Model-based process optimization of black soldier fly egg production.

Black soldier fly (BSF) larvae (Hermetia illucens) serve as a valuable protein source for animal feed. Limiting factors in the industrial rearing of BSF are the reproduction process and egg output. Studies indicate the potential to shorten preoviposition time and increase egg output through better utilization of environmental variables, such as temperature and light, in industrial settings. Excessive stimulation, however, can lead to stress, elevated production costs, and reduced egg numbers, emphasizing the need for a delicate balance. This study addresses these challenges by investigating controlled manipulation of environmental variables to stimulate mating and enhance egg production, thereby developing a comprehensive model encompassing the adult fly life cycle, mating, and egg production. Model parameters were fitted using literature data, and the model's plausibility was tested through simulations. Using the model and optimal control methods, the calculated dynamic trajectories for environmental variables when compared to the standard approach in a constant environment demonstrated higher output and shorter production cycles at reasonable energy costs. Applications for this model-based optimization are demonstrated for various scenarios, highlighting the practical utility and versatility of the developed model. This study contributes valuable insights for improving rearing practices of BSF through environmental stimulation, offering potential advancements in egg production efficiency and overall sustainability.

Epidemic management with admissible and robust invariant sets.

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing, quarantining and vaccination. We describe the admissible and maximal robust positively invariant (MRPI) sets of these two models via the theory of barriers. We show how the sets may be used in the management of epidemics, for both perfect and imperfect/uncertain models, detailing how intervention strategies may be specified such that the hard infection cap is never breached, regardless of the basic reproduction number. The results are clarified with detailed examples.

A comprehensive dynamic growth and development model of Hermetia illucens larvae.

Larvae of Hermetia illucens, also commonly known as black soldier fly (BSF) have gained significant importance in the feed industry, primarily used as feed for aquaculture and other livestock farming. Mathematical models such as the Von Bertalanffy growth model and dynamic energy budget models are available for modelling the growth of various organisms but have their demerits for their application to the growth and development of BSF. Also, such dynamic models were not yet applied to the growth of the BSF larvae despite models proven to be useful for automation of industrial production process (e.g. feeding, heating/cooling, ventilation, harvesting, etc.). This work primarily focuses on developing a model based on the principles of the afore mentioned models from literature that can provide accurate mathematical description of the dry mass changes throughout the life cycle and the transition of development phases of the larvae. To further improve the accuracy of these models, various factors affecting the growth and development such as temperature, feed quality, feeding rate, moisture content in feed, and airflow rate are developed and integrated into the dynamic growth model. An extensive set of data was aggregated from various literature and used for the model development, parameter estimation and validation. Models describing the environmental factors were individually validated based on the data sets collected. In addition, the dynamic growth model was also validated for dry mass evolution and development stage transition of larvae reared on different substrate feeding rates. The developed models with the estimated parameters performed well, highlighting their potential application in decision-support systems and automation for large scale production.

Response to IL-6 trans- and IL-6 classic signalling is determined by the ratio of the IL-6 receptor α to gp130 expression: fusing experimental insights and dynamic modelling.

BACKGROUND: Interleukin-6 is a pleiotropic cytokine with high clinical relevance and an important mediator of cellular communication, orchestrating both pro- and anti-inflammatory processes. Interleukin-6-induced signalling is initiated by binding of IL-6 to the IL-6 receptor α and subsequent binding to the signal transducing receptor subunit gp130. This active receptor complex initiates signalling through the Janus kinase/signal transducer and activator of transcription pathway. Of note, IL-6 receptor α exists in a soluble and a transmembrane form. Binding of IL-6 to membrane-bound IL-6 receptor α induces anti-inflammatory classic signalling, whereas binding of IL-6 to soluble IL-6 receptor α induces pro-inflammatory trans-signalling. Trans-signalling has been described to be markedly stronger than classic signalling. Understanding the molecular mechanisms that drive differences between trans- and classic signalling is important for the design of trans-signalling-specific therapies. These differences will be addressed here using a combination of dynamic mathematical modelling and molecular biology. METHODS: We apply an iterative systems biology approach using set-based modelling and validation approaches combined with quantitative biochemical and cell biological analyses. RESULTS: The combination of experimental analyses and dynamic modelling allows to relate the observed differences between IL-6-induced trans- and classic signalling to cell-type specific differences in the expression and ratios of the individual subunits of the IL-6 receptor complex. Canonical intracellular Jak/STAT signalling is indifferent in IL-6-induced trans- and classic signalling. CONCLUSION: This study contributes to the understanding of molecular mechanisms of IL-6 signal transduction and underlines the power of combined dynamical modelling, model-based validation and biological experiments. The opposing pro- and anti-inflammatory responses initiated by IL-6 trans- and classic signalling depend solely on the expression ratios of the subunits of the entire receptor complex. By pointing out the importance of the receptor expression ratio for the strength of IL-6 signalling this study lays a foundation for future precision medicine approaches that aim to selectively block pro-inflammatory trans-signalling. Furthermore, the derived models can be used for future therapy design.

Comparison of Different Calibration Methods in a Non-invasive ICP Assessment Model.

OBJECTIVE: Previously we described the method of continuous intracranial pressure (ICP) estimation using arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). The model was constructed using reference patient data. Various individual calibration strategies were used in the current attempt to improve the accuracy of this non-invasive ICP (nICP) assessment tool. MATERIALS AND METHODS: Forty-one patients (mean, 52 years; range, 18-77 years) with severe brain injuries were studied. CBFV in the middle cerebral artery (MCA), ABP and invasively assessed ICP were simultaneously recorded for 1 h. Recording was repeated at days 2, 4 and 7. In the first recording, invasively assessed ICP was recorded to calibrate the nICP procedure by means of either a constant shift of nICP (snICP), a constant shift of nICP/ABP ratio (anICP) or by including this recording for a model reconstruction (cnICP). At follow-up days, the calibrated nICP procedures were applied and the results compared to the original nICP. RESULTS: In 76 follow-up recordings, the mean differences (Bias), the SD and the mean absolute differences (ΔICP) between ICP and the nICP methods were (in mmHg): nICP, -5.6 ± 5.72, 6.5; snICP, +0.7 ± 6.98, 5.5, n.s.; anICP, +1.0 ± 7.22, 5.6, n.s.; cnICP, -3.4 ± 5.68, 5.4, p < 0.001. In patients with craniotomy (n = 19), the nICP was generally higher than ICP. This overestimation could be reduced by cnICP calibration, but not completely avoided. DISCUSSION: Constant shift calibrations (snICP, anICP) decrease the Bias to ICP, but increase SD and, therefore, increase the 95% confidence interval (CI = 2 × SD). This calibration method cannot be recommended. Compared to nICP, the cnICP method reduced the Bias and slightly reduced SD, and showed significantly decreased ΔICP. Compared to snICP and anICP, the Bias was higher. This effect was probably caused by the patients with craniotomy. CONCLUSION: The cnICP calibration method using initial recordings for model reconstruction showed the best results.

Identification of growth phases and influencing factors in cultivations with AGE1.HN cells using set-based methods.

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.

Photonic crystal light collectors in fish retina improve vision in turbid water.

Despite their diversity, vertebrate retinae are specialized to maximize either photon catch or visual acuity. Here, we describe a functional type that is optimized for neither purpose. In the retina of the elephantnose fish (Gnathonemus petersii), cone photoreceptors are grouped together within reflecting, photonic crystal-lined cups acting as macroreceptors, but rod photoreceptors are positioned behind these reflectors. This unusual arrangement matches rod and cone sensitivity for detecting color-mixed stimuli, whereas the photoreceptor grouping renders the fish insensitive to spatial noise; together, this enables more reliable flight reactions in the fish's dim and turbid habitat as compared with fish lacking this retinal specialization.

ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative-quantitative modeling.

SUMMARY: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if-then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLab(TM)-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. AVAILABILITY: ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/

A predictive computational model of the kinetic mechanism of stimulus-induced transducer methylation and feedback regulation through CheY in archaeal phototaxis and chemotaxis.

BACKGROUND: Photo- and chemotaxis of the archaeon Halobacterium salinarum is based on the control of flagellar motor switching through stimulus-specific methyl-accepting transducer proteins that relay the sensory input signal to a two-component system. Certain members of the transducer family function as receptor proteins by directly sensing specific chemical or physical stimuli. Others interact with specific receptor proteins like the phototaxis photoreceptors sensory rhodopsin I and II, or require specific binding proteins as for example some chemotaxis transducers. Receptor activation by light or a change in receptor occupancy by chemical stimuli results in reversible methylation of glutamate residues of the transducer proteins. Both, methylation and demethylation reactions are involved in sensory adaptation and are modulated by the response regulator CheY. RESULTS: By mathematical modeling we infer the kinetic mechanisms of stimulus-induced transducer methylation and adaptation. The model (deterministic and in the form of ordinary differential equations) correctly predicts experimentally observed transducer demethylation (as detected by released methanol) in response to attractant and repellent stimuli of wildtype cells, a cheY deletion mutant, and a mutant in which the stimulated transducer species is methylation-deficient. CONCLUSIONS: We provide a kinetic model for signal processing in photo- and chemotaxis in the archaeon H. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a CheY-dependent feedback on transducer demethylation.

Identification of Archaea-specific chemotaxis proteins which interact with the flagellar apparatus.

BACKGROUND: Archaea share with bacteria the ability to bias their movement towards more favorable locations, a process known as taxis. Two molecular systems drive this process: the motility apparatus and the chemotaxis signal transduction system. The first consists of the flagellum, the flagellar motor, and its switch, which allows cells to reverse the rotation of flagella. The second targets the flagellar motor switch in order to modulate the switching frequency in response to external stimuli. While the signal transduction system is conserved throughout archaea and bacteria, the archaeal flagellar apparatus is different from the bacterial one. The proteins constituting the flagellar motor and its switch in archaea have not yet been identified, and the connection between the bacterial-like chemotaxis signal transduction system and the archaeal motility apparatus is unknown. RESULTS: Using protein-protein interaction analysis, we have identified three proteins in Halobacterium salinarum that interact with the chemotaxis (Che) proteins CheY, CheD, and CheC2, as well as the flagella accessory (Fla) proteins FlaCE and FlaD. Two of the proteins belong to the protein family DUF439, the third is a HEAT_PBS family protein. In-frame deletion strains for all three proteins were generated and analyzed as follows: a) photophobic responses were measured by a computer-based cell tracking system b) flagellar rotational bias was determined by dark-field microscopy, and c) chemotactic behavior was analyzed by a swarm plate assay. Strains deleted for the HEAT_PBS protein or one of the DUF439 proteins proved unable to switch the direction of flagellar rotation. In these mutants, flagella rotate only clockwise, resulting in exclusively forward swimming cells that are unable to respond to tactic signals. Deletion of the second DUF439 protein had only minimal effects. HEAT_PBS proteins could be identified in the chemotaxis gene regions of all motile haloarchaea sequenced so far, but not in those of other archaeal species. Genes coding for DUF439 proteins, however, were found to be integral parts of chemotaxis gene regions across the archaeal domain, and they were not detected in other genomic context. CONCLUSION: Altogether, these results demonstrate that, in the archaeal domain, previously unrecognized archaea-specific Che proteins are essential for relaying taxis signaling to the flagellar apparatus.

Quantitative analysis of signal transduction in motile and phototactic cells by computerized light stimulation and model based tracking.

To investigate the responses of Halobacterium salinarum to stimulation with light (phototaxis and photokinesis), we designed an experimental setup consisting of optical devices for automatic video image acquisition and computer-controlled light stimulation, and developed algorithms to analyze physiological responses of the cells. Cells are categorized as motile and nonmotile by a classification scheme based on the square displacement of cell positions. Computerized tracking based on a dynamic model of the stochastic cell movement and a Kalman filter-based algorithm allows smoothed estimates of the cell tracks and the detection of physiological responses to complex stimulus patterns. The setup and algorithms were calibrated which allows quantitative measurements and systematic analysis of cellular sensing and response. Overall, the setup is flexible, extensible, and consists mainly of commercially available products. This facilitates modifications of the setup and algorithms for physiological studies of the motility of cells or microorganisms.

Flagellar rotation in the archaeon Halobacterium salinarum depends on ATP.

Halobacterium salinarum swims with the help of a polarly inserted flagellar bundle. In energized cells, the flagellar motors rotate continuously, occasionally switching the rotational sense. Starving cells become immotile as the energy level drops. Presumably, there is a threshold of energy required for flagellar rotation. When starved, immotile cells are energized by exposure to light, the speed of flagellar rotation increases gradually to its steady state over several minutes. Since the light-driven proton pump bacteriorhodopsin energizes the cell membrane to the maximal level within a fraction of a second, the delay in reaching the maximal swimming speed suggests that the halobacterial flagellar motor may not be driven directly by proton motive force. Swimming cells, which obtain their energy exclusively through light-driven proton pumping, become immotile within 20 min when treated with N,N'-dicyclohexylcarbodiimide (DCCD), an inhibitor of the proton translocating ATP synthase. However, flagellar motility in DCCD-treated cells can be restored by the addition of L-arginine, which serves as a fermentative energy source and restores the cytoplasmic ATP level in the presence of DCCD. This suggests that flagellar motor rotation depends on ATP, and this is confirmed by the observation that motility is increased strongly by L-arginine at zero proton motive force levels. The flagellar motor may be driven either by ATP directly or by an ATP-generated ion gradient that is not coupled directly to the proton gradient or the proton motive force of the cell.