Homeostasis in a feed forward loop gene regulatory motif

Area of Science:

• Systems Biology
• Molecular Biology
• Computational Biology

Background:

• Cellular internal states are influenced by external environmental factors like temperature.
• Homeostasis describes a system's ability to maintain a stable internal state despite external fluctuations.
• Gene regulatory networks (GRNs) often contain recurring sub-networks known as motifs, suggesting functional importance.

Purpose of the Study:

• To investigate the hypothesis that GRN motifs contribute to cellular homeostasis.
• To demonstrate that the feed-forward loop (FFL) GRN motif exhibits homeostatic behavior.
• To introduce and apply the concept of infinitesimal homeostasis and 'chair points' for analyzing GRN function.

Main Methods:

• Mathematical analysis using the concept of infinitesimal homeostasis, defined by critical points (zero derivative) in the input-output map.
• Identification of 'chair points' where the second derivative also vanishes, indicating a plateau or homeostasis region.
• Application of implicit differentiation to locate these critical points in a standard model of the FFL GRN.

Main Results:

• The feed-forward loop (FFL) GRN motif was shown to produce homeostasis.
• Analytical deduction confirmed the occurrence of chair points in the FFL GRN model.
• The identified chair points are linked to the regulation of specific mRNA production.

Conclusions:

• The feed-forward loop motif is a functional unit capable of generating homeostasis within GRNs.
• The mathematical framework of infinitesimal homeostasis and chair points provides a method for identifying homeostatic regions.
• This approach can potentially be extended to analyze homeostasis in other complex GRNs and understand its persistence.