Modeling Antibiotic Concentrations in the Vicinity of Antibiotic-Producing Bacteria at the Micron Scale

ABSTRACT

It is generally thought that antibiotics confer upon the producing bacteria the ability to inhibit or kill neighboring microorganisms, thereby providing the producer with a significant competitive advantage. Were this to be the case, the concentrations of emitted antibiotics in the vicinity of producing bacteria might be expected to fall within the ranges of MICs that are documented for a number of bacteria. Furthermore, antibiotic concentrations that bacteria are punctually or chronically exposed to in environments harboring antibiotic-producing bacteria might fall within the range of minimum selective concentrations (MSCs) that confer a fitness advantage to bacteria carrying acquired antibiotic resistance genes. There are, to our knowledge, no available in situ measured antibiotic concentrations in the biofilm environments that bacteria typically live in. The objective of the present study was to use a modeling approach to estimate the antibiotic concentrations that might accumulate in the vicinity of bacteria that are producing an antibiotic. Fick’s law was used to model antibiotic diffusion using a series of key assumptions. The concentrations of antibiotics within a few microns of single producing cells could not reach MSC (8 to 16 μg/L) or MIC (500 μg/L) values, whereas the concentrations around aggregates of a thousand cells could reach these concentrations. The model outputs suggest that single cells could not produce an antibiotic at a rate sufficient to achieve a bioactive concentration in the vicinity, whereas a group of cells, each producing the antibiotic, could do so.

IMPORTANCE It is generally assumed that a natural function of antibiotics is to provide their producers with a competitive advantage. If this were the case, sensitive organisms in proximity to producers would be exposed to inhibitory concentrations. The widespread detection of antibiotic resistance genes in pristine environments suggests that bacteria are indeed exposed to inhibitory antibiotic concentrations in the natural world. Here, a model using Fick’s law was used to estimate potential antibiotic concentrations in the space surrounding producing cells at the micron scale. Key assumptions were that per-cell production rates drawn from the pharmaceutical manufacturing industry are applicable in situ, that production rates were constant, and that produced antibiotics are stable. The model outputs indicate that antibiotic concentrations in proximity to aggregates of a thousand cells can indeed be in the minimum inhibitory or minimum selective concentration range.

INTRODUCTION

Aquatic and terrestrial environments can become contaminated with antibiotic residues via multiple exposure pathways, including municipal and pharmaceutical manufacturing wastewater effluents, land application of animal or human waste as fertilizer, irrigation with reclaimed wastewater, and the use of antibiotics for crop protection or aquaculture (1). There is an emerging concern that in some instances environmental antibiotic concentrations may select for resistance, even though their concentrations may be well below that required to inhibit growth, the MIC. Notably, the minimum selective concentration (MSC) is the lowest concentration at which resistance is predicted to be selected for and at which resistant bacteria will have a selective growth advantage in the presence of the antibiotic over isogenic sensitive bacteria (2). The MSC may be several hundredfold lower than the MIC.

Many antibiotics used in human medicine or food production are naturally produced by bacteria or fungi or are semisynthetic derivatives of these products (3). In the natural world, there are thought to be varied functions for chemicals, whose primary function may not, in fact, be antibiosis. For example, antibiotics in nature are involved in communication between microorganisms of the same or different species (4–8). At subinhibitory concentrations (sub-MICs), many antibiotics repress or activate the expression of a large number of transcripts in different bacteria; this property is associated with their function as environmental signaling agents (9). Nevertheless, antibiotics can inhibit the growth of neighboring populations, providing a selective advantage for the acquisition of nutrients and space for growth (10). Bacteria that carry genes conferring resistance to multiple classes of antibiotics have been isolated from environments that have never come into contact with humans (11). This implies that in nature, the concentrations of antibiotics in proximity to producing microorganisms are sufficient to suppress or kill sensitive neighboring bacteria, enriching for resistant individuals in the process. Furthermore, bacteria able to metabolize antibiotics are readily isolated from environmental matrices (12). This indicates that at least in some environments, antibiotic concentrations are high enough that catabolic pathways have evolved to use them as growth substrates.

In the present study, a modeling approach was used to estimate the antibiotic concentrations that might be found in the immediate environment of antibiotic-producing bacteria. To describe this process, normal diffusion-reaction equations were used (13–15). A key assumption was that antibiotic production rates that are reported in the fermentation literature reflect that which could be expressed in situ. We specifically sought to determine if the antibiotic concentration gradient in the vicinity of producing bacteria could encompass the ranges expected for MICs and MSCs and, if so, at what distance from the producing cells. We found that antibiotic concentrations could, in some instances, reach the range of micrograms per milliliter or even milligrams per liter within a few microns of aggregates of producing cells.

RESULTS

Distribution of the lowest MIC₅₀ and estimated MSC of the most commonly used antibiotics.

The distribution of the lowest observed MIC₅₀ and estimated MSC boundaries of 111 antibiotics are shown in Fig. 1. The lowest observed MIC₅₀, the sample size-adjusted lowest MICs (MSC upper boundary), and predicted no-effect concentrations (PNECs; MSC lower boundary) for all the antibiotics tested ranged from 2 μg/L to 128 μg/L, from 0.064 μg/L to 500 μg/L, and from 0.008 μg/L to 64 μg/L, respectively. The corresponding concentrations that captured 80% of all tested antibiotics were 500 μg/L, 16 μg/L, and 8 μg/L, respectively (Fig. 1). These values were used for comparison purposes and interpret the biological meaning of the estimated antibiotic concentration through our modeling. Thus, an antibiotic concentration of 500 μg/L would exert an inhibitory effect on exposed bacteria, an antibiotic concentration of 16 μg/L could provide resistant bacteria an advantage over susceptible bacteria, and a concentration of 8 μg/L would have no effect on bacterial growth (16).

FIG 1.

Distribution of the lowest observed MIC₅₀ (A), size-adjusted lowest MICs (MSC upper boundaries) (B), and predicted no-effect concentrations (C) for the 111 antibiotics tested by Bengtsson-Palme and Larsson (16).

Estimated antibiotic concentrations in the vicinity of producing cells.

The antibiotic concentration gradient profile in the vicinity of producer cells was modeled, assuming a highest and lowest production scenario (Fig. 2). The estimated antibiotic concentration surrounding a bacterium or aggregate of bacteria decreased by 2 orders of magnitude for every order of magnitude increase in distance from the producer(s). As expected, the antibiotic concentration increased proportionally with the number of antibiotic-producing cells.

FIG 2.

Estimated antibiotic concentration gradient profiles in the vicinity of the producer cells assuming the highest (left) and lowest (right) production scenarios. In the highest production scenario, an antibiotic production rate of 1 × 10⁻¹⁴ g/h per cell and an antibiotic diffusion coefficient of 0.7 × 10⁻⁶ cm²/s were assumed. In the lowest production scenario, an antibiotic production rate of 1 × 10⁻¹⁴ g/h per cell and an antibiotic diffusion coefficient of 0.7 × 10⁻⁶ cm²/s were assumed. A predicted no-effect concentration (PNEC) of 8 μg/L, minimal selective concentration (MSC) of 16 μg/L, and MIC₅₀ of 500 μg/L were selected as cutoffs.

Assuming a highest production scenario (Fig. 2), using an antibiotic production rate of 1 × 10⁻¹⁴ g/h per cell and an antibiotic diffusion coefficient of 0.7 × 10⁻⁶ cm²/s, the estimated antibiotic concentration in the volume surrounding a single antibiotic-producing bacterium at a distance of 1 μm from the cell was 0.31 μg/L. Under this scenario, at least 30 aggregate antibiotic-producing bacteria would be required to reach concentrations in the range of the MSC (8 to 16 μg/L) at a distance of 1 μm. To achieve antibiotic concentrations above the MIC₅₀ of 500 μg/L at a distance of 1 μm, at least 1.6 × 10³ cells producing together in an aggregate would be required. The minimal numbers of cells required to get antibiotic concentrations in the MSC range of 8 to 16 μg/L at distances of 10, 100, and 1,000 μm were estimated at 500, 3 × 10⁴, and 3 × 10⁶ cells, respectively. Aggregates of 1 × 10⁴, 2 × 10⁶, and >1 × 10⁸ cells would be required to reach an antibiotic concentration above the MIC₅₀ of 500 μg/L at distances of 10, 100, and 1,000 μm from producers.

Assuming a lowest production scenario (Fig. 2), with an antibiotic production rate of 1 × 10⁻¹⁸ g/h per cell and an antibiotic diffusion coefficient of 6 × 10⁻⁶ cm²/s, the estimated antibiotic concentration in the volume surrounding a bacterium at 1 μm outside a cell would be 3 × 10⁻⁶μg/L. To reach antibiotic concentrations in the range of 8 to 16 μg/L and above 500 μg/L at a distance of 1 μm, at least 1.6 × 10⁶ cells and 1.6 × 10⁸ producing cells would be required.

Impact of antibiotic production rate on the estimated antibiotic concentrations in the vicinity of producing cells.

The antibiotic concentration in the vicinity of producer cells as a function of the antibiotic production rate is shown in Fig. 3. Based on the fermentation literature, the antibiotic production rate under controlled conditions ranged from 1 × 10⁻¹⁸ to 1 × 10⁻¹⁴ g/h per cell (see Table S1 in the supplemental material). A 1 log reduction of the antibiotic production rate decreased by 1 order of magnitude the estimated antibiotic concentration surrounding a bacterium or cell aggregates (Fig. 3).

FIG 3.

Estimated antibiotic concentrations at increasing distances (1 to 10,000 μm) from the producer cells as a function of the antibiotic production rate. Values within the figure refer to the antibiotic concentrations at that point, in log micrograms per liter. A predicted no-effect concentration (PNEC) of 8 μg/L, minimal selective concentration (MSC) of 16 μg/L, and MIC₅₀ of 500 μg/L were selected as cutoffs.

To achieve antibiotic concentrations above 8 μg/L (PNEC) and 500 μg/L (MIC₅₀) in the volume surrounding bacterial producers at a distance of 1 μm, cell aggregates comprising more than 2 × 10⁶ cells and 2 × 10⁸ cells, respectively, producing antibiotic at a constant rate of 1 × 10⁻¹⁸ g/h per cell would be required (Fig. 3). For each log reduction in the antibiotic production rate, the number of cells producing antibiotic has to be 10-fold larger in order to maintain similar antibiotic concentrations in the surrounding area. Likewise, for every 10-fold increase in distance from the antibiotic-producing bacteria, the number of cells producing an antibiotic at a certain production rate should be 100-fold larger to maintain similar antibiotic concentrations (Fig. 3).

DISCUSSION

In the present study, a modeling approach was used to estimate the antibiotic concentrations that might be found in the immediate environment of antibiotic-producing microorganisms in a spherical, three-dimensional structure of an aggregate. Modeling estimates indicate that a single cell could not produce enough antibiotic to reach a proximal PNEC concentration of 8 μg/L (Fig. 2). However, antibiotic concentrations in the range of the MSC (8 to 16 μg/L) would be found within 1 μm of aggregates as small as 30 antibiotic-producing cells, in the case of the highest production scenario. This indicates that to synthetize a meaningful amount of antibiotic in nature, it would be necessary to reach a critical mass of cells, as has been found in previous studies (17). One mechanism that bacteria have adopted to regulate the production of antimicrobial compounds is quorum sensing (18). Scanning electrochemical microscopy (SECM) observation of small-molecule production by bacterial biofilms revealed that quorum sensing-dependent behaviors are observed by aggregates consisting of as few as 500 cells (19).

Bacterial aggregates in nature often contain ~10¹ to 10⁵ cells (19–22). Based on our model, the estimated amount of antibiotic produced by a bacterial aggregate of 10⁵ cells may be high enough (8 to 16 μg/L) to have an impact on neighboring aggregates positioned up to 100 μm away from the producers. Antibiotic concentrations in the range of 8 to 16 μg/L could provide neighboring resistant bacteria a competitive advantage compared to isogenic sensitive bacteria (23). The resistant populations selected at sub-MICs could represent a greater challenge to manage than those selected at MIC, since they do not lose their resistance traits in the absence of antimicrobials, making them more stable (24, 25). Antibiotic pressure at low concentrations can select for resistant phenotypes or cells with an increased mutation rate (26). Likewise, recombination and horizontal gene transfer, including induced transfer of plasmids and transposons, can be induced when bacteria are exposed to sub-MICs of some antibiotics (23, 27).

Antibiotics at higher concentrations can inhibit the growth of neighboring populations, providing a selective advantage for the acquisition of nutrients and space for growth (10). In the present study, an antibiotic concentration of >500 μg/L was established as an MIC value that would exert an inhibitory effect on adjacent bacteria (Fig. 1). Assuming a highest production scenario, bacterial aggregates of 1,600, 3 × 10⁴, and 2 × 10⁶ cells producing antibiotic at a constant rate would result in concentrations of ~500 μg/L in their vicinity at 1, 10, and 100 μm, respectively. In contrast, under the lowest production scenario, bacterial aggregates containing more than 1 × 10⁶ or 1 × 10⁷ cells would be required to reach antibiotic concentrations in the MSC (8 to 16 μg/L) and MIC (>500 g/L) ranges in the vicinity of 1 μm, respectively.

The modeling approach used here is predicated on a number of important assumptions (Table 1). Notably, the per-cell rates of antibiotic production were estimated on the basis of optimized commercial fermentations. There are, to our knowledge, no in situ measurements of antibiotic production rates at the spatial scale under consideration in the present study and thus no means of verifying if the fermentation values could represent the activity of a producing cell, or aggregate of cells, in a biofilm. The antibiotic concentrations estimated using the highest and the lowest production scenarios are the result of modeling a specific antibiotic production rate and antibiotic diffusion coefficient. Based on our model, a change in the antibiotic mass flow (g/h) or antibiotic diffusion coefficient (m²/s) would lead to a corresponding linear increase or decrease in the antibiotic production rate.

TABLE 1.

Model assumptions and identified potential limitations

Assumption	Limitation	Citation
Antibiotic-producing cells have the volume of E. coli but are spherical.	Bacteria such as Streptomyces spp. with a variety of complex structures and dimensions can be antibiotic producers.	28
Antibiotic production rates are estimated from published industrial fermentation data.	There are no in situ production measurements to validate the assumption.	None available
Antibiotic production rates are constant, and emissions are uniform across the cell surface.	There may be temporal and spatial heterogeneity.	29, 30
All cells within a microcolony are producing at a uniform rate and contributing equally to the flux of antibiotic.	Microcolonies may have significant chemical and physical heterogeneity influencing the activities of individual cells, depending on their location.	31
Microcolonies have a uniformly spherical architecture.	Microcolonies in biofilms can have a complex and dynamic structure.	20, 32
Emitted antibiotic molecules are not degraded or transformed.	Antibiotics may be subject to enzymatic or chemical transformation in proximity to the producing cells.	14, 15
Antibiotic molecules diffuse uniformly within biofilms following emission.	Effective diffusivities within biofilms are likely highly influenced by biofilm composition and physical heterogeneity and the chemical properties of the antibiotic.	14, 15

A set of assumptions concern the morphology of producing cells and microcolonies and the spatial and temporal uniformity of antibiotic emissions. In the present study, the volume of a producing cell was taken to be that of Escherichia coli and the cell shape to be spherical, whereas antibiotic-producing bacteria such as Streptomyces spp. have far more complex and variable cell morphologies (28). Assuming that all cells within an aggregate are contributing equally to the emission of an antibiotic from the surface of an aggregate is no doubt simplistic. Antibiotics and other secondary metabolites are not produced during the phase of active cell growth but rather when the growth is limited by some nutritional or other factor (33). This will be a condition that cells are experiencing most of the time. Finally, a series of assumptions concern the fate of an antibiotic once emitted into the surrounding environment. Essentially it is assumed that once produced, the antibiotic does not interact with the surrounding environment and is conserved. Homogeneous diffusion of the antibiotic is an oversimplification of what would be expected, considering heterogeneous bacterial aggregation with anisotropic diffusion coefficients (14, 15). The further the distance from the emitting cell(s), the less likely the assumption is to be valid. Overall, clearly the theoretical conclusions from the model outputs need to be challenged experimentally.

In order to benefit from the inhibitory or toxic properties of antibiotics, a minimum number of cells is necessary, as a single cell will not suffice to produce suitably elevated concentrations (Fig. 2 and 3). This result is consistent with the role of quorum sensing in regulating the production of at least some antibiotics (34–36).

Model outputs from the present study suggest that antibiotic concentrations in the micron scale environments that microorganisms live in can reach concentrations that are bioactive. Neighboring microorganisms that are sensitive to the antibiotic would be at a competitive disadvantage, whereas those bacteria that have intrinsic or acquired resistance would have a competitive advantage. These phenomena have evolved over millennia, whereas the “age of antibiotics” has only existed for about a hundred years and is a defining feature of the Anthropocene (11, 37, 38). The widespread use of antibiotics in agricultural and health care settings, and the widespread emission of antibiotic residues and resistant bacteria into the environment, have massively increased the environmental reservoir of antimicrobial resistance (AMR), and has contributed to the contemporary AMR crisis (39, 40). Results from the present study are in no way inconsistent with the need to reduce the pressure for AMR selection across the One Health continuum.

MATERIALS AND METHODS

Model and assumptions.

The concentration gradient of an antibiotic in the vicinity of cell producers was estimated based on Fick’s law of diffusion (13).

To estimate the radial concentration in the vicinity of an organism producing an antibiotic with a given mass flux, a simple mass balance equation can be written. It is also assumed that the antibiotic being produced does not undergo reactions or transformation but rather is conserved across the concentric spheres, assumed as control volumes for radial mass balances. Under such assumptions, it is possible to write the following mass balance:

$$\mathit{Co}\times R{o}^3=C_r\times R^3$$ (1)

where Co is the concentration emitted at the spherical surface, characterized by the radius Ro and the concentration Co. This mass is equated to the one present in the sphere with an arbitrary radius R (with R > Ro) and the corresponding concentration C_r. The factor 4/3 × π, required for calculating the sphere volume, has been removed from both sides of the equation, since it cancels out.

While equation 1 explains how a conservative antibiotic radially evolves in concentration for an idealized case of isotropic radial diffusion, no information is given on the amount of antibiotic mass being transported across radial control volumes. Such information is instead provided by Fick’s law of radial diffusion, which can be written as

$$J=\frac{-D\times \mathit{dC}}{\mathit{dr}}$$ (2)

where J is the produced antibiotic mass flow (kilograms per second per square meter), and D is the antibiotic diffusion coefficient (square meters per second).

Rearranging equation 2 as a function of the radial concentration gradient, we obtain

$$\frac{\mathit{dC}}{\mathit{dr}}=\frac{-J}{D}$$ (3)

which, upon integration, yields

$$C_r=\mathit{Co}-\frac{J}{D}\times R$$ (4)

Finally, it is possible to substitute Co in equation 4 with Co obtained from equation 1 and solve for C_r to find an expression that is independent of Co. Doing so, it is possible to obtain the antibiotic concentration in the vicinity of a spherical bacterium emitting an antibiotic with a given mass flux J:

$$C_r=\frac{\left(\frac{J}{D}\times R\right)}{[\left(\frac{R^3}{R{o}^3}\right)-1]}$$ (5)

where C_r is the antibiotic concentration (kilograms per meter cubed) surrounding a bacterium as a function of the distance from the antibiotic producer, R is the distance from the antibiotic cell producer (meters), and Ro is the radius of the bacterium or aggregate of cells (meters).

The model was based on the following parameters and assumptions (Table 1): (i) the dimensions of E. coli, namely, a bacterium with radius of 0.32 μm with a surface area of 4.2 μm² (41); (ii) a range of antibiotic production rate from 1 × 10⁻¹⁸ to 1 × 10⁻¹⁴ g/h per cell (this range was based on fermentation literature describing the antibiotic production yield of antibiotics produced by various microorganisms under controlled conditions [see Table S1 in the supplemental material]; fermentation antibiotic production rates of bacteria genetically modified to increase the antibiotic production yield were not used for the calculations); and (iii) a diffusion coefficient range from 0.7 × 10⁻⁶ to 6 × 10⁻⁶ cm²/s, based on observations for a broad range of antibiotics in water and polymer gel matrices (15, 42, 43). The model assumed (i) a constant antibiotic production rate uniformly emitted into the surrounding environment; (ii) an equal production rate for all bacterial cells within a spherical, three-dimensional structure of an aggregate; (iii) no antibiotic degradation or transformation by either biological or physical processes in the environment around the producer; (iv) uniform effective diffusivity within biofilm; (v) bacteria growing in spherical clusters; and (vi) all bacteria in the spherical, three-dimensional structure of the aggregate are resistant to the antibiotic produced and emitted into the environment.

Two scenarios were modeled to estimate the antibiotic concentration that would be in the volume surrounding a bacterium or aggregate at distances ranging from 1 to 1,000 μm from the producers: (i) a highest concentration scenario, assuming the highest published antibiotic production rate (1 × 10⁻¹⁴ g/h per cell; Table S1) and the lowest antibiotic diffusion coefficient (0.7 × 10⁻⁶ cm²/s); and (ii) a lowest concentration scenario, assuming the lowest antibiotic production rate (1 × 10⁻¹⁸ g/h per cell; Table S1) and the highest antibiotic diffusion coefficient (6 × 10⁻⁶ cm²/s). The antibiotic concentration in the vicinity of cell producers in relation to various antibiotic production rates (from 1 × 10⁻¹⁸ to 1 × 10⁻¹⁴ g/h per cell; Table S1) was also modeled.

Selection of MIC and minimum selective concentration cutoffs.

The estimated antibiotic concentrations were compared to environmental concentrations that might exert selection for resistant bacteria, such as the MIC and the minimal selection concentration (MSC) (16). Data of the MIC₅₀ and MSCs of 111 antibiotics were obtained from Bengtsson-Palme and Larsson (16). They proposed a method for estimating the predicted no-effect concentration (PNEC) with respect to the selection of antibiotic resistance based on the MICs. In brief, they obtained the data for MICs for each commonly used antibiotic available in the European Committee on Antimicrobial Susceptibility Testing (EUCAST) database (http://www.eucast.org/clinical_breakpoints/).

From these values, the 1% lowest observed MICs were identified, and to compensate for limited species coverage, the predicted lowest MICs adjusted for the number of tested species were extrapolated (what they term the “size-adjusted lowest MIC”), corresponding to the estimated upper boundary for the MSC. They then applied a safety factor of 10 and consider this value to be the PNEC, corresponding to the estimated lower boundary for the MSC. The distribution of both the lowest observed MIC₅₀ and the estimated MSC boundaries of all antibiotics tested were used to predict if the antibiotic concentration estimated through our modeling might exert a selecting pressure on bacteria in the vicinity of the producer. The lowest observed MIC₅₀ and MSC (for both upper and lower boundaries) that represented 80% of the 111 antibiotics tested were selected as a cutoff (Fig. 1).