Limits of entrainment of circadian neuronal networks

Circadian rhythmicity lies at the center of various important physiological and behavioral processes in mammals, such as sleep, metabolism, homeostasis, mood changes, and more. Misalignment of intrinsic neuronal oscillations with the external day-night cycle can disrupt such processes and lead to numerous disorders. In this work, we computationally determine the limits of circadian synchronization to external light signals of different frequency, duty cycle, and simulated amplitude. Instead of modeling circadian dynamics with generic oscillator models (e.g., Kuramoto-type), we use a detailed computational neuroscience model, which integrates biomolecular dynamics, neuronal electrophysiology, and network effects. This allows us to investigate the effect of small drug molecules, such as Longdaysin, and connect our results with experimental findings. To combat the high dimensionality of such a detailed model, we employ a matrix-free approach, while our entire algorithmic pipeline enables numerical continuation and construction of bifurcation diagrams using only direct simulation. We, thus, computationally explore the effect of heterogeneity in the circadian neuronal network, as well as the effect of the corrective therapeutic intervention of Longdaysin. Last, we employ unsupervised learning to construct a data-driven embedding space for representing neuronal heterogeneity.

Modelling the functional roles of synaptic and extra-synaptic γ-aminobutyric acid receptor dynamics in circadian timekeeping

In the suprachiasmatic nucleus (SCN), γ-aminobutyric acid (GABA) is a primary neurotransmitter. GABA can signal through two types of GABAA receptor subunits, often referred to as synaptic GABAA (gamma subunit) and extra-synaptic GABAA (delta subunit). To test the functional roles of these distinct GABAA in regulating circadian rhythms, we developed a multicellular SCN model where we could separately compare the effects of manipulating GABA neurotransmitter or receptor dynamics. Our model predicted that blocking GABA signalling modestly increased synchrony among circadian cells, consistent with published SCN pharmacology. Conversely, the model predicted that lowering GABAA receptor density reduced firing rate, circadian cell fraction, amplitude and synchrony among individual neurons. When we tested these predictions, we found that the knockdown of delta GABAA reduced the amplitude and synchrony of clock gene expression among cells in SCN explants. The model further predicted that increasing gamma GABAA densities could enhance synchrony, as opposed to increasing delta GABAA densities. Overall, our model reveals how blocking GABAA receptors can modestly increase synchrony, while increasing the relative density of gamma over delta subunits can dramatically increase synchrony. We hypothesize that increased gamma GABAA density in the winter could underlie the tighter phase relationships among SCN cells.

Interrogation of the perturbed gut microbiota in gouty arthritis patients through in silico metabolic modeling

Recent studies have shown perturbed gut microbiota associated with gouty arthritis, a metabolic disease characterized by an imbalance between uric acid production and excretion. To mechanistically investigate altered microbiota metabolism associated with gout disease, 16S rRNA gene amplicon sequence data from stool samples of gout patients and healthy controls were computationally analyzed through bacterial community metabolic models. Patient-specific community models constructed with the metagenomics modeling pipeline, mgPipe, were used to perform k-means clustering of samples according to their metabolic capabilities. The clustering analysis generated statistically significant partitioning of samples into a Bacteroides-dominated, high gout cluster and a Faecalibacterium-elevated, low gout cluster. The high gout cluster was predicted to allow elevated synthesis of the amino acids D-alanine and L-alanine and byproducts of branched-chain amino acid catabolism, while the low gout cluster allowed higher production of butyrate, the sulfur-containing amino acids L-cysteine and L-methionine, and the L-cysteine catabolic product H2S. By expanding the capabilities of mgPipe to provide taxa-level resolution of metabolite exchange rates, acetate, D-lactate and succinate exchanged from Bacteroides to Faecalibacterium were predicted to enhance butyrate production in the low gout cluster. Model predictions suggested that sulfur-containing amino acid metabolism generally and H2S more specifically could be novel gout disease markers.

Dynamic metabolic modelling predicts efficient acetogen-gut bacterium cocultures for CO-to-butyrate conversion

AIMS

While gas-fermenting acetogens have been engineered to secrete non-native metabolites such as butyrate, acetate remains the most thermodynamically favourable product. An alternative to metabolic engineering is to exploit native capabilities for CO-to-acetate conversion by coculturing an acetogen with a second bacterium that provides efficient acetate-butyrate conversion.

METHODS AND RESULTS

We used dynamic metabolic modelling to computationally evaluate the CO-to-butyrate conversion capabilities of candidate coculture systems by exploiting the diversity of human gut bacteria for anaerobic synthesis of butyrate from acetate and ethanol. A preliminary screening procedure based on flux balance analysis was developed to identify 48 gut bacteria which satisfied minimal growth rate and acetate-to-butyrate conversion requirements when cultured on minimal medium containing acetate and a simple sugar not consumed by the paired acetogen. A total of 170 acetogen/gut bacterium/sugar combinations were dynamically simulated for continuous growth using a 70/30 CO/CO₂ feed gas mixture and minimal medium computationally determined for each combination.

CONCLUSIONS

While coculture systems involving the acetogens Eubacterium limosum or Blautia producta yielded low butyrate productivities and CO-to-ethanol conversion had minimal impact on system performance, dynamic simulations predicted a large number of promising coculture designs with Clostridium ljungdahlii or C. autoethanogenum as the CO-to-acetate converter. Pairings with the gut bacterium Clostridium hylemonae or Roseburia hominis were particularly promising due to their ability to generate high butyrate productivities over a range of dilution rates with a variety of sugars. The higher specific acetate secretion rate of C. ljungdahlii proved more beneficial than the elevated growth rate of C. autoethanogenum for coculture butyrate productivity.

SIGNIFICANCE AND IMPACT OF THE STUDY

Our study demonstrated that metabolic modelling could provide useful insights into coculture design that can guide future experimental studies. More specifically, our predictions generated several favourable designs, which could serve as the first coculture systems realized experimentally.

Metabolic Modeling to Interrogate Microbial Disease: A Tale for Experimentalists

The explosion of microbiome analyses has helped identify individual microorganisms and microbial communities driving human health and disease, but how these communities function is still an open question. For example, the role for the incredibly complex metabolic interactions among microbial species cannot easily be resolved by current experimental approaches such as 16S rRNA gene sequencing, metagenomics and/or metabolomics. Resolving such metabolic interactions is particularly challenging in the context of polymicrobial communities where metabolite exchange has been reported to impact key bacterial traits such as virulence and antibiotic treatment efficacy. As novel approaches are needed to pinpoint microbial determinants responsible for impacting community function in the context of human health and to facilitate the development of novel anti-infective and antimicrobial drugs, here we review, from the viewpoint of experimentalists, the latest advances in metabolic modeling, a computational method capable of predicting metabolic capabilities and interactions from individual microorganisms to complex ecological systems. We use selected examples from the literature to illustrate how metabolic modeling has been utilized, in combination with experiments, to better understand microbial community function. Finally, we propose how such combined, cross-disciplinary efforts can be utilized to drive laboratory work and drug discovery moving forward.

Computational modeling of the gut microbiota reveals putative metabolic mechanisms of recurrent Clostridioides difficile infection

Approximately 30% of patients who have Clostridioides difficile infection (CDI) will suffer at least one incident of reinfection. While the underlying causes of CDI recurrence are poorly understood, interactions between C. difficile and commensal gut bacteria are thought to play an important role. In this study, an in silico pipeline was used to process 16S rRNA gene amplicon sequence data of 225 stool samples from 93 CDI patients into sample-specific models of bacterial community metabolism. Clustered metabolite production rates generated from post-diagnosis samples generated a high Enterobacteriaceae abundance cluster containing disproportionately large numbers of recurrent samples and patients. This cluster was predicted to have significantly reduced capabilities for secondary bile acid synthesis but elevated capabilities for aromatic amino acid catabolism. When applied to 16S sequence data of 40 samples from fecal microbiota transplantation (FMT) patients suffering from recurrent CDI and their stool donors, the community modeling method generated a high Enterobacteriaceae abundance cluster with a disproportionate large number of pre-FMT samples. This cluster also was predicted to exhibit reduced secondary bile acid synthesis and elevated aromatic amino acid catabolism. Collectively, these in silico predictions suggest that Enterobacteriaceae may create a gut environment favorable for C. difficile spore germination and/or toxin synthesis.

Pseudomonas aeruginosa reverse diauxie is a multidimensional, optimized, resource utilization strategy

Pseudomonas aeruginosa is a globally-distributed bacterium often found in medical infections. The opportunistic pathogen uses a different, carbon catabolite repression (CCR) strategy than many, model microorganisms. It does not utilize a classic diauxie phenotype, nor does it follow common systems biology assumptions including preferential consumption of glucose with an 'overflow' metabolism. Despite these contradictions, P. aeruginosa is competitive in many, disparate environments underscoring knowledge gaps in microbial ecology and systems biology. Physiological, omics, and in silico analyses were used to quantify the P. aeruginosa CCR strategy known as 'reverse diauxie'. An ecological basis of reverse diauxie was identified using a genome-scale, metabolic model interrogated with in vitro omics data. Reverse diauxie preference for lower energy, nonfermentable carbon sources, such as acetate or succinate over glucose, was predicted using a multidimensional strategy which minimized resource investment into central metabolism while completely oxidizing substrates. Application of a common, in silico optimization criterion, which maximizes growth rate, did not predict the reverse diauxie phenotypes. This study quantifies P. aeruginosa metabolic strategies foundational to its wide distribution and virulence including its potentially, mutualistic interactions with microorganisms found commonly in the environment and in medical infections.

Artificial consortium demonstrates emergent properties of enhanced cellulosic-sugar degradation and biofuel synthesis

Planktonic cultures, of a rationally designed consortium, demonstrated emergent properties that exceeded the sums of monoculture properties, including a >200% increase in cellobiose catabolism, a >100% increase in glycerol catabolism, a >800% increase in ethanol production, and a >120% increase in biomass productivity. The consortium was designed to have a primary and secondary-resource specialist that used crossfeeding with a positive feedback mechanism, division of labor, and nutrient and energy transfer via necromass catabolism. The primary resource specialist was Clostridium phytofermentans (a.k.a. Lachnoclostridium phytofermentans), a cellulolytic, obligate anaerobe. The secondary-resource specialist was Escherichia coli, a versatile, facultative anaerobe, which can ferment glycerol and byproducts of cellobiose catabolism. The consortium also demonstrated emergent properties of enhanced biomass accumulation when grown as biofilms, which created high cell density communities with gradients of species along the vertical axis. Consortium biofilms were robust to oxic perturbations with E. coli consuming O₂, creating an anoxic environment for C. phytofermentans. Anoxic/oxic cycling further enhanced biomass productivity of the biofilm consortium, increasing biomass accumulation ~250% over the sum of the monoculture biofilms. Consortium emergent properties were credited to several synergistic mechanisms. E. coli consumed inhibitory byproducts from cellobiose catabolism, driving higher C. phytofermentans growth and higher cellulolytic enzyme production, which in turn provided more substrate for E. coli. E. coli necromass enhanced C. phytofermentans growth while C. phytofermentans necromass aided E. coli growth via the release of peptides and amino acids, respectively. In aggregate, temporal cycling of necromass constituents increased flux of cellulose-derived resources through the consortium. The study establishes a consortia-based, bioprocessing strategy built on naturally occurring interactions for improved conversion of cellulose-derived sugars into bioproducts.

Astrocytic Modulation of Neuronal Activity in the Suprachiasmatic Nucleus: Insights from Mathematical Modeling

The suprachiasmatic nucleus (SCN) of the hypothalamus consists of a highly heterogeneous neuronal population networked together to allow precise and robust circadian timekeeping in mammals. While the critical importance of SCN neurons in regulating circadian rhythms has been extensively studied, the roles of SCN astrocytes in circadian system function are not well understood. Recent experiments have demonstrated that SCN astrocytes are circadian oscillators with the same functional clock genes as SCN neurons. Astrocytes generate rhythmic outputs that are thought to modulate neuronal activity through pre- and postsynaptic interactions. In this study, we developed an in silico multicellular model of the SCN clock to investigate the impact of astrocytes in modulating neuronal activity and affecting key clock properties such as circadian rhythmicity, period, and synchronization. The model predicted that astrocytes could alter the rhythmic activity of neurons via bidirectional interactions at tripartite synapses. Specifically, astrocyte-regulated extracellular glutamate was predicted to increase neuropeptide signaling from neurons. Consistent with experimental results, we found that astrocytes could increase the circadian period and enhance neural synchronization according to their endogenous circadian period. The impact of astrocytic modulation of circadian rhythm amplitude, period, and synchronization was predicted to be strongest when astrocytes had periods between 0 and 2 h longer than neurons. Increasing the number of neurons coupled to the astrocyte also increased its impact on period modulation and synchrony. These computational results suggest that signals that modulate astrocytic rhythms or signaling (e.g., as a function of season, age, or treatment) could cause disruptions in circadian rhythm or serve as putative therapeutic targets.

A population balance model to modulate shear for the control of aggregation in Taxus suspension cultures

Cellular aggregation in plant suspension cultures directly affects the accumulation of high value products, such as paclitaxel from Taxus. Through application of mechanical shear by repeated, manual pipetting through a 10 ml pipet with a 1.6 mm aperture, the mean aggregate size of a Taxus culture can be reduced without affecting culture growth. When a constant level of mechanical shear was applied over eight generations, the sheared population was maintained at a mean aggregate diameter 194 μm lower than the unsheared control, but the mean aggregate size fluctuated by over 600 μm, indicating unpredictable culture variability. A population balance model was developed to interpret and predict disaggregation dynamics under mechanical shear. Adjustable parameters involved in the breakage frequency function of the population balance model were estimated by nonlinear optimization from experimentally measured size distributions. The optimized model predictions were in strong agreement with measured size distributions. The model was then used to determine the shear requirements to successfully reach a target aggregate size distribution. This model will be utilized in the future to maintain a culture with a constant size distribution with the goal of decreasing culture variability and increasing paclitaxel yields.

Metabolic modelling of chronic wound microbiota predicts mutualistic interactions that drive community composition

AIMS

To identify putative mutualistic interactions driving community composition in polymicrobial chronic wound infections using metabolic modelling.

METHODS AND RESULTS

We developed a 12 species metabolic model that covered 74% of 16S rDNA pyrosequencing reads of dominant genera from 2963 chronic wound patients. The community model was used to predict species abundances averaged across this large patient population. We found that substantially improved predictions were obtained when the model was constrained with genera prevalence data and predicted abundances were averaged over 5000 ensemble simulations with community participants randomly determined according to the experimentally determined prevalences. Staphylococcus and Pseudomonas were predicted to exhibit a strong mutualistic relationship that resulted in community growth rate and diversity simultaneously increasing, suggesting that these two common chronic wound pathogens establish dominance by cooperating with less harmful commensal species. In communities lacking one or both dominant pathogens, other mutualistic relationship including Staphylococcus/Acinetobacter, Pseudomonas/Serratia and Streptococcus/Enterococcus were predicted consistent with published experimental data.

CONCLUSIONS

Mutualistic interactions were predicted to be driven by crossfeeding of organic acids, alcohols and amino acids that could potentially be disrupted to slow chronic wound disease progression.

SIGNIFICANCE AND IMPACT OF THE STUDY

Approximately 2% of the US population suffers from nonhealing chronic wounds infected by a combination of commensal and pathogenic bacteria. These polymicrobial infections are often resilient to antibiotic treatment due to the nutrient-rich wound environment and species interactions that promote community stability and robustness. The simulation results from this study were used to identify putative mutualistic interactions between bacteria that could be targeted to enhance treatment efficacy.

Predicting the performance of pressure filtration processes by coupling computational fluid dynamics and discrete element methods

To obtain a fundamental understanding of the various factors affecting pressure filtration performance, we developed a coupled computational fluid dynamics (CFD) and discrete element method (DEM) model for simulating the effect of solvent flow through the solid particle cake. The model was validated using data collected by filtering mixtures of spherical glass beads and deionized water through a dead-end cell over a range of applied pressures. Numerical experiments were performed to study the effects of particle properties, liquid properties and operating conditions on filtration performance. The model predicted that the filtrate flow rate could be strongly affected by the mean size of the particles, the presence of small particles (i.e. fines) in the particle distribution, the viscosity of the liquid, and particle deformation leading to cake compression. Our study demonstrated that CFD-DEM modeling is a powerful approach for understanding cake filtration processes and predicting filtration performance.

Metabolic modeling of bacterial co-culture systems predicts enhanced carbon monoxide-to-butyrate conversion compared to monoculture systems

We used metabolic modeling to computationally investigate the potential of bacterial coculture system designs for CO conversion to the platform chemical butyrate. By taking advantage of the native capabilities of wild-type strains, we developed two anaerobic coculture designs by combining Clostridium autoethanogenum for CO-to-acetate conversion with bacterial strains that offer high acetate-to-butyrate conversion capabilities: the environmental bacterium the human gut bacteriumEubacterium rectale. When grown in continuous stirred tank reactor on a 70/0/30 CO/H₂/N₂ gas mixture, the C. autoethanogenum-C Kluyveri co-culture was predicted to offer no mprovement in butyrate volumetric productivity compared to an engineered C. autoethanogenum monoculture despite utilizing vinyl acetate as a secondary carbon source for C. kluyveri growth enhancement. A coculture consisting of C. autoethanogenum and C. kluyveri engineered in silico to eliminate hexanoate synthesis was predicted to enhance both butyrate productivity and titer. The C. autoethanogenum-E. rectale coculture offered similar improvements in butyrate productivity without the need for metabolic engineering when glucose was provided as a secondary carbon source to enhance E. rectale growth. A bubble column model developed to assess the potential for large-scale butyrate production of the C. autoethanogenum-E. rectale design predicted that a 40/30/30 CO/H₂/N₂ gas mixture and a 5 m column length would be preferred to enhance C. autoethanogenum growth and counteract CO inhibitory effects on E. rectale.

In Silico Metabolic Design of Two-Strain Biofilm Systems Predicts Enhanced Biomass Production and Biochemical Synthesis

Engineered biofilm consortia have the potential to solve important biotechnological problems that have proved difficult for monoculture biofilms and planktonic consortia, such as conversion of lignocellulosic material to useful biochemicals. While considerable experimental progress has been reported for engineering and characterizing biofilm consortia, the field still lacks in silico tools for simulation, design, and optimization of stable, robust, and productive designed consortia. We developed biofilm consortia metabolic models for two coculture systems centered around the ecological design motif of a primary cell type that utilizes a supplied electron donor and secretes acetate as a byproduct and a secondary cell type that consumes the acetate, relieving byproduct inhibition on the primary cell type and enhancing overall system biomass. The models presented in this paper predict that distinct metabolic niches for the two cell types could be established by supplying electron donors and acceptors at opposite ends of the biofilm and that acetate consumption by the secondary cell type could increase total biomass accumulation and the synthesis of valuable biochemicals, such as isobutanol, by the primary cell type. System tunability is enhanced when each cell type is supplied with a unique terminal electron acceptor at opposite ends of the biofilm rather than competing for a common electron acceptor. Our model provides good qualitative agreement with data for a synthetic Escherichia coli coculture system, suggesting that the proposed design rules may have wide applicability to engineered biofilm consortia.

Suboptimal community growth mediated through metabolite crossfeeding promotes species diversity in the gut microbiota

The gut microbiota represent a highly complex ecosystem comprised of approximately 1000 species that forms a mutualistic relationship with the human host. A critical attribute of the microbiota is high species diversity, which provides system robustness through overlapping and redundant metabolic capabilities. The gradual loss of bacterial diversity has been associated with a broad array of gut pathologies and diseases including malnutrition, obesity, diabetes and inflammatory bowel disease. We formulated an in silico community model of the gut microbiota by combining genome-scale metabolic reconstructions of 28 representative species to explore the relationship between species diversity and community growth. While the individual species offered a broad range of metabolic capabilities, communities optimized for maximal growth on simulated Western and high-fiber diets had low diversities and imbalances in short-chain fatty acid (SCFA) synthesis characterized by acetate overproduction. Community flux variability analysis performed with the 28-species model and a reduced 20-species model suggested that enhanced species diversity and more balanced SCFA production were achievable at suboptimal growth rates. We developed a simple method for constraining species abundances to sample the growth-diversity tradeoff and used the 20-species model to show that tradeoff curves for Western and high-fiber diets resembled Pareto-optimal surfaces. Compared to maximal growth solutions, suboptimal growth solutions were characterized by higher species diversity, more balanced SCFA synthesis and lower exchange rates of crossfed metabolites between more species. We hypothesized that modulation of crossfeeding relationships through host-microbiota interactions could be an important means for maintaining species diversity and suggest that community metabolic modeling approaches that allow multiobjective optimization of growth and diversity are needed for more realistic simulation of complex communities.

Incorporating hydrodynamics into spatiotemporal metabolic models of bubble column gas fermentation

Gas fermentation has emerged as a technologically and economically attractive option for producing renewable fuels and chemicals from carbon monoxide (CO) rich waste streams. LanzaTech has developed a proprietary strain of the gas fermentating acetogen Clostridium autoethanogenum as a microbial platform for synthesizing ethanol, 2,3-butanediol, and other chemicals. Bubble column reactor technology is being developed for the large-scale production, motivating the investigation of multiphase reactor hydrodynamics. In this study, we combined hydrodynamics with a genome-scale reconstruction of C. autoethanogenum metabolism and multiphase convection-dispersion equations to compare the performance of bubble column reactors with and without liquid recycle. For both reactor configurations, hydrodynamics was predicted to diminish bubble column performance with respect to CO conversion, biomass production, and ethanol production when compared with bubble column models in which the gas phase was modeled as ideal plug flow plus axial dispersion. Liquid recycle was predicted to be advantageous by increasing CO conversion, biomass production, and ethanol and 2,3-butanediol production compared with the non-recycle reactor configuration. Parametric studies performed for the liquid recycle configuration with two-phase hydrodynamics showed that increased CO feed flow rates (more gas supply), smaller CO gas bubbles (more gas-liquid mass transfer), and shorter column heights (more gas per volume of liquid per time) favored ethanol production over acetate production. Our computational results demonstrate the power of combining cellular metabolic models and two-phase hydrodynamics for simulating and optimizing gas fermentation reactors.

Microbiota dysbiosis in inflammatory bowel diseases: in silico investigation of the oxygen hypothesis

BACKGROUND

Inflammatory bowel diseases (IBD), which include ulcerative colitis and Crohn's disease, cause chronic inflammation of the digestive tract in approximately 1.6 million Americans. A signature of IBD is dysbiosis of the gut microbiota marked by a significant reduction of obligate anaerobes and a sharp increase in facultative anaerobes. Numerous experimental studies have shown that IBD is strongly correlated with a decrease of Faecalibacterium prausnitzii and an increase of Escherichia coli. One hypothesis is that chronic inflammation induces increased oxygen levels in the gut, which in turn causes an imbalance between obligate and facultative anaerobes.

RESULTS

To computationally investigate the oxygen hypothesis, we developed a multispecies biofilm model based on genome-scale metabolic reconstructions of F. prausnitzii, E. coli and the common gut anaerobe Bacteroides thetaiotaomicron. Application of low bulk oxygen concentrations at the biofilm boundary reproduced experimentally observed behavior characterized by a sharp decrease of F. prausnitzii and a large increase of E. coli, demonstrating that dysbiosis consistent with IBD disease progression could be qualitatively predicted solely based on metabolic differences between the species. A diet with balanced carbohydrate and protein content was predicted to represent a metabolic "sweet spot" that increased the oxygen range over which F. prausnitzii could remain competitive and IBD could be sublimated. Host-microbiota feedback incorporated via a simple linear feedback between the average F. prausnitzii concentration and the bulk oxygen concentration did not substantially change the range of oxygen concentrations where dysbiosis was predicted, but the transition from normal species abundances to severe dysbiosis was much more dramatic and occurred over a much longer timescale. Similar predictions were obtained with sustained antibiotic treatment replacing a sustained oxygen perturbation, demonstrating how IBD might progress over several years with few noticeable effects and then suddenly produce severe disease symptoms.

CONCLUSIONS

The multispecies biofilm metabolic model predicted that oxygen concentrations of ∼1 micromolar within the gut could cause microbiota dysbiosis consistent with those observed experimentally for inflammatory bowel diseases. Our model predictions could be tested directly through the development of an appropriate in vitro system of the three species community and testing of microbiota-host interactions in gnotobiotic mice.

Metabolic modeling of a chronic wound biofilm consortium predicts spatial partitioning of bacterial species

Background

Chronic wounds are often colonized by consortia comprised of different bacterial species growing as biofilms on a complex mixture of wound exudate. Bacteria growing in biofilms exhibit phenotypes distinct from planktonic growth, often rendering the application of antibacterial compounds ineffective. Computational modeling represents a complementary tool to experimentation for generating fundamental knowledge and developing more effective treatment strategies for chronic wound biofilm consortia.

Results

We developed spatiotemporal models to investigate the multispecies metabolism of a biofilm consortium comprised of two common chronic wound isolates: the aerobe Pseudomonas aeruginosa and the facultative anaerobe Staphylococcus aureus. By combining genome-scale metabolic reconstructions with partial differential equations for metabolite diffusion, the models were able to provide both temporal and spatial predictions with genome-scale resolution. The models were used to analyze the metabolic differences between single species and two species biofilms and to demonstrate the tendency of the two bacteria to spatially partition in the multispecies biofilm as observed experimentally. Nutrient gradients imposed by supplying glucose at the bottom and oxygen at the top of the biofilm induced spatial partitioning of the two species, with S. aureus most concentrated in the anaerobic region and P. aeruginosa present only in the aerobic region. The two species system was predicted to support a maximum biofilm thickness much greater than P. aeruginosa alone but slightly less than S. aureus alone, suggesting an antagonistic metabolic effect of P. aeruginosa on S. aureus. When each species was allowed to enhance its growth through consumption of secreted metabolic byproducts assuming identical uptake kinetics, the competitiveness of P. aeruginosa was further reduced due primarily to the more efficient lactate metabolism of S. aureus. Lysis of S. aureus by a small molecule inhibitor secreted from P. aeruginosa and/or P. aeruginosa aerotaxis were predicted to substantially increase P. aeruginosa competitiveness in the aerobic region, consistent with in vitro experimental studies.

Conclusions

Our biofilm modeling approach allows the prediction of individual species metabolism and interspecies interactions in both time and space with genome-scale resolution. This study yielded new insights into the multispecies metabolism of a chronic wound biofilm, in particular metabolic factors that may lead to spatial partitioning of the two bacterial species. We believe that P. aeruginosa lysis of S. aureus combined with nutrient competition is a particularly relevant scenario for which model predictions could be tested experimentally.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0334-8) contains supplementary material, which is available to authorized users.

Inhibitory and excitatory networks balance cell coupling in the suprachiasmatic nucleus: A modeling approach

Neuronal coupling contributes to circadian rhythms formation in the suprachiasmatic nucleus (SCN). While the neurotransmitter vasoactive intestinal polypeptide (VIP) is considered essential for synchronizing the oscillations of individual neurons, γ-aminobutyric acid (GABA) does not have a clear functional role despite being highly concentrated in the SCN. While most studies have examined the role of either GABA or VIP, our mathematical modeling approach explored their interplay on networks of SCN neurons. Tuning the parameters that control the release of GABA and VIP enabled us to optimize network synchrony, which was achieved at a peak firing rate during the subjective day of about 7Hz. Furthermore, VIP and GABA modulation could adjust network rhythm amplitude and period without sacrificing synchrony. We also performed simulations of SCN networks to phase shifts during 12h:12h light-dark cycles and showed that GABA networks reduced the average time for the SCN model to re-synchronize. We hypothesized that VIP and GABA balance cell coupling in the SCN to promote synchronization of heterogeneous oscillators while allowing flexibility for adjustment to environmental changes.

Spatiotemporal modeling of microbial metabolism

BACKGROUND

Microbial systems in which the extracellular environment varies both spatially and temporally are very common in nature and in engineering applications. While the use of genome-scale metabolic reconstructions for steady-state flux balance analysis (FBA) and extensions for dynamic FBA are common, the development of spatiotemporal metabolic models has received little attention.

RESULTS

We present a general methodology for spatiotemporal metabolic modeling based on combining genome-scale reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in time and spatially varying environments. Our solution procedure involves spatial discretization of the partial differential equation model followed by numerical integration of the resulting system of ordinary differential equations with embedded linear programs using DFBAlab, a MATLAB code that performs reliable and efficient dynamic FBA simulations. We demonstrate our methodology by solving spatiotemporal metabolic models for two systems of considerable practical interest: (1) a bubble column reactor with the syngas fermenting bacterium Clostridium ljungdahlii; and (2) a chronic wound biofilm with the human pathogen Pseudomonas aeruginosa. Despite the complexity of the discretized models which consist of 900 ODEs/600 LPs and 250 ODEs/250 LPs, respectively, we show that the proposed computational framework allows efficient and robust model solution.

CONCLUSIONS

Our study establishes a new paradigm for formulating and solving genome-scale metabolic models with both time and spatial variations and has wide applicability to natural and engineered microbial systems.

Genome-scale modelling of microbial metabolism with temporal and spatial resolution

Most natural microbial systems have evolved to function in environments with temporal and spatial variations. A major limitation to understanding such complex systems is the lack of mathematical modelling frameworks that connect the genomes of individual species and temporal and spatial variations in the environment to system behaviour. The goal of this review is to introduce the emerging field of spatiotemporal metabolic modelling based on genome-scale reconstructions of microbial metabolism. The extension of flux balance analysis (FBA) to account for both temporal and spatial variations in the environment is termed spatiotemporal FBA (SFBA). Following a brief overview of FBA and its established dynamic extension, the SFBA problem is introduced and recent progress is described. Three case studies are reviewed to illustrate the current state-of-the-art and possible future research directions are outlined. The author posits that SFBA is the next frontier for microbial metabolic modelling and a rapid increase in methods development and system applications is anticipated.

Circadian Gating of the Mammalian Cell Cycle Restriction Point: A Mathematical Analysis

A critical decision in the mammalian cell cycle is whether to pass through the restriction point (R-point) or enter the cell cycle. In this letter, we modeled the decision-making system of the mammalian cell cycle entry and the simulated circadian regulation of the R-point driven by external epithelial growth factor (EGF) patterns. Our conceptual model replicated key signaling behaviors observed experimentally, suggesting that the proposed network captured the essential system features. The model revealed the dramatic importance of the EGF dynamics on promoting cell proliferation, showed that the EGF signal duration was more important than the signal strength for driving cells past the R-point, and suggested that the loss of circadian control of the cell cycle entry could be associated with cancer development.

Metabolic modeling of synthesis gas fermentation in bubble column reactors

BACKGROUND

A promising route to renewable liquid fuels and chemicals is the fermentation of synthesis gas (syngas) streams to synthesize desired products such as ethanol and 2,3-butanediol. While commercial development of syngas fermentation technology is underway, an unmet need is the development of integrated metabolic and transport models for industrially relevant syngas bubble column reactors.

RESULTS

We developed and evaluated a spatiotemporal metabolic model for bubble column reactors with the syngas fermenting bacterium Clostridium ljungdahlii as the microbial catalyst. Our modeling approach involved combining a genome-scale reconstruction of C. ljungdahlii metabolism with multiphase transport equations that govern convective and dispersive processes within the spatially varying column. The reactor model was spatially discretized to yield a large set of ordinary differential equations (ODEs) in time with embedded linear programs (LPs) and solved using the MATLAB based code DFBAlab. Simulations were performed to analyze the effects of important process and cellular parameters on key measures of reactor performance including ethanol titer, ethanol-to-acetate ratio, and CO and H2 conversions.

CONCLUSIONS

Our computational study demonstrated that mathematical modeling provides a complementary tool to experimentation for understanding, predicting, and optimizing syngas fermentation reactors. These model predictions could guide future cellular and process engineering efforts aimed at alleviating bottlenecks to biochemical production in syngas bubble column reactors.

Dynamic flux balance analysis for synthetic microbial communities

Dynamic flux balance analysis (DFBA) is an extension of classical flux balance analysis that allows the dynamic effects of the extracellular environment on microbial metabolism to be predicted and optimised. Recently this computational framework has been extended to microbial communities for which the individual species are known and genome-scale metabolic reconstructions are available. In this review, the authors provide an overview of the emerging DFBA approach with a focus on two case studies involving the conversion of mixed hexose/pentose sugar mixtures by synthetic microbial co-culture systems. These case studies illustrate the key requirements of the DFBA approach, including the incorporation of individual species metabolic reconstructions, formulation of extracellular mass balances, identification of substrate uptake kinetics, numerical solution of the coupled linear program/differential equations and model adaptation for common, suboptimal growth conditions and identified species interactions. The review concludes with a summary of progress to date and possible directions for future research.

Dynamic model-based analysis of furfural and HMF detoxification by pure and mixed batch cultures of S. cerevisiae and S. stipitis

Inhibitory compounds that result from biomass hydrolysis are an obstacle to the efficient production of second-generation biofuels. Fermentative microorganisms can reduce compounds such as furfural and 5-hydroxymethyl furfural (HMF), but detoxification is accompanied by reduced growth rates and ethanol yields. In this study, we assess the effects of these furan aldehydes on pure and mixed yeast cultures consisting of a respiratory deficient mutant of Saccharomyces cerevisiae and wild-type Scheffersomyces stipitis using dynamic flux balance analysis. Uptake kinetics and stoichiometric equations for the intracellular reduction reactions associated with each inhibitor were added to genome-scale metabolic reconstructions of the two yeasts. Further modification of the S. cerevisiae metabolic network was necessary to satisfactorily predict the amount of acetate synthesized during HMF reduction. Inhibitory terms that captured the adverse effects of the furan aldehydes and their corresponding alcohols on cell growth and ethanol production were added to attain qualitative agreement with batch experiments conducted for model development and validation. When the two yeasts were co-cultured in the presence of the furan aldehydes, inoculums that reduced the synthesis of highly toxic acetate produced by S. cerevisiae yielded the highest ethanol productivities. The model described here can be used to generate optimal fermentation strategies for the simultaneous detoxification and fermentation of lignocellulosic hydrolysates by S. cerevisiae and/or S. stipitis.

Dynamic metabolic modeling of a microaerobic yeast co-culture: predicting and optimizing ethanol production from glucose/xylose mixtures

BACKGROUND

A key step in any process that converts lignocellulose to biofuels is the efficient fermentation of both hexose and pentose sugars. The co-culture of respiratory-deficient Saccharomyces cerevisiae and wild-type Scheffersomyces stipitis has been identified as a promising system for microaerobic ethanol production because S. cerevisiae only consumes glucose while S. stipitis efficiently converts xylose to ethanol.

RESULTS

To better predict how these two yeasts behave in batch co-culture and to optimize system performance, a dynamic flux balance model describing co-culture metabolism was developed from genome-scale metabolic reconstructions of the individual organisms. First a dynamic model was developed for each organism by estimating substrate uptake kinetic parameters from batch pure culture data and evaluating model extensibility to different microaerobic growth conditions. The co-culture model was constructed by combining the two individual models assuming a cellular objective of total growth rate maximization. To obtain accurate predictions of batch co-culture data collected at different microaerobic conditions, the S. cerevisiae maximum glucose uptake rate was reduced from its pure culture value to account for more efficient S. stipitis glucose uptake in co-culture. The dynamic co-culture model was used to predict the inoculum concentration and aeration level that maximized batch ethanol productivity. The model predictions were validated with batch co-culture experiments performed at the optimal conditions. Furthermore, the dynamic model was used to predict how engineered improvements to the S. stipitis xylose transport system could improve co-culture ethanol production.

CONCLUSIONS

These results demonstrate the utility of the dynamic co-culture metabolic model for guiding process and metabolic engineering efforts aimed at increasing microaerobic ethanol production from glucose/xylose mixtures.

Genome-based Modeling and Design of Metabolic Interactions in Microbial Communities

Biotechnology research is traditionally focused on individual microbial strains that are perceived to have the necessary metabolic functions, or the capability to have these functions introduced, to achieve a particular task. For many important applications, the development of such omnipotent microbes is an extremely challenging if not impossible task. By contrast, nature employs a radically different strategy based on synergistic combinations of different microbial species that collectively achieve the desired task. These natural communities have evolved to exploit the native metabolic capabilities of each species and are highly adaptive to changes in their environments. However, microbial communities have proven difficult to study due to a lack of suitable experimental and computational tools. With the advent of genome sequencing, omics technologies, bioinformatics and genome-scale modeling, researchers now have unprecedented capabilities to analyze and engineer the metabolism of microbial communities. The goal of this review is to summarize recent applications of genome-scale metabolic modeling to microbial communities. A brief introduction to lumped community models is used to motivate the need for genome-level descriptions of individual species and their metabolic interactions. The review of genome-scale models begins with static modeling approaches, which are appropriate for communities where the extracellular environment can be assumed to be time invariant or slowly varying. Dynamic extensions of the static modeling approach are described, and then applications of genome-scale models for design of synthetic microbial communities are reviewed. The review concludes with a summary of metagenomic tools for analyzing community metabolism and an outlook for future research.

A population balance equation model of aggregation dynamics in Taxus suspension cell cultures

The nature of plant cells to grow as multicellular aggregates in suspension culture has profound effects on bioprocess performance. Recent advances in the measurement of plant cell aggregate size allow for routine process monitoring of this property. We have exploited this capability to develop a conceptual model to describe changes in the aggregate size distribution that are observed over the course of a Taxus cell suspension batch culture. We utilized the population balance equation framework to describe plant cell aggregates as a particulate system, accounting for the relevant phenomenological processes underlying aggregation, such as growth and breakage. We compared model predictions to experimental data to select appropriate kernel functions, and found that larger aggregates had a higher breakage rate, biomass was partitioned asymmetrically following a breakage event, and aggregates grew exponentially. Our model was then validated against several datasets with different initial aggregate size distributions and was able to quantitatively predict changes in total biomass and mean aggregate size, as well as actual size distributions. We proposed a breakage mechanism where a fraction of biomass was lost upon each breakage event, and demonstrated that even though smaller aggregates have been shown to produce more paclitaxel, an optimum breakage rate was predicted for maximum paclitaxel accumulation. We believe this is the first model to use a segregated, corpuscular approach to describe changes in the size distribution of plant cell aggregates, and represents an important first step in the design of rational strategies to control aggregation and optimize process performance.

Analysis of aggregate size as a process variable affecting paclitaxel accumulation in Taxus suspension cultures

Plant cell aggregates have long been implicated in affecting cellular metabolism in suspension culture, yet the rigorous characterization of aggregate size as a process variable and its effect on bioprocess performance has not been demonstrated. Aggregate fractionation and analysis of biomass-associated product is commonly used to assess the effect of aggregation, but we establish that this method is flawed under certain conditions and does not necessarily agree with comprehensive studies of total culture performance. Leveraging recent advances to routinely measure aggregate size distributions, we developed a simple method to manipulate aggregate size and evaluate its effect on the culture as a whole, and found that Taxus suspension cultures with smaller aggregates produced significantly more paclitaxel than cultures with larger aggregates in two cell lines over a range of aggregate sizes, and where biomass accumulation was equivalent before elicitation with methyl jasmonate. Taxus cuspidata (T. cuspidata) P93AF cultures with mean aggregate sizes of 690 and 1,100 μm produced 22 and 11 mg/L paclitaxel, respectively, a twofold increase for smaller aggregates, and T. cuspidata P991 cultures with mean aggregate sizes of 400 and 840 μm produced 6 and 0.3 mg/L paclitaxel, respectively, an increase of 20-fold for smaller aggregates. These results demonstrate the importance of validating experiments aimed at a specific phenomenon with total process studies, and provide a basis for treating aggregate size as a targeted process variable for rational control strategies.

Dynamic flux balance modeling of microbial co-cultures for efficient batch fermentation of glucose and xylose mixtures

Sequential uptake of pentose and hexose sugars that compose lignocellulosic biomass limits the ability of pure microbial cultures to efficiently produce value-added bioproducts. In this work, we used dynamic flux balance modeling to examine the capability of mixed cultures of substrate-selective microbes to improve the utilization of glucose/xylose mixtures and to convert these mixed substrates into products. Co-culture simulations of Escherichia coli strains ALS1008 and ZSC113, engineered for glucose and xylose only uptake respectively, indicated that improvements in batch substrate consumption observed in previous experimental studies resulted primarily from an increase in ZSC113 xylose uptake relative to wild-type E. coli. The E. coli strain ZSC113 engineered for the elimination of glucose uptake was computationally co-cultured with wild-type Saccharomyces cerevisiae, which can only metabolize glucose, to determine if the co-culture was capable of enhanced ethanol production compared to pure cultures of wild-type E. coli and the S. cerevisiae strain RWB218 engineered for combined glucose and xylose uptake. Under the simplifying assumption that both microbes grow optimally under common environmental conditions, optimization of the strain inoculum and the aerobic to anaerobic switching time produced an almost twofold increase in ethanol productivity over the pure cultures. To examine the effect of reduced strain growth rates at non-optimal pH and temperature values, a break even analysis was performed to determine possible reductions in individual strain substrate uptake rates that resulted in the same predicted ethanol productivity as the best pure culture.

Characterization of aggregate size in Taxus suspension cell culture

Plant cells grow as aggregates in suspension culture, but little is known about the dynamics of aggregation, and no routine methodology exists to measure aggregate size. In this study, we evaluate several different methods to characterize aggregate size in Taxus suspension cultures, in which aggregate diameters range from 50 to 2,000 microm, including filtration and image analysis, and develop a novel method using a specially equipped Coulter counter system. We demonstrate the suitability of this technology to measure plant cell culture aggregates, and show that it can be reliably used to measure total biomass accumulation compared to standard methods such as dry weight. Furthermore, we demonstrate that all three methods can be used to measure an aggregate size distribution, but that the Coulter counter is more reliable and much faster, and also provides far better resolution. While absolute measurements of aggregate size differ based on the three evaluation techniques, we show that linear correlations are sufficient to account for these differences (R(2) > 0.99). We then demonstrate the utility of the novel Coulter counter methodology by monitoring the dynamics of a batch process and find that the mean aggregate size increases by 55% during the exponential growth phase, but decreases during stationary phase. The results indicate that the Coulter counter method can be routinely used for advanced process characterization, particularly to study the relationship between aggregate size and secondary metabolite production, as well as a source of reliable experimental data for modeling aggregation dynamics in plant cell culture.

Steady-state and dynamic flux balance analysis of ethanol production by Saccharomyces cerevisiae

Steady-state and dynamic flux balance analysis (DFBA) was used to investigate the effects of metabolic model complexity and parameters on ethanol production predictions for wild-type and engineered Saccharomyces cerevisiae. Three metabolic network models ranging from a single compartment representation of metabolism to a genome-scale reconstruction with seven compartments and detailed charge balancing were studied. Steady-state analysis showed that the models generated similar wild-type predictions for the biomass and ethanol yields, but for ten engineered strains the seven compartment model produced smaller ethanol yield enhancements. Simplification of the seven compartment model to two intracellular compartments produced increased ethanol yields, suggesting that reaction localisation had an impact on mutant phenotype predictions. Further analysis with the seven compartment model demonstrated that steady-state predictions can be sensitive to intracellular model parameters, with the biomass yield exhibiting high sensitivity to ATP utilisation parameters and the biomass composition. The incorporation of gene expression data through the zeroing of metabolic reactions associated with unexpressed genes was shown to produce negligible changes in steady-state predictions when the oxygen uptake rate was suitably constrained. Dynamic extensions of the single and seven compartment models were developed through the addition of glucose and oxygen uptake expressions and transient extracellular balances. While the dynamic models produced similar predictions of the optimal batch ethanol productivity for the wild type, the single compartment model produced significantly different predictions for four implementable gene insertions. A combined deletion/overexpression/insertion mutant with improved ethanol productivity capabilities was computationally identified by dynamically screening multiple combinations of the ten metabolic engineering strategies. The authors concluded that extensive compartmentalisation and detailed charge balancing can be important for reliably screening metabolic engineering strategies that rely on modification of the global redox balance and that DFBA offers the potential to identify novel mutants for enhanced metabolite production in batch and fed-batch cultures.

Small-world network models of intercellular coupling predict enhanced synchronization in the suprachiasmatic nucleus

The suprachiasmatic nucleus (SCN) of the hypothalamus is a multioscillator system that drives daily rhythms in mammalian behavior and physiology. Based on recent data implicating vasoactive intestinal polypeptide (VIP) as the key intercellular synchronizing agent, we developed a multicellular SCN model to investigate the effects of cellular heterogeneity and intercellular connectivity on circadian behavior. A 2-dimensional grid was populated with 400 model cells that were heterogeneous with respect to their uncoupled rhythmic behavior (intrinsic and damped pacemakers with a range of oscillation periods) and VIP release characteristics (VIP producers and nonproducers). We constructed small-world network architectures in which local connections between VIP producing cells and their 4 nearest neighbors were augmented with random connections, resulting in long-range coupling across the grid. With only 10% of the total possible connections, the small-world network model was able to produce similar phase synchronization indices as a mean-field model with VIP producing cells connected to all other cells. Partial removal of random connections decreased the synchrony among neurons, the amplitude of VIP and cAMP response element binding protein oscillations, the mean period of intrinsic periods across the population, and the percentage of oscillating cells. These results indicate that small-world connectivity provides the optimal compromise between the number of connections and control of circadian amplitude and synchrony. This model predicts that small decreases in long-range VIP connections in the SCN could have dramatic effects on period and amplitude of daily rhythms, features commonly described with aging.

Optimization of Fed-Batch Saccharomyces cerevisiae Fermentation Using Dynamic Flux Balance Models

We developed a dynamic flux balance model for fed-batch Saccharomyces cerevisiae fermentation that couples a detailed steady-state description of primary carbon metabolism with dynamic mass balances on key extracellular species. Model-based dynamic optimization is performed to determine fed-batch operating policies that maximize ethanol productivity and/or ethanol yield on glucose. The initial volume and glucose concentrations, the feed flow rate and dissolved oxygen concentration profiles, and the final batch time are treated as decision variables in the dynamic optimization problem. Optimal solutions are generated to analyze the tradeoff between maximal productivity and yield objectives. We find that for both cases the prediction of a microaerobic region is significant. The optimization results are sensitive to network model parameters for the growth associated maintenance and P/O ratio. The results of our computational study motivate continued development of dynamic flux balance models and further exploration of their application to productivity optimization in biochemical reactors.