Model Predictive Control With Guaranteed Feasibility of Inequality Path Constraints.

This article concerns nonlinear model predictive control (MPC) with guaranteed feasibility of inequality path constraints (PCs). For MPC with PCs, the existing methods, such as direct multiple shooting, cannot guarantee feasibility of PCs because the PCs are enforced at finitely many time points only. Therefore, this article presents a novel MPC framework that is capable of not only achieving stability control but also guaranteeing feasibility of PCs during the rolling optimization stages of MPC. Under the above MPC framework, an algorithm is first proposed by applying the semi-infinite programming technique to the rolling optimization of MPC. However, it takes heavy computational time to achieve guaranteed feasibility of PCs. Therefore, to guarantee feasibility of PCs meanwhile effectively reducing the computation burden of the closed-loop system, an event-triggered sampling mechanism is constructed in the above path-constrained MPC algorithm. Moreover, sufficient conditions are given for asymptotic convergence of the closed-loop systems. Finally, the effectiveness of the proposed results is illustrated via a cart-damper-spring system.

Electrostatic potentials of atomic nanostructures at metal surfaces quantified by scanning quantum dot microscopy.

The discrete and charge-separated nature of matter - electrons and nuclei - results in local electrostatic fields that are ubiquitous in nanoscale structures and relevant in catalysis, nanoelectronics and quantum nanoscience. Surface-averaging techniques provide only limited experimental access to these potentials, which are determined by the shape, material, and environment of the nanostructure. Here, we image the potential over adatoms, chains, and clusters of Ag and Au atoms assembled on Ag(111) and quantify their surface dipole moments. By focusing on the total charge density, these data establish a benchmark for theory. Our density functional theory calculations show a very good agreement with experiment and allow a deeper analysis of the dipole formation mechanisms, their dependence on fundamental atomic properties and on the shape of the nanostructures. We formulate an intuitive picture of the basic mechanisms behind dipole formation, allowing better design choices for future nanoscale systems such as single-atom catalysts.

Toward a modeling, optimization, and predictive control framework for fed-batch metabolic cybergenetics.

Biotechnology offers many opportunities for the sustainable manufacturing of valuable products. The toolbox to optimize bioprocesses includes extracellular process elements such as the bioreactor design and mode of operation, medium formulation, culture conditions, feeding rates, and so on. However, these elements are frequently insufficient for achieving optimal process performance or precise product composition. One can use metabolic and genetic engineering methods for optimization at the intracellular level. Nevertheless, those are often of static nature, failing when applied to dynamic processes or if disturbances occur. Furthermore, many bioprocesses are optimized empirically and implemented with little-to-no feedback control to counteract disturbances. The concept of cybergenetics has opened new possibilities to optimize bioprocesses by enabling online modulation of the gene expression of metabolism-relevant proteins via external inputs (e.g., light intensity in optogenetics). Here, we fuse cybergenetics with model-based optimization and predictive control for optimizing dynamic bioprocesses. To do so, we propose to use dynamic constraint-based models that integrate the dynamics of metabolic reactions, resource allocation, and inducible gene expression. We formulate a model-based optimal control problem to find the optimal process inputs. Furthermore, we propose using model predictive control to address uncertainties via online feedback. We focus on fed-batch processes, where the substrate feeding rate is an additional optimization variable. As a simulation example, we show the optogenetic control of the ATPase enzyme complex for dynamic modulation of enforced ATP wasting to adjust product yield and productivity.

Concept for the Real-Time Monitoring of Molecular Configurations during Manipulation with a Scanning Probe Microscope.

A bold vision in nanofabrication is the assembly of functional molecular structures using a scanning probe microscope (SPM). This approach requires continuous monitoring of the molecular configuration during manipulation. Until now, this has been impossible because the SPM tip cannot simultaneously act as an actuator and an imaging probe. Here, we implement configuration monitoring using experimental data other than images collected during the manipulation process. We model the manipulation as a partially observable Markov decision process (POMDP) and approximate the actual configuration in real time using a particle filter. To achieve this, the models underlying the POMDP are precomputed and organized in the form of a finite-state automaton, allowing the use of complex atomistic simulations. We exemplify the configuration monitoring process and reveal structural motifs behind measured force gradients. The proposed methodology marks an important step toward the piece-by-piece creation of supramolecular structures in a robotic and possibly automated manner.

Fast, inexpensive, and reliable HPLC method to determine monomer fractions in poly(3-hydroxybutyrate-co-3-hydroxyvalerate).

The determination of the monomer fractions in polyhydroxyalkanoates is of great importance for research on microbial-produced plastic material. The development of new process designs, the validation of mathematical models, and intelligent control strategies for production depend enormously on the correctness of the analyzed monomer fractions. Most of the available detection methods focus on the determination of the monomer fractions of the homopolymer poly(3-hydroxybutyrate). Only a few can analyze the monomer content in copolymers such as poly(3-hydroxybutyrate-co-3-hydroxyvalerate), which usually require expensive measuring devices, a high preparation time or the use of environmentally harmful halogenated solvents such as chloroform or dichloromethane. This work presents a fast, simple, and inexpensive method for the analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) with high-performance liquid chromatography. Samples from a bioreactor experiment for the production of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) with Cupriavidus necator H16 were examined regarding their monomer content using the new method and gas chromatography analysis, one of the most frequently used methods in literature. The results from our new method were validated using gas chromatography measurements and show excellent agreement.Key points∙ The presented HPLC method is an inexpensive, fast and environmentally friendly alternative to existing methods for quantification of monomeric composition of PHBV.∙ Validation with state of the art GC measurement exhibits excellent agreement over a broad range of PHBV monomer fractions.

Quantitative imaging of electric surface potentials with single-atom sensitivity.

Because materials consist of positive nuclei and negative electrons, electric potentials are omnipresent at the atomic scale. However, due to the long range of the Coulomb interaction, large-scale structures completely outshine small ones. This makes the isolation and quantification of the electric potentials that originate from nanoscale objects such as atoms or molecules very challenging. Here we report a non-contact scanning probe technique that addresses this challenge. It exploits a quantum dot sensor and the joint electrostatic screening by tip and surface, thus enabling quantitative surface potential imaging across all relevant length scales down to single atoms. We apply the technique to the characterization of a nanostructured surface, thereby extracting workfunction changes and dipole moments for important reference systems. This authenticates the method as a versatile tool to study the building blocks of materials and devices down to the atomic scale.

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.

Mathematical 3D modelling and sensitivity analysis of multipolar radiofrequency ablation in the spine.

Radiofrequency ablation is a valuable tool in the treatment of many diseases, especially cancer. However, controlled heating up to apoptosis of the desired target tissue in complex situations, e.g. in the spine, is challenging and requires experienced interventionalists. For such challenging situations a mathematical model of radiofrequency ablation allows to understand, improve and optimise the outcome of the medical therapy. The main contribution of this work is the derivation of a tailored, yet expandable mathematical model, for the simulation, analysis, planning and control of radiofrequency ablation in complex situations. The dynamic model consists of partial differential equations that describe the potential and temperature distribution during intervention. To account for multipolar operation, time-dependent boundary conditions are introduced. Spatially distributed parameters, like tissue conductivity and blood perfusion, allow to describe the complex 3D environment representing diverse involved tissue types in the spine. To identify the key parameters affecting the prediction quality of the model, the influence of the parameters on the temperature distribution is investigated via a sensitivity analysis. Simulations underpin the quality of the derived model and the analysis approach. The proposed modelling and analysis schemes set the basis for intervention planning, state- and parameter estimation, and control.

Activation of D2 autoreceptors alters cocaine-induced locomotion and slows down local field oscillations in the rat ventral tegmental area.

Psychoactive substances affecting the dopaminergic system induce locomotor activation and, in high doses, stereotypies. Network mechanisms underlying the shift from an active goal-directed behavior to a "seemingly purposeless" stereotypic locomotion remain unclear. In the present study we sought to determine the relationships between the behavioral effects of dopaminergic drugs and their effects on local field potentials (LFPs), which were telemetrically recorded within the ventral tegmental area (VTA) of freely moving rats. We used the D2/D3 agonist quinpirole in a low, autoreceptor-selective (0.1 mg/kg, i.p.) and in a high (0.5 mg/kg, i.p.) dose, and a moderate dose of cocaine (10 mg/kg, i.p.). In the control group, power spectrum analysis revealed a prominent peak of LFP power in the theta frequency range during active exploration. Cocaine alone stimulated locomotion, but had no significant effect on the peak of the LFP power. In contrast, co-administration of low dose quinpirole with cocaine markedly altered the pattern of locomotion, from goal-directed exploratory behavior to recurrent motion resembling locomotor stereotypy. This behavioral effect was accompanied by a shift of the dominant theta power toward a significantly lower (by ∼15%) frequency. High dose quinpirole also provoked an increased locomotor activity with signs of behavioral stereotypies, and also induced a shift of the dominant oscillation frequency toward the lower range. These results demonstrate a correlation between the LFP oscillation frequency within the VTA and a qualitative aspect of locomotor behavior, perhaps due to a variable level of coherence of this region with its input or output areas.

Model-based derivation, analysis and control of unstable microaerobic steady-states--considering Rhodospirillum rubrum as an example.

Microaerobic (oxygen-limited) conditions are critical for inducing many important microbial processes in industrial or environmental applications. At very low oxygen concentrations, however, the process performance often suffers from technical limitations. Available dissolved oxygen measurement techniques are not sensitive enough and thus control techniques, that can reliable handle these conditions, are lacking. Recently, we proposed a microaerobic process control strategy, which overcomes these restrictions and allows to assess different degrees of oxygen limitation in bioreactor batch cultivations. Here, we focus on the design of a control strategy for the automation of oxygen-limited continuous cultures using the microaerobic formation of photosynthetic membranes (PM) in Rhodospirillum rubrum as model phenomenon. We draw upon R. rubrum since the considered phenomenon depends on the optimal availability of mixed-carbon sources, hence on boundary conditions which make the process performance challenging. Empirically assessing these specific microaerobic conditions is scarcely practicable as such a process reacts highly sensitive to changes in the substrate composition and the oxygen availability in the culture broth. Therefore, we propose a model-based process control strategy which allows to stabilize steady-states of cultures grown under these conditions. As designing the appropriate strategy requires a detailed knowledge of the system behavior, we begin by deriving and validating an unstructured process model. This model is used to optimize the experimental conditions, and identify properties of the system which are critical for process performance. The derived model facilitates the good process performance via the proposed optimal control strategy. In summary the presented model-based control strategy allows to access and maintain microaerobic steady-states of interest and to precisely and efficiently transfer the culture from one stable microaerobic steady-state into another. Therefore, the presented approach is a valuable tool to study regulatory mechanisms of microaerobic phenomena in response to oxygen limitation alone. Biotechnol. Bioeng. 2014;111: 734-747. © 2013 Wiley Periodicals, Inc.

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.

Integrating cellular metabolism into a multiscale whole-body model.

Cellular metabolism continuously processes an enormous range of external compounds into endogenous metabolites and is as such a key element in human physiology. The multifaceted physiological role of the metabolic network fulfilling the catalytic conversions can only be fully understood from a whole-body perspective where the causal interplay of the metabolic states of individual cells, the surrounding tissue and the whole organism are simultaneously considered. We here present an approach relying on dynamic flux balance analysis that allows the integration of metabolic networks at the cellular scale into standardized physiologically-based pharmacokinetic models at the whole-body level. To evaluate our approach we integrated a genome-scale network reconstruction of a human hepatocyte into the liver tissue of a physiologically-based pharmacokinetic model of a human adult. The resulting multiscale model was used to investigate hyperuricemia therapy, ammonia detoxification and paracetamol-induced toxication at a systems level. The specific models simultaneously integrate multiple layers of biological organization and offer mechanistic insights into pathology and medication. The approach presented may in future support a mechanistic understanding in diagnostics and drug development.

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/

Heterogeneity reduces sensitivity of cell death for TNF-stimuli.

BACKGROUND: Apoptosis is a form of programmed cell death essential for the maintenance of homeostasis and the removal of potentially damaged cells in multicellular organisms. By binding its cognate membrane receptor, TNF receptor type 1 (TNF-R1), the proinflammatory cytokine Tumor Necrosis Factor (TNF) activates pro-apoptotic signaling via caspase activation, but at the same time also stimulates nuclear factor κB (NF-κB)-mediated survival pathways. Differential dose-response relationships of these two major TNF signaling pathways have been described experimentally and using mathematical modeling. However, the quantitative analysis of the complex interplay between pro- and anti-apoptotic signaling pathways is an open question as it is challenging for several reasons: the overall signaling network is complex, various time scales are present, and cells respond quantitatively and qualitatively in a heterogeneous manner. RESULTS: This study analyzes the complex interplay of the crosstalk of TNF-R1 induced pro- and anti-apoptotic signaling pathways based on an experimentally validated mathematical model. The mathematical model describes the temporal responses on both the single cell level as well as the level of a heterogeneous cell population, as observed in the respective quantitative experiments using TNF-R1 stimuli of different strengths and durations. Global sensitivity of the heterogeneous population was quantified by measuring the average gradient of time of death versus each population parameter. This global sensitivity analysis uncovers the concentrations of Caspase-8 and Caspase-3, and their respective inhibitors BAR and XIAP, as key elements for deciding the cell's fate. A simulated knockout of the NF-κB-mediated anti-apoptotic signaling reveals the importance of this pathway for delaying the time of death, reducing the death rate in the case of pulse stimulation and significantly increasing cell-to-cell variability. CONCLUSIONS: Cell ensemble modeling of a heterogeneous cell population including a global sensitivity analysis presented here allowed us to illuminate the role of the different elements and parameters on apoptotic signaling. The receptors serve to transmit the external stimulus; procaspases and their inhibitors control the switching from life to death, while NF-κB enhances the heterogeneity of the cell population. The global sensitivity analysis of the cell population model further revealed an unexpected impact of heterogeneity, i.e. the reduction of parametric sensitivity.

Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks.

BACKGROUND: Mathematical modeling and analysis have become, for the study of biological and cellular processes, an important complement to experimental research. However, the structural and quantitative knowledge available for such processes is frequently limited, and measurements are often subject to inherent and possibly large uncertainties. This results in competing model hypotheses, whose kinetic parameters may not be experimentally determinable. Discriminating among these alternatives and estimating their kinetic parameters is crucial to improve the understanding of the considered process, and to benefit from the analytical tools at hand. RESULTS: In this work we present a set-based framework that allows to discriminate between competing model hypotheses and to provide guaranteed outer estimates on the model parameters that are consistent with the (possibly sparse and uncertain) experimental measurements. This is obtained by means of exact proofs of model invalidity that exploit the polynomial/rational structure of biochemical reaction networks, and by making use of an efficient strategy to balance solution accuracy and computational effort. CONCLUSIONS: The practicability of our approach is illustrated with two case studies. The first study shows that our approach allows to conclusively rule out wrong model hypotheses. The second study focuses on parameter estimation, and shows that the proposed method allows to evaluate the global influence of measurement sparsity, uncertainty, and prior knowledge on the parameter estimates. This can help in designing further experiments leading to improved parameter estimates.

Mathematical modeling and analysis of force induced bone growth.

Bone is a dynamic living tissue that undergoes continuous adaptation of its mass and structure in response to mechanical and biological environment demands. Studies of bone adaptation have focused on metabolic or mechanical stimulus, but mathematical models of bone adaptation considering both, are not available by now. In this paper, we propose a mathematical model of bone adaptation during a remodeling cycle due to mechanical stimulus with the introduction of osteocytes as mechanotransducers. The model captures qualitatively very well the bone adaptation and cell interactions during the bone remodeling.