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

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

Computational Complexity of Atomic Chemical Reaction Networks

Informally, a chemical reaction network is "atomic" if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational complexity of deciding whether a given network is atomic according to each of these definitions. Our first definition, primitive atomic, which requires each reaction to preserve the total number of atoms, is to shown to be equivalent to mass conservation. Since it is known that it can be decided in polynomial time whether a given chemical reaction network is mass-conserving, the equivalence gives an efficient algorithm to decide primitive atomicity. Another definition, subset atomic, further requires that all atoms are species. We show that deciding whether a given network is subset atomic is in $\textsf{NP}$, and the problem "is a network subset atomic with respect to a given atom set" is strongly $\textsf{NP}$-$\textsf{Complete}$. A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et al., further requires that each species has a sequence of reactions splitting it into its constituent atoms. We show that there is a $\textbf{polynomial-time algorithm}$ to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is $\textbf{decidable}$. We show that the reachability problem for reachably atomic networks is $\textsf{Pspace}$-$\textsf{Complete}$. Finally, we demonstrate equivalence relationships between our definitions and some special cases of another existing definition of atomicity due to Gnacadja

TRPM7 regulates proliferation and polarisation of macrophages.

Ion channels play pivotal roles in regulating important functions of macrophages, such as cytokine and chemokine production, migration, proliferation, phagocytosis and others. In this study, we have identified the transient receptor potential cation channel, subfamily M, member 7 (TRPM7) for the first time in macrophages. TRPM7 activity is differentially regulated in macrophages, i.e. current density in TRPM7 is significantly larger in anti-inflammatory M2-type macrophages than in untreated and in pro-inflammatory M1-type macrophages, whereas mRNA levels of TRPM7 remain unchanged upon cell polarisation. The specific TRPM7 inhibitors NS8593 and FTY720 abolish proliferation of macrophages induced by interleukin-4 (IL-4) and macrophage colony-stimulating factor (M-CSF), respectively, whereas proliferation arrest was not accompanied by induction of apoptosis or necrosis in macrophages. Furthermore, NS8593 and FTY720 prevented polarisation of macrophages towards the anti-inflammatory M2 phenotype. Inhibition of TRPM7 reduced IL-4-induced upregulation of arginase-1 (Arg1) mRNA levels and Arg1 activity, and abolished the inhibitory effects of IL-4 or M-CSF on LPS-induced TNF-α production by macrophages. In summary, our data suggest a main role of TRPM7 in the regulation of macrophage proliferation and polarisation

Divide and Conquer: High Resolution Structural Information on TRP Channel Fragments

Understanding how proteins facilitate signaling and substrate transport across biological membranes is an important frontier of structural biology. Membrane proteins are the doors and windows of cells: many membrane proteins are gates of entry into or exit from cells or cellular compartments, and others allow cells to sense their environment. One important multifunctional family of membrane proteins is the transient receptor potential (TRP) family of ion channels. TRP channels have recently been the subject of multiple structural analyses, both low resolution electron microscopy studies (reviewed by Moiseenkova-Bell and Wensel in this issue [p. 239]) and the divide and conquer approach of determining high resolution crystal structures of channel fragments, reviewed here.Molecular and Cellular Biolog

Defects in TRPM7 channel function deregulate thrombopoiesis through altered cellular Mg2+ homeostasis and cytoskeletal architecture

Mg2+ plays a vital role in platelet function, but despite implications for life-threatening conditions such as stroke or myocardial infarction, the mechanisms controlling [Mg2+](i) in megakaryocytes (MKs) and platelets are largely unknown. Transient receptor potential melastatin-like 7 channel (TRPM7) is a ubiquitous, constitutively active cation channel with a cytosolic alpha-kinase domain that is critical for embryonic development and cell survival. Here we report that impaired channel function of TRPM7 in MKs causes macrothrombocytopenia in mice (Trpm7(fl/fl-Pf4Cre)) and likely in several members of a human pedigree that, in addition, suffer from atrial fibrillation. The defect in platelet biogenesis is mainly caused by cytoskeletal alterations resulting in impaired proplatelet formation by Trpm7(fl/fl-Pf4Cre) MKs, which is rescued by Mg2+ supplementation or chemical inhibition of non-muscle myosin IIA heavy chain activity. Collectively, our findings reveal that TRPM7 dysfunction may cause macrothrombocytopenia in humans and mice

TRPM2 channels are essential for regulation of cytokine production in lung interstitial macrophages

Interstitial macrophages (IMs) are essential for organ homeostasis, inflammation, and autonomous immune response in lung tissues, which are achieved through polarization to a pro-inflammatory M1 and an M2 state for tissue repair. Their remote parenchymal localization and low counts, however, are limiting factors for their isolation and molecular characterization of their specific role during tissue inflammation. We isolated viable murine IMs in sufficient quantities by coculturing them with stromal cells and analyzed mRNA expression patterns of transient receptor potential (TRP) channels in naïve and M1 polarized IMs after application of lipopolysaccharide (LPS) and interferon γ. M-RNAs for the second member of the melastatin family of TRP channels, TRPM2, were upregulated in the M1 state and functional channels were identified by their characteristic currents induced by ADP-ribose, its specific activator. Most interestingly, cytokine production and secretion of interleukin-1α (IL-1α), IL-6 and tumor necrosis factor-α in M1 polarized but TRPM2-deficient IMs was significantly enhanced compared to WT cells. Activation of TRPM2 channels by ADP-ribose (ADPR) released from mitochondria by ROS-produced H2O2 significantly increases plasma membrane depolarization, which inhibits production of reactive oxygen species by NADPH oxidases and reduces cytokine production and secretion in a negative feedback loop. Therefore, TRPM2 channels are essential for the regulation of cytokine production in M1-polarized murine IMs. Specific activation of these channels may promote an anti-inflammatory phenotype and prevent a harmful cytokine storm often observed in COVID-19 patients

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