Overview

To sum up, we developed three models. Firstly, we constructed a population growth model for Pseudomonas aeruginosa using growth differential equations to calculate the concentrations of bacteria and viruses over time. This model revealed the required burst size and infection rate for the virus to rapidly infect the entire colony. Subsequently, we conducted flux balancing analysis on a modified Pseudomonas aeruginosa metabolic model by incorporating reactions related to the cyclic-di-GMP pathway. Simulation results showed that insertion of yhjH and wspF genes significantly inhibited cell growth and biofilm formation. Finally, we constructed another differential equation model to investigate the impact of insertion of aiiiA and ytnP genes on quorum sensing in Pseudomonas aeruginosa. By calculating critical points of the equations, our experiment demonstrated that the insertion of these genes significantly increased the activation threshold of quorum sensing and decreased its releasing threshold. Overall, our models support the notion that the insertion of our selected genes significantly impairs biofilm formation in Pseudomonas aeruginosa, suggesting that mild bacteriophage therapy may serve as an effective treatment method.

Quorum Sensing Model

Reference: Dockery JD, Keener JP. A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull Math Biol. 2001 Jan;63(1):95-116. doi: 10.1006/bulm.2000.0205. PMID: 11146885.

Quorum sensing is a process by which bacteria communicate with each other to coordinate behavior based on their population density. They do this through the production, release, and sensing of signaling molecules called autoinducers. Now, let’s break down the components in the given description related to modeling quorum sensing:

A (Autoinducer)	3 - oxo - C12 - HSL : a specific type of signaling molecule, that can be detected by other bacteria to help them gauge the population density.
R (LasR protein)	When the autoinducer (3 - oxo - C12 - HS) binds to LasR, it forms a complex that can then activate the expression of certain genes.
P (complex of A and R)	This complex is crucial for the transmission of the quorum sensing signal within the bacterial community.
ρ (cell density)	The ratio of cell volume to the space volume.

1. Formulas

Originally, this system aims to regulate expression of the elastase LasB and was therefore named the las system. The two enzymes, LasB elastase and LasA elastase, are responsible for elastolytic activity which destroys elastin-containing human lung tissue and causes pulmonary hemorrhages associated with P. aeruginosa infections. The las system is composed of lasI, the autoinducer synthase gene responsible for synthesis of the autoinducer 3-oxo-C12-HSL, and the lasR gene that codes for transcriptional activator protein. The LasR/3-oxo-C12-HSL dimer, which is the activated form of LasR, activates a variety of genes, but preferentially promotes lasI activity. The las system is positively controlled by both GacA and Vfr, which are needed for transcription of lasR. The transcription of lasI is also repressed by the inhibitor RsaL. The upper equations describes the kinetics of this system.

Next, use the default parameters to solve the above system of equations, which results in the following picture:

We want to check how many equilibrium points are in the ode system. The picture below shows the stable line for this system, where the blue line indicates the stable line for equation (20), and the others indicate the stable line for equation (21) corresponds to different ρ. For example, the yellow line has only one common point with the blue one, which means that when ρ=0.15, there is only one equilibrium point in the ode system. There is only one equilibrium point when ρ is small. As ρ increases, the number of equilibrium points gradually becomes two, three, two, and eventually one.

Our purpose is to simulate the impact of the insertion of the two genes aiiA and ytnP on quorum sensing. The function of these two genes is to degrade AHLs, corresponds to the variable A mentioned above. Inserting these two genes is equivalent to increasing kA.

2. Purpose of our model

Taking kA as a variable, try to deduce the relationship between the ρ and kA to reach the critical condition of a single equilibrium point.

3. Model Construction

4. Solution

By computing the contour of 0 on the two surfaces, the relationship between the critical ρ and kA to reach a single equilibrium point is deduced as shown in the figure below:

5. Conclusion

As kA increases, ρ increases significantly.

Therefore, after the insertion of aiiA and ytnP , as kA increases, ρ also increases significantly. P. aeruginosa requires higher densities to activate the quorum sensing mechanism. (The quorum sensing effect also disappears faster when the density of P. aeruginosa decreases)

6. Coding Material

Flux Balance Analysis (FBA)

1. Summary

In enhancing our investigative scope beyond wet-lab experiments, we turned to computational simulations to delve into the impacts of integrating the yhjH and wspF genes into Pseudomonas aeruginosa. The choice of employing Flux Balance Analysis (FBA) as our computational tool stemmed from its proven efficacy in exploring metabolic pathways and potential alterations in microbial behavior upon genetic modifications. By constructing a metabolic model of Pseudomonas aeruginosa using FBA, we aimed to simulate the introduction of the aforementioned genes and envisage their implications on bacterial physiology in a controlled, computational setting

This metabolic modeling enabled us to hypothesize and quantify the effects of yhjH and wspF gene insertion on biofilm formation and bacterial growth rates, particularly in antibiotic environments. FBA facilitated a systematic exploration of how these genes might interact with the metabolic network of P. aeruginosa , providing a platform to predict their roles in altering biofilm dynamics and growth patterns. Our simulations unveiled that both genes could significantly mitigate biofilm formation and retard the growth of P. aeruginosa , with the inhibitory effects escalating approximately linearly with the intensification of gene activity levels.

The integration of FBA in our study not only augmented the depth of our analysis but also provided a computational lens through which we could scrutinize the multifaceted interactions between gene insertions and metabolic responses. This fusion of computational and experimental methodologies allowed for a more comprehensive understanding of the molecular and metabolic orchestrations governing the behavior of Pseudomonas aeruginosa in response to yhjH and wspF gene insertions, thereby bridging the gap between in silico predictions and in vitro observations. Through the amalgamation of FBA-based simulations with wet-lab findings, we have achieved a more holistic view of the gene-metabolism interplay in Pseudomonas aeruginosa, enriching our overall investigative narrative.

* wspF intensity is the intensity of the inserted wspF gene, measured by the upper limit of the flow rate of the diguanylate cycle reaction. The specific relationship is: upper limit=0.0025+0.00005 * strength

** yhjH intensity is the intensity of the inserted yhjH gene, measured by the lower limit of the flow rate of the photosodiesterase reaction. The specific relationship is: lower limit=0.02 * strength

*** Growth index is an indicator of the growth rate of Pseudomonas aeruginosa, with larger values indicating faster growth; Biofilm index is an indicator of biofilm formation, with higher values resulting in more biofilms being formed

Please refer to Experimental process for details

2. Experimental process

First, import the cobrapy package and load the iJN1436 model (BiGG)

2.1 Add c-di-GMP pathway

Then add metabolites to the model: c-di-gmp, its synthesis reaction diguanylate_cyclase (DGC), catabolism reaction phosphodiesterase, and binding reaction with the target protein (the reaction is called *sink*)

The relationship between c-di-gmp and the target reaction is then established.

Because c-di-gmp binds to alg44 protein (gene_id=PP_1286) and promotes PALGSKT response, here add constraints to limit the rate of PALGSKT c-di-gmp binding number is linear: flux = 10 x binding

2.2 Adding biofilm

Add the variable biofilm to the model as an indicator of biofilm formation, constraints:

(1)The amount of biofilm formed should be less than the sum of the constituents.

(2)The amount of biofilm formed should be less than 20 times the amount of each component.

Biofilm constituents include five fucoidan polysaccharides (alginate) and N-acetyl-D-glucosamine, a constituent of Pel polysaccharides.

The Psl polysaccharide and another constituent of Pel are not considered because the model has only an uptake pathway but not a secretory pathway regarding the Psl constituent mannose, and glucose is the main uptake. In addition, the model does not contain rhamnose and N-acetyl-D-galactosamine

Modeling cell growth in the absence of antibiotics

The above results show that, under this condition:

* Cells grew at a rate: μ = 0.586h^-1

* Doubling Time: ln 2 / μ= 1.18 h

* Low production of biofilm and c-di-gmp

2.3 Addition of antibiotics

The mechanism of action of the antibiotics used is to inhibit transcription or translation. This was achieved by limiting the BIOMASS_KT2440_WT3 growth indicator response.

Add the variable antibiotic as an indicator of the antibiotic.

Set the dose of antibiotic to 0.1 mmol/(gDryweight hour)

Constrain the relationship between antibiotic intake and biofilm: antibiotic = dose - biofilm

Relationship between target response and antibiotic intake: flux < 0.6 x (1 - antibiotics/dose)

Calculate cell growth and biofilm formation in the presence of antibiotics.

The above results show that:

* There was a decrease in cell growth rate, from 0.586 originally to 0.502.

* The doubling time has changed from 1.18h to 1.38h.

* There is a certain amount of biofilm production and c-di-gmp also binds to its target protein.

The detailed composition of the biofilm is then exported

2.4 Simulation of gene insertion

First, simulate the insertion of yhjH .

Since yhjH is a PDE, it was simulated by increasing the lower limit of the PDE response.

The above results show that:

Due to the insertion of yhjH , there is a certain reduction in the formation of biological periplasm and a certain reduction in the rate of cell growth in the antibiotic environment as the rate of PDE reaction increases.

The insertion of wspF was then simulated. Since wspF is able to inhibit the expression of wspF as DGC, it was simulated here by limiting the rate of DGC reaction.

The above results show that:

After the insertion of wspF , as the DCG reaction was gradually inhibited, the formation of the biological periplasm was significantly reduced, and the growth rate of the cell was significantly decreased.

3. Conclusion

In this experiment, a new model was constructed by adding c-di-GMP-related metabolites and reactions, indicator variables of biofilm formation, and beta-lactamase inhibitor antibiotics to the existing Pseudomonas aeruginosa model iJN1463.

The new model was able to better predict the growth and biofilm formation of Pseudomonas aeruginosa in the presence of beta-lactamase inhibitor antibiotics.

The insertion of wspF and yhjH genes was simulated separately using the new model and conclusions were drawn:

The insertion of both genes was able to inhibit biofilm formation and reduce bacterial growth in the antibiotic environment.

4. Code description

We employ Python and Cobrapy to conduct flux balance analysis. Building upon the BiGG iJN1436 metabolic model, we incorporate additional metabolites, including c-di-gmp, its production reaction diguanylate_cyclase (DGC), its consumption reaction phosphodiesterase, and its binding reaction. We also introduce linear constraints into the c-di-gmp binding reaction and the reactions catalized by its binding enzyme, simulating its activation potential. Furthermore, variables for biofilm and antibiotics are incorporated into the model. The biofilm value is calculated based on the flux of several biofilm-forming polysaccharides. Antibiotic constraints, including its target growth reaction and biofilm, are also included to simulate its inhibitory effect on cell growth and biofilm formation. We simulate gene insertion effects by altering the upper or lower bound of c-di-gmp-related reactions. The results demonstrate significant inhibition of biofilm formation upon gene insertion. Our code is embedded within the report document.

Reference

1. King ZA, Lu JS, Dräger A, Miller PC, Federowicz S, Lerman JA, Ebrahim A, Palsson BO, and Lewis NE. BiGG Models: A platform for integrating, standardizing, and sharing genome-scale models (2016) Nucleic Acids Research 44(D1):D515-D522. doi:10.1093/nar/gkv1049

2. Ebrahim A, Lerman JA, Palsson BO, Hyduke DR. 2013, COBRApy: COnstraints-Based Reconstruction and Analysis for Python. BMC Syst Bio 7: 74.

3. Zachary A. King, Andreas Dräger, Ali Ebrahim, Nikolaus Sonnenschein, Nathan E. Lewis, and Bernhard O. Palsson (2015) Escher: A web application for building, sharing, and embedding data-rich visualizations of biological pathways, PLOS Computational Biology 11(8): e1004321. doi:10.1371/journal.pcbi.1004321

A Population Growth Model for P. aeruginosa

Modifying the filamentous bacteriophage pf4 could impact Pseudomonas aeruginosa’s growth and other attributes due to their interdependent relationship. pf4 promotes biofilm formation crucial for bacterial survival and pathogenicity. It also shields the bacteria from antibiotics, affecting treatment efficacy. Furthermore, pf4 helps modulate host immune responses to favor infection, aiding the bacterium in evading host immune detection. Certain pf4 variants reduce virulence-associated traits in Pseudomonas aeruginosa, indicating that pf4 modifications can influence bacterial virulence and potentially growth. pf4 is also integral for biofilm development, stress tolerance, and genetic variant formation in Pseudomonas aeruginosa, which are vital for its survival, growth, and pathogenicity under various conditions. Hence, any alteration to pf4 could potentially affect these interactions and subsequently the growth and other phenotypic traits of Pseudomonas aeruginosa. [1], [2], [3].