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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

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Design Principles for Perfect Adaptation in Biological Networks with Nonlinear Dynamics.

Priyan Bhattacharya¹, Karthik Raman², Arun K Tangirala^3,4

¹Department of Chemical Engineering, IIT Madras, Chennai, Tamil Nadu, 600036, India.

Bulletin of Mathematical Biology

|July 3, 2024

Summary

This study identifies network architectures enabling perfect adaptation to environmental changes. It reveals two key structures—incoherent feed-forward (IFF) and negative feedback with buffer (NFB)—essential for biological system regulation.

Keywords:

Biological adaptation Global adaptation Global stability Homeostasis Network dynamics Non-linear dynamics Signed digraph

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Visualizing Visual Adaptation

Visualizing Visual Adaptation

Published on: April 24, 2017

Area of Science:

Systems biology
Synthetic biology
Nonlinear dynamics

Background:

Biological systems require adaptation to environmental disturbances for stable function.
Understanding the relationship between network structure and emergent properties like adaptation is crucial.

Purpose of the Study:

To develop a nonlinear systems theory framework for identifying design principles of perfect adaptation.
To determine mathematical conditions and network architectures enabling adaptation to external disturbances.

Main Methods:

Utilizing nonlinear systems theory to derive mathematical conditions for perfect adaptation.
Translating these conditions into structural requirements for biological networks.
Analyzing network architectures including incoherent feed-forward (IFF) and negative feedback loops (NFB).

Main Results:

Identified precise mathematical conditions for perfect adaptation to constant input disturbances.
Determined that only incoherent feed-forward (IFF) and negative feedback with buffer (NFB) architectures can provide local adaptation across the entire state space.
Established global asymptotic stability for steady states under constant disturbances.
Discussed limitations of certain IFF networks with downstream connections.

Conclusions:

Two fundamental network architectures, IFF and NFB, are necessary for achieving adaptation in biological systems.
The developed framework provides a systematic approach to understanding and designing adaptive biological networks.
Simulation studies validate the theoretical findings on network adaptation principles.