Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.

Metabolic network modeling of microbial communities provides an in-depth understanding of community-wide metabolic and regulatory processes. Compared to single organism analyses, community metabolic network modeling is more complex because it needs to account for interspecies interactions. To date, most approaches focus on reconstruction of high-quality individual networks so that, when combined, they can predict community behaviors as a result of interspecies interactions. However, this conventional method becomes ineffective for communities whose members are not well characterized and cannot be experimentally interrogated in isolation. Here, we tested a new approach that uses community-level data as a critical input for the network reconstruction process. This method focuses on directly predicting interspecies metabolic interactions in a community, when axenic information is insufficient. We validated our method through the case study of a bacterial photoautotroph–heterotroph consortium that was used to provide data needed for a community-level metabolic network reconstruction. Resulting simulations provided experimentally validated predictions of how a photoautotrophic cyanobacterium supports the growth of an obligate heterotrophic species by providing organic carbon and nitrogen sources. J. Cell. Physiol. 231: 2339–2345, 2016. © 2016 The Authors. Journal of Cellular Physiology Published by Wiley Periodicals, Inc.

Anthropogenic activities, especially dam operations, often induce larger and more frequent stage fluctuations than those occurring in natural rivers. However, long‐term impacts of such flow variations on thermal and biogeochemical dynamics of the associated hyporheic zone (HZ) are poorly understood. In this study, we built a heterogeneous, two‐dimensional, thermo‐hydro‐biogeochemical model for an aerobic respiration dominated river system. Our results revealed important interactions between subdaily to weekly flow variations and mean flow conditions controlled by snowpack at the watershed. High‐frequency stage fluctuations had their strongest thermal and biogeochemical impacts when mean river stage was low during fall and winter. In an abnormal drought year (2015) with low river stages during summer and early fall, high‐frequency stage fluctuations caused the HZ to be warmer than average. Furthermore, high‐frequency stage fluctuation enhanced all biogeochemical reactions by increasing nutrient supply and creating more oxygenated conditions. Overall carbon consumption in the HZ increased due to high‐frequency flow variations. Thermal dynamics altered by high‐frequency stage fluctuation impacted biogeochemical reactions in the HZ less than effects imposed by enhanced nutrient and oxygen supply. In addition to these results, we demonstrated that the HZ's hydrogeologic properties control flow paths that influence residence times and nutrient supply and consequently control spatial distribution of biogeochemical reaction hot spots in the HZ. Here we provide scientific basis for assessing potential ecological consequences of high‐frequency flow variations in a regulated river, as well as guidance for maximizing potential benefits—or minimizing drawbacks—of dam regulation to riverine ecosystems.

Predictive biogeochemical modeling requires data-model integration that enables explicit representation of the sophisticated roles of microbial processes that transform substrates. Data from high-resolution organic matter (OM) characterization are increasingly available and can serve as a critical resource for this purpose, but their incorporation into biogeochemical models is often prohibited due to an over-simplified description of reaction networks. To fill this gap, we proposed a new concept of biogeochemical modeling—termed substrate-explicit modeling—that enables parameterizing OM-specific oxidative degradation pathways and reaction rates based on the thermodynamic properties of OM pools. Based on previous developments in the literature, we characterized the resulting kinetic models by only two parameters regardless of the complexity of OM profiles, which can greatly facilitate the integration with reactive transport models for ecosystem simulations by alleviating the difficulty in parameter identification. The two parameters include maximal growth rate (μ^max) and harvest volume (V_h) (i.e., the volume that a microbe can access for harvesting energy). For every detected organic molecule in a given sample, our approach provides a systematic way to formulate reaction kinetics from chemical formula, which enables the evaluation of the impact of OM character on biogeochemical processes across conditions. In a case study of two sites with distinct OM thermodynamics using ultra high-resolution metabolomics datasets derived from Fourier transform ion cyclotron resonance mass spectrometry analyses, our method predicted how oxidative degradation is primarily driven by thermodynamic efficiency of OM consistent with experimental rate measurements (as shown by correlation coefficients of up to 0.61), and how biogeochemical reactions can vary in response to carbon and/or oxygen limitations. Lastly, we showed that incorporation of enzymatic regulations into substrate-explicit models is critical for more reasonable predictions. This result led us to present integrative biogeochemical modeling as a unifying framework that can ideally describe the dynamic interplay among microbes, enzymes, and substrates to address advanced questions and hypotheses in future studies. Altogether, the new modeling concept we propose in this work provides a foundational platform for unprecedented predictions of biogeochemical and ecosystem dynamics through enhanced integration with diverse experimental data and extant modeling approaches.

The soil microbiome performs many functions that are key to ecology, agriculture, and nutrient cycling. However, because of the complexity of this ecosystem we do not know the molecular details of the interactions between microbial species that lead to these important functions.

Microbial communities organize into spatial patterns that are largely governed by interspecies interactions. This phenomenon is an important metric for understanding community functional dynamics, yet the use of spatial patterns for predicting microbial interactions is currently lacking. Here we propose supervised deep learning as a new tool for network inference. An agent-based model was used to simulate the spatiotemporal evolution of two interacting organisms under diverse growth and interaction scenarios, the data of which was subsequently used to train deep neural networks. For small-size domains (100 µm × 100 µm) over which interaction coefficients are assumed to be invariant, we obtained fairly accurate predictions, as indicated by an average R2 value of 0.84. In application to relatively larger domains (450 µm × 450 µm) where interaction coefficients are varying in space, deep learning models correctly predicted spatial distributions of interaction coefficients without any additional training. Lastly, we evaluated our model against real biological data obtained using Pseudomonas fluorescens and Escherichia coli co-cultures treated with polymeric chitin or N-acetylglucosamine, the hydrolysis product of chitin. While P. fluorescens can utilize both substrates for growth, E. coli lacked the ability to degrade chitin. Consistent with our expectations, our model predicted context-dependent interactions across two substrates, i.e., degrader-cheater relationship on chitin polymers and competition on monomers. The combined use of the agent-based model and machine learning algorithm successfully demonstrates how to infer microbial interactions from spatially distributed data, presenting itself as a useful tool for the analysis of more complex microbial community interactions.