Team:British Columbia/modeling results

Simulation Results

We ran 1200-generation simulations using the parameters and starting conditions listed in Table 1. To predict the outcome of phage-assisted biofilm dispersal under two different systems-one in which phage particles and DspB are produced, and the other in which only phage particles are generated-we performed simulations by setting the DspB production rate, S, to 1) 0.0001 and 2) 0. To determine whether the phage infection rate and half-life are critical to the design and engineering of biofilm-degradation systems, we applied sensitivity analyses using a reasonably comprehensive range of values for the parameters.

The Binary Outcome

Biofilm Death

Figure 1: The simulated behavior of the biofilm and phage populations over 1200 mins (20 hrs). The percent of the total biofilm population remaining after phage introduction (blue) sharply declines at 400 min. This coincides with the sharp increase of the percent of the biofilm population infected by phage (green). The phage population (here, represented by the P-factor) peaks shortly after 400 mins. These features suggest that the accumulation of phage particles in the biofilm between 0 and 400 min triggers mass host cell lysis leading to the destruction of the biofilm at the 1200^th min.

Figure 2: The dynamics of the extracellular concentrations of AIP (purple) and DspB (red) over 1200 mins (20 hrs). The maximum level of AIP concentration and the activation threshold level are indicated by the upper and lower dashed lines, respectively. AIP concentration is shown to steadily decrease over time, but does not fall below the threshold level during the 1200 mins. This is due to the relatively high rate of AIP degradation rate arbitrarily set for this simulation. DspB concentration rises rapidly at 400 min, coinciding with decrease in biofilm population and increase in phage population (indicated in Figure 1), and then peaks at 600 min when the biofilm population is substantially reduced.

Biofilm Survival

Figure 3: The simulated behavior of the biofilm and phage populations over 1200 mins (20 hrs) in a system where DspB production is absent (i.e. S = 0). The phage population (orange) experiences rapid decline at the beginning, when the phage particles attempt to infect the bacteria at the surface of the biofilm, resulting in a small subpopulation of infected bacteria (green). However, the total biofilm population (blue) is minimally impacted. The relatively constant biofilm and phage populations suggest that the phage is repeatedly attempting infection at the biofilm surface but fails to penetrate into the biofilm structure. This simulation demonstrates that DspB greatly facilitates phage invasion into the biofilm structure, as shown in Collins et al. (2007).

Figure 4: The dynamics of the extracellular concentrations of AIP (purple) and DspB (red) over 1200 mins (20 hrs). The maximum level of AIP concentration and the activation threshold level are indicated by the upper and lower dashed lines, respectively. AIP concentration is shown to steadily decrease over time, but does not fall below the threshold level during the 1200 mins. This is due to the relatively high rate of AIP degradation rate arbitrarily set for this simulation. DspB is completely absent.

Sensitivity Analyses

Phage virulence is critical to successful biofilm dispersal

A

B

C

Figure 5: Sensitivity analysis of the phage infection rate parameter, κ. A range of values for the infection rate is used. The infection rate is shown to have some impact on the dynamics of the total biofilm population (panel A), the infected biofilm subpopulation (panel B), and the phage population (panel C). When the rate is high (>=0.4), further rate increase has a diminishing effect on the population dynamics. When the rate is low (<=0.2), further decrease renders the phage particles ineffective for biofilm degradation (panel A and B). This analysis suggests that the phage must be sufficiently virulent for biofilm dispersal to occur. Interaction between the phage and the target biofilm bacteria is an important component in the design of biofilm-degradation systems.

Half-life is not an outcome-determining factor

A

B

C

Figure 6: Sensitivity analysis of the phage half-life parameter, η. A broad range of values for the phage half-life is investigated. The half-life has little, if any, effect on the dynamics of biofilm (panel A and B) and phage (panel C) populations, and therefore is not a critical factor for biofilm dispersal. Unless the phage has an extremely short lifespan, it is not a major concern in phage-biofilm system design.

Discussion

Although our model was initially developed to simulate the behavior of our genetically engineered (GE) system, it can be applied to predict the dynamics of other biofilm systems that are introduced to a biofilm matrix-degrading phage. By setting the model parameters to values that represent the properties of a real-world biofilm system, we can simulate scenarios where the biofilms are exposed to a GE phage functionally similar to ours. We can also incorporate information on the properties of the phage by modifying certain parameters. Our model can be used to perform in silico phage-assisted biofilm-degradation experiments. By changing various parameters that represent properties of the biofilm bacteria or phage, we can simulate different phage-biofilm systems. Our model can also assist the designing similar synthetic biology systems. The sensitivity analyses demonstrated here can be performed to weigh the importance of properties that may impact the design of the system.

Table 1: List of parameters and starting conditions used for simulations.