Spatiotemporally Heterogeneous Population Dynamics of Gut Bacteria Inferred from Fecal Time Series Data

ABSTRACT A priority in gut microbiome research is to develop methods to investigate ecological processes shaping microbial populations in the host from readily accessible data, such as fecal samples. Here, we demonstrate that these processes can be inferred from the proportion of ingested microorganisms that is egested and their egestion time distribution, by using general mathematical models that link within-host processes to statistics from fecal time series. We apply this framework to Drosophila melanogaster and its gut bacterium Acetobacter tropicalis. Specifically, we investigate changes in their interactions following ingestion of a food bolus containing bacteria in a set of treatments varying the following key parameters: the density of exogenous bacteria ingested by the flies (low/high) and the association status of the host (axenic or monoassociated with A. tropicalis). At 5 h post-ingestion, ~35% of the intact bacterial cells have transited through the gut with the food bolus and ~10% are retained in a viable and culturable state, leaving ~55% that have likely been lysed in the gut. Our models imply that lysis and retention occur over a short spatial range within the gut when the bacteria are ingested from a low density, but more broadly in the host gut when ingested from a high density, by both gnotobiotic and axenic hosts. Our study illustrates how time series data complement the analysis of static abundance patterns to infer ecological processes as bacteria traverse the host. Our approach can be extended to investigate how different bacterial species interact within the host to understand the processes shaping microbial community assembly.

Taken together, these results indicate that the bacteria retain the plasmid even in association with the Drosophila host, and GFP is stably present even in the absence of antibiotic selection.
Text S1B. Assessing the quality of the automated counting method The number of particles (microsphere and bacteria) recovered from feces and in inoculum were quantified using the opensource image analysis software CellProfiler (4) and supplemented by manual counting. CellProfiler allows automated counting by discriminating particles based on size, shape, and color. Parameters for particle detections were determined by comparing automated and manual counts over several images. Parameters were chosen such that the particles were identified appropriately and matched visual inspection. To determine the quality of the automated counts, we randomly chose 10 additional images and quantified the particle abundance by both methods. We saw consistency between the two methods, for both microspheres and GFP-labeled A. tropicalis (Fig S2).
Text S1C. Estimating proportions of ingested A. tropicalis that are retained by, egested out of, and lost in the fly Ingested bacteria only have three mutually exclusive fates: 1. Intact bacteria are egested out; 2. Intact bacteria are retained in the host over the experiment; or 3. Bacteria are lost due to lysis. To clarify our calculations, we will walk through the procedure using data values from one of the three replicate experiments in Microbial Fate Experiment (first row of Axenic fly treatment, Table 1). We calculate proportion of ingested bacteria that is egested in both Egestion Time Experiment and Microbial Fate Experiment.
1. The first step is to quantify the number of cells ingested by the fly relative to the number of ingested microspheres. Assuming that flies ingested cells and microspheres indiscriminately, this ratio equals the ratio of cells to microspheres in the inoculum, which was measured in each replicate experiment (0.289 cells/microsphere in this example). Then using the numbers of cells retained (Equation S1 .5) and ingested, we have Equation S1 .6 Proportion of ingested bacteria that is retained= Number of cells retained Number of cells ingested = 70783.39 cells/fly 813007.5 cells/fly = 0.087 6. Lastly, we calculate the proportion of ingested A. tropicalis that is lysed by the end of the experiment.

Equation S1.7
Proportion of ingested bacteria that is lysed = 1 − (Proportion of bacteria that is egested) − (Proportion of bacteria that is retained) We performed the same calculations for all samples and the results are shown in Table 1. Across both Axenic and Gnotobiotic samples, we observed statistically significant proportions of ingested bacteria that are egested, retained, and lysed (t-test against null hypothesis that mean = 0. Mean ± SEM = 0.25 ± 0.10, p=0.048; 0.09 ± 0.02, p=0.005; and 0.66 ± 0.11, p=0.002, respectively). Importantly, proportion of ingested bacteria that is egested are similar between Egestion Time Experiment and Microbial Fate Experiment (LA: mean ± SEM = 0.25 ± 0.12 and 0.18 ± 0.08, respectively. LG: 0.30 ± 0.18 and 0.53 ± 0.11, respectively), implying consistency between the experiments.
In these calculations, we ignored the possibility of bacteria reproduction in the host. If reproduction is present, then actual proportion of bacteria that is lysed would be higher than our calculated estimate. Suppose that there is some reproduction, z, in the host. Then the actual proportion of bacteria that is lysed is Equation S1.8 Proportion of ingested bacteria that is lysed The value in Table 1 for the proportion of ingested bacteria that is egested would then be too high by a factor of 2.
The proportion of ingested bacteria that is retained was also calculated using the number of microspheres egested to estimate the number of bacteria ingested, in Equation S1.4 and Equation S1.1. If half the microspheres were retained rather than egested, the estimated number of bacteria ingested would be low by a factor of 2. Then instead of Equation S1.6 for the proportion of ingested bacteria that is retained, we would have Equation S1 .10 Proportion of ingested bacteria that is retained= Number of cells retained Number of cells ingested = 70783.39 cells/fly 2 × 813007.5 cells/fly = 0.044 The value in Table 1 for the proportion of ingested bacteria that is retained also would be too high by a factor of 2.
Therefore, if not all ingested microspheres are egested, the actual values of the proportions of ingested bacteria that are egested and retained would be lower than the values in Table 1, and the values of the proportion of ingested bacteria that is lysed would be higher. However, this has no effect on our qualitative conclusion: some of the ingested bacteria are egested and retained intact, while many are lysed in the host.
Text S1D. Calculating the proportion of particles recovered in Microbial Fate Experiment Here we derive the proportion of particles recovered that was used to generate Table 1, as explained in Text S1C. To clarify the calculation, we will walk through the procedure using data values from the first replicate experiment (first row in Axenic fly treatment,  This is the number of microspheres ingested by a fly in Axenic Immediate sample. We assume that a fly in Axenic Passaged sample also ingested the same number of microspheres. Furthermore, because microspheres were scarce in our 5-24 h and 24-48 h samples, we assume that all ingested microspheres were egested by 5 h. We counted the number of microspheres recovered in hourly samples from the Passaged flies, and summing these over 5 h gives the total number of microspheres recovered from the feces (e.g. 91194.54 microspheres/fly). We calculate the proportion of particles recovered for a replicate experiment using the number of microspheres recovered and egested.

Equation S1.13
Proportion Note that we calculate proportion of particles recovered using numbers of microspheres recovered from feces (relative to the estimated number of microspheres egested). In the experiments, both microspheres and bacteria were homogeneously distributed on the experimental food, and fecal samples were collected indiscriminately. We therefore assume that the proportion of particles recovered is the same for bacteria as it is for microspheres.
As noted above, we also assume that the same proportion of particles recovered applies to all samples within a replicate experiment, including both Axenic and Gnotobiotic flies. To test this assumption and validate the estimates of proportion of particles recovered, we re-calculate the proportion of ingested bacteria that is egested using the proportion of particles recovered, and compare the results to the values in Table 1. The values in Table 1 did not use the proportion of particles recovered (Equation S1.3). Therefore, if this alternative calculation (AC) leads to similar values as Table 1, then we conclude that our estimate for the proportion of particles recovered is sound. To test our assumption that the proportion of particles recovered (calculated using Axenic flies) also applies to Gnotobiotic flies, we re-calculate the proportion of bacteria that is egested using the Gnotobiotic flies. To clarify AC, we will walk through its calculation using data values from the second replicate experiment (first row in Gnotobiotic fly treatment, Table 1).
In AC, we assume that each fly in The proportion of ingested bacteria that is egested using numbers of cells egested (Equation S1 .15) and ingested (Equation S1 .14) under AC is Equation S1 .16 Proportion of ingested bacteria that is egested = Number of cells egested Number of cells ingested = 215667 cells / fly 308153 cells / fly = 0.7 Calculating the proportion of ingested bacteria that is egested with (AC) and without (Equation S1 .3) the proportion of particles recovered led to similar values (mean ± SEM = 0.45 ± 0.26 and 0.53 ± 0.11, respectively) across Gnotobiotic samples. We conclude that our calculation of the proportion of particles recovered is sound.
Text S1E. Conversion factor between microscopy (cells/ml) and spiral plater (CFU/ml) bacterial counts Here we derive the conversion factor between microscopy and spiral plater that was used in Text S1C and Text S1D. Quantification of retained A. tropicalis involves two different methods to count the number of bacteria: fecal samples under fluorescent microscopy (measured in cells/ml) and fly homogenate samples on spiral plater (measured in CFU/ml).
The two approaches have different ranges for measurable microbial densities. We must calculate the conversion factor between the two methods so that measurements by the two methods can both be used. We calculated the conversion factor by the following. We grew a culture of GFP-labeled A. tropicalis overnight, and re-suspended the culture in PBS. We serially diluted the culture, such that some dilutions are within the measurable range for the spiral plater, whereas others are within the measurable range for microscopy. For each serial dilution, we regressed microscopy or spiral plater measurements against the dilution factor of the sample to obtain a slope between measurements and dilution. We thus obtained paired slopes ( for spiral plater against dilution factor and for microscopy against dilution factor) for each sample: Text S1F. Summary of calculations for Table 1 Here we summarize compactly how the quantities estimated in Text S1C, Text S1D, and Text S1E were used to get the numbers in Table 1. Terms in the calculations are in one of three typefaces to distinguish whether they were directly observed or indirectly inferred. Each typeface describes the following: Normal type: Data collected by directly observing samples (e.g. feces from Axenic Passaged flies, inoculum used in a replicate experiment).
Italic type: Inferred from calculation using data on same fly type only.
Bold face type: Inferred from calculation using, in whole or part, data from another fly type.
(1) Proportion of particles recovered (Text S1D) 0.034 = Number of microspheres recovered from feces Axenic Passaged fly Number of microspheres ingested

Number of microspheres ingested = Number of cells ingested ´ Number of microspheres in inoculum Number of cells in inoculum
Number of cells ingested = Number of CFU ingested Axenic Immediate fly ´ Conversion factor Text S1E Proportion of particles recovered is calculated using samples from same fly type: Axenic Passaged and Axenic Immediate samples. Once the proportion is calculated, however, the same proportion is also applied to Gnotobiotic Passaged flies in the same replicate experiment.
(2) Proportion of ingested bacteria that is egested (Text S1C) Calculating the proportion of ingested bacteria that is retained involves the number of cells ingested. As above, we use the proportion of particles recovered to calculate the number of cells ingested. Proportion of particles recovered is calculated from data on Axenic flies. We assume that the proportion of particles recovered is the same within a replicate experiment for both Axenic and Gnotobiotic fecal samples. Therefore, calculating the proportion of ingested bacteria that is retained for Axenic flies would only involve data from the same fly type. The calculation for Gnotobiotic flies, however, would involve data from another fly type.

= 1 − Proportion of ingested bacteria that is egested − Proportion of ingested bacteria that is retained
The proportion of ingested bacteria that is retained in Axenic Passaged samples would only involve data from the same fly type, whereas the proportion of ingested bacteria that is retained in Gnotobiotic Passaged samples would involve data from another fly type.