Author Contributions
Conceptualization, K.C., B.M., C.B. and F.M.; Methodology, K.C., B.M., C.B. and F.M.; Software, L.F. and F.M.; Validation, K.C., L.F., B.M., C.B. and F.M.; Formal analysis, K.C., L.F. and F.M.; Investigation, K.C., L.F. and F.M.; Resources, B.M., C.B. and F.M.; Writing—original draft preparation, K.C., L.F., B.M., C.B. and F.M.; Writing—review and editing, K.C., B.M., C.B. and F.M.; Visualization, K.C., L.F. and F.M.; Supervision, B.M., C.B. and F.M.; Project administration, B.M., C.B. and F.M.; Funding acquisition, B.M., C.B. and F.M. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Attachment domain , grid of the stochastic algorithm with, in yellow, the elements with attached bacteria and non-zero values of attachment probability of matrix .
Figure 1.
Attachment domain , grid of the stochastic algorithm with, in yellow, the elements with attached bacteria and non-zero values of attachment probability of matrix .
Figure 2.
Effect of the ratio of probability values against values on bacterial attachment characteristics using 2D one-species model for (a) roughness coefficient, (b) maximum thickness, (c) mean thickness on bacteria only, (d) mean thickness on the whole surface (including voids). A total of 50 simulations were performed with and . Color grade indicates the average value of each bacterial attachment criterium according to or values.
Figure 2.
Effect of the ratio of probability values against values on bacterial attachment characteristics using 2D one-species model for (a) roughness coefficient, (b) maximum thickness, (c) mean thickness on bacteria only, (d) mean thickness on the whole surface (including voids). A total of 50 simulations were performed with and . Color grade indicates the average value of each bacterial attachment criterium according to or values.
Figure 3.
A 2D simulation of attachment for with (a) , (b) , (c) , (d) .
Figure 3.
A 2D simulation of attachment for with (a) , (b) , (c) , (d) .
Figure 4.
Two-dimensional illustrations of algorithm extensions for : (a) Attachment of three species of bacteria with 40 (yellow), 60 (blue), and 100 (red) elements, respectively, and other probabilities equal . (b) Attachment on a non-plane surface with , . (c) Attachment on an inhomogeneous plane surface with at the left, in the middle, at the right, . (d) Attachment with and variable values for and : and for the 100 first elements, and then and .
Figure 4.
Two-dimensional illustrations of algorithm extensions for : (a) Attachment of three species of bacteria with 40 (yellow), 60 (blue), and 100 (red) elements, respectively, and other probabilities equal . (b) Attachment on a non-plane surface with , . (c) Attachment on an inhomogeneous plane surface with at the left, in the middle, at the right, . (d) Attachment with and variable values for and : and for the 100 first elements, and then and .
Figure 5.
Effect of iron on the microscopic parameters obtained for mono-, dual- and three-species sessile cells. Effect of 0.8 M, 8 M, and 80 M of iron on the (A) biovolume, (B) roughness coefficient, (C) surface-to-biovolume ratio, (D) mean thickness, and (E) maximum thickness of mono-species (S. gordonii—Sg, P. gingivalis—Pg, and T. denticola—Td), dual-species (S. gordonii-P. gingivalis: SgPg, S. gordonii-T. denticola: SgTd, P. gingivalis-T. denticola: PgTd), and three-species (S. gordonii-P. gingivalis-T. denticola: SgPgTd) 2 h sessile growth. The microscopic parameters were calculated on the total bacteria in each condition (comprising all cells irrespective of individual species). * indicates p-value < 0.05.
Figure 5.
Effect of iron on the microscopic parameters obtained for mono-, dual- and three-species sessile cells. Effect of 0.8 M, 8 M, and 80 M of iron on the (A) biovolume, (B) roughness coefficient, (C) surface-to-biovolume ratio, (D) mean thickness, and (E) maximum thickness of mono-species (S. gordonii—Sg, P. gingivalis—Pg, and T. denticola—Td), dual-species (S. gordonii-P. gingivalis: SgPg, S. gordonii-T. denticola: SgTd, P. gingivalis-T. denticola: PgTd), and three-species (S. gordonii-P. gingivalis-T. denticola: SgPgTd) 2 h sessile growth. The microscopic parameters were calculated on the total bacteria in each condition (comprising all cells irrespective of individual species). * indicates p-value < 0.05.
Figure 6.
Representative microscopic images of bacteria attached at 2 h in mono-, two-, and three-species conditions. The 2 h sessile cells of various conditions (mono-species: S. gordonii—Sg, P. gingivalis—Pg, T. denticola—Td; dual-species: S. gordonii-P. gingivalis: SgPg, S. gordonii-T. denticola: SgTd, P. gingivalis-T. denticola: PgTd; three-species: S. gordonii-P. gingivalis-T. denticola: SgPgTd) were stained using Styo®9 and were visualized using the Leica TCS-SP5 confocal laser scanning microscope. The images are representative of the total bacteria in each condition (comprising all cells irrespective of individual species). The images of these 2 h sessile cells grown at three different iron concentrations (0.8 M, 8 M, and 80 M) were compared. A maximum z-projection of the Z stack was taken using 40× oil immersion objective lens for T. denticola mono-species condition while the 63× oil immersion objective lens was used for the remaining. A numerical zoom of 2 was applied. The scale (10 m) is shown on the bottom right corner of each image.
Figure 6.
Representative microscopic images of bacteria attached at 2 h in mono-, two-, and three-species conditions. The 2 h sessile cells of various conditions (mono-species: S. gordonii—Sg, P. gingivalis—Pg, T. denticola—Td; dual-species: S. gordonii-P. gingivalis: SgPg, S. gordonii-T. denticola: SgTd, P. gingivalis-T. denticola: PgTd; three-species: S. gordonii-P. gingivalis-T. denticola: SgPgTd) were stained using Styo®9 and were visualized using the Leica TCS-SP5 confocal laser scanning microscope. The images are representative of the total bacteria in each condition (comprising all cells irrespective of individual species). The images of these 2 h sessile cells grown at three different iron concentrations (0.8 M, 8 M, and 80 M) were compared. A maximum z-projection of the Z stack was taken using 40× oil immersion objective lens for T. denticola mono-species condition while the 63× oil immersion objective lens was used for the remaining. A numerical zoom of 2 was applied. The scale (10 m) is shown on the bottom right corner of each image.
Figure 7.
Effect of iron and interspecies association on attachment of each species in either mono- or multi-species sessile cells. The concentration of individual species (CFU/mL) in different conditions (mono-species: S. gordonii-Sg, P. gingivalis-Pg and T. denticola-Td; dual-species: S. gordonii-P. gingivalis: SgPg, S. gordonii-T. denticola: SgTd, P. gingivalis-T. denticola: PgTd; three-species: S. gordonii-P. gingivalis-T. denticola: SgPgTd) were compared at 0.8 M, 8 M, and 80 M of iron. The graph shows the concentration of S. gordonii (A), concentration of P. gingivalis (B), and concentration of T. denticola (C) in the different 2 h sessile cells. All initial inoculums contained 2.8 × 10 cells of S. gordonii and/or 1.2 × 10 cells of P. gingivalis and/or 6.3 × 10 cells of T. denticola in the various conditions. * indicates p-value < 0.05.
Figure 7.
Effect of iron and interspecies association on attachment of each species in either mono- or multi-species sessile cells. The concentration of individual species (CFU/mL) in different conditions (mono-species: S. gordonii-Sg, P. gingivalis-Pg and T. denticola-Td; dual-species: S. gordonii-P. gingivalis: SgPg, S. gordonii-T. denticola: SgTd, P. gingivalis-T. denticola: PgTd; three-species: S. gordonii-P. gingivalis-T. denticola: SgPgTd) were compared at 0.8 M, 8 M, and 80 M of iron. The graph shows the concentration of S. gordonii (A), concentration of P. gingivalis (B), and concentration of T. denticola (C) in the different 2 h sessile cells. All initial inoculums contained 2.8 × 10 cells of S. gordonii and/or 1.2 × 10 cells of P. gingivalis and/or 6.3 × 10 cells of T. denticola in the various conditions. * indicates p-value < 0.05.
Figure 8.
Two-dimensional simulations of biofilms attachment at 8 M of iron: (a) Sg (red), (b) Pg (blue), (c) Td (yellow), (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd.
Figure 8.
Two-dimensional simulations of biofilms attachment at 8 M of iron: (a) Sg (red), (b) Pg (blue), (c) Td (yellow), (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd.
Figure 9.
The 2D slices, generated with ImageJ software V1.43m from biofilm stacks obtained using Leica TCS-SP5 confocal laser scanning microscope, and obtained at 8 M iron for (a) Sg, (b) Pg, (c) Td, (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd. Their respective X–Z projection or thickness (z) along the X axis is shown. The scale (10 m) is shown on the top right corner of each image.
Figure 9.
The 2D slices, generated with ImageJ software V1.43m from biofilm stacks obtained using Leica TCS-SP5 confocal laser scanning microscope, and obtained at 8 M iron for (a) Sg, (b) Pg, (c) Td, (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd. Their respective X–Z projection or thickness (z) along the X axis is shown. The scale (10 m) is shown on the top right corner of each image.
Figure 10.
Three-dimensional simulations of biofilms attachment at 8 M of iron: (a) Sg (red), (b) Pg (blue), (c) Td (yellow), (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd.
Figure 10.
Three-dimensional simulations of biofilms attachment at 8 M of iron: (a) Sg (red), (b) Pg (blue), (c) Td (yellow), (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd.
Figure 11.
Representative 3D images generated with Imaris Viewer 9.6 software from biofilm stacks obtained using Leica TCS-SP5 confocal laser scanning microscope, and obtained at 8 M iron for (a) Sg, (b) Pg, (c) Td, (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd. The scale (20 m) is shown on the bottom left corner of each image.
Figure 11.
Representative 3D images generated with Imaris Viewer 9.6 software from biofilm stacks obtained using Leica TCS-SP5 confocal laser scanning microscope, and obtained at 8 M iron for (a) Sg, (b) Pg, (c) Td, (d) SgPg, (e) SgTd, (f) PgTd, (g) SgPgTd. The scale (20 m) is shown on the bottom left corner of each image.
Table 1.
Two-dimensional oral bacterial attachment model fitting using experimental biological values at 0.8 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Table 1.
Two-dimensional oral bacterial attachment model fitting using experimental biological values at 0.8 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Bacteria | | | | | | | | | |
---|
Sg | 365 | | 0.10 | 0.10 | 0.27 | 0.01 | 0.03 | 0.08 | 0.16 |
Pg | 29 | | 0.06 | 0.10 | 0.31 | 0.01 | 0 | 0.03 | 0.21 |
Td | 99 | | 0.01 | 0.10 | 0.02 | 0.02 | 0 | 0.05 | 0.12 |
| | | | | | | | | |
SgPg | 240 | 0.05 | 0.20 | | 0.28 | 0.02 | 0.01 | 0.02 | 0.18 |
SgTd | 126 | 0.001 | 0.25 | | 0.12 | 0 | 0.07 | 0.40 | 0.45 |
PgTd | 75 | 0.25 | 0.001 | | 0.28 | 0.01 | 0.03 | 0.35 | 0.02 |
SgPgTd | 500 | | | | 0.23 | 0.06 | 0.22 | 0.70 | 0.37 |
Table 2.
Two-dimensional oral bacterial attachment model fitting using experimental biological values at 8 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Table 2.
Two-dimensional oral bacterial attachment model fitting using experimental biological values at 8 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Bacteria | | | | | | | | | |
---|
Sg | 360 | | 0.10 | 0.10 | 0.28 | 0 | 0.02 | 0.03 | 0 |
Pg | 28 | | 0.06 | 0.10 | 0.34 | 0 | 0 | 0.04 | 0.29 |
Td | 39 | | 0.01 | 0.10 | 0 | 0.03 | 0 | 0.02 | 0.30 |
| | | | | | | | | |
SgPg | 340 | 0.05 | 0.20 | | 0.18 | 0.02 | 0 | 0 | 0.20 |
SgTd | 800 | 0.25 | 0.001 | | 0.21 | 0.05 | 0.06 | 0.19 | 0.05 |
PgTd | 110 | 0.25 | 0.001 | | 0.31 | 0.01 | 0.08 | 1.00 | 0.34 |
SgPgTd | 560 | | | | 0.03 | 0.02 | 0.01 | 0.05 | 0.27 |
Table 3.
Two-dimensional oral bacterial attachment model fitting using experimental biological values at 80 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Table 3.
Two-dimensional oral bacterial attachment model fitting using experimental biological values at 80 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Bacteria | | | | | | | | | |
---|
Sg | 315 | | 0.10 | 0.10 | 0.31 | 0 | 0.02 | 0.01 | 0.02 |
Pg | 29 | | 0.06 | 0.10 | 0.36 | 0.02 | 0 | 0.08 | 0.24 |
Td | 16 | | 0.01 | 0.10 | 0 | 0 | 0 | 0.17 | 0.31 |
| | | | | | | | | |
SgPg | 400 | 0.001 | 0.25 | | 0.11 | 0.02 | 0.04 | 0.05 | 0.13 |
SgTd | 970 | 0.25 | 0.001 | | 0.18 | 0.06 | 0.07 | 0.20 | 0.02 |
PgTd | 110 | 0.25 | 0.001 | | 0.28 | 0.01 | 0.09 | 1.43 | 0.57 |
SgPgTd | 545 | | | | 0 | 0.01 | 0.03 | 0 | 0.21 |
Table 4.
Three-dimensional oral bacterial attachment model fitting using experimental biological values at 8 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Table 4.
Three-dimensional oral bacterial attachment model fitting using experimental biological values at 8 M of iron. Relative errors are computed on the mean of 100 simulations (0 represents a value less than ).
Bacteria | | | | | | | | | |
---|
Sg | 78,000 | | 0.20 | 0.03 | 0.22 | 0.01 | 0.08 | 0.10 | 0.12 |
Pg | 5900 | | 0.20 | 0.03 | 0.30 | 0.01 | 0 | 0.05 | 0.07 |
Td | 7300 | | 0.08 | 0.10 | 0.06 | 0.02 | 0 | 0.09 | 0.06 |
| | | | | | | | | |
SgPg | 70,000 | 0.05 | 0.20 | | 0.16 | 0 | 0 | 0.04 | 0.07 |
SgTd | 166,000 | 0.2 | 0.02 | | 0.18 | 0.01 | 0.03 | 0.01 | 0.02 |
PgTd | 24,000 | 0.25 | 0.001 | | 0.25 | 0.01 | 0.08 | 0.90 | 0.90 |
SgPgTd | 114,000 | | | | 0.01 | 0.02 | 0.01 | 0.06 | 0.06 |
Table 5.
Ratios between attachment parameters for mono-bacterial microcolonies.
Table 5.
Ratios between attachment parameters for mono-bacterial microcolonies.
Iron Concentration and Model | Bacteria | | | |
---|
0.8 M 2D model | Sg | | | 1 |
Pg | | | |
Td | | | |
8 M 2D model | Sg | | | 1 |
Pg | | | |
Td | | | |
8 M 3D model | Sg | | | |
Pg | | | |
Td | | | |
80 M 2D model | Sg | | | 1 |
Pg | | | |
Td | | | |