
Network Motif ◽  
Network Motifs ◽  
Ode Models ◽  
Regulatory Systems ◽  
Nonlinear Delay Differential Equations ◽  
Cell Signaling Networks ◽  
Analytical Relations ◽  
Delay Differential

AbstractBiological regulatory systems, such as cell signaling networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. Network motif models focus on small sub-networks to provide quantitative insight into overall behavior. However, such models often overlook time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equation (DDE) models, both analytically and numerically. We find many broadly applicable results, including parameter reduction versus canonical ordinary differential equation (ODE) models, analytical relations for converting between ODE and DDE models, criteria for when delays may be ignored, a complete phase space for autoregulation, universal behaviors of feedforward loops, a unified Hill-function logic framework, and conditions for oscillations and chaos. We conclude that explicit-delay modeling simplifies the phenomenology of many biological networks and may aid in discovering new functional motifs.

scholarly journals Nonlinear delay differential equations and their application to modeling biological network motifs

2020 ◽  
Author(s):  
David S. Glass ◽  
Xiaofan Jin ◽  
Ingmar H. Riedel-Kruse
Keyword(s):  
Differential Equations ◽  
Biological Networks ◽  
Delay Differential Equations ◽  
Network Motif ◽  
Network Motifs ◽  
Mathematical Form ◽  
Unified Framework ◽  
Regulatory Systems ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential

AbstractBiological regulatory systems, such as transcription factor or kinase networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. “Network motif” models focus on small sub-networks to provide quantitative insight into overall behavior. However, conventional network motif models often ignore time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equations (DDEs), both analytically and numerically. We find many broadly applicable results, such as the reduction in number of parameters compared to canonical descriptions via ordinary differential equations (ODE), criteria for when delays may be ignored, a complete phase space for autoregulation, explicit dependence of feedforward loops on a difference of delays, a unified framework for Hill-function logic, and conditions for oscillations and chaos. We emphasize relevance to biological function throughout our analysis, summarize key points in non-mathematical form, and conclude that explicit-delay modeling simplifies the phenomenological understanding of many biological networks and may aid in discovering new functional motifs.

NMDB: NETWORK MOTIF DATABASE ENVISAGED AND EXPLICATED FROM HUMAN DISEASE SPECIFIC PATHWAYS

2014 ◽  
Vol 22 (01) ◽  
pp. 89-100 ◽  
Author(s):  
ABHAY PRATAP ◽  
SETU TALIYAN ◽  
TIRATHA RAJ SINGH
Keyword(s):  
Biological Networks ◽  
Human Disease ◽  
Biological Network ◽  
Metabolic Diseases ◽  
Network Motif ◽  
Network Motifs ◽  
Efficient Detection ◽  
Single Input ◽  
Motif Database ◽  
Disease Specific

The study of network motifs for large number of networks can aid us to resolve the functions of complex biological networks. In biology, network motifs that reappear within a network more often than expected in random networks include negative autoregulation, positive autoregulation, single-input modules, feedforward loops, dense overlapping regulons and feedback loops. These network motifs have their different dynamical functions. In this study, our main objective is to examine the enrichment of network motifs in different biological networks of human disease specific pathways. We characterize biological network motifs as biologically significant sub-graphs. We used computational and statistical criteria for efficient detection of biological network motifs, and introduced several estimation measures. Pathways of cardiovascular, cancer, infectious, repair, endocrine and metabolic diseases, were used for identifying and interlinking the relation between nodes. 3–8 sub-graph size network motifs were generated. Network Motif Database was then developed using PHP and MySQL. Results showed that there is an abundance of autoregulation, feedforward loops, single-input modules, dense overlapping regulons and other putative regulatory motifs in all the diseases included in this study. It is believed that the database will assist molecular and system biologists, biotechnologists, and other scientific community to encounter biologically meaningful information. Network Motif Database is freely available for academic and research purpose at: http://www.bioinfoindia.org/nmdb .

scholarly journals A Natural Homotopy Analysis Method for Nonlinear Delay Differential Equations

2019 ◽  
Vol 1 (2) ◽  
pp. 86-90
Author(s):  
Aminu Barde
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Delay Differential Equations ◽  
Analysis Method ◽  
Linear Delay ◽  
Homotopy Analysis ◽  
Nonlinear Delay Differential Equations ◽  
Functional Differential ◽  
Delay Differential

Delay differential equation (DDEs) is a type of functional differential equation arising in numerous applications from different areas of studies, for example biology, engineering population dynamics, medicine, physics, control theory, and many others. However, determining the solution of delay differential equations has become a difficult task more especially the nonlinear type. Therefore, this work proposes a new analytical method for solving non-linear delay differential equations. The new method is combination of Natural transform and Homotopy analysis method. The approach gives solutions inform of rapid convergence series where the nonlinear terms are simply computed using He's polynomial. Some examples are given, and the results obtained indicate that the approach is efficient in solving different form of nonlinear DDEs which reduces the computational sizes and avoid round-off of errors.

scholarly journals Application of dynamic expansion tree for finding large network motifs in biological networks

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e6917 ◽  
Author(s):  
Sabyasachi Patra ◽  
Anjali Mohapatra
Keyword(s):  
Biological Networks ◽  
Protein Function ◽  
Large Scale ◽  
Network Motif ◽  
Graph Isomorphism ◽  
Interaction Network ◽  
Motif Finding ◽  
Network Motifs ◽  
Large Network ◽  
Scalable Network

Network motifs play an important role in the structural analysis of biological networks. Identification of such network motifs leads to many important applications such as understanding the modularity and the large-scale structure of biological networks, classification of networks into super-families, and protein function annotation. However, identification of large network motifs is a challenging task as it involves the graph isomorphism problem. Although this problem has been studied extensively in the literature using different computational approaches, still there is a lot of scope for improvement. Motivated by the challenges involved in this field, an efficient and scalable network motif finding algorithm using a dynamic expansion tree is proposed. The novelty of the proposed algorithm is that it avoids computationally expensive graph isomorphism tests and overcomes the space limitation of the static expansion tree (SET) which makes it enable to find large motifs. In this algorithm, the embeddings corresponding to a child node of the expansion tree are obtained from the embeddings of a parent node, either by adding a vertex or by adding an edge. This process does not involve any graph isomorphism check. The time complexity of vertex addition and edge addition are O(n) and O(1), respectively. The growth of a dynamic expansion tree (DET) depends on the availability of patterns in the target network. Pruning of branches in the DET significantly reduces the space requirement of the SET. The proposed algorithm has been tested on a protein–protein interaction network obtained from the MINT database. The proposed algorithm is able to identify large network motifs faster than most of the existing motif finding algorithms.

scholarly journals Identifying Representative Network Motifs for Inferring Higher-order Structure of Biological Networks

2018 ◽  
Author(s):  
Wang Tao ◽  
Yadong Wang ◽  
Jiajie Peng ◽  
Chen Jin
Keyword(s):  
Biological Networks ◽  
Motif Discovery ◽  
Network Motif ◽  
Low Frequency ◽  
Organizational Structures ◽  
Higher Order ◽  
Order Structure ◽  
Network Motifs ◽  
Scalable Algorithm ◽  
Significant Patterns

AbstractNetwork motifs are recurring significant patterns of inter-connections, which are recognized as fundamental units to study the higher-order organizations of networks. However, the principle of selecting representative network motifs for local motif based clustering remains largely unexplored. We present a scalable algorithm called FSM for network motif discovery. FSM accelerates the motif discovery process by effectively reducing the number of times to do subgraph isomorphism labeling. Multiple heuristic optimizations for subgraph enumeration and subgraph classification are also adopted in FSM to further improve its performance. Experimental results show that FSM is more efficient than the compared models on computational efficiency and memory usage. Furthermore, our experiments indicate that large and frequent network motifs may be more appropriate to be selected as the representative network motifs for discovering higher-order organizational structures in biological networks than small or low-frequency network motifs.

An iterative scheme for the oscillation criteria of a nonlinear delay differential equation with several deviating arguments

2021 ◽  
pp. 2250071
Author(s):  
R. Basu
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Deviating Arguments ◽  
First Order ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

This paper deals with the oscillatory results of first order nonlinear delay differential equations with several deviating arguments by employing an iterative process. The results presented here has improved the outcomes of [1, 2, 8]. Various examples are solved in MATLAB software to illustrate the relevance of the main results.

Overview of Gene Regulatory Network Inference Based on Differential Equation Models

2020 ◽  
Vol 21 (11) ◽  
pp. 1054-1059
Author(s):  
Bin Yang ◽  
Yuehui Chen
Keyword(s):  
Differential Equation ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Network Inference ◽  
New Drugs ◽  
Gene Regulatory Network Inference ◽  
Ode Models ◽  
Differential Equation Models ◽  
Linear Ode ◽  
Gene Regulatory

: Reconstruction of gene regulatory networks (GRN) plays an important role in understanding the complexity, functionality and pathways of biological systems, which could support the design of new drugs for diseases. Because differential equation models are flexible androbust, these models have been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates the differential equation models for reverse engineering gene regulatory networks. We introduce three kinds of differential equation models, including ordinary differential equation (ODE), time-delayed differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are utilized to search the optimal structures and parameters of differential equation models. This investigation could provide a comprehensive understanding of differential equation models, and lead to the discovery of novel differential equation models.

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