Stochastic evolutionary dynamics of bimatrix games

Evolutionary game dynamics of two-player asymmetric games in finite populations is studied. We consider two roles in the game, roles α and β. α-players and β-players interact and gain payoffs. The game is described by a pair of matrices, which is called bimatrix. One's payoff in the game is interpreted as its fecundity, thus strategies are subject to natural selection. In addition, strategies can randomly mutate to others. We formulate a stochastic evolutionary game dynamics of bimatrix games as a frequency-dependent Moran process with mutation. We analytically derive the stationary distribution of strategies under weak selection. Our result provides a criterion for equilibrium selection in general bimatrix games.     

One-third rules with equality: Second-order evolutionary stability conditions in finite populations

The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650] describes a robustness criterion for evolution in a finite population: If at an A-frequency of 1/3, the fitness of an A player is greater (smaller) than the fitness of a B player, then a single A mutant that appears in a population of otherwise all B has a fixation probability greater (smaller) than the neutral threshold 1/N, the inverse population size. We examine the case where at an A-frequency of 1/3, the fitness of an A player is exactly equal to the fitness of a B player. We find that in this case the relative magnitude of the cross payoffs matters: If the payoff of A against B is larger (smaller) than the payoff of B against A, then a single A mutant has a fixation probability larger (smaller) than 1/N. If the cross payoffs coincide, we are in the special case of a partnership game, where the deviation cost from an inefficient equilibrium is exactly balanced by the potential gain of switching to the payoff dominant equilibrium. We show that in this case the fixation probability of A is lower than 1/N. Finally, we illustrate our findings by a language game with differentiated costs of signals.     

Differences in β-strand Populations of Monomeric Aβ40 and Aβ42

Using homonuclear ¹H NOESY spectra, with chemical shifts, ³J_H^N_H^α scalar couplings, residual dipolar couplings, and ¹H-¹⁵N NOEs, we have optimized and validated the conformational ensembles of the amyloid-β 1–40 (Aβ40) and amyloid-β 1–42 (Aβ42) peptides generated by molecular dynamics simulations. We find that both peptides have a diverse set of secondary structure elements including turns, helices, and antiparallel and parallel β-strands. The most significant difference in the structural ensembles of the two peptides is the type of β-hairpins and β-strands they populate. We find that Aβ42 forms a major antiparallel β-hairpin involving the central hydrophobic cluster residues (16–21) with residues 29–36, compatible with known amyloid fibril forming regions, whereas Aβ40 forms an alternative but less populated antiparallel β-hairpin between the central hydrophobic cluster and residues 9–13, that sometimes forms a β-sheet by association with residues 35–37. Furthermore, we show that the two additional C-terminal residues of Aβ42, in particular Ile-41, directly control the differences in the β-strand content found between the Aβ40 and Aβ42 structural ensembles. Integrating the experimental and theoretical evidence accumulated over the last decade, it is now possible to present monomeric structural ensembles of Aβ40 and Aβ42 consistent with available information that produce a plausible molecular basis for why Aβ42 exhibits greater fibrillization rates than Aβ40.     

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.     

Method for the complete separation of radioactively labeled human γ-globin chains from pre-βA chains on CM-cellulose chromatography: Use of cold carrier globin chains

Carboxymethyl (CM)-cellulose chromatography of globins is the technique used most frequently in analysis of hemoglobin synthesis. However, if this method is to be reliable in cases where only small amounts of fetal hemoglobin (α₂γ₂) compared to adult hemoglobin (α₂β₂^A) are synthesized, it is important to obtain a clean separation of γ chains from pre-β^A chains. In the past, it has been found that small amounts of pre-β^A chains tend to elute with the γ chains. Radioactively labeled γ chains can be completely and reproducibly separated from small amounts of labeled pre-β^A chains by the addition of unlabeled β^J chains (Hb J Baltimore = β16 Gly → Asp) which elute at the same position as the pre β^A chains, thus increasing the quantity of this peak and allowing a clean separation from the γ chains.     

The replicator equation on graphs

We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their immediate neighbors. We consider three different update rules, called 'birth-death', 'death-birth' and 'imitation'. A fourth update rule, 'pairwise comparison', is shown to be equivalent to birth-death updating in our model. We use pair approximation to describe the evolutionary game dynamics on regular graphs of degree k. In the limit of weak selection, we can derive a differential equation which describes how the average frequency of each strategy on the graph changes over time. Remarkably, this equation is a replicator equation with a transformed payoff matrix. Therefore, moving a game from a well-mixed population (the complete graph) onto a regular graph simply results in a transformation of the payoff matrix. The new payoff matrix is the sum of the original payoff matrix plus another matrix, which describes the local competition of strategies. We discuss the application of our theory to four particular examples, the Prisoner's Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game.     

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.     

Individual variation evades the Prisoner's Dilemma

Background  

The Prisoner's Dilemma (PD) is a widely used paradigm to study cooperation in evolutionary biology, as well as in fields as diverse as moral philosophy, sociology, economics and politics. Players are typically assumed to have fixed payoffs for adopting certain strategies, which depend only on the strategy played by the opponent. However, fixed payoffs are not realistic in nature. Utility functions and the associated payoffs from pursuing certain strategies vary among members of a population with numerous factors. In biology such factors include size, age, social status and expected life span; in economics they include socio-economic status, personal preference and past experience; and in politics they include ideology, political interests and public support. Thus, no outcome is identical for any two different players.     

Coevolution of Quantum and Classical Strategies on Evolving Random Networks

We study the coevolution of quantum and classical strategies on weighted and directed random networks in the realm of the prisoner’s dilemma game. During the evolution, agents can break and rewire their links with the aim of maximizing payoffs, and they can also adjust the weights to indicate preferences, either positive or negative, towards their neighbors. The network structure itself is thus also subject to evolution. Importantly, the directionality of links does not affect the accumulation of payoffs nor the strategy transfers, but serves only to designate the owner of each particular link and with it the right to adjust the link as needed. We show that quantum strategies outperform classical strategies, and that the critical temptation to defect at which cooperative behavior can be maintained rises, if the network structure is updated frequently. Punishing neighbors by reducing the weights of their links also plays an important role in maintaining cooperation under adverse conditions. We find that the self-organization of the initially random network structure, driven by the evolutionary competition between quantum and classical strategies, leads to the spontaneous emergence of small average path length and a large clustering coefficient.     

Cholesterol-dependent regulation of adenosine A2A receptor-mediated anion secretion in colon epithelial cells

Cholesterol affects diverse biological processes, in many cases by modulating the function of integral membrane proteins. In this study we have investigated the role of cholesterol in the adenosine-dependent regulation of ion transport in colonic epithelial cells. We observed that methyl-β-cyclodextrin (MβCD), a cholesterol-sequestering molecule, enhanced adenosine A_2A receptor-activated transepithelial short circuit current (I_sc), but only from the basolateral side. Cholesterol is a major constituent of membrane microdomains, called lipid rafts that also contain sphingolipids. However, studies with the sphingomyelin-degrading enzyme, sphingomyelinase, and the cholesterol-binding agent, filipin, indicated that the change in the level of cholesterol alone was sufficient to control the adenosine-modulated I_sc. Cholesterol depletion had a major effect on the functional selectivity of A_2A receptors. Under control conditions, adenosine activated I_sc more potently than the specific A_2A agonist, CGS-21680, and the current was inhibited by XE991, an inhibitor of cAMP-dependent K⁺ channels. Following cholesterol depletion, CGS-21680 activated I_sc more potently than adenosine, and the current was inhibited by clotrimazole, an inhibitor of Ca²⁺-activated K⁺ (IK1) channels. Co-immunoprecipitation experiments revealed that A_2A receptors associate with IK1 channels following cholesterol depletion. These results suggest that cholesterol content in colonic epithelia affects adenosine-mediated anion secretion by controlling agonist-selective signaling.     

Synthesis and characterization of 1H-phenanthro[9,10-d]imidazole derivatives as multifunctional agents for treatment of Alzheimer's disease

BackgroundAlzheimer's disease (AD) is a progressive neurodegenerative brain disorder that is characterized by dementia, cognitive impairment, and memory loss. Diverse factors are related to the development of AD, such as increased level of β-amyloid (Aβ), acetylcholine, metal ion deregulation, hyperphosphorylated tau protein, and oxidative stress.MethodsThe following methods were used: organic syntheses of 1H-phenanthro[9,10-d]imidazole derivatives, inhibition of self-mediated and metal-induced Aβ_1–42 aggregation, inhibition studies for acetylcholinesterase and butyrylcholinesterase, anti-oxidation activity studies, CD, MTT assay, transmission electron microscopy, dot plot assay, gel electrophoresis, Western blot, and molecular docking studies.ResultsWe synthesized and characterized a new type of 1H-phenanthro[9,10-d]imidazole derivatives as multifunctional agents for AD treatment. Our results showed that most of these derivatives exhibited strong Aβ aggregation inhibitory activity. Compound 9g had 74% Aβ_1–42 aggregation inhibitory effect at 10 μM concentration with its IC₅₀ value of 6.5 μM for self-induced Aβ_1–42 aggregation. This compound also showed good inhibition of metal-mediated (Cu^2 + and Fe^2 +) and acetylcholinesterase-induced Aβ_1–42 aggregation, as indicated by using thioflavin T assay, transmission electron microscopy, gel electrophoresis, and Western blot. Besides, compound 9g exhibited cholinesterase inhibitory activity, with its IC₅₀ values of 0.86 μM and 0.51 μM for acetylcholinesterase and butyrylcholinesterase, respectively. In addition, compound 9g showed good anti-oxidation effect with oxygen radical absorbance capacity (ORAC) value of 2.29.ConclusionsCompound 9g was found to be a potent multi-target-directed agent for Alzheimer's disease.General significanceCompound 9g could become a lead compound for further development as a multi-target-directed agent for AD treatment.     

Novel 8-hydroxyquinoline derivatives targeting β-amyloid aggregation,metal chelation and oxidative stress against Alzheimer’s disease

A series of multitargeted 8-hydroxyquinoline derivatives were designed and synthesized for the treatment of Alzheimer’s disease (AD). In vitro studies indicated that most of the prepared compounds exhibited significant inhibitory effects against self-induced Aβ_1?42 aggregation and potential antioxidant properties especially compound 5b (IC₅₀?=?5.64?μM for self-induced Aβ aggregation; the oxygen radical absorbance capacity using fluorescein (ORAC-FL) value is 2.63 Trolox equivalents). Notably, 5b can chelate biometals and inhibit Cu²⁺/Zn²⁺-induced Aβ_1?42 aggregation. The cell assays showed that 5b had excellent protective effects against oxidative toxin H₂O₂ and presented low neurotoxicity in PC12 cells. Furthermore, 5b could penetrate the blood–brain barrier (BBB) in vitro and did not show any acute toxicity in mice at doses up to 2000?mg/kg in vivo. Our findings provide a rationale for the potential application of compound 5b as a lead compound in AD therapy.     

Discovery of novel 2,5-dihydroxyterephthalamide derivatives as multifunctional agents for the treatment of Alzheimer’s disease

A series of 2,5-dihydroxyterephthalamide derivatives were designed, synthesized and evaluated as multifunctional agents for the treatment of Alzheimer’s disease. In vitro assays demonstrated that most of the derivatives exhibited good multifunctional activities. Among them, compound 9d showed the best inhibitory activity against both RatAChE and EeAChE (IC₅₀?=?0.56?μM and 5.12?μM, respectively). Moreover, 9d exhibited excellent inhibitory effects on self-induced Aβ_1–42 aggregation (IC₅₀?=?3.05?μM) and Cu²⁺-induced Aβ_1–42 aggregation (71.7% at 25.0?μM), and displayed significant disaggregation ability to self- and Cu²⁺-induced Aβ_1–42 aggregation fibrils (75.2% and 77.2% at 25.0?μM, respectively). Furthermore, 9d also showed biometal chelating abilities, antioxidant activity, anti-neuroinflammatory activities and appropriate BBB permeability. These multifunctional properties highlight 9d as promising candidate for further studies directed to the development of novel drugs against AD.     

Measurement of the Attachment and Assembly of Small Amyloid-β Oligomers on Live Cell Membranes at Physiological Concentrations Using Single-Molecule Tools

It is thought that the pathological cascade in Alzheimer's disease is initiated by the formation of amyloid-β (Aβ) peptide complexes on cell membranes. However, there is considerable debate about the nature of these complexes and the type of solution-phase Aβ aggregates that may contribute to their formation. Also, it is yet to be shown that Aβ attaches strongly to living cell membranes, and that this can happen at low, physiologically relevant Aβ concentrations. Here, we simultaneously measure the aggregate size and fluorescence lifetime of fluorescently labeled Aβ_1-40 on and above the membrane of cultured PC12 cells at near-physiological concentrations. We find that at 350 nM Aβ concentration, large (>>10 nm average hydrodynamic radius) assemblies of codiffusing, membrane-attached Aβ molecules appear on the cell membrane together with a near-monomeric species. When the extracellular concentration is 150 nM, the membrane contains only the smaller species, but with a similar degree of attachment. At both concentrations, the extracellular solution contains only small (∼2.3 nm average hydrodynamic radius) Aβ oligomers or monomers. We conclude that at near-physiological concentrations only the small oligomeric Aβ species are relevant, they are capable of attaching to the cell membrane, and they assemble in situ to form much larger complexes.     

Hemoglobins Austin and Waco: two hemoglobins with substitutions in the alpha 1 beta 2 contact region.

Hemoglobins (Hbs) Austin and Waco were detected by their electrophoretic migration on cellulose acetate (pH 8.4) and citrate agar (pH 6.2). By these methods, both variants migrated between Hbs A and F. Globin chain analysis at pH 8.6 indicated that the mutant β chain of Hb Austin was faster moving than the β^A chain; however, the mutant chain of Hb Waco was indistinguishable from the β^A chain by this technique. The two variants were isolated by ion-exchange column chromatography. Sequence studies demonstrated a substitution of serine (Hb Austin) and lysine (Hb Waco) for arginine at position 40 in the β chain. These mutations involve an amino acid residue in the α₁β₂ contact region, which, before this report, had been considered invariant in all hemoglobin sequences. Hb Austin was found to exist as dimers when oxygenated and as tetramers when deoxygenated. The equilibrium constant (K_d) for the tetramer to dimer transition was approximately 300 × 10^?6m, as calculated from sedimentation velocity studies. This variant also had high oxygen affinity, a much reduced heme-heme interaction, and a normal Bohr effect. The functional properties of Hb Waco were similar to those of Hb A.     

Nucleotide Binding States of Subunit A of the A-ATP Synthase and the Implication of P-Loop Switch in Evolution

The crystal structures of the nucleotide-empty (A_E), 5′-adenylyl-β,γ-imidodiphosphate (A_PNP)-bound, and ADP (A_DP)-bound forms of the catalytic A subunit of the energy producer A₁A_O ATP synthase from Pyrococcus horikoshii OT3 have been solved at 2.47 Å and 2.4 Å resolutions. The structures provide novel features of nucleotide binding and depict the residues involved in the catalysis of the A subunit. In the A_E form, the phosphate analog SO₄²⁻ binds, via a water molecule, to the phosphate binding loop (P-loop) residue Ser238, which is also involved in the phosphate binding of ADP and 5′-adenylyl-β,γ-imidodiphosphate. Together with amino acids Gly234 and Phe236, the serine residue stabilizes the arched P-loop conformation of subunit A, as shown by the 2.4-Å structure of the mutant protein S238A in which the P-loop flips into a relaxed state, comparable to the one in catalytic β subunits of F₁F_O ATP synthases. Superposition of the existing P-loop structures of ATPases emphasizes the unique P-loop in subunit A, which is also discussed in the light of an evolutionary P-loop switch in related A₁A_O ATP synthases, F₁F_O ATP synthases, and vacuolar ATPases and implicates diverse catalytic mechanisms inside these biological motors.     

Polymorphism of Alzheimer's Aβ17-42 (p3) Oligomers: The Importance of the Turn Location and Its Conformation

Aβ_17-42 (so-called p3) amyloid is detected in vivo in the brains of individuals with Alzheimer's disease or Down's syndrome. We investigated the polymorphism of Aβ_17-42 oligomers based on experimental data from steady-state NMR measurements, electron microscopy, two-dimensional hydrogen exchange, and mutational studies, using all-atom molecular-dynamics simulation with explicit solvent. We assessed the structural stability and the populations. Our results suggest that conformational differences in the U-turn of Aβ_17-42 lead to polymorphism in β-sheet registration and retention of an ordered β-strand organization at the termini. Further, although the parallel Aβ_17-42 oligomer organization is the most stable of the conformers investigated here, different antiparallel Aβ_17-42 organizations are also stable and compete with the parallel architectures, presenting a polymorphic population. In this study we propose that 1), the U-turn conformation is the primary factor leading to polymorphism in the assembly of Aβ_17-42 oligomers, and is also coupled to oligomer growth; and 2), both parallel Aβ_17-42 oligomers and an assembly of Aβ_17-42 oligomers that includes both parallel and antiparallel organizations contribute to amyloid fibril formation. Finally, since a U-turn motif generally appears in amyloids formed by full proteins or long fragments, and since to date these have been shown to exist only in parallel architectures, our results apply to a broad range of oligomers and fibrils.     

Effects of Hydroxylated Carbon Nanotubes on the Aggregation of Aβ16–22 Peptides: A Combined Simulation and Experimental Study

The pathogenesis of Alzheimer’s disease (AD) is associated with the aggregation of amyloid-β (Aβ) peptides into toxic aggregates with β-sheet character. In a previous computational study, we showed that pristine single-walled carbon nanotubes (SWCNTs) can inhibit the formation of β-sheet-rich oligomers in the central hydrophobic core fragment of Aβ (Aβ_16–22). However, the poor solubility of SWCNTs in water hinders their use in biomedical applications and nanomedicine. Here, we investigate the influence of hydroxylated SWCNT, a water-soluble SWCNT derivative, on the aggregation of Aβ_16–22 peptides using all-atom explicit-water replica exchange molecular dynamics simulations. Our results show that hydroxylated SWCNTs can significantly inhibit β-sheet formation and shift the conformations of Aβ_16–22 oligomers from ordered β-sheet-rich structures toward disordered coil aggregates. Detailed analyses of the SWCNT-Aβ interaction reveal that the inhibition of β-sheet formation by hydroxylated SWCNTs mainly results from strong electrostatic interactions between the hydroxyl groups of SWCNTs and the positively charged residue K16 of Aβ_16–22 and hydrophobic and aromatic stacking interactions between SWCNTs and F19 and F20. In addition, our atomic force microscopy and thioflavin T fluorescence experiments confirm the inhibitory effect of both pristine and hydroxylated SWCNTs on Aβ_16–22 fibrillization, in support of our previous and present replica exchange molecular dynamics simulation results. These results demonstrate that hydroxylated SWCNTs efficiently inhibit the aggregation of Aβ_16–22; in addition, they offer molecular insight into the inhibition mechanism, thus providing new clues for the design of therapeutic drugs against amyloidosis.     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.