Sensitivity analysis and efficient algorithms for some economic lot-sizing and scheduling problems

Many of optimization problems can be decomposed into a number of easier subproblems of the same type. Then dynamic programming (DP) seems to be a natural way to obtain an optimal solution. A straightforward application of DP usually leads to algorithms whose running time heavily depends on the magnitude of the input data. It has been shown in the thesis that it is possible to improve the complexity status of straightforward DP algorithms for different optimization problems, arising in production planning and scheduling, by means of a sensitivity analysis that allows to shrink the state space and to reduce thereby the amount of unnecessary computations. Using the suggested approach, we transform DP algorithms into polynomial ones and into so-called fully polynomial time approximation schemes.Viele Optimierungsprobleme können als Menge einfacherer Subprobleme dargestellt werden. Dynamische Programmierung (DP) ist dann ein offensichtliches Verfahren eine optimale Lösung zu finden. Eine direkte Anwendung der DP führt aber in den meisten Fällen zu Algorithmen, deren Laufzeiten sehr von der Größe des Inputs abhängen. In der vorliegenden Dissertation wirt an bestimmten Produktionsplanungs- und Schedulingproblemen gezeigt, dass man die Laufzeit der auf DP basierenden Algorithmen verbessern kann, falls eine Art von Sensitivitätsanalyse nachträglich verwendet wird. Mit den vorgestellten Methoden werden solche Algorithmen in polynomiale Algorithmen und in so genannten vollpolynomiale Approximationsschematas transformiert

TRPM6 and TRPM7 differentially contribute to the relief of heteromeric TRPM6/7 channels from inhibition by cytosolic Mg2+ and Mg center dot ATP

TRPM6 and its homologue TRPM7 are alpha-kinase-coupled divalent cation-selective channels activated upon reduction of cytosolic levels of Mg2+ and Mg center dot ATP. TRPM6 is vital for organismal Mg2+ balance. However, mechanistically the cellular role and functional nonredundancy of TRPM6 remain incompletely understood. Comparative analysis of native currents in primary cells from TRPM6-versus TRPM7-deficient mice supported the concept that native TRPM6 primarily functions as a constituent of heteromeric TRPM6/7 channels. However, heterologous expression of the human TRPM6 protein engendered controversial results with respect to channel characteristics including its regulation by Mg2+ and Mg center dot ATP. To resolve this issue, we cloned the mouse TRPM6 (mTRPM6) cDNA and compared its functional characteristics to mouse TRPM7 (mTRPM7) after heterologous expression. Notably, we observed that mTRPM6 and mTRPM7 differentially regulate properties of heteromeric mTRPM6/7 channels: In the presence of mTRPM7, the extreme sensitivity of functionally expressed homomeric mTRPM6 to Mg2+ is tuned to higher concentrations, whereas mTRPM6 relieves mTRPM7 from the tight inhibition by Mg center dot ATP. Consequently, the association of mTRPM6 with mTRPM7 allows for high constitutive activity of mTRPM6/7 in the presence of physiological levels of Mg2+ and Mg center dot ATP, thus laying the mechanistic foundation for constant vectorial Mg2+ transport specifically into epithelial cells

Elucidating the role of the TRPM7 alpha-kinase: TRPM7 kinase inactivation leads to magnesium deprivation resistance phenotype in mice

TRPM7 is an unusual bi-functional protein containing an ion channel covalently linked to a protein kinase domain. TRPM7 is implicated in regulating cellular and systemic magnesium homeostasis. While the biophysical properties of TRPM7 ion channel and its function are relatively well characterized, the function of the TRPM7 enzymatically active kinase domain is not understood yet. To investigate the physiological role of TRPM7 kinase activity, we constructed mice carrying an inactive TRPM7 kinase. We found that these mice were resistant to dietary magnesium deprivation, surviving three times longer than wild type mice; also they displayed decreased chemically induced allergic reaction. Interestingly, mutant mice have lower magnesium bone content compared to wild type mice when fed regular diet; unlike wild type mice, mutant mice placed on magnesium-depleted diet did not alter their bone magnesium content. Furthermore, mouse embryonic fibroblasts isolated from TRPM7 kinase-dead animals exhibited increased resistance to magnesium deprivation and oxidative stress. Finally, electrophysiological data revealed that the activity of the kinase-dead TRPM7 channel was not significantly altered. Together, our results suggest that TRPM7 kinase is a sensor of magnesium status and provides coordination of cellular and systemic responses to magnesium deprivation

TRPM6 and TRPM7—Gatekeepers of human magnesium metabolism

AbstractHuman magnesium homeostasis primarily depends on the balance between intestinal absorption and renal excretion. Magnesium transport processes in both organ systems – next to passive paracellular magnesium flux – involve active transcellular magnesium transport consisting of an apical uptake into the epithelial cell and a basolateral extrusion into the interstitium. Whereas the mechanism of basolateral magnesium extrusion remains unknown, recent molecular genetic studies in patients with hereditary hypomagnesemia helped gain insight into the molecular nature of apical magnesium entry into intestinal brush border and renal tubular epithelial cells. Patients with Hypomagnesemia with Secondary Hypocalcemia (HSH), a primary defect in intestinal magnesium absorption, were found to carry mutations in TRPM6, a member of the melastatin-related subfamily of transient receptor potential (TRP) ion channels. Before, a close homologue of TRPM6, TRPM7, had been characterized as a magnesium and calcium permeable ion channel vital for cellular magnesium homeostasis. Both proteins share the unique feature of an ion channel fused to a kinase domain with homology to the family of atypical alpha kinases. The aim of this review is to summarize the data emerging from clinical and molecular genetic studies as well as from electrophysiologic and biochemical studies on these fascinating two new proteins and their role in human magnesium metabolism

TRPM5, a taste-signaling transient receptor potential ion-channel, is a ubiquitous signaling component in chemosensory cells

<p>Abstract</p> <p>Background</p> <p>A growing number of TRP channels have been identified as key players in the sensation of smell, temperature, mechanical forces and taste. TRPM5 is known to be abundantly expressed in taste receptor cells where it participates in sweet, amino acid and bitter perception. A role of TRPM5 in other sensory systems, however, has not been studied so far.</p> <p>Results</p> <p>Here, we systematically investigated the expression of TRPM5 in rat and mouse tissues. Apart from taste buds, where we found TRPM5 to be predominantly localized on the basolateral surface of taste receptor cells, TRPM5 immunoreactivity was seen in other chemosensory organs – the main olfactory epithelium and the vomeronasal organ. Most strikingly, we found solitary TRPM5-enriched epithelial cells in all parts of the respiratory and gastrointestinal tract. Based on their tissue distribution, the low cell density, morphological features and co-immunostaining with different epithelial markers, we identified these cells as brush cells (also known as tuft, fibrillovesicular, multivesicular or caveolated cells). In terms of morphological characteristics, brush cells resemble taste receptor cells, while their origin and biological role are still under intensive debate.</p> <p>Conclusion</p> <p>We consider TRPM5 to be an intrinsic signaling component of mammalian chemosensory organs, and provide evidence for brush cells being an important cellular correlate in the periphery.</p

Elucidating the role of the TRPM7 alpha-kinase: TRPM7 kinase inactivation leads to magnesium deprivation resistance phenotype in mice

TRPM7 is an unusual bi-functional protein containing an ion channel covalently linked to a protein kinase domain. TRPM7 is implicated in regulating cellular and systemic magnesium homeostasis. While the biophysical properties of TRPM7 ion channel and its function are relatively well characterized, the function of the TRPM7 enzymatically active kinase domain is not understood yet. To investigate the physiological role of TRPM7 kinase activity, we constructed mice carrying an inactive TRPM7 kinase. We found that these mice were resistant to dietary magnesium deprivation, surviving three times longer than wild type mice; also they displayed decreased chemically induced allergic reaction. Interestingly, mutant mice have lower magnesium bone content compared to wild type mice when fed regular diet; unlike wild type mice, mutant mice placed on magnesium-depleted diet did not alter their bone magnesium content. Furthermore, mouse embryonic fibroblasts isolated from TRPM7 kinase-dead animals exhibited increased resistance to magnesium deprivation and oxidative stress. Finally, electrophysiological data revealed that the activity of the kinase-dead TRPM7 channel was not significantly altered. Together, our results suggest that TRPM7 kinase is a sensor of magnesium status and provides coordination of cellular and systemic responses to magnesium deprivation

Band-like arrangement of taste-like sensory cells at the gastric groove: evidence for paracrine communication

The discovery of taste-related elements within the gastrointestinal tract has led to a growing interest in the mechanisms and physiological significance of chemosensory monitoring of chymus composition. Previous work suggests that brush cells located in the "gastric groove," which parallels the "limiting ridge," a structure in rodents that divides the fundus from the corpus, are candidate sensory cells. A novel sectioning technique revealed that these cells are arranged in a palisade-like manner forming a band which borders the whole length of the corpus epithelium. Using transgenic PLC beta 2 promoter-GFP mice and specific antibodies, we have demonstrated that most of these cells express gustducin, PLC beta 2, and TRPM5; typical signaling proteins of gustatory sensory "type II" cells. These molecular features strongly suggest that the cells may be capable of sensing nutrient or non-nutrient constituents of the ingested food. Since there is no evidence that brush cells are endocrine cells, attempts were made to explore how such putative chemosensory cells might transmit the information to "effector" cells. It was found that most of the cells express the neuronal nitric oxide synthase (NOS) suggesting some paracrine interaction with adjacent cells. Moreover, they also express choline acetyltransferase (ChAT) as well as the vesicular protein SNAP25, indicating the potential for cholinergic transmission, possibly with subjacent enteric nerve fibers

Rescaled coordinate descent methods for linear programming

We propose two simple polynomial-time algorithms to find a positive solution to Ax=0Ax=0 . Both algorithms iterate between coordinate descent steps similar to von Neumann’s algorithm, and rescaling steps. In both cases, either the updating step leads to a substantial decrease in the norm, or we can infer that the condition measure is small and rescale in order to improve the geometry. We also show how the algorithms can be extended to find a solution of maximum support for the system Ax=0Ax=0 , x≥0x≥0 . This is an extended abstract. The missing proofs will be provided in the full version