Team:British Columbia/modeling description

We developed a mathematical model that describes the dynamics of the biofilm structure (in terms of bacterial population size) and the interactions among the major components, including the engineered phage and DispersinB (DspB) protein. We used numerical simulations to predict the impact of phage and DspB release on the biofilm structure. We also investigated the weight of each parameter to the design of our system with sensitivity analysis. Possible scenarios of biofilm degradation suggested by our model are investigated.

The biofilm system assumes a simple planar geometry characterized by depth, D, and cross-sectional area, A (Figure 1). The density and distribution of the biofilm bacterial population, extracellular polymeric substance (EPS), and dissolved components (e.g. AIP and metabolites) are uniform throughout the biofilm structure. Assuming that each biofilm bacterium occupies a spherical volume of diameter, d, and the surrounding EPS extends this volume by a constant, Α, each bacterium takes up a cubic volume of (Α + d)^3.

The total bacterial population, B, is divided into two subpopulations: 1) the carrier bacteria, B_i, which are infected with the engineered phage and 2) the non-carrier bacteria, B_u, which are uninfected but susceptible to phage infection upon exposure. We separate the carrier bacteria subpopulation further into two subpopulations: 1) the bacteria infected with the phage in latent phase, B_l , and 2) those infected with the phage in lytic phase, B_L. The total population, B_T , undergo logistic growth at rate Ρ_T limited by the carrying capacity, K; the uninfected, B_u , and infected, B_i , subpopulations grow at rates Ρ_u and Ρ_i, respectively. The following differential equations describe the dynamics of the two infected subpopulations, where p is the portion of latent bacteria, Π the rate of transition from latent to lytic phase, and Λ the rate of lysis:

Equations

The carrying capacity is related to the maximum biofilm thickness, since both are determined by the genetic predisposition of the constituent bacteria and environmental factors. The carrying capacity can be coarsely estimated using Equation 1 by letting D equal to the maximum thickness.

Equations

Initially, only the engineered S. aureus bacteria will be introduced to the biofilm. In response to the presence of AIP, they will generate and release the first batch of phage particles. A proportion of these phage particles, Κ, will successfully infect and integrate its genetic information into the host genome. Once infected, a bacterium is subject to lysis probability of Λ; upon lysis, the bacterium will release R number of phage particles. The dynamics of the phage particles is governed by half-life, t_1/2.