Axiomatizations of two types of Shapley values for games on union closed systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication. © 2010 The Author(s)

The Role of Extramembranous Cytoplasmic Termini in Assembly and Stability of the Tetrameric K+-Channel KcsA

Membrane-active alcohol 2,2,2-trifluoroethanol has been proven to be an attractive tool in the investigation of the intrinsic stability of integral membrane protein complexes by taking K+-channel KcsA as a suitable and representative ion channel. In the present study, the roles of both cytoplasmic N and C termini in channel assembly and stability of KcsA were determined. The N terminus (1–18 residues) slightly increased tetramer stability via electrostatic interactions in the presence of 30 mol.% acidic phosphatidylglycerol (PG) in phosphatidylcholine lipid bilayer. Furthermore, the N terminus was found to be potentially required for efficient channel (re)assembly. In contrast, truncation of the C terminus (125–160 residues) greatly facilitated channel reversibility from either a partially or a completely unfolded state, and this domain was substantially involved in stabilizing the tetramer in either the presence or absence of PG in lipid bilayer. These studies provide new insights into how extramembranous parts play their crucial roles in the assembly and stability of integral membrane protein complexes

Lipid-mediated Wnt protein stabilization enables serum-free culture of human organ stem cells

Wnt signalling proteins are essential for culture of human organ stem cells in organoids, but most Wnt protein formulations are poorly active in serum-free media. Here we show that purified Wnt3a protein is ineffective because it rapidly loses activity in culture media due to its hydrophobic nature, and its solubilization requires a detergent, CHAPS (3-[(3-cholamidopropyl) dimethylammonio]-1-propanesulfonate), that interferes with stem cell self-renewal. By stabilizing the Wnt3a protein using phospholipids and cholesterol as carriers, we address both problems: Wnt activity remains stable in serum-free media, while non-toxic carriers allow the use of high Wnt concentrations. Stabilized Wnt3a supports strongly increased self-renewal of organ and embryonic stem cells and the serum-free establishment of human organoids from healthy and diseased intestine and liver. Moreover, the lipophilicity of Wnt3a protein greatly facilitates its purification. Our findings remove a major obstacle impeding clinical applications of adult stem cells and offer advantages for all cell culture uses of Wnt3a protein

Caspase-8 binding to cardiolipin in giant unilamellar vesicles provides a functional docking platform for bid

Caspase-8 is involved in death receptor-mediated apoptosis in type II cells, the proapoptotic programme of which is triggered by truncated Bid. Indeed, caspase-8 and Bid are the known intermediates of this signalling pathway. Cardiolipin has been shown to provide an anchor and an essential activating platform for caspase-8 at the mitochondrial membrane surface. Destabilisation of this platform alters receptor-mediated apoptosis in diseases such as Barth Syndrome, which is characterised by the presence of immature cardiolipin which does not allow caspase-8 binding. We used a simplified in vitro system that mimics contact sites and/or cardiolipin-enriched microdomains at the outer mitochondrial surface in which the platform consisting of caspase-8, Bid and cardiolipin was reconstituted in giant unilamellar vesicles. We analysed these vesicles by flow cytometry and confirm previous results that demonstrate the requirement for intact mature cardiolipin for caspase-8 activation and Bid binding and cleavage. We also used confocal microscopy to visualise the rupture of the vesicles and their revesiculation at smaller sizes due to alteration of the curvature following caspase-8 and Bid binding. Biophysical approaches, including Laurdan fluorescence and rupture/tension measurements, were used to determine the ability of these three components (cardiolipin, caspase-8 and Bid) to fulfil the minimal requirements for the formation and function of the platform at the mitochondrial membrane. Our results shed light on the active functional role of cardiolipin, bridging the gap between death receptors and mitochondria

An AFM study of solid-phase bilayers of unsaturated PC lipids and the lateral distribution of the transmembrane model peptide WALP23 in these bilayers

An altered lipid packing can have a large influence on the properties of the membrane and the lateral distribution of proteins and/or peptides that are associated with the bilayer. Here, it is shown by contact-mode atomic force microscopy that the surface topography of solid-phase bilayers of PC lipids with an unsaturated cis bond in their acyl chains shows surfaces with a large number of line-type packing defects, in contrast to the much smoother surfaces observed for saturated PC lipids. Di-n:1-PC (n = 20, 22, 24) and (16:0,18:1)-PC (POPC) were used. Next, the influence of an altered lipid environment on the lateral distribution of the single α-helical model peptide WALP23 was studied by incorporating the peptide in the bilayers of di-n:1-PC (n = 20, 22, 24) and (16:0,18:1)-PC unsaturated lipids. The presence of WALP23 leads to an increase in the number of packing defects but does not lead to the formation of the striated domains that were previously observed in bilayers of saturated PC lipids and WALP. This is ascribed to the less efficient lateral lipid packing of the unsaturated lipids, while the increase in packing defects is probably an indirect effect of the peptide. Finally, the fact that an altered lipid packing affects the distribution of WALP23 is also confirmed in an additional experiment where the solvent TFE (2,2,2-trifluorethanol) is added to bilayers of di-16:0-PC/WALP23. At 3.5 vol% TFE, the previous striated ordering of the peptide is abolished and replaced by loose lines

Differential Actions of Chlorhexidine on the Cell Wall of Bacillus subtilis and Escherichia coli

Chlorhexidine is a chlorinated phenolic disinfectant used commonly in mouthwash for its action against bacteria. However, a comparative study of the action of chlorhexidine on the cell morphology of Gram-positive and Gram-negative bacteria is lacking. In this study, the actions of chlorhexidine on the cell morphology were identified with the aids of electron microscopy. After exposure to chlorhexidine, numerous spots of indentation on the cell wall were found in both Bacillus subtilis and Escherichia coli. The number of indentation spots increased with time of incubation and increasing chlorhexidine concentration. Interestingly, the dented spots found in B. subtilis appeared mainly at the hemispherical caps of the cells, while in E. coli the dented spots were found all over the cells. After being exposed to chlorhexidine for a prolonged period, leakage of cellular contents and subsequent ghost cells were observed, especially from B subtilis. By using 2-D gel/MS-MS analysis, five proteins related to purine nucleoside interconversion and metabolism were preferentially induced in the cell wall of E. coli, while three proteins related to stress response and four others in amino acid biosynthesis were up-regulated in the cell wall materials of B. subtilis. The localized morphological damages together with the biochemical and protein analysis of the chlorhexidine-treated cells suggest that chlorhexidine may act on the differentially distributed lipids in the cell membranes/wall of B. subtilis and E. coli