Optimal control of self-organized dynamics in cellular signal transduction

We demonstrate how model-based optimal control can be exploited in biological and biochemical modelling applications in several ways. In the first part, we apply optimal control to a detailed kinetic model of a glycolysis oscillator, which plays a central role in immune cells, in order to analyse potential regulatory mechanisms in the dynamics of associated signalling pathways. We demonstrate that the formulation of inverse problems with the aim to determine specific time-dependent input stimuli can provide important insight into dynamic regulations of self-organized cellular signal transduction. In the second part, we present an optimal control study aimed at target-oriented manipulation of a biological rhythm, an internal clock mechanism related to the circadian oscillator. This oscillator is responsible for the approximate endogenous 24 h (latin: circa dies) day-night rhythm in many organisms. On the basis of a kinetic model for the fruit fly Drosophila, we compute switching light stimuli via mixed-integer optimal control that annihilate the oscillations for a fixed time interval. Insight gained from such model-based specific manipulation may be promising in biomedical applications.     

Combinatorial integral approximation

We are interested in structures and efficient methods for mixed-integer nonlinear programs (MINLP) that arise from a first discretize, then optimize approach to time-dependent mixed-integer optimal control problems (MIOCPs). In this study we focus on combinatorial constraints, in particular on restrictions on the number of switches on a fixed time grid. We propose a novel approach that is based on a decomposition of the MINLP into a NLP and a MILP. We discuss the relation of the MILP solution to the MINLP solution and formulate bounds for the gap between the two, depending on Lipschitz constants and the control discretization grid size. The MILP solution can also be used for an efficient initialization of the MINLP solution process. The speedup of the solution of the MILP compared to the MINLP solution is considerable already for general purpose MILP solvers. We analyze the structure of the MILP that takes switching constraints into account and propose a tailored Branch and Bound strategy that outperforms cplex on a numerical case study and hence further improves efficiency of our novel method.     

Direkte potentiometrische st?rungsfreie Fluoridbestimmung in Mineral-, Trink- und Brauchw?ssern

Zusammenfassung Das von Chang et al. [5] kürzlich entdeckte Verfahren, Fluorid neben großen Aluminiummengen durch Dekomplexierung mit Hilfe von Tiron zu bestimmen, wurde von uns überprüft und dessen Brauchbarkeit in bezug auf Störelemente und Mengenbereich erweitert.Theoretisch wie praktisch konnte bewiesen werden, daß Tiron (Dinatrium-brenzcatechin-3,5-disulfonat) tatsächlich in der Lage ist, Fluoridionen aus allen seinen Komplexen, wie z. B. aus denen mit Al³⁺, Fe³⁺, TiO²⁺, Mg²⁺, SiO₂, H₃BO₃, freizusetzen und somit die direkte potentiometrische Bestimmung der Fluoridionen auch in Lösungen unbekannter Zusammensetzung zu ermöglichen. Im Gegensatz zu den in herkömmlichen TISABs (total ionic strength adjustment buffers) enthaltenen Komplexbildnern [6, 9, 15] komplexiert das Tiron Lanthanionen kaum, wodurch gegenüber der Messung mit TISAB der Leerwert erniedrigt und der Lanthanfluorideinkristall der Elektrode geschont wird. Gleichzeitig werden auch pH und Ionenstärke durch Tiron geregelt.Der Fluoridgehalt natürlicher Wässer wurde direkt nach Zugabe von 0,06 M Tironlösung bei pH 6,5 bestimmt. In akratischen und hypotonischen Wässern können bis zu 0,2 mg F^–/l mit ±3 % und mit geringerer Genauigkeit noch bis zu 0,01 mg erfaßt werden. Für hypertonische Wässer wird die Erstellung einer entsprechenden Eichkurve empfohlen. Bei Säuerlingen und künstlich mit CO₂ versetzten Wässern nimmt der Fluoridgehalt der Wasserproben in der Originalflasche mit der Zeit der Lagerung ständig ab.

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Direct potentiometric determination of fluoride in mineral, drinking and industrial waters without interferences

Summary The method recently discovered by Chang et al. [5] to determine fluoride in presence of huge amounts of aluminium by means of decomplexation with the aid of tiron, was checked by us; the determination limits were extended and the method was also investigated concerning other substances.Theoretical calculations and practical measuring could prove the reagent tiron (pyrocatechol 3,5-disodium disulphonate) to be able to liberate fluoride from several complexes, e.g. from Al³⁺, Fe³⁺, TiO²⁺, Mg²⁺, SiO₂, H₃BO₃ etc.; so the direct determination of fluoride in solutions of unknown composition becomes possible by means of tiron.In contrast to those complexing agents present in common TISABs [6, 9, 15] (total ionic strength adjustment buffers) tiron hardly complexes lanthanum-ions; therefore the value of the reagent blank is lowered compared with the measured value in presence of TISAB, and the LaF₃ single-crystal of the electrode is saved. Simultaneously pH and ionic-strength are regulated by the reagent.The determination of fluorine is recommended in 0.03 M solutions of tiron at pH 6.5. In akratic and hypertonic waters down to 0.2 mg of F^–/l can be determined. In the linear region of the calibration graph the accuracy is ±3 %.It has been shown that the fluoride content of originally bottled water samples declines steadily with the time of storage, particularly if the sample is acidic or CO₂ is added artificially.

     

Qualitativer Nachweis von Phosphat in pulverf?rmigen Mineralproben

Ohne Zusammenfassung

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Qualitative test for phosphate in powdered mineral samples

     

An SR1/BFGS SQP algorithm for nonconvex nonlinear programs with block-diagonal Hessian matrix

We present a quasi-Newton sequential quadratic programming (SQP) algorithm for nonlinear programs in which the Hessian of the Lagrangian function is block-diagonal. Problems with this characteristic frequently arise in the context of optimal control; for example, when a direct multiple shooting parametrization is used. In this article, we describe an implementation of a filter line-search SQP method that computes search directions using an active-set quadratic programming (QP) solver. To take advantage of the block-diagonal structure of the Hessian matrix, each block is approximated separately by quasi-Newton updates. For nonconvex instances, that arise, for example, in optimum experimental design control problems, these blocks are often found to be indefinite. In that case, the block-BFGS quasi-Newton update can lead to poor convergence. The novel aspect in this work is the use of SR1 updates in place of BFGS approximations whenever possible. The resulting indefinite QPs necessitate an inertia control mechanism within the sparse Schur-complement factorization that is carried out by the active-set QP solver. This permits an adaptive selection of the Hessian approximation that guarantees sufficient progress towards a stationary point of the problem. Numerical results demonstrate that the proposed approach reduces the number of SQP iterations and CPU time required for the solution of a set of optimal control problems.     

Structure and dynamics of water in nonionic reverse micelles: A combined time-resolved infrared and small angle x-ray scattering study

We study the structure and reorientation dynamics of nanometer-sized water droplets inside nonionic reverse micelles (water/Igepal-CO-520/cyclohexane) with time-resolved mid-infrared pump-probe spectroscopy and small angle x-ray scattering. In the time-resolved experiments, we probe the vibrational and orientational dynamics of the O-D bonds of dilute HDO:H(2)O mixtures in Igepal reverse micelles as a function of temperature and micelle size. We find that even small micelles contain a large fraction of water that reorients at the same rate as water in the bulk, which indicates that the polyethylene oxide chains of the surfactant do not penetrate into the water volume. We also observe that the confinement affects the reorientation dynamics of only the first hydration layer. From the temperature dependent surface-water dynamics, we estimate an activation enthalpy for reorientation of 45 ± 9 kJ mol(-1) (11?±?2 kcal mol(-1)), which is close to the activation energy of the reorientation of water molecules in ice.     

Rapid determination of fluorine in solid samples

A rapid method for the determination of fluorine in various matrices of geochemical and environmental interest is described. After fusion with NaOH, the sample is dissolved by means of tiron (= pyrocatechol-3,5-disulfonic acid, disodium salt), which acts both as buffer substance and as superior masking agent for cations exhibiting strong complexes with fluoride, e.g. Al, Fe, Ti etc. The final determination is done by means of the fluoride sensitive electrode without further separation.The applicability of the method has been checked for various silicates, bauxite, phosphates, soils, coal and plant material. A detection limit of 10 µg/g can be achieved, which is sufficient in many cases. The overall precision is better than ±10%.Dedicated to Prof. Dr.K. L. Komarek on occasion of his 60th birthday.     

Bestimmung des in Form von Kassiterit vorkommenden Zinns

Zusammenfassung Zur Ermittlung des in Gesteinen als Kassiterit vorliegenden Zinnanteils wird die gemahlene Probe mit Ammoniodid in einem Reagensglas zweimal sublimiert und anschließend in wäßriger Weinsäure/Ascorbinsäure gelöst. Nach Dekantieren und Waschen des unlöslichen Rückstandes erfolgt die Zinnbestimmung mit Hydrid-AAS aus weinsaurer Lösung; die Querstörungen dieser Endbestimmung sind als gering zu bezeichnen. Hauptproblem sind Kontaminationen aus den Gefäßen, die durch Spülen bzw. Stehenlassen mit verdünnter Weinsäure vermieden werden können.Die Selektivität des Verfahrens wird durch Anwendung auf Mineralien dokumentiert, wobei als Referenzmethode die spektrographische Bestimmung des Gesamtgehalts dient.In Schwermineralfraktionen wurden 53–79% des Zinns als in Kassiterit vorkommend gefunden.

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Determination of tin occurring bound in cassiterite

Summary For the determination of the amount of tin being present in rocks as cassiterite, the powdered sample is sublimed twice with ammonium iodide within a test tube, and subsequently dissolved in aqueous tartaric/ascorbic acid. After decantation and washing of the insoluble residue, the determination of tin is performed by hydride-AAS from tartaric acid solution; the cross interferences of this final determination are small. The chief experimental problem has been the contamination from vessels, which can however be avoided by rinsing and soaking with diluted tartaric acid. The selectivity of the procedure is documented by the application to some minerals, in comparison with the spectrographic determination of the total amount of tin as a reference.In fractions of the heavy minerals, 53–79% of the total tin has been found to be present as cassiterite.