Microfluidic and mathematical modeling of aquatic microbial communities

Abstract

Aquatic microbial communities contribute fundamentally to biogeochemical transformations in natural ecosystems, and disruption of these community can lead to ecological disasters such as harmful algal blooms. Microbial communities are highly dynamic, and their composition and function are tightly controlled by the biophysical (e. g. light, fluid flow and temperature) and biochemical (e.g. chemical gradients, and cell concentration) parameters of the surrounding environment. Due to the large number of environmental factors involved, a systematic understanding of the microbial community-environment interactions is lacking. In this article, we show that microfluidic platforms present a unique opportunity to recreate well defined environmental factors in a laboratory setting in a high throughput way, enabling quantitative studies of microbial communities that are amenable to theoretical modeling. The focus of this article is on aquatic microbial communities, but the microfluidic and mathematical models discussed here can be readily applied to investigate other microbiomes.

Introduction

Microbial communities are important players for the sustainability of aquatic ecological systems: being responsible for primary production of organic carbon, decomposition of organic matter, and recycling of nutrients. They are essential to ensure the robustness and adaptability of aquatic ecosystems functions. It is well established that the composition of a set of micro-organisms of a specific body of water (e.g. lake or pond) is shaped by the abiotic parameters of the space they live in [1], including light, temperature, nutrient availability and pH (See Figure 1a). Altering abiotic parameters can lead to serious negative impact to the stability of the microbial community. A particular example is the problem of harmful algal blooms (HABs), where certain microalgae or cyanobacteria suddenly outgrow other species and end up dominating aquatic microbial communities. The toxins produced by HABs endanger other aquatic animals such as fishes, and deplete water resources both for drinking water and recreational uses. Even though the occurrence of HABs is increasing due to climate change and population expansion [2–4], quantitative understanding of how environmental factors break the balance within microbial communities are largely unknown. In this perspective article, we will focus on recent developments in microfluidic technology for recreating well defined biotic and abiotic factors of microbial communities in the laboratory and their applications for quantitatively studying the spatial and temporal dynamics of microbiomes. Emphasis will be given to studies of aquatic microbial communities. For reviews of microfluidic platforms for basic microbial coculture technology, please refer to Refs [5, 6]. For reviews of microfluidic platforms for algae biotech, please refer to Ref [7]. Finally, for reviews on microfluidic platforms for the general topic of microbial ecology, please refer to Ref. [8].

Fig. 1. Modeling microbial community.

a. The function and dynamics of microbial community is governed by both biotic and abiotic parameters. Biotic parameters include the composition and spatial organization of the photosynthetic cells and their associated bacterial cells. Abiotic parameters include temperature, light and chemical gradients. b. Microfluidic platforms for modeling community organization, and their physical and chemical environment. Modeling of microbial community organization can be categorized into two basic forms, one is with direct physical contact among cells of different strains; and the other is with a well-defined spatial separation. In both cases, cells can be confined using microtraps, microchambers and microdroplets. In direct physical cell contact, cells of different strains can be pre-mixed, and then confined. In the case of physical separation, cells of different strains are separated by a chemically permeable interface. Modeling of biophysical factors can be performed by manipulating light and temperature gradients. Modeling of biochemical gradients includes generating chemical gradients via diffusion or convective flow. c. Mathematical modeling approaches with different degrees of complexity and detail can be used to investigate theoretically the dynamics and structure of microbial communities. Microfluidics can be used to estimate model parameters, perform model selection and test the predictions of mathematical models. This integration between microfluidics and mathematical modeling will strengthen our quantitative understanding of aquatic microbial communities.

State of the art technology for investigating microbial communities

Field study and lab culture

Microbial communities for environmental applications are traditionally studied by investigating field samples or laboratory synthetic communities. Field studies are essential for identifying relevant microbial strains in a realistic environmental setting, and are largely empowered by the rapid advancement of sequencing technologies including 16S rRNA sequencing and metagenomics. For example, by collecting and analyzing bloom samples from Lake Taihu for over about a year, Zhu et al. identified the alternate succession of two dominate cyanobacterial species that correlated with temperature and nitrogen concentration, and revealed a nitrogen co-pathway in the nitrogen cycle via the interplay between the candidate associated bacteria and the cyanobacteria [9]. Microbial communities in environmental samples are usually very complex and the abiotic factors of a wide-open system in nature cannot be controlled easily. Lab culture, on the other hand, is an alternative with better controlled abiotic environments for studies of both natural and artificial microbial communities, at the expense of less realistic environmental settings and the impossibility of working with nonculturable bacteria. Lab culture technologies [10–14] include batch cultures and chemostats. These are the main approaches used today, they provide abundant material for molecular analysis and omics methods including transcriptomics and metabolomics, they allow us to identify the genotypes and phenotypes of microbes in the community and to discover the chemical mechanisms underlying their interaction. For example, using a test tube platform, Richter et al. studied a microbial community that includes the marine algae Chlorella spp. and their associated bacteria for potential applications in biofuel production. Two associated bacterial species were identified that correlated with fast growth rate and high lipid production of the algae, and the loss of these bacteria led to carbon limitation and oxidative stress of the algae [15].

As studies on aquatic microbials move towards a more quantitative understanding, in particular, covering multiple levels of biological organization (molecular, cellular and cell culture) and expanding into investigation of changes in microbial community composition in response to well controlled environmental cues, several limitations of traditional lab culture approaches are noted. Traditional lab culture techniques only provide limited environmental control. Concerning the chemical environment, batch cultures are subjected to the initial amount of chemicals in the growth medium which change over the course of an experiment. Chemostats can maintain a certain chemical composition, however, the constant removing of culture and adding of fresh medium could make it challenging for some phytoplankton species [intended as either microalgae or cyanobacteria [16]] to grow. Concerning the physical environment, phytoplankton cultures suffer from self-shading by which cells at the surface or near the walls of a container experience higher light intensity compared to cells in the middle of the container. This can be partly compensated by shaking, which can however cause cells to still experience light intensity fluctuations and unwanted shear stresses. Lack of precise environmental control, together with the relatively large amount of reagents required, limits the ability and throughput of traditional lab culture approaches. This is especially important for screening a large range and number of abiotic environmental factors and of microbial communities. The exponentially fed batch culture [17] is an intermediate approach between batch cultures and chemostats, and despite being based on earlier bioreactor designs for industrial fermentation [18], has only recently being adopted in the experimental ecology and microbiology literature. In this approach, fresh medium is continuously supplied to a culture, proportionally to its volume, and is periodically set back to the initial volume. By doing so, the culture is kept in a continuously exponential growth phase, while maintaining approximately constant chemical composition, although the temporal variation in the surface-to-volume ratio has been argued to affect ecological dynamics [17].

Microfluidic modeling of microbial community

Microfluidic technologies have greatly expanded the capabilities of precise environmental control of microbial cell cultures in a lab setting, as well as their throughput and quantitative readout. The unique contribution of the microfluidic platform is the ability to construct a microbial community with designated compositional and spatial arrangement, and to provide a well-defined and stable biophysical and biochemical environment. Additionally, the small size of microfluidic devices allows for fast molecular transport and high throughput, and the compatibility with microscopes allows for real time monitoring of the microbial community dynamics. Also important is the fact that microfluidic technologies allow us to work with viable but nonculturable microbes from environmental samples [19], which can lead to their identification and, occasionally, to the discovery of conditions that allow their co-culturing.

Modeling microbial community organization

Broadly speaking, there are two categories of microfluidic platforms for co-culture studies, which differ for the physical arrangement of the two (or more) cell types. One is for cells of different types to be in direct contact; the other is for them to be physically separated by a permeable interface (Fig. 1b). Using these two types of platform, one is able to reveal differential roles of chemical or physical interactions between cells of different types in the function of the microbial community of interest.

For cells of different types in direct physical contact, existing microfluidic cell cultivation platforms include microtraps, microchambers, and microdroplets (Fig. 1b). In these three platforms, a co-culture can be easily realized via the introduction of pre-mixed microbes. Microtraps have been designed to trap algal cells using size restriction with the dimension of the trap size in the order of a few micrometers for cell growth study [20–22]. This method works well with a monolayer of trapped cells perfused with media through connected channels, and have been used successfully in studies of synthetic bacteria cocultures [23, 24]. Microchambers or microwells with a typical size of a few hundred micrometers have been used for algal growth study [25, 26]. Although they have not yet been employed for investigating algal-associated communities, the capability of microchambers for coculture has been demonstrated in other microbial communities. For example, Guo et al. studied single-cell variability in an array of microwells using a coculture system of Escherichia coli and Enterobacter cloacae [27]. The microfluidic platform enabled them to investigate the heterogeneity of cell growth rate at the single-cell level. They found that interactions between different strains promoted heterogeneity of growth rate variation among cells of the same strain. We note that the throughput of the micro-trap and micro-chamber platforms depends on the number of traps/chambers that are physically patterned on a chip. Droplet-based microfluidics is not limited by the size of the chip, and has thus demonstrated an extremely high throughput capability, in that it can produce large numbers of independent microbial communities, each with a droplet of its own, through the creation or merging of droplets [28, 29]. Droplet-based platforms have been used directly to work with environmental samples with low cell concentration, and successfully isolated relevant strains that were unidentified and/or unculturable previously [28, 30]. Furthermore, the locations of the droplets can be easily controlled by electrical fields in a digital microfluidics platform [31, 32]. Recently, droplet-based microfluidics has been used to study algae-associated microbial communities. Ohan et al. isolated and identified Pseudomonas spp. from samples collected directly from freshwater and sediment, which promoted the growth of Chlorella sorokiniana (a green alga) [28]. Droplet based platform also demonstrated an ability to rapidly create and screen a large number of synthetic communities (order of 100,000), enabling the bottom-up assembly and functional selection of de novo microbial communities [29].

A unique capability of microfluidics for co-culture platforms is to place microbes of different types in a well-defined spatial organization (Fig. 1b). These platforms allow one to separate the roles of chemically and physically mediated interactions in microbial communities. An important example of chemically mediated interaction is carbon cycling in the phytoplankton-associated microbial community, in which phytoplankton provides organic carbon to bacteria. In contrast, an example of physically mediated interaction is the type VI secretion system - a machinery used by gram-negative bacteria to inject proteins through cell wall/membrane into adjacent cells. To decouple the physically and chemically mediated interactions among microbials of different types, a number of microfluidic platforms have been developed in which a permeable interface is introduced to prevent physical contact, while allowing for chemical exchange. Examples of permeable interface are microsieves [33], narrow connecting channels [34], and permeable membranes [35–37]. To control the physical distance of various cell types, clever spatial arrangements have been developed, controlling the relative position and distance between individual strains via careful design of the microchambers layout [35]. This work enables one to understand the roles of physical separation in the growth stability of a co-culture system. Microdroplet platforms offer a high throughput way of coculturing with defined physical separation by encapsulating one microbial strain in a gel microdroplet surrounded by a liquid culture of another strain. Such technique has been developed and used for studying the role of physical confinement on tumor transformation in the current literature [38, 39]. We note that this method can be easily extended to microbial cocultures. We also note that the recent development of 3D printing using soft materials offers an opportunity to construct complex, three-dimensional arrangements of multiple cell types [40].

Modeling the physical and chemical environment

Microfluidic platforms have played instrumental roles in recreating natural environments in a laboratory setting for quantitative studies of microbial communities. Light is an important abiotic factor for photosynthetic microbes as it is a fundamental energy source for many microbes. The advancement of modern electronics has allowed precise control of the intensity, spectrum and spatial distribution of light over microfluidic platforms with ease. Light gradients over an array of microchambers have been realized by placing a light control layer, or a Liquid Crystal Display (LCD), directly on top of a Light-Emitting Diode (LED) light source as shown in Fig. 1b [25]. Using this platform, Graham et al. were able to control the intensity and the spectral composition of light over each individual microchambers. They revealed that the onset of light saturation of cyanobacteria Synechococcus Elongatus is 41 ± 2 μmol∙m⁻²∙s⁻¹, and that S. Elongatus growth preferred red light over blue light at high light intensities. Another light control method is to project a light pattern directly onto a microfluidic platform using a digital light processing (DLP) projector (Fig. 1b). This method allows generation of complex micro-scale light patterns and has been used to study light sensitive cell motility [41–44]. Lam et al. used a DLP projector together with a LED light source with maximum brightness of 100 lumens and a 4x lens to project patterns with 20 um pixel resolution, which controlled the local swarming behavior of the phototactic alga Euglena gracilis [42]. In addition to direct illumination, evanescent field illumination using waveguides and surface plasmons has been explored for microfluidic algal cultures. This approach offers high-intensity light localized at the surface, a feature that has been exploited for bioenergy applications in which cell cultures or biofilms were grown on a surface [45–47]. This approach can be easily extended for investigating phytoplankton-bacteria communities. We note that inexpensive and individually addressable LED arrays have been introduced as a light source for 96 well plate platforms [48, 49]. Chen et al. designed an array of 8×12 650 nm LEDs individually addressable by 6 serial microcontrollers, which was placed underneath the 96 well plate with a transparent bottom [48]. This design was capable of screening light intensity on algal growth up to 120 μmol∙cm⁻² with temporal resolution of 10 μs.

Microbial growth depends sensitively on temperature. Temperature control has been developed previously in microfluidic platforms for biochemical reactions that require thermal cycling [50–53], such as the Polymerase Chain Reaction (PCR), for the preparation of thermal sensitive materials [54], and for the investigation of temperature-dependent biological processes such as oocyte membrane permeability in oocyte cryopreservation [55, 56]. Heating and cooling, as well as sensing and feedback control are important components of temperature control [57–59]. Utilizing convective heat exchange, hot and cold liquids can be introduced to the side channels as shown in Fig. 1b and a temperature gradient is established in the cell chamber [60, 61]. This liquid-perfusing approach is compatible with the design principles and fabrication methods of microfluidic channels, and can thus be easily incorporated with other microfluidic compartments. Fig. 1b also shows a method for generating temperature gradients using an electric current. Here, one can drive heat into the system with microheaters [62–64] or out of the system with thermoelectric coolers (TEC) [65, 66]. These devices can be connected to control circuits, which facilitates a feedback control. A drawback of this method is poor optical access since high electrical and thermal conductivity usually comes with low optical transmission. To achieve imaging compatibility, one can adopt either a careful design for the geometry, or alternative transparent materials such as ITO (indium tin oxide) coated glass. Infrared laser has also been used to efficiently heat up aqueous solutions in a microfluidic chamber by selecting radiation wavelengths to match absorption spectra of a particular liquid/solution [67, 68]. This method features rapid temperature ramping ability, while meeting the requirements for laser instrumentation.

Chemical gradients are primary ways of communication among cells, and are thus important abiotic factors for regulating cell-cell interactions and controlling the compositional evolution of microbial communities. Microfluidics presents a platform for precise control of the chemical environment of microbial communities. There are generally two ways to generate chemical gradients: diffusion-based and convective flow-based gradient generation. Diffusion-based gradient generation utilizes molecular diffusion through porous media, such as agarose gels [26]. Here, the time for gradient generation depends on molecular diffusion, a relatively slow process. It is important to design the size of the device such that the gradient establishment time is fast enough for the specific study question. Fig. 1b shows an example of a diffusion-based microfluidic device. Here, the gradient establishment time can be estimated as L²/(4D), where L is the length between the source and sink channels, and D is the diffusion coefficient of the molecules of interest. For example, for a distance of 1 mm between source and sink channels, the gradient establishment time for a small molecule in solution such as a sugar (glucose, diffusion coefficient = 670 μm²/s in water at 25°C) is about 12 minutes. In addition, the diffusion-based method allows the simultaneous generation of well-controlled chemical gradients of two different chemicals by introducing the chemical solutions in the sink and the source channels, respectively [69]. For convective, flow-based gradient generation, chemicals are mixed through convective flows, which feature fast mixing times. Fig. 1b shows an example of convective, flow-based gradient generation, consisting of a set of serpentine channels and T-junctions imprinted in PDMS [70, 71]. At each successive T-junction, fluids of different chemical concentration are mixed, and a chemical gradient is established at the outlet of the serpentine channels. The advantage of the convective, flow-based gradient generation is its speed, which can be established at milli-seconds time scales [72]. The disadvantage is that it typically introduces a flow in the area where cells reside, which may influence cell behavior of certain cell types. Besides chemical gradients, the temporal variation of the chemical environment can also be controlled via microfluidics [21]. One important requirement for studying phytoplankton growth is long term cell culture (on the order of days), which can be easily maintained using the diffusion-based microfluidic platform through the use of syringe pumps. We note that physical and chemical gradients can be generated over the cell culture platforms discussed in the previous section.

In their native states, some phytoplankton cells require open surfaces for adequate gas transport and light. PDMS, the most popular material for microfluidics, is permeable to gases including oxygen and CO2, which facilitates gas transport from photosynthetic activity in the device. A systematic investigation of the similarities and differences between open and closed systems, however, is yet unavailable and will require both experimental and computational efforts. In addition to PDMS, hydrogels such as agarose gel have also been used in microfluidics. Agarose gel polymerizes quickly and is permeable to the growth media, thus supporting long-term culture of phytoplankton cells while preventing sample evaporation [26, 69].

Current understanding of phytoplankton and the associated bacteria communities

The two major players in phytoplankton-associated bacterial communities are the cyanobacteria/microalgae (phytoplankton) and the associated bacteria (Fig. 2). Prokaryotic cyanobacteria and eukaryotic microalgae are primary producers capable of carbon fixation through photosynthesis. Certain bacterial communities have been found to associate with phytoplankton species [73, 74] by colonizing the zone rich in extracellular products surrounding phytoplanktonic cells (i.e., the phycosphere) [75]. These associated bacteria can have various ecological interactions with the phytoplankton, yet direct measurement and quantification are limited, in part due to the lack of high throughput tools [76]. A specific phytoplankton-associated bacterial community is defined by the environment they live in. For example, in Lake Taihu, HABs are dominated by cyanobacteria Microcystis sp. and the most abundant associated bacteria are identified to belong to the phylum of Proteobacteria [73, 9].

Fig. 2. Mutualistic and competitive interactions within the phytoplankton-associated bacteria community.

Phytoplankton and the associated bacteria are engaged in mutualistic interactions in which phytoplankton provides organic carbon to the associated bacteria and, in return, associated bacteria provide micro/macro nutrients in a form that can be more readily uptaken by phytoplankton. Competitive interactions include competition for nutrients and light within phytoplankton, competition for nutrients among the associated bacteria, and the secretion of algicides from the associated bacteria to inhibit algal growth.

Interactions among phytoplankton (e. g. between microalgae and cyanobacteria) are usually competitive (Fig. 2), as they all compete for light, inorganic carbon and other resources. It has been proposed that these competitions are mediated by allelochemicals. In lab settings, both spent medium and membrane separated chambers have been used to identify the use of allelochemicals in signaling between phytoplankton cells. Spent medium from cultures of the freshwater cyanobacterium Oscillatoria sp. was found to reduce the total number of Microcystis cells, with different Microcystis genotypes showing dissimilar susceptibility [77]. Coculturing two cyanobacteria, Planktothrix and Microcystis, using a membrane separated coculture chamber resulted in reduced growth, cell size, and trichome length of Planktothrix, as well as reduced initial growth and increased number of intracellular metabolites of Microcystis, indicating a strong chemical response induced by Planktothrix [78]. Some specific allelochemicals mediating phytoplankton interactions have also been identified. For example, Leão et al. found that the mixture of two secondary metabolites, portoamides A and B, produced and secreted by Oscillatoria sp. synergistically inhibited the growth of the green alga Chlorella vulgaris [79]. Song et al. found that M. aeruginosa inhibits growth of C. vulgaris via the release of linoleic acid, and the release is controlled by a positive feedback mechanism stimulated by nitric oxide produced by C. vulgaris [80]. Also, toxins produced by cyanobacteria including microcystin-LR (MC-LR) and anatoxin-a (ATX) were found to affect the physiology of a group of phytoplankton: MC-LR + ATX reduced the chlorophyll-a concentration of Microcystis strain LE-3; ATX but not MC-LR reduced nitrogen fixation by Anabaena UTEX B377; and MC-LR + ATX synergistically increased growth of the microalga Selenastrum capricornutum [81].

Interspecific interactions between phytoplankton and the associated bacteria can be mutualistic (i. e. mutually beneficial) (Fig. 2), and the reported interspecific interactions identified to date are largely chemically mediated. The phytoplankton exude rich organic molecules to their vicinity, which are necessary resources for heterotrophic bacteria. This zone, where interactions between bacteria and primary producers take place, has been described as the phycosphere, as an analogy to the plant root associated rhizosphere. Bacteria can colonize the phycosphere by raising micronutrients availability and re-mineralizing macronutrients in exchange for organic carbons. Important mutualistic interactions include the cycling of carbon (C) between phytoplankton and bacteria, as well as bacteria increasing macronutrients and micronutrients availability for the phytoplankton. A number of works has illustrated the importance of phytoplankton-bacteria mutualistic interactions through carbon cycling [82–84]. Here, the phytoplankton takes in CO₂ and converts it to organic carbon (e. g. sugars) through photosynthesis that can be consumed by heterotrophic bacteria. In return, bacteria produce CO₂ through respiration, thus helping to increase inorganic carbon availability within the microenvironment of the microbial community. In a recent study of carbon fixation of two microalgal species relevant for biofuel production, it was found that microalgae with attached bacteria were able to fix more carbon than axenic culture did. This result was obtained by stable isotope tracing and high spatial resolution mass spectrometry imaging (NanoSIMS) [85]. Bacteria can also increase the availability of macronutrients for phytoplankton, including nitrogen (N), phosphorous (P) and sulfur (S) [86, 9, 87, 88]. They do this through nutrient pathways with complementary functions to the phytoplankton: recent work from field studies in lake Taihu revealed that phytoplankton and the associated bacteria synergistically perform N cycling. It has been suggested that regulating this co-pathway has the potential of disrupting harmful algal blooms [89, 9]. Similarly, P transference between Microcystis and the attached bacterium Pseudomonas has been revealed by isotope tracing, which could maintain a high P concentration in the microenvironment, indicating that bacteria could serve as a temporary P bank for the phytoplankton [87]. Furthermore, cross-feeding on macronutrients can be combined with bacterial growth-regulating strategies. A bloom-forming marine HAB diatom and an associated bacterium were found to exchange nutrients: organosulfur from the diatom and ammonia from the bacterium. At the same time, the bacteria synthesized a signaling molecule, indole-3-acetic acid, from algal-secreted and self-produced tryptophan to promote algal cell division [88]. Lastly, in addition to macronutrients, bacteria in the phycosphere could also increase the micronutrient availability for the phytoplankton. Bacteria Marinobacter in close association with marine microalgae was found to produce iron-siderophores with high photolysis rates that increased algal iron uptake by >20-fold [89]. Another important micronutrient in phytoplankton-bacteria mutualism is vitamin B-12. Concluded from a survey on 27 HAB species, most HAB forming microalgae were vitamin B-1 and B-12 auxotrophs, thus requiring exogenous supply [90]. Microalgae and bacteria can establish a facultative mutualistic relationship in which algae provide fixed carbon and bacteria provide B-12, and active transport is likely involved in this interaction [91–93]. Microcystis in cyanobloom samples lack the B-12 biosynthesis pathway, which was found only in the associated bacteria. Bacteria such as the rhizobia can synthesize B-12 and have been proposed to be also involved in N cycling and oxidative stress reduction of Microcystis [94, 74, 86].

In contrast to mutualistic interactions, a group of bloom-residing bacteria are antagonistic against the phytoplankton, and have been referred to as algicidal bacteria, inhibiting proliferation or even causing cell lysis of phytoplankton [95] (Fig. 2). Algicidal activities against Microcystis aeruginosa have been identified in bacterial species including Pseudomonas, Aeromonas, and Bacillus. The fermentation liquid of Pseudomonas aeruginosa was found to inhibit protein and carbohydrate synthesis of M. aeruginosa and damage its cell membrane by lipid peroxidation [96]. Aeromonas veronii isolated from Microcystis colonies collected in Lake Kinneret was found to produce algicidal secondary metabolites, including lumichrome, and the production was increased when conditioned by the cyanobacteria spent medium in contrast to A. veronii monoculture [97]. In addition, some strains were shown to regulate the production of algicidal compounds by quorum sensing (QS), including AHL-mediated QS in Aeromonas sp. GLY-2107 and NprR-NprX QS in Bacillus sp. S51107, both strains isolated from Lake Taihu [98, 99]. Although there has not been evidence showing the ability of M. aeruginosa in regulating the QS behavior of the associated bacteria, some microalgae and cyanobacteria were found to produce chemical compounds capable of QS (de)activation. Chlamydomonas was found to synthesize vitamin B-2 (riboflavin) and its derivative lumichrome, which were able to stimulate Las R receptors in P. aeruginosa. A novel acylase was identified in Anabaena sp. PCC7120, which can function as a quorum quencher of AHL-based QS [100]. Both mutualistic and antagonistic interactions are important in the context of cyanoHABs, since micronutrients such as vitamins and trace metals are necessary for sustaining a rapidly growing bloom, and could be a limiting factor at the pre bloom onset stage with overloaded N and P; also, large biomass accumulated during blooms makes it a tempting resource for heterotrophic bacteria to exploit without payment.

In addition to chemically mediated interactions, direct cell-cell interactions via physical contact also play important roles in modulating phytoplankton associated microbial community dynamics. Physical attachment of bacteria was shown to facilitate the diverse metabolic responses of microalgae [85], and it was found that the bacterial community composition of free-living bacteria differs from that of bacterial communities attached to Microcystis colonies, with variation in community composition based on colony size [101]. In addition, comparing mixed cocultures and membrane separated chamber cocultures of green algae Oocystis marsonii and M. aeruginosa showed that mixed culturing was required for growth inhibition of O. marsonii by M. aeruginosa, from which it was argued that cell-cell contact was important in allelopathic interactions of phytoplankton species [102]. However, these results could also be due to the dilution effect of large volume lab cultures and the long time required for diffusion to achieve equilibrium across membrane-separated culture chambers. To reveal the nature of the interactions, there is a need for precise physical and chemical microenvironment control that could be addressed using microfluidics as discussed in the previous section. In addition to cell-cell contact, spatial self-organization of microbial cells has also been found to affect community dynamics. For example, modeling marine particulate organic matter using micron-sized polysaccharide particles, Ebrahimi et al. revealed that clustering of degrader bacteria promoted cooperation through public goods secretion when diffusion of oligosaccharide was low. [103]

Interactions in the phytoplankton-associated microbial communities are modulated by the environment. The allelopathic interactions between two toxic cyanoHAB genera - Microcystis and Anabaena (Dolichospermum) were found to depend on the nutrients (N, P) levels as Anabaena dominated under low N conditions, while Microcystis dominated under low P as well as when both nutrients were replete [104]. Also, increasing temperature and light intensity were shown to favor Dolichospermum flos-aquae in the competition against M. aeruginosa [105]. In addition, abiotic factors could also regulate the equilibrium of the vitamin B-12 mediated mutualism of phytoplankton and bacteria [106, 9], as well as the antagonistic algicidal behavior of bacteria [107].

Taken together, a unique feature of experimental studies of microbial communities using microfluidic platforms is their ability to establish well defined environmental parameters, and to provide quantitative results that can be used to parametrize and test mathematical models of community structure and dynamics. We anticipate that these studies together with mathematical modeling will allow us to discover the underlying principles of how microbial interactions affect community composition under controlled microenvironments.

Mathematical modeling of microbial communities

Microbial communities in the environment are complex and interactions between species vary as environmental conditions change over time, which makes dynamic mathematical modeling a necessary tool for understanding these communities [108, 109]. Mathematical modeling can help us identify the most relevant quantities and parameters that affect the biodiversity and stability of microbial communities, with the ultimate goal of predicting their dynamics and composition, and designing successful management efforts.

A variety of different approaches have been developed to investigate microbial community dynamics, with different degrees of detail and complexity depending on available knowledge of the specific study system at hand, of its fundamental biology and of the biochemical interactions within it. Modeling approaches can be broadly classified in five categories: i) dynamic and community flux balance analysis, ii) coarse-grained metabolic models, iii) consumer-resource models, iv) generalized Lotka-Volterra equations, and v) network and game theoretical approaches (Fig. 1c).

Dynamic and community flux balance analysis are computational approaches that use information on intracellular biochemical reactions, metabolic pathways and metabolic interactions among different species in a community together with stoichiometric, thermodynamics and ecosystem constraints to predict community composition [110, 111]. Typically, these models have too many parameters to be learned from data, and thus rely on quasi-steady state and optimality assumptions to solve a multi-dimensional optimization problem. In simple situations in which the metabolic networks and metabolic dependencies among members of a microbial consortium are known, these approaches agree with available experimental data. However, these models require lots of information about the system of interest, which is typically not available except for the best-studied model systems. In the near future though, such information is likely to become more readily available due to the rise of metagenomic and metabolomic approaches. Because these models use detailed information at the molecular and biochemical level, and because they rely on solving complex optimization problems, analytical insight into the conditions that allow species coexistence and community stability are not achievable, and one needs to rely on computation alone.

Information on intracellular metabolic networks and metabolic co-dependencies among different members of a microbial community can also be used to construct coarse-grained resource allocation models [112], which can be used to explore community assembly and community dynamics [113, 114]. These models are based on the observation that the amount of an enzyme limits the maximal flux through the biochemical reaction it catalyzes. Using a biochemical resource allocation model, Sharma and Steuer modelled cyanobacteria phototrophic growth and co-existence of two competing phytoplankton strains with different carbon and nitrogen metabolic capabilities, and found that the strain with higher affinity towards extracellular nitrogen excluded the other with lower affinity under constant light condition, while seasonally varying light and nitrogen gave rise to the coexistence and alternate domination of the two [113].

An alternative approach, which requires less information on intracellular metabolic networks, is inspired by MacArthur’s consumer-resource model [115] and has recently found renewed interest in the literature that looks at the stability of competitive communities with more species than resources available (a study questions often referred to as the “paradox of the plankton”) [116–118]. Consumer-resource models are kinetic models based on the consumption of nutrients in the environment by different species that may have different resource preferences, growth rates, and nutrient uptake rates. Within this modeling framework, Posfai et al. included trade-offs in the capability of different species to utilize a set of different nutrients simultaneously, and found that limited number of nutrients could allow coexistence of an unlimited number of species, if specific conditions are met for the resource supply rate and the metabolic preferences of the species in the community [117]. Consumer-resource models that are more tailored to describing microbial communities have also been developed, and showed that the fact that microbes can dynamically update resource consumption based on nutrient availability can promote species coexistence [114], and that trade-offs similar to those considered by Posfai et al. may arise from constraints on proteome allocation to different tasks [119]. Using a consumer-resource model, Goldford et al. found that nonspecific cross-feeding of metabolic byproducts promotes coexistence of competitors growing on a single carbon source, and that communities assembled by the model have a stable function according to the type of resources available, with species-level diversity and functionality [120].

In the absence of information on the relative uptake rates of different nutrients, one can rely on a mathematical framework that has found widespread application in the theoretical ecology literature, that of the generalized Lotka-Volterra equations, which do not model explicitly the dynamics of resources but rather adopt pairwise interaction strengths between species to model how the abundance of one affects the growth rate of another. Early studies [121] of the relationship between the stability and diversity of ecological communities were based on generalized Lotka-Volterra equations with random pairwise interactions and initiated a very fruitful line of investigation that is still very active today [122–125]. Besides being of interest for fundamental questions related to the stability-diversity relationship, these models have also found application for the interpretation of laboratory experiments with microbial populations [126–128], and estimation of pairwise interaction coefficients can be easily performed in the lab [129]. In the context of phytoplankton and associated bacteria, Grant et al. adopted this framework to study the mutualism of a B-12-requiring alga and a B-12-providing bacteria in coculture: experimental results were well fitted by describing the active B-12 production of the bacteria when the alga was the only carbon source [93].

Finally, a modeling approach that requires even less information on the system of interest combines ideas from networks and game theory, in which microbial interactions are studied as strategic games. These approaches have also been useful for exploring the stability of microbial communities and how it is affected by the interactions within the community [130–132, 125]. Despite these approaches cannot typically provide information on the temporal dynamics of population abundances in complex microbial communities, or of the biochemical composition of the extracellular environment, they can be very successful for predicting statistical properties of stable states of microbial communities, as shown for example by Goyal et al. which explained multiple stable states of competitive microbial communities using only ranked nutrient preferences, and assembly rules governed by the stable marriage problem from economic game theory [132].

Even though we have presented five modeling frameworks as distinct and complementary, hybrid approaches that combine two or more frameworks have been proposed and are becoming increasingly more popular. For example, networks models that simulate generalized Lotka-Volterra dynamics have been considered extensively in the literature on the stability-diversity relationship [123, 133–136] and game theoretic, network approaches that also include information from metabolic analysis have been developed [137, 138]. Ultimately, the choice of modeling framework depends on biological and biochemical knowledge available for the system of interest, and on the study question at hand. Microfluidic platforms can help us parametrize mathematical models, investigate the metabolic co-dependencies that are often introduced in such models, and ultimately test their predictions.

Future perspectives

Looking ahead, we believe that integrating microfluidic and mathematical modeling will enable us to develop a mechanistic understanding that governs the dynamics of aquatic microbial communities, especially the interactions between phytoplankton and the associated bacteria, under environmental controls. The microfluidic approaches will allow us to manipulate the physical and the chemical environment, as well as to prescribe the spatial structure and connectivity of microbial habitats, thus leading to a more realistic model of environmental feedbacks on community dynamics. Mathematical modeling can identify key biophysical and biochemical parameters, inform the design of microfluidic devices, so that they resemble the spatial organization of natural landscapes, preserving the statistical properties of landscape connectivity and environmental heterogeneity and fluctuations. Several pioneering works using millifluidics and microfluidics devices have shown the effects of spatial structure and heterogeneity on microbial community dynamics [35, 139–143]. Quantitative measurements from the microfluidic studies can be input to theoretical models, and in return, results from mathematical computation can inform future microfluidic experiments. We anticipate that this integrated approach will accelerate our understanding and coming up with solutions to urgent contemporary problems such as the occurrence of HABs [144–146]. One enabling capability to note is to model HABs across a freshwater-to-marine continuum [147], where different blooming species dominate different natural habitats from head water to estuaries. In this platform, a connected network of microhabitats can be constructed with environmental gradients, and input pulses of certain chemicals can be introduced to represent seasonal nutrient loading. These experiments together with mathematical modeling can accelerate greatly our understanding of how the vast number environmental parameters impact on the spatial and evolution of the aquatic microbial communities.