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Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.
Heating efficiency of magnetic nanoparticles decreases with gradual immobilization in hydrogels
(2019)
Enzyme-catalyzed reactions have been designed to mimic various Boolean logic gates in the general framework of unconventional biomolecular computing. While some of the logic gates, particularly OR, AND, are easy to realize with biocatalytic reactions and have been reported in numerous publications, some other, like NXOR, are very challenging and have not been realized yet with enzyme reactions. The paper reports on a novel approach to mimicking the NXOR logic gate using the bell-shaped enzyme activity dependent on pH values. Shifting pH from the optimum value to the acidic or basic values by using acid or base inputs (meaning 1,0 and 0,1 inputs) inhibits the enzyme reaction, while keeping the optimum pH (assuming 0,0 and 1,1 input combinations) preserves a high enzyme activity. The challenging part of the present approach is the selection of an enzyme with a well-demonstrated bell-shape activity dependence on the pH value. While many enzymes can satisfy this condition, we selected pyrroloquinoline quinone (PQQ)-dependent glucose dehydrogenase as this enzyme has the optimum pH center-located on the pH scale allowing the enzyme activity change by the acidic and basic pH shift from the optimum value corresponding to the highest activity. The present NXOR gate is added to the biomolecular “toolbox” as a new example of Boolean logic gates based on enzyme reactions.
Monitoring the cellular metabolism of bacteria in (bio)fermentation processes is crucial to control and steer them, and to prevent undesired disturbances linked to metabolically inactive microorganisms. In this context, cell-based biosensors can play an important role to improve the quality and increase the yield of such processes. This work describes the simultaneous analysis of the metabolic behavior of three different types of bacteria by means of a differential light-addressable potentiometric sensor (LAPS) set-up. The study includes Lactobacillus brevis, Corynebacterium glutamicum, and Escherichia coli, which are often applied in fermentation processes in bioreactors. Differential measurements were carried out to compensate undesirable influences such as sensor signal drift, and pH value variation during the measurements. Furthermore, calibration curves of the cellular metabolism were established as a function of the glucose concentration or cell number variation with all three model microorganisms. In this context, simultaneous (bio)sensing with the multi-organism LAPS-based set-up can open new possibilities for a cost-effective, rapid detection of the extracellular acidification of bacteria on a single sensor chip. It can be applied to evaluate the metabolic response of bacteria populations in a (bio)fermentation process, for instance, in the biogas fermentation process.