Simulation of catalase-dependent tolerance of microbial biofilm to hydrogen peroxide with a biofilm computer model

Hydrogen peroxide (HP) is a common disinfectant and antiseptic. When applied to a biofilm, it may be expected that the top layer of the biofilm would be killed by HP, the HP would penetrate further, and eventually eradicate the entire biofilm. However, using the Biofilm.jl computer model, we demonstrate a mechanism by which the biofilm can persist, and even become thicker, in the indefinite treatment with an HP solution at concentrations that are lethal to planktonic microorganisms. This surprising result is found to be dependent on the neutralization of HP by dead biomass, which provides protection for living biomass deeper within the biofilm. Practically, to control a biofilm, this result leads to the concept of treating with an HP dose exceeding a critical threshold concentration rather than a sustained, lower-concentration treatment.

hydrogen peroxide, consumption of hydrogen peroxide by catalase-containing cells, and diffusion of hydrogen 38 peroxide into the biofilm. The biofilm is simulated as a uniformly thick film growing in a continuous stirred-39 tank reactor. A companion paper describes the equations and the code for their numerical solution in detail 40 [35]. We are not aware of any prior modeling work on the problem of continuous treatment of a biofilm with 41 hydrogen peroxide. 42 2 Methods

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Simulations are conducted with Biofilm.jl [36], which models a one-dimensional biofilm within a stirred tank 44 reactor. Details are provided in [35] on the governing equations, numerical methods, and application of the 45 solver to a number of test cases. In this paper, the governing equations are described followed by a high-level 46 description of the numerical methods. 47 The model solves for the concentrations of particulates and substrates within the tank (X t and S t ), The live and dead biomass L and D is solved for within the tank. The initial concentrations are set to 56 X t:L = X 0 t:L and X t:D = X 0 t:D and the temporal change is described by for j = [L, D]. The first term on the right-hand-side (RHS) describes the growth of particulate and µ j is the where k dis is the disinfection neutralization rate coefficient. The initial concentrations of the substrates glucose and hydrogen peroxide are set to S t:G = S 0 t:G and 68 S t:H = S 0 t:H and the temporal change is described by for k = [G, H]. The first term on the RHS describes the consumption of substrates due to the growth of particulates and Y j,k is the yield coefficient of substrate on biomass and for this problem where Y G,L is non-zero because glucose is consumed by the growth of live biomass but Y H,L = 0 since hydrogen peroxide is neither produced or consumed. Furthermore, the dead biomass does not consume or produce either glucose or hydrogen peroxide and both Y G,D and Y H,D are zero. The second term on the RHS is the flow of substrate into and out of the tank. The flow of glucose into the tank is a constant S in:G . The flow of hydrogen peroxide into the tank controls the dosing and is given as The third term on the RHS of Eq. 4 is the flux of substrate into the biofilm due to diffusion. The last term 70 is the source of substrate and is zero for glucose and describes the neutralization of hydrogen peroxide due 71 to living and dead biomass, i.e., The live and dead biomass L and D is solved for within the tank. The initial concentrations are set to 75 X b:L = X 0 b:L and X b:D = X 0 b:D . The temporal changes are described by for j = [L, D]. The first term on the RHS describes the growth of biomass and uses the growth rates in 77 Eq. 2. The second term describes the vertical transport of particulates due to growth and sources at deeper 78 depths in the biofilm characterized by the growth velocity v(z), i.e., where P tot = Nx j=1 P b:j and ρ j is the density of the particulates. The final term in Eq. 6 is the source of for k = [G, H]. The first term on the RHS describes diffusion and D e:k is the diffusion coefficient. The boundary conditions on the diffusion term are 1) no-flux at the bottom of the biofilm and 2) at the top of the biofilm the diffusion of substrate from the tank is equal to the flux into the biofilm. For the top boundary condition, a boundary layer is added of thickness L L within the tank, and the flux matching condition can be written as The second term in the RHS of Eq. 8 is the consumption of substrate due to biomass growth and the third 85 provides the source of substrates using Eq. 5.

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The thickness of the biofilm is initially set to L f = L 0 f and then the temporal dynamics are described by where the first term on the RHS is the growth velocity at the top of the biofilm (see Eq. 7). The second 89 term is the detachment velocity modeled as v det = K det L 2 f and K det is the detachment coefficient. The solver was run with a number of different cases. The standard parameters are provided in Table 1  withstood ongoing continuous dosing with the biocide (Fig. 1). When the biocide was discontinued, the 113 biofilm returned within a day to its pre-treatment steady-state thickness (Fig. 1).

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Biofilms persisted despite continuous exposure to high concentrations of HP. The steady state biofilm 115 thickness was larger than the pre-treatment thickness for HP dose concentrations up to 3,400 g/m 3 (Fig. 2a).

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Only when the HP concentration was increased beyond this amount did the steady-state biofilm thickness 117

Parameter
Value Description Biocide neutralization rate for live and dead biomass ρ L | ρ D 2.5e5 | 2.5e5 g/m 3 Density of live and dead biomass Number of grid points used to discretize biofilm   The distribution of live and dead cells within the biofilm was complex and non-uniform (Fig. 4a). Dead 137 cells outnumbered live cells only in the topmost layer of the biofilm (Fig. 4a). Whereas live cells constituted 138 100% of cells in untreated biofilm, the mean live cell volume fraction in the treated biofilms was 68%. The 139 volumetric consumption rate of glucose inside the biofilm was reduced in HP treated biofilms (Fig. 4b). This 140 was not due to lower availability of glucose as the glucose concentration in the treated biofilm was higher 141 than that in the untreated biofilm (Fig. 3b). The reduction in glucose consumption rate was likely due to 142 the reduced volume fraction of live, metabolically active cells in the treated biofilm.    When the neutralization of hydrogen peroxide mediated by dead cells was turned off, the biofilm became 146 susceptible to killing (Fig. 5). Compared to the base case simulation that used both live and dead cell 147 neutralization of HP, turning off dead cell neutralization resulted in the biofilm thickness decaying toward zero 148 (Fig. 5a) as well as the elimination of live cells (Fig. 5b). Doses of HP, that in the baseline simulation were well 149 tolerated, eliminated the biofilm in a simulation where dead cell neutralization of HP was turned off (Fig. 6).

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For example, whereas a biofilm in which both live and dead cells neutralize HP withstood a continuous dose 151 of 16,600 g/m 3 , a dose of just 200 g/m 3 fully decimated a biofilm in which dead cell neutralization was 152 turned off (Fig. 6). Curiously, turning off the neutralization of hydrogen peroxide mediated by live cells had 153 little influence on biofilm susceptibility (Fig. 5, Fig. 6). Therefore, it appears that the catalytic activity of 154 dead cells versus HP is critical to robust biofilm protection, but not that of live cells.

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When the concentration of the growth-limiting substrate, glucose, was decreased, the biofilm became less 157 tolerant (Fig. 7). Decreasing glucose from 100 g/m 3 in the base case to about 16 g/m 3 resulted in the 158 elimination of the biofilm when subjected to the standard HP dose (Fig. 7). Conversely, increasing the 159 influent concentration of glucose made the biofilm somewhat more tolerant (Fig. 7). the biofilm, leading to a standing gradient in biocide concentration within the biofilm (Fig. 3b).

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The ability of aggregated microorganisms to neutralize hydrogen peroxide and prevent its penetration into  We propose a simplified conceptual model to explain the remarkable tolerance of biofilm to HP and the 187 ability of the biofilm to maintain this defense indefinitely (Fig. 8). This model conceptualizes a zone at 188 the top layer of the biofilm that is predominantly dead cells and an active zone beneath this layer that is 189 predominantly living cells. In reality the biofilm is not sharply stratified but harbors gradients in dead and  The results of this study also support the biofouling control strategy of reducing nutrients available to 242 support biofilm growth. Reducing nutrient availability not only reduced innate fouling potential prior to 243 biocide treatment, it also reduces the ability of the biofilm to persist during continuous HP exposure (Fig. 7). This study received no funding.

Competing interests 252
All authors declare no financial or non-financial competing interests.

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Data Availability

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No data is used in this study. The simulated results are produced with Biofilm.jl, which is described in the 255 subsequent section.

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Code Availability

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The results in this study are produced with the Biofilm.jl software, which is freely available with an MIT