Multiscale study of bacterial growth: Experiments and model to understand the impact of gas exchange on global growth

Using a millifluidics and macroscale setup, we study quantitatively the impact of gas exchange on bacterial growth. In millifluidic environments, the permeability of the incubator materials allows an unlimited oxygen supply by diffusion. Moreover, the efficiency of diffusion at small scales makes the supply instantaneous in comparison with the cell division time. In hermetic closed vials, the amount of available oxygen is low. The growth curve has the same trend but is quantitatively different from the millifluidic situation. The analysis of all the data allows us to write a quantitative modeling enabling us to capture the entire growth process.

Figure 1

Photographs of the incubators used in this study. Incubator 1 (a) is a 100-ml Erlenmeyer flask with a porous cap; incubator 2 (b) is a 9-ml sealed vial; incubator 3 (c) corresponds to 5-$\mu \mathrm{l}$ droplets either in permeable or sealed tube; and finally, incubator 4 (d) corresponds to 1-$\mu \mathrm{l}$ droplets in permeable tube.

Figure 2

Description of the symbols, geometries, exchange conditions, and sizes associated with each incubator used in this study.

Figure 3

Growth curves of Escherichia coli (a) and of Staphylococcus aureus (b) for various incubation conditions. (Top) The black triangles correspond to droplets in permeable tubing (incubator 3: $\mu =0.75{\text{h}}^{-1}$, stationary population $9.0\times {10}^9\mathrm{CFU}$/ml), the blue circles to Erlenmeyer (incubator 1: $\mu =0.41{\text{h}}^{-1}$, stationary population $9.0\times {10}^9$ CFU/ml), the green triangle to droplets in airtight tubing (incubator 3: $\mu =0.65{\text{h}}^{-1}$, stationary population $1.2\times {10}^9$ CFU/ml), the pink stars to microdroplets (incubator 4: $\mu =0.71{\text{h}}^{-1}$, stationary population $1.0\times {10}^{10}$ CFU/ml), the filled red diamonds to vial (incubator 2 with $V_{\text{aq}}$ = 9 ml: $\mu =0.43{\text{h}}^{-1}$, stationary population $8.5\times {10}^9$ CFU/ml), the orange diamonds to vial (incubator 2 with $V_{\text{aq}}$ = 4.5 ml, $V_{\text{oil}}$ = 4.5 ml: $\mu =0.51{\text{h}}^{-1}$, stationary population $1.0\times {10}^9$ CFU/ml), and the open diamonds to vial (incubator 2 with $V_{\text{aq}}$ = 3 ml, $V_{\text{oil}}$ = 6 ml: $\mu =0.56{\text{h}}^{-1}$, stationary population $3.0\times {10}^9$ CFU/ml). (Bottom) The black triangles correspond to droplets in permeable tubing (incubator 3: $\mu =0.31{\text{h}}^{-1}$, stationary population $3.0\times {10}^8$ CFU/ml), the blue circles to erlenmeyer (incubator 1: $\mu =0.26{\text{h}}^{-1}$, stationary population $4.0\times {10}^8$ CFU/ml), the green triangle to droplets in airtight tubing (incubator 3: $\mu =0.31{\text{h}}^{-1}$, stationary population $6.0\times {10}^8$ CFU/ml), the filled red diamonds to vial (incubator 2 with $V_{\text{aq}}=9$ ml $\mu =0.21{\text{h}}^{-1}$, stationary population $2.0\times {10}^8$ CFU/ml), and the open red diamonds to vial (incubator 2 with $V_{\text{aq}}$ = 2 ml, $V_{\text{oil}}$ = 7 ml $\mu =0.17{\text{h}}^{-1}$, stationary population $1.0\times {10}^8$ CFU/ml). Stationary populations vary up to one order of magnitude, and growth rates show variations of factor two according to the incubation conditions. Note that aerated droplets and microdroplets (usual micromillifluidic conditions) exhibit the same stationary populations than in Erlenmeyer flasks conditions, but a higher growth rate.

Figure 4

Stationary phase population of E. coli for various concentrations in growth medium (LB) after growth in incubator 1 for 48 h (a). Stationary phase population of S. aureus for various concentrations in growth medium (TSB) after growth in incubator 1 for 48 h (b). Black arrows show working concentrations.

Figure 5

Growth curves of E. coli in 15.5 g/liter of LB at ${30}^{\circ }\mathrm{C}$ in droplets in permeable tubings (black triangles) and sealed vials (red diamonds). The red diamond with dark edges corresponds to population measured in the sealed vial after allowing gas exchanges by replacing its airtight cap by a permeable one.

Figure 6

Growth curves of S. aureus in 80 g/liter of TSB at ${30}^{\circ }\mathrm{C}$ in droplets (black triangles) and sealed vials (red diamonds). The empty green diamond is the population measured in an opened vial surrounded by air, whereas the filled green diamond is the population measured in the same conditions but with an exclusive nitrogen surrounding gas. Black and red curves are shown as references of, respectively, optimum gas exchanges conditions in droplets and no gas exchanges in sealed vials.

Figure 7

Results obtained by model resolution in the biphasic case (vial with a ratio medium:oil of 4:3). The top left graph (a) presents the configuration and boundary conditions used for the calculations. Top right graph (b) shows the population field in the aqueous phase of the incubator. Bottom left graph (c) displays the oxygen concentration field, and bottom right graph (d) corresponds to the nutrient concentration field. Population and oxygen profiles evidence the apparition of heterogeneities within the medium in this biphasic case.

Figure 8

Results obtained by model resolution in the droplet case (5 $\mu \mathrm{l}$ droplet in a permeable tube). The top left graph (a) presents the configuration and boundary conditions used for the calculations. Top right graph (b) shows the population field in the incubator. The bottom left graph (c) displays the oxygen concentration field, and the bottom right graph (d) corresponds to the nutrient concentration field. Even though a weak gradient appears in the oxygen field, we can notice from these graphs that the whole medium can be considered as homogeneous during growth.

Figure 9

Results obtained by model resolution in the incubator 2 case (vial with a variable ratio medium:oil). The top left graph (a) shows the population field for a medium:oil ratio of 1:0 (i.e., no oil). The top right graph (b) presents the population in the aqueous phase of the incubator for a ratio of 6:1; the bottom left graph (c) for a ratio of 4:3; and the bottom right graph (d) corresponds to a ratio of 2:5. The profile in the absence of oil shows that the medium remains homogeneous in the absence of gas reservoir. When oil can supply oxygen (three other graphs), growth is improved in a small layer close from the interface where diffusion is efficient.

Figure 10

Top right optical picture (a) of the periphery of the drop. Top left optical picture (c) of the center of the drop. Picture (b) corresponds to picture (a) after numerical processing; picture (d) corresponds to picture (c) after processing. After numerical processing, we count the number of white pixels corresponding to the bacteria and divide it by the total number of the zone (i.e., of the periphery or of the center). After 15 h, the concentration of bacteria is 2.1 times greater in the periphery than in the center.

Figure 11

Comparison between experimental and model results for E. coli. The top graph (a) represents the global growth curves obtained from experiments (discrete symbols) and from the corresponding calculations (solid lines). Red data correspond to growth in incubator 2 (vial) with stationary populations increasing with the amount of oil (from top to bottom, ratios of medium:oil are 1:2, 1:1, 1:0), black data to growth in incubator 3 (droplets in permeable tubes), green data to growth in the airtight incubator 3 (droplets in airtight tubes), and magenta data correspond to growth in incubator 4 (microdroplets in permeable tubes). The left bottom graph (b) sums up the growth rates measured for each growth configuration as a function of the characteristic length of the incubators. Faint symbols represent the experimental data and bright symbols correspond to the data extracted form the modelings. The right bottom graph (c) uses the same nomenclature to present the stationary phase populations versus the characteristic length of the incubators.

Figure 12

Comparison between experimental and model results for S. aureus. The top graph (a) represents the global growth curves obtained from experiments (discrete symbols) and from the corresponding calculations (solid and dot-dashed lines). Red data correspond to growth in incubator 2 (vial, dark red used for vial without oil for the sake of clarity), black data to growth in incubator 3 (droplets in permeable tubes). The empty symbols and dot-dashed lines correspond to growth in 80 g/liter medium instead of the 30 g/liter usually used. The left bottom graph (b) sums up the growth rates measured for each growth configuration as a function of the characteristic length of the incubators. Faint symbols represent the experimental data and bright symbols correspond to the data extracted from the modelings. The right bottom graph (c) uses the same nomenclature to present the stationary phase populations versus the characteristic length of the incubators.