Mutation-selection equilibrium in games with mixed strategies

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n×n payoff matrix. Players can use mixed strategies, which are given by the vector (p₁,…,p_n). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S_n. We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.     

Strategy selection in structured populations

Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix . We study a mutation and selection process. For weak selection strategy A is favored over B if and only if σa+b>c+σd. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games.     

Two-Electron Reactions S2QB → S0QB and S3QB → S1QB are Involved in Deactivation of Higher S States of the Oxygen-Evolving Complex of Photosystem II

The oxygen-evolving complex of Photosystem II cycles through five oxidation states (S₀-S₄), and dark incubation leads to 25% S₀ and 75% S₁. This distribution cannot be reached with charge recombination reactions between the higher S states and the electron acceptor Q_B⁻. We measured flash-induced oxygen evolution to understand how S₃ and S₂ are converted to lower S states when the electron required to reduce the manganese cluster does not come from Q_B⁻. Thylakoid samples preconditioned to make the concentration of the S₁ state 100% and to oxidize tyrosine Y_D were illuminated by one or two laser preflashes, and flash-induced oxygen evolution sequences were recorded at various time intervals after the preflashes. The distribution of the S states was calculated from the flash-induced oxygen evolution pattern using an extended Kok model. The results suggest that S₂ and S₃ are converted to lower S states via recombination from S₂Q_B⁻ and S₃Q_B⁻ and by a slow change of the state of oxygen-evolving complex from S₃ and S₂ to S₁ and S₀ in reactions with unspecified electron donors. The slow pathway appears to contain two-electron routes, S₂Q_B → S₀Q_B, and S₃Q_B → S₁Q_B. The two-electron reactions dominate in intact thylakoid preparations in the absence of chemical additives. The two-electron reaction was replaced by a one-electron-per-step pathway, S₃Q_B → S₂Q_B → S₁Q_B in PS II-enriched membrane fragments and in thylakoids measured in the presence of artificial electron acceptors. A catalase effect suggested that H₂O₂ acts as an electron donor for the reaction S₂Q_B → S₀Q_B but added H₂O₂ did not enhance this reaction.     

Regulation of MKP-1 expression and MAPK activation by PARP-1 in oxidative stress: a new mechanism for the cytoplasmic effect of PARP-1 activation

Previously, it was suggested that the release of nuclearly formed ADP-ribose polymers or ADP-ribosylated proteins could be responsible for the cytosolic and mitochondrial effects of poly(ADP-ribose) polymerase (PARP)-1 activation in oxidative stress. In this report, we provide a novel alternative mechanism. We found that reactive oxygen species-activated PARP-1 regulated the activation of JNK and p38 mitogen-activated protein kinases (MAPKs) because inhibition of PARP-1 by pharmacons, small interfering RNA silencing of PARP-1 expression, or the transdominant expression of enzymatically inactive PARP-1 resulted in the inactivation of these MAPKs. This regulation was achieved by increased expression and enlarged cytoplasmic localization of MAPK phosphatase-1 (MKP-1) upon PARP-1 inhibition in oxidative stress because changes in MKP-1 expression were reflected in the phosphorylation states of JNK and p38. Furthermore, we found that in MKP-1-silenced cells, PARP inhibition was unable to exert its protective effect, indicating the pivotal roles of JNK and p38 in mediating the oxidative-stress-induced cell death as well as that of increased MKP-1 expression in mediating the protective effect of PARP inhibition. We suggest that regulation of a protein that can directly influence cytoplasmic signaling cascades at the expression level represents a novel mechanism for the cytoplasmic action of PARP-1 inhibition.     

Picture representation during REM dreams: A redox molecular hypothesis

A novel molecular hypothesis about visual perception and imagery has recently been proposed (Bókkon, 2009; BioSystems). Namely, external electromagnetic visible photons are converted into electrical signals in the retina and are then conveyed to V1. Next, these retinotopic electrical signals (spike-related electrical signals along classical axonal-dendritic pathways) can be converted into synchronized bioluminescent biophoton signals (inside the neurons) by neurocellular radical reactions (redox processes) in retinotopically organized V1 mitochondrial cytochrome oxidase-rich visual areas. The bioluminescent photonic signals (inside the neurons) generated by neurocellular redox/radical reactions in synchronized V1 neurons make it possible to produce computational biophysical pictures during visual perception and imagery. Our hypothesis is in line with the functional roles of reactive oxygen and nitrogen species in living cells and states that this is not a random process, but rather a strict mechanism used in signaling pathways. Here, we suggest that intrinsic biophysical pictures can also emerge during REM dreams.     

Characterization of chromate-sensitive and-tolerant mutants of<Emphasis Type="Italic">Schizosaccharomyces pombe</Emphasis>

Stable chromium(VI)-sensitive and -tolerant mutants were obtained by induced mutagenesis of Schizosaccharomyces pombe lysine and leucine auxotrophic heterothallic strains 6chr+ and 9chr+. Eleven of them were selected for further studies. Fast transport of 51CrO4(2-) was detected in a representative sensitive mutant, chr-51S, while the tolerant mutant chr1-66T and the parental strain 6chr+ exhibited significantly lower 51CrO4(2-) uptake. The segregation of tetrads of three selected CrVI-tolerant mutants, chr1-66T, chr1-14T and chr2-04T, strongly indicated that tolerance was determined by single mutations. Random spore analysis proved that the mutations of chr1-66T and chr1-14T were allelic and the mutation of mutant chr2-04T was not allelic with the mutation of chr1-66T. Recombinants carrying the ura4D18 selective marker were created for transformation experiments. Two of them (chr1-661T and chr2-046T) can be used to clone and identify the genes responsible for their CrVI tolerance phenotype.     

Effect of polyanion on the acidic conformational transition of native and denatured ferricytochrome c. Circular dichroism study

Interaction of polyanion poly(vinylsulfate) with oxidized cytochrome c (cyt c) significantly affects the protein main characteristics. One of them, pKa value of acidic transition, was shifted from an apparent pKa value 2.5 (typical for cyt c in low ionic strength solvent) to approximately 5.20 +/- 0.15 upon polyanion binding to the protein, pointing to a likely involvement of histidines 26 and/or 33 in the protein acidic transition in complex with the polyanion. The acidic transition followed at 6 different wavelengths all over circular dichroism spectrum, monitoring different parts of the protein structure, revealed basically two-state character process. Only ellipticity at 262 nm indicated a low-cooperative pH-induced conformational transition in heme region with an apparent pKa approximately 4.34 +/- 0.25 in accordance with absorbance change at 620 nm. Polyanion also interacts with chemically-denatured (in the presence of 9 mol/l urea) state of the protein as it follows from stabilization of protein residual structure at acidic pH and its effect on pKa value of acidic transition of chemically-denatured cyt c. Destabilization effect of polyanions on native and, on the other hand, stabilization influence on partially unfolded conformations of the protein are discussed with an implication for their chaperone-like properties in vivo and in vitro.     

Production of bacteriolytic enzymes by mycoparasitic Trichoderma strains

Eighteen mycoparasitic Trichoderma strains were tested for their ability to degrade heat-inactivated Bacillus cereus var. mycoides, B. megaterium, B. subtilis, Escherichia coli, Micrococcus luteus, Pseudomonas aeruginosa and Serratia marcescens cells. The non-inductive and inductive ferment broths of five strains with good degrading abilities towards B. subtilis were investigated for specific degrading enzyme activities. In addition to trypsin- and chymotrypsin-like protease activities, -1,4-N-acetyl-glucosaminidase (NAGase) was also secreted. Strain Trichoderma harzianum T19 had the most outstanding degrading abilities. The extracellular degrading enzymes of this strain were separated on a Sephadex G-150 column, and their preliminary characterization was performed. The results demonstrated that muramidase-like activities are present in the ferment broth of this T. harzianum strain.     

Malate dehydrogenases--structure and function

Malate dehydrogenases (MDH, L-malate:NAD oxidoreductase, EC 1.1.1.37), catalyze the NAD/NADH-dependent interconversion of the substrates malate and oxaloacetate. This reaction plays a key part in the malate/aspartate shuttle across the mitochondrial membrane, and in the tricarboxylic acid cycle within the mitochondrial matrix. They are homodimeric molecules in most organisms, including all eukaryots and the most bacterial species. The enzymes share a common catalytic mechanism and their kinetic properties are similar, which demonstrates a high degree of structural similarity. The three-dimensional structures and elements essential for catalysis are conserved between mitochondrial and cytoplasmic forms of MDH in eukaryotic cells even though these isoenzymes are only marginally related at the level of primary structure.     

A phosphoserine/threonine-binding pocket in AGC kinases and PDK1 mediates activation by hydrophobic motif phosphorylation

The growth factor-activated AGC protein kinases RSK, S6K, PKB, MSK and SGK are activated by serine/threonine phosphorylation in the activation loop and in the hydrophobic motif, C-terminal to the kinase domain. In some of these kinases, phosphorylation of the hydrophobic motif creates a specific docking site that recruits and activates PDK1, which then phosphorylates the activation loop. Here, we discover a pocket in the kinase domain of PDK1 that recognizes the phosphoserine/phosphothreonine in the hydrophobic motif by identifying two oppositely positioned arginine and lysine residues that bind the phosphate. Moreover, we demonstrate that RSK2, S6K1, PKBalpha, MSK1 and SGK1 contain a similar phosphate-binding pocket, which they use for intramolecular interaction with their own phosphorylated hydrophobic motif. Molecular modelling and experimental data provide evidence for a common activation mechanism in which the phosphorylated hydrophobic motif and activation loop act on the alphaC-helix of the kinase structure to induce synergistic stimulation of catalytic activity. Sequence conservation suggests that this mechanism is a key feature in activation of >40 human AGC kinases.