Understanding photosynthetic biofilm productivity and structure through 2D simulation

Abstract

We present a spatial model describing the growth of a photosynthetic microalgae biofilm. In this 2D-model we consider photosynthesis, cell carbon accumulation, extracellular matrix excretion, and mortality. The rate of each of these mechanisms is given by kinetic laws regulated by light, nitrate, oxygen and inorganic carbon. The model is based on mixture theory and the behaviour of each component is defined on one hand by mass conservation, which takes into account biological features of the system, and on the other hand by conservation of momentum, which expresses the physical properties of the components. The model simulates the biofilm structural dynamics following an initial colonization phase. It shows that a 75 μm thick active region drives the biofilm development. We then determine the optimal harvesting period and biofilm height which maximize productivity. Finally, different harvesting patterns are tested and their effect on biofilm structure are discussed. The optimal strategy differs whether the objective is to recover the total biofilm or just the algal biomass.

Fig 1. Schematic representation of the biological model scheme, including the external supplies and the metabolic pathways.

The arrows represent the mass exchanges induced by biochemical reactions between the components which are represented by the rectangles.

Fig 2. Biofilm volume fractions and composition at different times: t = 5, t = 15, t = 25 and t = 35 days from left to right.

The first row represents the whole biofilm volume fraction B = A + N + E. The second row represents the microalgae volume fraction M = A + N. The third row represents the extra cellular matrix volume fraction E. Finally the last row represents the ratio of living biomass over the whole biomass, namely 100 × M/B.

Fig 3. Distribution of the dissolved components for a biofilm starting from a single spot colony.

The inorganic nitrogen concentration (first line), inorganic carbon distribution (second line) and oxygen distribution (third line) are represented at times t = 5, t = 15, t = 25 and t = 35 days (from left to right). The purple dotted line represents the biofilm front defined as the largest value for the biofilm gradient.

Fig 4. Photosynthesis rate in the biofilm (φ_Phot, see S2 Text for the detailed mathematical expression) at times t = 5, t = 15, t = 25 and t = 35 days for a biofilm starting from a single spot colony.

The purple dotted line represents the biofilm front.

Fig 5. Relative contributions to photosynthesis rate of different terms considered at time t = 15 days (except Fig 5H at time t = 30 days); see S2 Text for the expression of these terms.

Fig 5A: Normalized photosynthesis rate $\frac{{\phi }_{Phot}}{N{\mu }_{Phot}{\rho }_M}$. Fig 5B: Photosynthesis limitation by liquid f_Liquid. Fig 5C: Relative light intensity $\widehat{I}$. Fig 5D: Photosynthesis limitation by light f_Light using Haldane law. Fig 5E: Photosynthesis limitation by functional biomass quota f_Droop. Fig 5F: Photosynthesis limitation by inorganic carbon $f_{[C{O}_2]}$. Fig 5G: Photosynthesis limitation by oxygen f_Oxy at time t = 15 days. Fig 5H: Photosynthesis limitation by oxygen: f_Oxy at time t = 30 days.

Fig 6. Relative difference between excretion and death rates, functional biomass production, inorganic carbon transfer rate and oxygen ransfer rate at day 15 (see S2 Text for the expression of these terms).

Fig 6A: Relative difference (Δ in %) between fluxes for ECM excretion and death. Fig 6B: Functional biomass production rate φ_Func. Fig 6C: Inorganic carbon supply ${\phi }_{Henry}^C$. Fig 6D: Oxygen supply ${\phi }_{Henry}^O$.

Fig 7. Biofilm volume fractions and composition at different times: t = 5, t = 10, t = 15 and t = 20 days from left to right.

First row: whole biofilm volume fraction B = A + N + E. Second row: microalgae volume fraction M = A + N. Third row: extra cellular matrix volume fraction E. Last row: ratio (%) of living biomass over the whole biomass M/B.

Fig 8. Concentration of the dissolved components at times t = 5, t = 10, t = 15 and t = 20 days for a biofilm starting from a three spot colony.

First line: substrate distribution (S). Second line: inorganic carbon distribution (C). Third line: oxygen distribution (O). The purple dotted line represents the biofilm outer contour defined as the largest value for the biofilm gradient.

Fig 9. Daily production rates obtained using 1D numerical simulation (ie. uniform scraping pattern) for different biofilm components and biofilm compositions with respect to harvest period and height.

Fig 9A: Daily production rate of dry biofilm (A + N + E). Fig 9B: Daily production rate of dry ECM (E). Fig 9C: Daily production rate of dry microalgae (A + N). Fig 9D: Biofilm composition: dry biomass percentage within microalgae (A + N)/(A + N + E).

Fig 10. Biofilm (first row) and photosynthesis rate (second row) over an harvesting period.

Harvest is performed every 6.5 days, using battlement scraping shape of width 250μm. The first column, at time t = 0, represents biofilm and photosynthesis rate immediately after the harvest and the last column 6 days after harvest (or equivalently half a day before the second harvest). The columns in between represent the intermediary times t = 2 and t = 4 days after harvest. All these subfigures correspond to square domain of length L_x = L_z = 3 · 10⁻³.