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We extend a three-stage anaerobic digestion model by incorporating microbial mortality into the hydrolysis of particulate organic matter. The model describes hydrolysis, acidogenesis, and methanogenesis, each with distinct dilution and decay rates, and accounts for non-monotonic growth in order to capture substrate inhibition. Two hydrolysis mechanisms are considered: a first-order formulation and a biomass-dependent one. The latter distinguishes hydraulic washout from intrinsic mortality and leads to different persistence conditions. For both models, we establish well-posedness and prove the positivity and boundedness of solutions. We then characterize all equilibria and analyze their local stability with respect to key operating parameters. The inclusion of microbial mortality provides a more general and biologically relevant framework, thereby enriching the qualitative dynamics compared to the classical AM2 model.
To match the growing demand for bio-methane production, anaerobic digesters need to embrace the co-digestion of different feedstocks; in addition, to improve the techno-economic performance, an optimal and time-varying adaptation of the input diet is required. These operation modes constitute a very hard challenge for the limited instrumentation and control equipment typically installed aboard full-scale plants. A model-based predictive approach may be able to handle such control problem, but the identification of reliable predictive models is limited by the low information content typical of the data available from full-scale plants' operations, which entail high parametric uncertainty. In this work, the application of a tube-based robust nonlinear model predictive control (NMPC) is proposed to regulate bio-methane production over a period of diet change in time, while warranting safe operation and dealing with uncertainties. In view of its upcoming validation on a true small pilot-scale plant, the NMPC capabilities are assessed via numerical simulations designed to resemble as much as possible the experimental setup, along with some practical final considerations.
The Richards equation (RE) is widely used to model water flow in unsaturated soils, but its performance in persistently wet grassland systems remains uncertain. This is particularly relevant in Irish grasslands, where soils often remain close to saturation for extended periods and seasonal waterlogging is common. Here, we evaluate the RE against three soil moisture datasets from County Wexford, Ireland, spanning different locations, soil types, and observation periods. We show that the standard RE formulation systematically over-predicts soil moisture under prolonged near-saturated conditions. We find that this arises from the commonly used Feddes plant water uptake function, which suppresses water losses under anaerobic conditions, despite continued evaporation from near-saturated soils. To address this limitation, we introduce a simple modification that retains a small non-zero water loss rate in the anaerobic regime. The modified model produces substantially improved agreement with observations across all three datasets. These results provide a systematic evaluation of RE-based soil moisture modelling in Irish grasslands. More broadly, they identify an important limitation of co
The anaerobic co-digestion of slaughterhouse wastewater and food waste offers a sustainable approach to waste treatment and biogas production. However, limited literature was found on the study of ferric oxide as conductive material in co-digestion of the two substrates. This study evaluates the effect of ferric oxide on biogas yield, organic matter removal, and kinetics of anaerobic co-digestion. Five batch tests were performed: four with varying ferric oxide doses and one control. Results showed that ferric oxide significantly enhanced total solids (TS) and volatile solids (VS) reduction. The reactor with 0.5 g ferric oxide per 800 mL working volume achieved the highest TS and VS reduction, corresponding to the maximum methane yield of 9878.95 L methane per kg volatile solid. At this optimal dosage, biogas production increased by 81 percent compared to the control. However, further increases in ferric oxide above the optimal dosage concentration decreases biogas yield, indicating a threshold beyond which inhibitory effects occur. In addition, at this optimal dosage, reduction in BOD and COD was observed due to enhanced microbial activity. Furthermore, ferric oxide stabilizes anae
Fluorosurfactant-stabilized microdroplets hold significant promise for a wide range of applications, owing to their biological and chemical inertness. However, conventional synthetic routes for fluorosurfactants typically require multiple reaction steps and stringent conditions, such as high temperatures and anaerobic environments. This complexity poses a significant limitation to the development of fluorosurfactant synthesis and their subsequent applications in droplet-based systems. In this work, we present a robust two-step synthesis of fluorosurfactants with tunable functionalities. Microdroplets stabilized by these fluorosurfactants exhibit enhanced stability and biocompatibility. Notably, these fluorosurfactants facilitate the formation of nanodroplets that efficiently transport and concentrate fluorophores with high selectivity. Furthermore, we demonstrate that colloidal self-assemblies with tunable morphologies can be engineered by modulating interactions between the fluorosurfactants and colloidal particles. Our synthetic approach provides a strategy for the rapid production of functional fluorosurfactants under mild conditions, enabling droplet-based microfluidic techniqu
In many applications of biotechnology, measurements are available at different sampling rates, e.g., due to online sensors and offline lab analysis. Offline measurements typically involve time delays that may be unknown a priori due to the underlying laboratory procedures. This multirate (MR) setting poses a challenge to Kalman filtering, where conventionally measurement data is assumed to be available on an equidistant time grid and without delays. This tutorial paper derives the MR version of an extended Kalman filter (EKF) based on sample state augmentation, and applies it to the anaerobic digestion (AD) process in a simulative agricultural setting. The performance of the MR-EKF is investigated for various scenarios including varying delay lengths, measurement noise levels, plant-model mismatch (PMM), and initial state error. Provided with an adequate tuning, the MR-EKF can reliably estimate the process state and, thus, appropriately fuse the delayed offline measurements and smooth the noisy online measurements. Because of the sample state augmentation approach, the delay length of offline measurements does not critically effect the performance of the state estimation, provided
Anaerobic digestion (AD) offers a sustainable biotechnology to recover resources from carbon-rich wastewater, such as food-processing wastewater. Despite crude wastewater characterisation, the impact of detailed chemical fingerprinting on AD remains underexplored. This study investigated the influence of fermentation-wastewater composition and operational parameters on AD over time to identify critical factors influencing reactor biodiversity and performance. Eighteen reactors were operated under various operational conditions using mycoprotein fermentation wastewater. Detailed chemical analysis fingerprinted the molecules in the fermentation wastewater throughout AD including sugars, sugar alcohols and volatile fatty acids (VFAs). Sequencing revealed distinct microbiome profiles linked to temperature and reactor configuration, with mesophilic conditions supporting a more diverse and densely connected microbiome. Significant elevations in Methanomassiliicoccus were correlated to high butyric acid concentrations and decreased biogas production, further elucidating the role of this newly discovered methanogen. Dissimilarity analysis demonstrated the importance of individual molecules
The energy dissipated by a living organism is commonly identified with heat generation. However, as cells exchange metabolites with their environment they also dissipate energy in the form of chemical entropy. How dissipation is distributed between exchanges of heat and chemical entropy is largely unexplored. Here, we analyze an extensive experimental database recently created [1] to investigate how microbes partition dissipation between thermal and chemical entropy during growth. We find that aerobic respiration exchanges little chemical entropy and dissipation is primarily due to heat production, as commonly assumed. However, we also find several types of anaerobic metabolism that produce as much chemical entropy as heat. Counterintuitively, instances of anaerobic metabolisms such as acetotrophic methanogenesis and sulfur respiration are endothermic. We conclude that, because of their metabolic versatility, microbes are able to exploit all combinations of heat and chemical entropy exchanges that result in a net production of entropy.
Approximately 1.4 Ga after life first appeared, atmospheric oxygen suddenly jumped by more than an order of magnitude over a 20-50 Ma period. The contrast between these two timescales does not seem to be due to any sudden, large amplitude change in external forcing. However, it could be due to processes intrinsic to the geobiological system itself, namely, positive feedback between atmospheric oxygen and photosynthetic bacteria: More oxygen leads to more photosynthesis, which leads to more oxygen, and so on. Already-published feedbacks include buildup of an ozone shield and nutrient production by oxidative weathering. The feedback proposed here is the 15-fold greater efficiency of aerobic vs anaerobic respiration and the tight coupling of respiration and photosynthesis inside the cell. As in the climate system, feedback leads to tipping points, where a rapid, large amplitude change in the state of the system occurs. For the geobiological system, the GOE is the tipping point, and the long buildup before the GOE is the gradual oxidation of the crust and ocean, due either to burial of organic matter, oxidation of volcanic gases, or escape of hydrogen to space. The feedback hypothesis
Uncertainty quantification is critical for ensuring adequate predictive power of computational models used in biology. Focusing on two anaerobic digestion models, this article introduces a novel generalized Bayesian procedure, called VarBUQ, ensuring a correct tradeoff between flexibility and computational cost. A benchmark against three existing methods (Fisher's information, bootstrapping and Beale's criteria) was conducted using synthetic data. This Bayesian procedure offered a good compromise between fitting ability and confidence estimation, while the other methods proved to be repeatedly overconfident. The method's performances notably benefitted from inductive bias brought by the prior distribution, although it requires careful construction. This article advocates for more systematic consideration of uncertainty for anaerobic digestion models and showcases a new, computationally efficient Bayesian method. To facilitate future implementations, a Python package called 'aduq' is made available.
Evolutionary theorizing resembles building an aircraft while also piloting it; new results change the scaffold for older ideas, requiring revised strategy to remain airborne. A calculated kinetic pathway exists that, under explicit quantitative assumptions, delivers the SGC (Standard Genetic Code). The pathway and evidence for it is summarized below, striving for a clearer, more complete account than was possible during its construction. Beginning with experimental amino acid-RNA interactions, code assignments are fused, codes divide and an early coding crescendo is tested for homogeneous assignments, which are then selected for independent survival in a near-empty biotic world. During escape from the site of origin and diaspora, a near-complete SGC becomes dominant by supporting proficient division. Crescendo, escape and diaspora together comprise a near-ideal least selection for a Standard Genetic Code that specifically served LUCA, likely a free-living anaerobic thermophilic microbe. Selection during diaspora conceivably made persistence across gigayears feasible.
The escalating impacts of climate change and the increasing demand for sustainable development and natural resource management necessitate innovative technological solutions. Quantum computing (QC) has emerged as a promising tool with the potential to revolutionize these critical areas. This review explores the application of quantum machine learning and optimization techniques for climate change prediction and enhancing sustainable development. Traditional computational methods often fall short in handling the scale and complexity of climate models and natural resource management. Quantum advancements, however, offer significant improvements in computational efficiency and problem-solving capabilities. By synthesizing the latest research and developments, this paper highlights how QC and quantum machine learning can optimize multi-infrastructure systems towards climate neutrality. The paper also evaluates the performance of current quantum algorithms and hardware in practical applications and presents realistic cases, i.e., waste-to-energy in anaerobic digestion, disaster prevention in flooding prediction, and new material development for carbon capture. The integration of these q
In this study, the impact of turbulent diffusion on mixing of biochemical reaction models is explored by implementing and validating different models. An original codebase called CHAD (Coupled Hydrodynamics and Anaerobic Digestion) is extended to incorporate turbulent diffusion and validate it against results from OpenFOAM with 2D Rayleigh-Taylor Instability and lid-driven cavity simulations. The models are then tested for the applications with Anaerobic Digestion - a widely used wastewater treatment method. The findings demonstrate that the implemented models accurately capture turbulent diffusion when provided with an accurate flow field. Specifically, a minor effect of chemical turbulent diffusion on biochemical reactions within the anaerobic digestion tank is observed, while thermal turbulent diffusion significantly influences mixing. By successfully implementing turbulent diffusion models in CHAD, its capabilities for more accurate anaerobic digestion simulations are enhanced, aiding in optimizing the design and operation of anaerobic digestion reactors in real-world wastewater treatment applications.
Photosynthetic microbes have evolved and successfully adapted to the ever-changing environmental conditions in complex microhabitats throughout almost all ecosystems on Earth. In the absence of light, they can sustain their biological functionalities through aerobic respiration, and even in anoxic conditions through anaerobic metabolic activity. For a suspension of photosynthetic microbes in an anaerobic environment, individual cellular motility is directly controlled by its photosynthetic activity, i.e. the intensity of the incident light absorbed by chlorophyll. The effects of the metabolic activity on the collective motility on the population level, however, remain elusive so far. Here, we demonstrate that at high light intensities, a suspension of photosynthetically active microbes exhibits a stable reverse sedimentation profile of the cell density due to the microbes' natural bias to move against gravity. With decreasing photosynthetic activity, and therefore suppressed individual motility, the living suspension becomes unstable giving rise to coherent bioconvective flows. The collective motility is fully reversible and manifests as regular, three-dimensional plume structures,
Iron (Fe) reduction is one of Earth's most ancient microbial metabolisms, but after atmosphere-ocean oxygenation, this anaerobic process was relegated to niche anoxic environments below the water and soil surface. However, new technologies to monitor redox processes at the microscale relevant to microbial cells have recently revealed that the oxygen (O2) concentrations controlling the distribution of aerobic and anaerobic metabolisms are more heterogeneous than previously believed. To explore how O2 levels regulate microbial Fe reduction, we cultivated a facultative Fe-reducing bacterium using a cutting-edge microfluidic reactor integrated with transparent planar O2 sensors. Contrary to expectations, microbial growth induced Fe(III)-oxide (ferrihydrite) reduction under fully oxygenated conditions without forming O2-depleted microsites. Batch incubations highlighted the importance of the process at a larger scale, fundamentally changing our understanding of Fe cycling from the conceptualization of metal and nutrient mobility in the subsurface to our interpretation of Fe mineralogy in the rock record.
In this paper, we study a well known two-step anaerobic digestion model in a configuration of two chemostats in series. This model is an eight-dimensional system of ordinary differential equations. Since the reaction system has a cascade structure, we show that the eight-order model can be reduced to a four-dimensional one. Using general growth rates, we provide an in-depth mathematical analysis of the asymptotic behavior of the system. First, we determine all the steady states of the model where there can be more than fifteen equilibria with a non-monotonic growth rate. Then, the necessary and sufficient conditions of existence and local stability of all steady states are established according to the operating parameters: the dilution rate, the input concentrations of the two nutrients, and the distribution of the total process volume considered. The operating diagrams are then analyzed theoretically to describe the asymptotic behavior of the process according to the four control parameters. There can be seventy regions with rich behavior where the system may exhibit bistability or tristability with the coexistence of both microbial species in the two bioreactors.
Standard methods for modeling anaerobic digestion processes assume homogeneous conditions inside the tank and thus suffer from the negligence of hydrodynamics. In this work, we present the software toolbox Coupled Hydrodynamics and Anaerobic Digestion (CHAD), a novel parallelized solver that is capable of utilizing CFD results as the basis for Anaerobic digestion model No.1 (ADMno1) simulations. CHAD uses a particle-based Lagrangian CFD solver i.e., DualSPHysics (DSPH) as input and provides for a parallelized, C++ code implementation of the standard ADMno1. This paper demonstrates a conceptual and numerical verification of the toolbox and outlines the future pathway to enhance the approach.
Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable process monitoring to guarantee stable operating conditions at all times. Unscented Kalman filters (UKF) are an established tool for nonlinear state estimation, and there exist numerous variants of UKF implementations, treating state constraints, improvements of numerical performance and different noise cases. So far, however, a unified comparison of proposed methods emphasizing the algorithmic details is lacking. The present study thus examines multiple unconstrained and constrained UKF variants, addresses aspects crucial for direct implementation and applies them to a simplified AD model. The constrained UKF considering additive noise delivered the most accurate state estimations. The long run time of the underlying optimization could be vastly reduced through pre-calculated gradients and Hessian of the associated cost function, as well as by reformulation of the cost function as a quadratic program. However, unconstrained UKF variants showed lower run times at competitive estimation accuracy. This study provides useful advice to practitioners working with nonlinear Kalman filters by pa
Dynamic operation of anaerobic digestion plants requires advanced process monitoring and control. Different simplifications of the Anaerobic Digestion Model No. 1 (ADM1) have been proposed recently, which appear promising for model-based process automation and state estimation. As a fundamental requirement, observability and identifiability of these models are analyzed in this work, which was pursued through algebraic and geometric analysis. Manual algebraic assessment was successfull for small models such as the ADM1-R4 and simplified versions of the ADM1-R3, which were derived in this context. However, for larger model classes the algebraic approach showed to be insufficient. By contrast, the geometric approach, implemented in the STRIKE_GOLDD toolbox, allowed to show observability for more complex models (including ADM1-R4 and ADM1-R3), employing two independent algorithms. The present study lays the groundwork for state observer design, parameter estimation and advanced control resting upon ADM1-based models.
Probabilistic Graphical Models (PGMs) are generative models of complex systems. They rely on conditional independence assumptions between variables to learn sparse representations which can be visualized in a form of a graph. Such models are used for domain exploration and structure discovery in poorly understood domains. This work introduces a novel technique to perform sparse graph recovery by optimizing deep unrolled networks. Assuming that the input data $X\in\mathbb{R}^{M\times D}$ comes from an underlying multivariate Gaussian distribution, we apply a deep model on $X$ that outputs the precision matrix $\hatΘ$, which can also be interpreted as the adjacency matrix. Our model, uGLAD, builds upon and extends the state-of-the-art model GLAD to the unsupervised setting. The key benefits of our model are (1) uGLAD automatically optimizes sparsity-related regularization parameters leading to better performance than existing algorithms. (2) We introduce multi-task learning based `consensus' strategy for robust handling of missing data in an unsupervised setting. We evaluate model results on synthetic Gaussian data, non-Gaussian data generated from Gene Regulatory Networks, and prese