Application of proper orthogonal decomposition for evaluation of coherent structures and energy contents in microbial biofilms

Abstract

Microbial biofilms are structured communities of surface-associated microbial populations embedded in a matrix of extracellular polysaccharides that provide protection for biofilm cells. Among the wide plethora of microbial species adept at forming biofilms, the fungal pathogen Candida albicans (C. albicans), is one of the most notable. C. albicans biofilm development occurs in a series of sequential steps over a period of 24 h. Various quantitative and microscopic methods are available for the monitoring and evaluation of biofilms, including several innovative real-time methods for the evaluation of the cell-to-cell dynamics occurring during biofilm formation. These methods utilize biosensors which capture electrical, acoustic, and reflectance signals in bacterial populations (Li et al., 2021; Li et al., 2020; Kim et al., 2021; Paredes et al., 2021; Reipa et al., 2021). Additionally, machine learning, deep learning and other computational approaches have progressively been incorporated in the field of microbiology (Qu et al., 2019; Goodswen et al., 2021; Zhang et al., 2021; Ghannam and Techtmann, 2021; Rani et al., 2021; Berg et al., 2019) including some studies in biofilms (Buetti-Dinh et al., 2019; Srivastava et al., 2020; Hartmann et al., 2021; Dimauro et al., 2021) but given the potential of machine and deep learning, this niche is in large need of collaborative work between microbiology and engineering or physics experts to propel machine learning to a higher level. Therefore, whilst promising advances have been made, there is an urgent need for extensive development to take place to study and comprehend the complex interaction of microbial pathogens during biofilm formation. Specifically, there is a lot left to be understood about biofilm energy kinetics, and who the active microbial populations are. We infer that biofilm formation is an extremely diverse phenomenon and that each microorganism exerts different pathways to form a biofilm. Thus, we reasoned on the need for a model that would allow us to study the energy kinetics during C. albicans biofilm development. Modal decomposition techniques (MDTs) commonly used in fluid mechanics are gaining popularity outside their original field and might help decipher some of the dynamically relevant structures of biofilm formation. MDTs permit the identification of coherent structures in fluids and have been used in complex applications of information obtained during a particular time-lapse. A common MDT, Proper Orthogonal Decomposition (POD), can be used in reduced order modelling and machine learning applications. POD allows decomposition of a physical field influenced by different variables that may affect its physical properties. We aimed to evaluate the applicability of this technique in the analysis of energy kinetics during microbial biofilm formation, more specifically C. albicans biofilms. Using POD, we were able to easily distinguish visually distinct modes of growth of C. albicans cells in PBS and RPMI in terms of energy accumulation during the kinetic experiment. Comparing both PBS and RPMI, RPMI contains more energetic and dynamically relevant structures than PBS.