Evolutionary snowdrift game incorporating costly punishment in structured populations

The role of punishment and the effects of a structured population in promoting cooperation are important issues. Within a recent model of snowdrift game (SG) incorporating a costly punishing strategy (P), we study the effects of a population connected through a square lattice. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α$\alpha$ so as to punish a non-cooperative (D) opponent by β$\beta$. Depending on α$\alpha$, β$\beta$, the cost-to-benefit ratio r$r$ in SG, and the initial conditions, the system evolves into different phases that could be homogeneous or inhomogeneous. The spatial structure imposes geometrical constraint on how one agent is affected by neighboring agents. Results of extensive numerical simulations, both for the steady state and the dynamics, are presented. Possible phases are identified and discussed, and isolated phases in the r–β$r\text{–}\beta$ space are identified as special local structures of strategies that are stable due to the lattice structure. In contrast to a well-mixed population where punishers are suppressed due to the cost of punishment, the altruistic punishing strategy can flourish and prevail for appropriate values of the parameters, implying an enhancement in cooperation by imposing punishments in a structured population. The system could evolve to a phase corresponding to the coexistence of C, D, and P strategies at some particular payoff parameters, and such a phase is absent in a well-mixed population. The pair approximation, a commonly used analytic approach, is extended from a two-strategy system to a three-strategy system. We show that the pair approximation can, at best, capture the numerical results only qualitatively. Due to the improper way of including spatial correlation imposed by the lattice structure, the approximation does not give the frequencies of C, D, and P accurately and fails to give the homogeneous AllD and AllP phases.     

Synthesis and structure of two tetranuclear osmium carbonyl isotopomers: a crystallographic isotope effect

A synthetic route to [Os4(mu-H)(mu-OH)(mu-CO)(CO)12] ( 1) has been devised through the activation of [Os4(CO)14] with Me3NO. The pyrolysis and photolysis of the reactant in the presence of a trace amount of water produces 1 in low yield. The solid-state structure of [Os4(mu-H)(mu-OH)(mu-CO)(CO)12 x H2O] (1 x H2O) reveals a butterfly Os4 skeleton with bridging H, OH and CO ligands as well as hydrogen-bonded molecules of water in the crystal lattice. A low-temperature 13C{1H} NMR spectroscopic study revealed a merry-go-round exchange of CO ligands around the Os3 plane containing the asymmetric bridging CO. The exposure of 1 x H2O to D2O yielded [Os4(mu-H)(mu-OD)(mu-CO)(CO)12]2. Although the solid-state, intramolecular structure of 2 closely matched that of 1 x H2O, the intermolecular structure did not: its crystal lattice contained no water of crystallization, a previously unreported crystallographic isotope effect.     

Synthesis and thermal chemistry of copper (I) guanidinates

Copper (I) guanidinate dimers were generated by a salt metathesis route and structurally characterized. The guanidinates differed from the known amidinate dimers because of a large torsion of the dimer ring. This had a direct effect on their thermal chemistry. The thermal reactivity was investigated by several methods, including a novel temperature-resolved, gas-phase method that was monitored by mass spectrometry. The copper guanidinates underwent carbodiimide deinsertion to produce copper metal at temperatures between 225 -and 250 degrees C in the gas phase and at 125 degrees C in solution. The amidinate investigated also showed copper deposition at 190 degrees C in the gas phase, and 135 degrees C in solution, but without carbodiimide deinsertion. The guanidinate compounds deposited crystalline copper at 225 degrees C in a simple chemical vapor deposition experiment.     

Pyrrole Denitrogenation and Fragmentation of Tetramethylethylenediamine Promoted by a NbII Cluster

A nitrogen center was abstracted from a pyrrolyl ring to form the dinuclear nitrido- and dienyl-bridged complex 1 during the reaction of [{(tmeda)Nb^IICl}₂(μ-Cl)₃Li(tmeda)] with the lithium salt of 2,5-dimethylpyrrole (tmeda=N,N,N′,N′-tetramethylethylenediamine). A second product from this reaction is the amido-carbene-hydride niobium complex 2 , which likewise forms under C−N bond cleavage.     

Synthesis and Structure of a Chromium(III) Complex Supported by a β-diketiminate and an Enediolate Ligand

Abstract  

The complex (bis(2,6-diisopropylphenyl)pentane-2,4-ketiminato)(9,10-dihydro-9,10-(ethenediolato)anthracene)(tetrahydrofuran)chromium(III) (1) has been synthesized and structurally characterized. Complex 1 crystallizes in the spacegroup Cc with the crystal cell parameters a = 22.285 (3) ?, b = 9.3317 (13) ?, c = 40.782 (6) ?, β = 99.338 (3)°, V = 8369 (2) ?³, and Z = 8. Two symmetry unique complex molecules were located in the asymmetric unit making Z′ = 2. The chromium atoms display square pyramidal coordination with THF located in the axial position. The previously neutral α-diketone moiety has been reduced by two electrons to an enediolate group with a corresponding increase of oxidation state of the chromium center.     

Synthesis of zinc, copper, nickel, cobalt, and iron complexes using tris(pyrazolyl)methane sulfonate ligands: a structural model for N,N,O binding in metalloenzymes

Ligands of intermediate steric bulk were designed to mimic metalloenzymes with histidine and carboxlyate binding sites. The reaction between tris(3-isopropylpyrazolyl)methane and butyllithium followed by SO3NMe3 in THF yielded the new ligand lithium tris(3-isopropylpyrazolyl)methane sulfonate (LiTpmsiPr). Various metal salts reacted with LiTpmsiPr to give the octahedral complexes M(TpmsiPr)2 (M = Zn, Cu, Ni, Co, Fe) in which each ligand has N,N,O binding to the metal. In the reaction between LiTpmsiPr and ZnCl2, in addition to the major product Zn(TpmsiPr)2, [LiTpmsiPrZnCl2].2THF was also formed as a minor product with a tetrahedral zinc atom coordinated to either N,N,Cl,Cl in the solid phase or N,N,N,Cl in acetonitrile solution. Although TpmsiPr is coordinatively flexible and can act as a bipodal or tripodal ligand, it appears to favor the formation of octahedral L2M complexes.     

Phenylamido and Diphenylamido Complexes of Chromium(II)

Abstract  Addition LiNHPh to a [(NacNac)Cr(μ-I)]₂ [NacNac = 2,4 pentane-N-N′-bis(2,6-diisopropylphenyl) ketiminato] in THF yields a dimeric anilido complex, 1, that crystallizes in P2₁/n with unit cell parameters a = 13.390(2) ?, b = 26.298(5) ?, c = 21.326(4) ?, β = 93.905(4)°, V = 7492(2) ?³ and Z = 4. The same reaction in the presence of aniline yields a monomeric anilido complex, 2, with a coordinated aniline molecule. Complex 2 crystallizes in P2 ₁ /c with unit cell parameters a = 28.530(5) ?, b = 10.8116(18) ?, c = 26.492(5) ?, β = 115.685(3)°, V = 7364(2) ?³ and Z = 8. Addition of aniline to isolated 1 yields 2. Addition of LiNPh₂ to [(NacNac)Cr(μ-I)]₂ in THF yields a monomeric complex that crystallizes in P2₁/n with the unit cell parameters a = 11.152(6) ?, b = 23.820(12) ?, c = 17.915(9) ?, β = 106.223(9)°, V = 4569(4) ?³ and Z = 4. All complexes have been spectroscopically and structurally characterized. Graphical Abstract  Addition of LiNHPh or LiNPh₂ to [(NacNac)Cr(μ-I)]₂ yields a dimeric or a monomeric complex whereas addition of LiNHPh in the presence of aniline yields the monomeric anilido complex.      

Synthesis and Structure of Chromium(II) Complexes Supported by Both a β-Diketiminate and an Amidinate Ligand

Abstract  

The complexes (bis(2,6-diisopropylphenyl)pentane-2,4-ketiminato)(μ₂-diisopropylacetamidinato) chromium(II) (1) and (bis(2,6-diisopropylphenyl)pentane-2,4-ketiminato)(μ₂-dicyclohexylacetamidinato) chromium(II) (2) have been synthesized and structurally characterized. Complex 1 crystallizes in space group Pbcn with crystal cell parameters a = 10.7183(13) ?, b = 16.4093(19) ?, c = 20.687(2) ?, V = 3,638.3(7) ?³ and Z = 4. Complex 2 crystallizes in triclinic space group P-1 with crystal cell parameters a = 10.750(3) ?, b = 12.174(3) ?, c = 16.308(4) ?, α = 75.903(4)°, β = 82.137(4)°, γ = 85.511(4), V = 2,048.4(8) ?³ and Z = 2. The complexes adopt a spiro distorted square planar geometry and have similar structural parameters.     

Identification of active compounds from medicinal plant extracts using gas chromatography-mass spectrometry and multivariate data analysis

Conventional methods of drug discovery from natural products include bioassay-guided fractionation, which is tedious and has low efficiency. The aim of this work is to develop a platform method to rapidly identify bioactive compounds from crude plant extracts and their partially purified fractions using multivariate data analysis (MVDA). Soxhlet extraction and liquid-liquid fractionation were used to prepare different extracts and fractions from the leaves of a medicinal plant, Ardisia elliptica. The extracts and fractions were analysed chemically using GC-MS, and their ability to inhibit platelet aggregation was investigated. Two MVDA methods were developed and optimised to analyse the results. In the first method, compounds with the highest contribution scores for biological activity calculated by different models were listed as potential antiplatelet compounds. For the second MVDA method, a correlation of the concentrations of constituents and biological activities in the various extracts and fractions for each compound was done. Compounds with the highest correlation coefficients were identified as potential antiplatelet compounds. One of the predicted components was isolated, purified and confirmed to possess antiplatelet effects. This platform method can be developed and optimised for other plant extracts and biological activities, thus reducing time and cost of drug discovery while improving efficiency.