( 6.1.26 ) Written and research done by Gio Kim
Introduction
Pseudomonas aeruginosa is a Gram negative bacterium commonly found in soil, water, and other environmental habitats. It is widely studied due to its high adaptation capabilities and its impact in CF patients. One of the most important of these mechanisms is quorum sensing, a communication system that allows bacterial cells to respond collectively to changes in population density.
One quorum sensing pathway found in P. aeruginosa is the RhlR/RhlI system. Within this system, the enzyme RhlI synthesizes the signaling molecule C4-HSL (N-butyryl-homoserine lactone). C4-HSL can bind to the regulatory protein RhlR, forming an activated receptor-ligand complex. The interactions between these molecules create a regulatory network in which signal production and signal detection become interconnected.
The purpose of this project was to construct a simplified computational model that captures several of its core interactions of the RhlR/RhlI system. Using Tellurium, a systems biology simulation platform, I modeled RhII production, C4-HSL synthesis, receptor ligand binding, molecular degradation, and a Hill-function based feedback mechanism. By simulating these interactions over time, I investigated how positive feedback influences the overall behavior of the system.
Methodology
The model was implemented in Tellurium using a reaction based framework consisting of four molecular species:
RhII
C4-HSL
RhlR
Complex
The simulation was initialized with the following concentrations:
RhII = 0.05
C4-HSL = 0
RhlR = 1.0
Complex = 0
A central feature of the model was the inclusion of a Hill function within the RhII production equation:
RhII Production = rhli_basal + rhli_act × (Complexⁿ / (Kⁿ + Complexⁿ))
where:
K = 0.4
n = 3
The Hill function introduces nonlinear activation into the system. When complex concentration is low relative to K, the activation term remains small. As complex concentration approaches K, the activation term increases more rapidly. Because n = 3, the response becomes steeper than a simple linear relationship, creating a threshold-like transition between low and high activation states.
Additional reactions included C4-HSL production by RhII, reversible binding between C4-HSL and RhlR to form the complex, and degradation pathways for RhII and C4-HSL. The simulation was run from 0 to 200 time units with 1000 computational steps.
Results
At the beginning of the simulation, complex concentration is zero. As a result, the Hill activation term contributes almost nothing to RhII production, leaving basal production as the primary source of RhII. This causes RhII concentration to increase only gradually during the early phase of the simulation.
As RhII accumulates, production of C4-HSL increases because C4-HSL synthesis is directly proportional to RhII concentration. The increasing concentration of C4-HSL allows more receptor-ligand complexes to form through interaction with RhlR.
As the Hill function depends on complex concentration, the growth of the complex eventually increases the activation term in the RhII production equation. Once complex concentration approaches the value of K, the activation term rises much more rapidly. This produces the steep increase observed in the RhII curve.
C4-HSL follows a similar pattern because its production depends on RhII. The C4-HSL curve rises more slowly at first and then accelerates as RhII concentration increases. Eventually, both species approach stable values as production and degradation rates become balanced.
The free RhlR concentration decreases throughout the simulation because it is continuously incorporated into receptor-ligand complexes. Since the binding reaction is reversible, some RhlR is regenerated through dissociation, preventing complete depletion. The concentration therefore approaches a low steady-state value rather than reaching zero.
The complex concentration increases throughout most of the simulation as more C4-HSL becomes available for binding. Eventually the rate of complex formation becomes balanced by the rate of dissociation, causing the curve to plateau.
Conclusion
This project used Tellurium to construct and analyze a simplified computational model inspired by the RhlR/RhlI quorum sensing pathway of Pseudomonas aeruginosa. By incorporating a Hill-function activation term, reversible receptor ligand binding, signal production, and degradation, the simulation generated a clear transition from slow initial growth to rapid activation before ultimately reaching a stable steady state.
The results demonstrate how nonlinear feedback can influence system behavior and highlight the usefulness of computational modeling for exploring biological networks. While the model is not intended to represent the full biological complexity of the RhlR/RhlI pathway, it provides a useful framework for understanding how mathematical relationships produce emergent dynamic behavior.
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References:
https://tellurium.readthedocs.io/ (Tellurium Simulation Framework)
https://pubmed.ncbi.nlm.nih.gov/9150205/ (Rhlr/Rhli P.Aeruginosa paper)
Caption: Figure A, Visualization of the output of the program (higher resolution picture at the bottom of the page)
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