Periodontal and Peri-Implant Microbiome Dysbiosis Is Associated With Alterations in the Microbial Community Structure and Local Stability

Periodontitis and peri-implantitis are common biofilm-mediated infectious diseases affecting teeth and dental implants and have been considered to be initiated with microbial dysbiosis. To further understand the essence of oral microbiome dysbiosis in terms of bacterial interactions, community structure, and microbial stability, we analyzed 64 plaque samples from 34 participants with teeth or implants under different health conditions using metagenomic sequencing. After taxonomical annotation, we computed the inter-species correlations, analyzed the bacterial community structure, and calculated the microbial stability in supra- and subgingival plaques from hosts with different health conditions. The results showed that when inflammation arose, the subgingival communities became less connective and competitive with fewer hub species. In contrast, the supragingival communities tended to be more connective and competitive with an increased number of hub species. Besides, periodontitis and peri-implantitis were associated with significantly increased microbial stability in subgingival microbiome. These findings indicated that the periodontal and peri-implant dysbiosis is associated with aberrant alterations in the bacterial correlations, community structures, and local stability. The highly connected hub species, as well as the major contributing species of negative correlations, should also be given more concern in future studies.

evaluate the impact of different factors on the compositions of the microbiome (Supplementary Figure   1A). The results indicated that supragingival and subgingival microbiome were significantly different.
This was confirmed by PCoA on the beta diversity of supra-and subgingival microbiome (Supplementary Figure 1B). Then we compared the alpha diversity using Chao1 and Shannon indices (Supplementary Figure 1C). The result showed that supragingival microbiome had significantly higher Chao1 index yet similar Shannon index when compared with subgingival microbiome. This indicated that the supragingival communities had higher species richness, however, some of the species were either too high or too little in abundance which resulted in poorer evenness in comparison. We then computed the core microbiome in supra-and subgingival communities (Supplementary Figure 1D).
Core species represented those bacteria members shared by at least 80% of individuals in either supraor subgingival microbiome with a minimum relative abundance of 0.1%. Detailed lists of core species were presented in Supplementary Table 4. We also compared the relative abundance of these core species between healthy and diseased individuals (Supplementary Figure 2). There were no significant differences in relative abundance in any of the core species, indicating that the core components of supragingival (or subgingival) communities were in a way constant and did not change with the shift of health conditions. We therefore took a further look into the community structure to figure out what factors differentiate the healthy and diseased microbiome as shown in the main text.

Stability analysis
Here we briefly review local asymptotic stability (henceforth, stability) and show how to analyze the stability of the oral microbiome through experimental data and numerical simulation.

Dynamical framework
Following May's assumptions, we consider the microbial community-which consists of S interacting species-as an autonomous system. The dynamical behavior of this system can be described by a set of ordinary differential equations: where ( ) represents, for example, the abundance of population at time , and is the function expressing the growth rate of population , which depends on the abundance of all populations. The point * > 0 is a feasible equilibrium if ( * ) = 0 for all .
Around the equilibrium, the trajectories can be described by considering a linearized system.
Suppose the system is resting at the equilibrium * , and that a sufficiently small perturbation is applied at time zero, (0) = * − (0). Then, by Taylor expansion: where is the Jacobian matrix of the system, = . The so-called "community matrix " is the Jacobian evaluated at * , and therefore: which is a system of homogeneous linear differential equations with constant coefficients. This system has solution: Moreover, if is diagonalizable, it can be decomposed as −1 where is a diagonal matrix whose diagonal coefficients are the eigenvalues of , and is a matrix whose columns are the corresponding right eigenvectors. In this case, the solution becomes: If all the eigenvalues of have negative real part, the small perturbation ( ) will eventually decay to zero. Thus, if we order the eigenvalues according to their real part, ( ,1 ) > ⋯ > ( , ), stability is exclusively determined by ( ,1 ). If ( ,1 ) < 0, the equilibrium is stable, and if ( ,1 ) > 0, the equilibrium is unstable.
In fact, ( ,1 ) describes the asymptotic decay rate of the system after perturbation. Thus, ( ,1 ) is often used as a measure of the system's stability. Following previous work, we here define the system's stability as − ( ,1 ).

Stability analysis using experimental data and numerical simulation
What mentioned above shows that the key to stability analysis is the construction of community matrix , can be constructed by the following two steps. Firstly, we generated the adjacency matrix from our taxonomical data. > 0 meant species received a positive effect from species , < 0 meant species received a positive effect from species while = 0 meant species had no effect on species . Secondly, we assigned the coefficients of as follows: where was a random variable obeying normal distribution ( , 2 ).
We then performed a series of numerical simulations by changing and . For each parameter combination, we performed 50 simulations ( Figure 5 and Supplementary Figure 3). The results showed that healthy subgingival communities possessed the worst stability while the diseased subgingival communities possessed the highest stability.

Supplementary Tables
Supplementary Table 1 HT and DT stand for healthy teeth and teeth with periodontitis, respectively. Note that the supragingival sample from subject HT-1 was discarded due to contamination during transportation.
The subgingival sample from subject DT-2 failed to pass quality control after filtration and was therefore discarded.

Supplementary Table 2. Detailed information of samples from dental implants.
HI and DI stand for healthy implants and implants with peri-implantitis, respectively. Note that the supragingival samples from subjects DI-4 and DI-5 were discarded due to contamination during transportation.  This indicates the core components of the supra-and subgingival microbiome did not change with the shift of health conditions. Figure 3. Other parameter sets of calculating local stability. Other parameter sets we used to compare stability among communities were shown. All these simulations showed the same result as in Figure 5, which proved the robustness of our findings.