Special Issue: Microbial Community Modeling: Prediction of Microbial Interactions and Community Dynamics

Microbial communities are networks of species, the interaction structure of which dynamically reorganizes in a varying environment. Even in a static condition, community dynamics are often difficult to predict due to highly nonlinear interspecies interactions. Understanding the fundamental principles of microbial interactions is therefore key for predicting and harnessing community function and properties. As extensively reviewed previously, mathematical models and computational methods that can predictively link interactions to community behaviors are indispensable tools for achieving this goal [1]

A Generalized Spatial Measure for Resilience of Microbial Systems

The emergent property of resilience is the ability of a system to return to an original state after a disturbance. Resilience may be used as an early warning system for significant or irreversible community transition; that is, a community with diminishing or low resilience may be close to catastrophic shift in function or an irreversible collapse. Typically, resilience is quantified using recovery time, which may be difficult or impossible to directly measure in microbial systems. A recent study in the literature showed that under certain conditions, a set of spatial-based metrics termed recovery length, can be correlated to recovery time, and thus may be a reasonable alternative measure of resilience. However, this spatial metric of resilience is limited to use for step-change perturbations. Building upon the concept of recovery length, we propose a more general form of the spatial metric of resilience that can be applied to any shape of perturbation profiles (for example, either sharp or smooth gradients). We termed this new spatial measure “perturbation-adjusted spatial metric of resilience” (PASMORE). We demonstrate the applicability of the proposed metric using a mathematical model of a microbial mat

Knowledge-informed Data-driven Modeling of Microbial Inactivation in Food

Prevention of the growth of harmful microorganisms in food products is an important requirement for ensuring food safety and quality. Mathematical models to predict the quantitative changes in microbial populations in food to the variations of environmental conditions are useful tools in this regard. Current approaches that use empirical formulation generate arbitrary forms of model equations, impeding systematic analysis towards identifying key factors governing microbial growth and inactivation in food. To address this challenge, we present a data-driven modeling pipeline that enables automatic discovery of model equations (through parsimonious selection of relevant terms in a pre-built library) without having to assume specific functional forms of equations a priori. Through case studies using literature data, we showed how one can systematically build and analyze microbial inactivation models using the pipeline to predict the changes in D-value (i.e., the time taken to reduce microbial population to 10% of the initial level) as a function of given input variables. We used Akaike information criterion to avoid overfitting without hurting model accuracy. The final model was integrated with global sensitivity analysis to evaluate the impacts of individual factors on target variables. We highlight that, besides enhanced performance in data fit, the ability to generate models of varying complexity by accounting for a trade-off between accuracy and interpretability is a unique feature with our approach, not shared by empirical methods. Due to its generality, the pipeline presented in this work is readily applicable to many other related non-linear systems without being limited to microbial inactivation dataset

CompLaB v1.0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism, and biofilm dynamics

Microbial activity and chemical reactions in porous media depend on the local conditions at the pore scale and can involve complex feedback with fluid flow and mass transport. We present a modeling framework that quantitatively accounts for the interactions between the bio(geo)chemical and physical processes and that can integrate genome-scale microbial metabolic information into a dynamically changing, spatially explicit representation of environmental conditions. The model couples a lattice Boltzmann implementation of Navier–Stokes (flow) and advection–diffusion-reaction (mass conservation) equations. Reaction formulations can include both kinetic rate expressions and flux balance analysis, thereby integrating reactive transport modeling and systems biology. We also show that the use of surrogate models such as neural network representations of in silico cell models can speed up computations significantly, facilitating applications to complex environmental systems. Parallelization enables simulations that resolve heterogeneity at multiple scales, and a cellular automaton module provides additional capabilities to simulate biofilm dynamics. The code thus constitutes a platform suitable for a range of environmental, engineering and – potentially – medical applications, in particular ones that involve the simulation of microbial dynamics

Integrating Ecological and Engineering Concepts of Resilience in Microbial Communities

Many definitions of resilience have been proffered for natural and engineered ecosystems, but a conceptual consensus on resilience in microbial communities is still lacking. We argue that the disconnect largely results from the wide variance in microbial community complexity, which range from compositionally simple synthetic consortia to complex natural communities, and divergence between the typical practical outcomes emphasized by ecologists and engineers. Viewing microbial communities as elasto-plastic systems that undergo both recoverable and unrecoverable transitions, we argue that this gap between the engineering and ecological definitions of resilience stems from their respective emphases on elastic and plastic deformation, respectively. We propose that the two concepts may be fundamentally united around the resilience of function rather than state in microbial communities and the regularity in the relationship between environmental variation and a community\u27s functional response. Furthermore, we posit that functional resilience is an intrinsic property of microbial communities and suggest that state changes in response to environmental variation may be a key mechanism driving functional resilience in microbial communities

Historical Contingency in Microbial Resilience to Hydrologic Perturbations

Development of reliable biogeochemical models requires a mechanistic consideration of microbial interactions with hydrology. Microbial response to and its recovery after hydrologic perturbations (i.e., resilience) is a critical component to understand in this regard, but generally difficult to predict because the impacts of future events can be dependent on the history of perturbations (i.e., historical contingency). Fundamental issues underlying this phenomenon include how microbial resilience to hydrologic perturbations is influenced by historical contingency and how their relationships vary depending on the characteristics of microbial functions. To answer these questions, we considered a simple microbial community composed of two species that redundantly consume a common substrate but specialize in producing distinct products and developed a continuous flow reactor model where the two species grow with trade-offs along the flow rate. Simulations of this model revealed that (1) the history of hydrologic perturbations can lead to the shifts in microbial populations, which consequently affect the community’s functional dynamics, and (2) while historical contingency in resilience was consistently predicted for all microbial functions, it was more pronounced for specialized functions, compared to the redundant function. As a signature of historical contingency, our model also predicted the emergence of hysteresis in the transitions across conditions, a critical aspect that can affect transient formation of intermediate compounds in biogeochemistry. This work presents microbial growth traits and their functional redundancy or specialization as fundamental factors that control historical contingencies in resilience

Regulation-Structured Dynamic Metabolic Model Provides a Potential Mechanism for Delayed Enzyme Response in Denitrification Process

In a recent study of denitrification dynamics in hyporheic zone sediments, we observed a significant time lag (up to several days) in enzymatic response to the changes in substrate concentration. To explore an underlying mechanism and understand the interactive dynamics between enzymes and nutrients, we developed a trait-based model that associates a community’s traits with functional enzymes, instead of typically used species guilds (or functional guilds). This enzyme-based formulation allows to collectively describe biogeochemical functions of microbial communities without directly parameterizing the dynamics of species guilds, therefore being scalable to complex communities. As a key component of modeling, we accounted for microbial regulation occurring through transcriptional and translational processes, the dynamics of which was parameterized based on the temporal profiles of enzyme concentrations measured using a new signature peptide-based method. The simulation results using the resulting model showed several days of a time lag in enzymatic responses as observed in experiments. Further, the model showed that the delayed enzymatic reactions could be primarily controlled by transcriptional responses and that the dynamics of transcripts and enzymes are closely correlated. The developed model can serve as a useful tool for predicting biogeochemical processes in natural environments, either independently or through integration with hydrologic flow simulators

Prediction of Neighbor-Dependent Microbial Interactions From Limited Population Data

Modulation of interspecies interactions by the presence of neighbor species is a key ecological factor that governs dynamics and function of microbial communities, yet the development of theoretical frameworks explicit for understanding context-dependent interactions are still nascent. In a recent study, we proposed a novel rule-based inference method termed the Minimal Interspecies Interaction Adjustment (MIIA) that predicts the reorganization of interaction networks in response to the addition of new species such that the modulation in interaction coefficients caused by additional members is minimal. While the theoretical basis of MIIA was established through the previous work by assuming the full availability of species abundance data in axenic, binary, and complex communities, its extension to actual microbial ecology can be highly constrained in cases that species have not been cultured axenically (e.g., due to their inability to grow in the absence of specific partnerships) because binary interaction coefficients – basic parameters required for implementing the MIIA – are inestimable without axenic and binary population data. Thus, here we present an alternative formulation based on the following two central ideas. First, in the case where only data from axenic cultures are unavailable, we remove axenic populations from governing equations through appropriate scaling. This allows us to predict neighbor-dependent interactions in a relative sense (i.e., fractional change of interactions between with versus without neighbors). Second, in the case where both axenic and binary populations are missing, we parameterize binary interaction coefficients to determine their values through a sensitivity analysis. Through the case study of two microbial communities with distinct characteristics and complexity (i.e., a three-member community where all members can grow independently, and a four-member community that contains member species whose growth is dependent on other species), we demonstrated that despite data limitation, the proposed new formulation was able to successfully predict interspecies interactions that are consistent with experimentally derived results. Therefore, this technical advancement enhances our ability to predict context-dependent interspecies interactions in a broad range of microbial systems without being limited to specific growth conditions as a pre-requisite