Parallel Factor Analysis: from "What Bacteria Are There?" to "What Are They Doing?"

A story on how a novel study design led to borrowing a method from an entirely different field.
Published in Microbiology
Parallel Factor Analysis: from "What Bacteria Are There?" to "What Are They Doing?"
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Prevention is Key in Dentistry

Many of us are familiar with the discomfort of slightly infected, bleeding gums, often a result of neglecting the interdental cleaning our dentist recommended. This condition is known as ‘gingivitis’, a common and reversible condition that is caused by the buildup of dental plaque. With proper oral hygiene, including regular tooth brushing and visits to the dentist, this condition can be easily managed. If neglected, it can escalate into more severe and irreversible conditions like periodontitis (causing bone loss) and caries (causing tooth loss).

Interestingly, gum infection and bleeding as a result of dental plaque buildup varies from person to person [1]. However, the current dental practice for everyone is to remove all plaque. If dentists could know which patients are and which are not susceptible to gingivitis, significant healthcare costs could be saved. Since dental plaque is a combination of bacteria and macromolecules, it makes sense to investigate the roles of the oral microbiome and salivary metabolome, as well as their interaction, in gingivitis susceptibility.

A Novel Study Design: Longitudinal and Multi-omics

In the paper, we present an “experimental gingivitis challenge” in which 41 volunteers were not allowed to brush their teeth for two weeks. Before, during and after the challenge phase we sampled their oral microbiome in various places in the mouth, the metabolome of their saliva, the amount of plaque on their teeth and the bleeding of the gums.

Timeline of experimental gingivitis challenge with analyses

Research often compares healthy and diseased people at a single time point. However, the dynamics of the oral microbiome composition and salivary metabolomics cannot be investigated this way. By sampling longitudinally, we could trace how the microbiome shifts as gingivitis develops and resolves. It is well known that bacteria in dental plaque react to the compounds that they are exposed to. For example, sugar is well-known to cause dental plaque bacteria to produce acid, leading to tooth deterioration. To investigate both the oral microbiome and salivary metabolome simultaneously we sampled various areas of the oral cavity as well as the saliva at the same time points. This should allow us to observe interactions between the oral microbiome and the salivary metabolome across time, which could reveal insights into how that interaction impacts gingivitis susceptibility.

The Critical Added Value of Interdisciplinary Research

Our research was part of the University of Amsterdam’s Research Priority Area on Personal Microbiome Health, which funded my PhD position. This initiative is interdisciplinary, involving collaboration between the Faculty of Science, Faculty of Dentistry (ACTA) and researchers specializing in fields such as public health, social and behavioural sciences and data science. For this project, the intersection between the data scientists and the dentists was critical for its success. As a data scientist, I would frequently consult with the microbiologists and dentists to ensure that our results made sense biologically. Only through the joint effort of applying the correct data analysis method and interpreting the results biologically were we able to write this paper.

‘Borrowing’ a Method from Another Field entirely

For instance, we quickly learned that conventional microbiome analysis methods were not sufficient for our kind of data. The repeated measurements over time created correlations between consecutive samples that complicated the modelling process.

Thankfully, my professor Age Smilde, suggested exploring multi-way analysis methods, which are commonly used in the fields of Chemometrics and Psychometrics. These methods can model data as a multi-dimensional cube of numbers – also known as a tensor – rather than as a flat table, allowing for a more sophisticated analysis. This approach led us to Parallel Factor Analysis [2,3], which is a generalization of Principal Component Analysis. By applying PARAFAC we could decompose this data cube into interpretable components that describe one biological phenomenon at a time. However, interpretation of the results was challenging.

 

Longitudinal microbiome data is often presented as a two-way data table with measurements (i.e. one sample for every subject-time point combination) in the rows and microbial abundances in the columns. This kind of data can be converted to a three-way array by putting all measurements for each time point in the third dimension.

What we learned

Using PARAFAC we discovered that certain bacterial subcommunities behaved very differently depending on the severity of the gingivitis. Health-associated bacteria like Rothia dentocariosa decrease, while pathogenic species like Porphyromonas gingivalis flourish in inflamed conditions. These insights suggest that monitoring shifts in bacterial populations over time could be a way to predict susceptibility to gingivitis. Further, the overlap between bacterial metabolic activity and the saliva metabolome reveals key pathways—such as those related to biofilm formation and virulence—that could serve as targets for therapeutic intervention.

Next steps

I have developed an R package called parafac4microbiome (now available on CRAN), which allows researchers to create PARAFAC models for their own longitudinal microbiome data. The package contains extensive documentation and example data, including the dataset from this study. If you feel like PARAFAC might be an interesting approach for your own data, I encourage you to check it out.

The Personal Microbiome Health community in Amsterdam is a vibrant and collaborative place. Many colleagues across many disciplines have already approached me to apply more complex multi-way methods to their datasets. Much of that work will be published soon, so watch this space!

References

[1] van der Veen, M. H., Volgenant, C. M. C., Keijser, B., ten Cate, J. (Bob) M. & Crielaard, W. Dynamics of red fluorescent dental plaque during experimental gingivitis—A cohort study. J. Dent. 48, 71–76 (2016).

[2] Carroll JD, Chang J-J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika. 1970;35:283–319.

[3] Harshman RA. Foundations of the PARAFAC procedure: Models and conditions for an" explanatory" multimodal factor analysis. 1970.

*** Poster image was generated using ChatGPT 4o under the supervision of the author. ***

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