Increasing aggregate size reduces single-cell organic carbon incorporation by hydrogel-embedded wetland microbes

Abstract Microbial degradation of organic carbon in sediments is impacted by the availability of oxygen and substrates for growth. To better understand how particle size and redox zonation impact microbial organic carbon incorporation, techniques that maintain spatial information are necessary to quantify elemental cycling at the microscale. In this study, we produced hydrogel microspheres of various diameters (100, 250, and 500 μm) and inoculated them with an aerobic heterotrophic bacterium isolated from a freshwater wetland (Flavobacterium sp.), and in a second experiment with a microbial community from an urban lacustrine wetland. The hydrogel-embedded microbial populations were incubated with 13C-labeled substrates to quantify organic carbon incorporation into biomass via nanoSIMS. Additionally, luminescent nanosensors enabled spatially explicit measurements of oxygen concentrations inside the microspheres. The experimental data were then incorporated into a reactive-transport model to project long-term steady-state conditions. Smaller (100 μm) particles exhibited the highest microbial cell-specific growth per volume, but also showed higher absolute activity near the surface compared to the larger particles (250 and 500 μm). The experimental results and computational models demonstrate that organic carbon availability was not high enough to allow steep oxygen gradients and as a result, all particle sizes remained well-oxygenated. Our study provides a foundational framework for future studies investigating spatially dependent microbial activity in aggregates using isotopically labeled substrates to quantify growth.


Methods: Numerical Modeling
The model for bacterial growth and decay within a hydrogel microsphere was based on the diffusion-reaction material balances for the relevant chemical species in the hydrogel exposed to a constant carbon (CB,S) and oxygen (CB,O2) concentration.A one-dimensional hydrogel with a fixed thickness (LF) and a spherical geometry was assumed in all cases.The hydrogel was assumed to contain both biomass and a cross-linked polymeric matrix, represented by inert biomass.The isolate model only considers the growth of Flavobacterium sp. on glucose with biomass initially uniformly distributed throughout the hydrogel matrix (Xi).The wetland community model considers the growth of three species on a carbon substrate with equivalent amounts of biomass for all three species uniformly distributed throughout the hydrogel matrix (Xi).The only difference between the one species and three species models were the kinetic parameters (Table S1-4) and initial biomass concentrations.
The conversion rate of a component is related to the stoichiometric coefficient (Aij) and the process rates to (ρj) through the equation ui=∑j Aijρ ρj.The index i refers to model components, while processes were marked by index j.Two types of components were present in the system, soluble (S) and particulate (X) substances [1].

Solute balances in the biofilm
Two model solutes (index i) were included in the model, with concentrations CF,i (mol/m3 biofilm): dissolved oxygen (O2) and glucose (S).Time-dependent mole balances for all solutes in the hydrogel included rates of reaction and transport by diffusion, eq. ( 1): % %& for the spherical hydrogel geometry.
The effective diffusion coefficients in the biofilm, DF,i, were chosen based on values reported in Stewart 2003 [2].The net rates for each soluble component, ri, were based on the stoichiometry and kinetics of carbon and oxygen consumption of each organism.Rates, kinetic expressions, stoichiometry, parameters are detailed in Tables S1-6.
The boundary condition at the hydrogel center (x=0) was set as zero-flux for all solutes, eq. ( 2): The external mass transfer resistance (diffusion boundary layer) was neglected for all solutes.Therefore, concentrations at the hydrogel surface (x=LF) were assumed to be equivalent with the bulk liquid concentrations, which were set to a constant value, eq. ( 3): with CB,i in mol/m 3 liquid.

Biomass balances in the hydrogel
Biomass within the hydrogels were modeled as a fixed thickness biofilm containing active biomass (Xi), inert biomass (Xinert), and a cross-linked hydrogel polymeric matrix, which was represented by inert biomass (Xinert) in the model [3].A constant hydrogel matrix density of was assumed for the hydrogel granule [3].Biomass was assumed to be uniformly distributed throughout the hydrogel matrix and comprise 1% of the total hydrogel matrix.Biomass decay was described by the death-regeneration concept and was assumed to be a fixed fraction (10%) of the growth rate [4][5][6]).
A time-dependent mole balances for all biomass component in the hydrogel including reaction rates and f, eq. ( 4): The net rates for each biomass component, ri, were based on the stoichiometry and kinetics of carbon and oxygen consumption of each organism.Rates, kinetic expressions, stoichiometry, parameters are detailed in Tables S1-6.
The advective velocity of the hydrogel matrix within the hydrogel was computed based on the total hydrogel matrix mass balance, eq. ( 5).
The boundary condition at the hydrogel center (x=0) was set as zero-flux for all biomass components, eq. ( 6): The boundary condition at the edge of the biofilm (x=LF) was set as an outflow boundary condition, where biomass growing past the edge of the hydrogel was assumed to exit the hydrogel.

Model solution
The model was implemented in COMSOL Multiphysics (v4.4,Comsol Inc., Burlington, MA).Model equations were solved with variable time step on a biofilm domain discretized with a maximum mesh size of 1 µm.The simulation times were in the order of seconds per case.All reported steady state results were in all conditions obtained after 300 days [7].

Table S1: Stoichiometric matrix of conversion reactions for
Table S2: Stoichiometric matrix of conversion reactions for the three species wetland community model

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Table S8 The number of cells analyzed per hydrogel microsphere size category, and how many cells as well as the percentage of cells which were statistically more active than the no-addition control cells.The model was built on a 300-day simulation of steady-state supply of carbon and oxygen to determine the gradients of biomass across microsphere diameters.

Figure S1 :
Figure S1: Picarro isotopic gas analysis showing 13 CO2 was generated from the Flavobacterium experiment growing on 13 C-labeled glucose and the wetland microbial community experiment growing on 13 C labeled protein.

Figure S2 :Figure S3 :
Figure S2:Isolate and wetland cells are more likely to be highly active in 100 µm microspheres using probability statistics.Inactive and low activity cells create a positively skewed distribution across all microsphere sizes, yet 100 µm spheres a higher proportion of active cells compared to larger sizes.The a & c) probability distribution functions are the statistical likelihood of a cell being within a specific Cnet range, and the b & d) cumulative distribution functions are the likelihood of a cell having a Cnet at that percent or lower.The Flavobacterium (a &b) and wetland community (c & d) analyses are shown with 100µm micropheres (purple circles), 250µm (yellow diamonds) and 500µm microspheres (pink triangles).Overall, the mean of cells in 100 µm microspheres were statistically more enriched for 13 C than the larger 250µm and 500µm microspheres that were not significantly different from each other.The size data for the isolate experiment resulted in distinct cumulative distribution functions (FigureS2b) using Kolmogorov-Smirnov tests (100µm-250µm D=0.469, 100µm-500µm D=0.315, 250µm-500µm D=0.332, all p<<0.05).The wetland community's cumulative distribution functions (FigureS2d) showed more highly active cells in 100 µm microspheres resulting in a distinct distribution (100 µm-250µm D=0.138 & p<<0.05, 100 µm-500 µm D=0.134 & p <<0.05) while the 250 µm and 500 µm distributions were not significantly distinct (250 µm-500 µm D=0.079 & p=0.280)

Figure S4 :
Figure S4:The 100 µm microspheres had a higher activity based on 15 N-atom percent excess (APE).Inactive and low activity cells created a positively skewed distribution across all microsphere sizes.All incubations were given a mixture of 15 N-algal protein and 15 N-ammonium to detect cells via nanoSIMS, including the control cells, therefore a cutoff for active/inactive is not shown.The a) probability distribution function and b) cumulative distribution function for 15 N-APE of the wetland microbial community analysis is shown with 100µm (purple circles), 250 µm (yellow diamonds) and 500 µm microspheres (pink triangles).This analysis created bins at 10% intervals to represent the percentage of analyzed cells whose 15 N-APE fell within a bin's range.

Figure S5 :
Figure S5: SYBR Gold stained Flavobacterium sp. on a z-stack maximum projection image of a 500 µm microsphere showing several regions outlined with red dashed circles, which are likely larger microporous cavities with higher abundances of microbial cells with higher activity.

Figure S6 :
Figure S6: Fluorescence confocal microscopy image of a cross section through the center of several hydrogel microspheres to reveal the oxygen concentration using nanosensors.The ratio of two fluorescent signals is shown on the scale bar where the oxygen intensity reading at 405nm excitation with 640 -660nm emission is divided by the reference signal at 405nm excitation with 435 -485 excitation.The ratio is inversely proportional to oxygen concentration where 0.3 is at saturation (~8 mg/L of oxygen) and 1.5 is the lowest oxygen concentration of around 2.7 mg/L based on the Stern-Volmer equation.

Figure S7 :
Figure S7: The Flavobacterium a) 250 µm microspheres (yellow diamonds) had a significantly lower decrease in oxygen concentration from the surface to 50 µm into the microsphere while the wetland b) 100 µm microspheres (purple circles) had a significantly lower oxygen concentration.The change in dissolved oxygen concentration is shown normalized across all microsphere diameter sizes where 0 represents the liquid/surface interface and the oxygen concentration drops moving further into the microspheres.

Figure S8 :
Figure S8:The isolate, Flavobacterium sp., is C-limited when modeled with varying organic C concentrations (1 µM up to 1000 µM) and never reaches oxygen limiting conditions at steady state.The model is built on a 300-day simulation of steady-state supply of C and oxygen to determine the gradients across microsphere diameters.The left-side panels model the C concentration across a) 100 µM diameter, b) 250 µM diameter, and c) 500 µM diameter microspheres.The right-side panels model the oxygen concentration within a microsphere when the population is fed each carbon concentration across a) 100 µM diameter , b) 250 µM diameter , and c) 500 µM diameter microspheres.

Figure S9 :
Figure S9: One-dimensional modeling of 3-member microbial community.Dotted lines represent the location of the center of 100 µm, 250 µm, and 500 µm diameter microspheres.The model was built on a 300-day simulation of steady-state supply of carbon and oxygen to determine the gradients of biomass across microsphere diameters.

Table S3 :
Kinetic rate expressions for Flavobacterium sp.model

Table S5 :
Modeling Parameters for values Flavobacterium sp.Model

Table S6 :
Modeling parameters for three species wetland model

Table S7 :
Initial values for three species wetland model