Replicator Dynamics and Evolutionary Stable Strategies in Heterogeneous Games

We generalise and extend the work of Iñarra and Laruelle (2011) by studying two person symmetric evolutionary games with two strategies, a heterogenous population with two possible types of individuals and incomplete information. Comparing such games with their classic homogeneous version vith complete information found in the literature, we show that for the class of anti-coordination games the only evolutionarily stable strategy vanishes. Instead, we find infinite neutrally stable strategies. We also model the evolutionary process using two different replicator dynamics setups, each with a different inheritance rule, and we show that both lead to the same results with respect to stability.

Evolution of Cooperation in the Snowdrift Game with Incomplete Information and Heterogeneous Population

Differently from previous studies of tag-based cooperation, we assume that individuals fail to recognize their own tag. Due to such incomplete information, the action taken against the opponent cannot be based on similarity, although it is still motivated by the tag displayed by the opponent. We present stability conditions for the case when individuals play unconditional cooperation, unconditional defection or conditional cooperation. We then consider the removal of one or two strategies. Results show that conditional cooperators are the most resilient agents against extinction and that the removal of unconditional cooperators may lead to the extinction of unconditional defectors.

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.

Emergence of Cooperation in Heterogeneous Population: A Discrete-Time Replicator Dynamics Analysis

The emergence of cooperation is analyzed in heterogeneous populations where individuals can be classified in two groups according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are able to identify the type of every other individual, but fail to recognize their own type, and thus behave under partial information conditions. The interactions between individuals are described by 2 × 2 symmetric games where individuals can either cooperate or defect. The evolution of such populations is studied in the framework of evolutionary game by means of the replicator dynamics. Overlapping generations are considered, so the replicator equations are formulated in discrete-time form. The well-posedness conditions of the system are derived. Depending on the parameters of the game, a restriction may exist for the generation length. The stability analysis of the dynamical system is carried out and a detailed description of the behavior of trajectories starting from the interior of the state-space is given. We find that, provided the conditions of well-posedness are verified, the linear stability of monomorphic states in the discrete-time replicator coincides with the one of the continuous case. Specific from the discrete-time case, a relaxed restriction for the generation length is derived, for which larger time-steps can be used without compromising the well-posedness of the replicator system.

The electrocatalytic and stoichiometric oxidation chemistry of binuclear ruthenium complexes incorporating the anionic tripod ligand {(η5-C5H5)Co[P(OCH3)2(=O)]3}-

The anionic tripod ligand NaLoMe (L_(oMe) - = [(η^5-C_5H_5)Co{P(O)(OCH_3)_2}_3]^-) reacts with RuO_4 in a biphasic reaction mixture of 1% H_2SO_4 and CCI_4 to afford [(L_(oMe) (HO)Ru^(IV) (µ-O)_2Ru ^(IV)(OH)(L_(oMe)] (1), which is treated with aqueous CF_3S0_3H to generate [(L_(oMe)(H_2O)Ru^(IV) (µ-O)_2R^(IV) (OH_2)(L_(oMe)][CF_3SO_3]_2 ([H_21][CF_3SO_3]_2). Addition of iodosobenzene to an acetonitrile solution of this salt yields [(L_(oMe)(O)Ru^v(µ-0)2Ru^v-(O)(_(LoMe)] (2). The dimer 1 can be reduced chemically or electrochemically to the Ru^(III)- Ru^(III) dimers [(L_(oMe)(H_20)Ru^(III) (µ-OH)_2Ru^(III) (OH_2)(L_(oMe)) ]^2+ and [(L_(oMe)) ^(III) (µ-0Hh(µ-0H2)Ru^(III) (L_(oMe)]^2+ which interconvert in aqueous media. Two electron processes dominate both the bulk chemistry and the electrochemistry of 1. Among these processes are the quasi-reversible Ru^(IV) - Ru^(IV)/Ru^(III)- Ru^(III) and Ru^(III)- Ru^(III)/ Ru^(II)- Ru^(II) reductions and a largely irreversible Ru^(V) - Ru^(V)/ Ru^(IV) - Ru^(IV)/oxidation. The dioxo dimer 2 oxidizes alcohols and aldehydes in organic media to afford 1 and the corresponding aldehydes and acids. Analogously, the Ru^(V) - Ru^(V)/ Ru^(IV)- Ru^(IV) redox wave mediates the electrooxidation of alcohols and aldehydes in aqueous buffer. In this system, substrates can be oxidized completely to CO_2. The kinetic behavior of these oxidations was examined by UV-vis and chronoamperometry, respectively, and the chemistry is typical of metal-oxo complexes, indicating that electronic coupling between two metal centers does not dramatically affect the metal-oxo chemistry. Dimer [H_21]^(2+) also reacts with alcohols, aldehydes, and triphenylphosphine in CH_3CN to afford Ru^(III)- Ru^(III) products including [(L_(oMe))CH_3CN) Ru^(III) (µ-OH)_2 Ru^(III) (NCCH_3)( L_(oMe))][CF_3SO_3]2 (characterized by X-ray crystallography) and the corresponding organic products. Reaction of 1 with formaldehyde in aqueous buffer quantitatively affords the triply bridged dimer [(L_(oMe)Ru^(III) (µ-OH)2- (µ-HCOO) Ru^(III) (L_(oMe)][CF_3SO_3] (characterized by X-ray crystallography). This reaction evidently proceeds by two parallel inner-sphere pathways, one of which is autocatalytic. Neither pathway exhibits a primary isotope effect suggesting the rate determining process could be the formation of an intermediate, perhaps a Ru^(IV) - Ru^(IV) formate adduct. The Ru^(III)- Ru^(III)formate adduct is easily oxidized to the Ru^(IV) - Ru^(IV) analog [(L_(oMe)Ru^(IV)(µ-OH)_2-(µ-HCOO) Ru^(IV) (L_(oMe)][CF_3SO_3], which, after isolation, reacts slowly with aqueous formaldehyde to generate free formate and the Ru^(III)- Ru^(III) formate adduct. These dimers function as catalysts for the electrooxidation of formaldehyde at low anodic potentials (+0.0 V versus SCE in aqueous buffer, pH 8.5) and enhance the activity of Nafion treated palladium/carbon heterogeneous fuel cell catalysts.

The design and synthesis of a true, heterogeneous, asymmetric catalyst

This work describes the design and synthesis of a true, heterogeneous, asymmetric catalyst. The catalyst consists of a thin film that resides on a high-surface- area hydrophilic solid and is composed of a chiral, hydrophilic organometallic complex dissolved in ethylene glycol. Reactions of prochiral organic reactants take place predominantly at the ethylene glycol-bulk organic interface.

The synthesis of this new heterogeneous catalyst is accomplished in a series of designed steps. A novel, water-soluble, tetrasulfonated 2,2'-bis (diphenylphosphino)-1,1'-binaphthyl (BINAP-4S0_3Na) is synthesized by direct sulfonation of 2,2'-bis(diphenylphosphino)-1,1'-binaphthyl (BINAP). The rhodium (I) complex of BINAP-4SO_3Na is prepared and is shown to be the first homogeneous catalyst to perform asymmetric reductions of prochiral 2-acetamidoacrylic acids in neat water with enantioselectivities as high as those obtained in non-aqueous solvents. The ruthenium (II) complex, [Ru(BINAP-4SO_3Na)(benzene)Cl]Cl is also synthesized and exhibits a broader substrate specificity as well as higher enantioselectivities for the homogeneous asymmetric reduction of prochiral 2-acylamino acid precursors in water. Aquation of the ruthenium-chloro bond in water is found to be detrimental to the enantioselectivity with some substrates. Replacement of water by ethylene glycol results in the same high e.e's as those found in neat methanol. The ruthenium complex is impregnated onto a controlled pore-size glass CPG-240 by the incipient wetness technique. Anhydrous ethylene glycol is used as the immobilizing agent in this heterogeneous catalyst, and a non-polar 1:1 mixture of chloroform and cyclohexane is employed as the organic phase.

Asymmetric reduction of 2-(6'-methoxy-2'-naphthyl)acrylic acid to the non-steroidal anti-inflammatory agent, naproxen, is accomplished with this heterogeneous catalyst at a third of the rate observed in homogeneous solution with an e.e. of 96% at a reaction temperature of 3°C and 1,400 psig of hydrogen. No leaching of the ruthenium complex into the bulk organic phase is found at a detection limit of 32 ppb. Recycling of the catalyst is possible without any loss in enantioselectivity. Long-term stability of this new heterogeneous catalyst is proven by a self-assembly test. That is, under the reaction conditions, the individual components of the present catalytic system self-assemble into the supported-catalyst configuration.

The strategies outlined here for the design and synthesis of this new heterogeneous catalyst are general, and can hopefully be applied to the development of other heterogeneous, asymmetric catalysts.

Multiplexed DNA-mediated electrochemistry

The aromatic core of double helical DNA possesses the unique and remarkable ability to form a conduit for electrons to travel over exceptionally long molecular distances. This core of π-stacked nucleobases creates an efficient pathway for charge transfer to proceed that is exquisitely sensitive to even subtle perturbations. Ground state electrochemistry of DNA-modified electrodes has been one of the major techniques used both to investigate and to harness the property of DNA-mediated charge transfer. DNA-modified electrodes have been an essential tool for both gaining insights into the fundamental properties of DNA and, due to the exquisite specificity of DNA-mediated charge transfer for the integrity of the π-stack, for use in next generation diagnostic sensing. Here, multiplexed DNA-modified electrodes are used to (i) gain new insights on the electrochemical coupling of metalloproteins to the DNA π-stack with relevance to the fundaments of in vivo DNA-mediated charge transfer and (ii) enhance the overall sensitivity of DNA-mediated reduction for use in the detection of low abundance diagnostic targets.

First, Methylene Blue (MB′) was covalently attached to DNA through a flexible C12 alkyl linker to yield a new redox reporter for DNA electrochemistry measurements with enhanced sensitivity. Tethered, intercalated MB′ was reduced through DNA-mediated charge transport. The redox signal intensity for MB′-dT-C12-DNA was found to be at least 3 fold larger than that of previously used Nile Blue (NB)-dT-DNA, which is coupled to the base stack via direct conjugation. The signal attenuation, due to an intervening mismatch, and therefore the degree of DNA-mediated reduction, does, however, depend on the DNA film morphology and the backfilling agent used to passivate the surface. These results highlight two possible mechanisms for the reduction of MB′ on the DNA-modified electrode that are distinguishable by their kinetics: reduction mediated by the DNA base pair stack and direct surface reduction of MB′ at the electrode. The extent of direct reduction at the surface can be minimized by overall DNA assembly conditions.

Next, a series of intercalation-based DNA-mediated electrochemical reporters were developed, using a flexible alkane linkage to validate and explore their DNA-mediated reduction. The general mechanism for the reduction of distally bound redox active species, covalently tethered to DNA through flexible alkyl linkages, was established to be an intraduplex DNA-mediated pathway. MB, NB, and anthraquinone were covalently tethered to DNA with three different covalent linkages. The extent of electronic coupling of the reporter was shown to correlate with the DNA binding affinity of the redox active species, supporting an intercalative mechanism. These electrochemical signals were shown to be exceptionally sensitive to a single intervening π-stack perturbation, an AC mismatch, in a densely packed DNA monolayer, which further supports that the reduction is DNA-mediated. Finally, this DNA-mediated reduction of MB occurs primarily via intra- rather than inter duplex intercalation, as probed through varying the proximity and integrity of the neighboring duplex DNA. Further gains to electrochemical sensitivity of our DNA-modified devices were then achieved through the application of electrocatalytic signal amplification using these solvent accessible intercalative reporters, MB-dT-C8, and hemoglobin as a novel electron sink. Electrocatalysis offers an excellent means of electrochemical signal amplification, yet in DNA based sensors, its application has been limited due to strict assembly conditions. We describe the use of hemoglobin as a robust and effective electron sink for electrocatalysis in DNA sensing on low density DNA films. Protein shielding of the heme redox center minimizes direct reduction at the electrode surface and permits assays on low density DNA films. Electrocatalysis of MB that is covalently tethered to the DNA by a flexible alkyl linkage allows for efficient interactions with both the base stack and hemoglobin. Consistent suppression of the redox signal upon incorporation of single CA mismatch in the DNA oligomer demonstrates that both the unamplified and the electrocatalytically amplified redox signals are generated through DNA-mediated charge transport. Electrocatalysis with hemoglobin is robust: it is stable to pH and temperature variations. The utility and applicability of electrocatalysis with hemoglobin is demonstrated through restriction enzyme detection, and an enhancement in sensitivity permits femtomole DNA sampling.

Finally, we expanded the application of our multiplexed DNA-modified electrodes to the electrochemical characterization of DNA-bound proteins containing [4Fe-4S] clusters. DNA-modified electrodes have become an essential tool for the characterization of the redox chemistry of DNA repair proteins that contain redox cofactors. Multiplexed analysis of EndonucleaseIII (EndoIII), a DNA repair protein containing a [4Fe-4S] cluster known to be accessible via DNA-mediated charge transport, elucidated subtle differences in the electrochemical behavior as a function of DNA morphology. DNA-bound EndoIII is seen to have two different electron transfer pathways for reduction, either through the DNA base stack or through direct surface reduction. Closely packed DNA films, where the protein has limited surface accessibility, produce electrochemical signals reflecting electron transfer that is DNA-mediated. The electrochemical comparison of EndoIII mutants, including a new family of mutations altering the electrostatics surrounding the [4Fe-4S] cluster, was able to be quantitatively performed. While little change in the midpoint potential was found for this family of mutants, significant variations in the efficiency of DNA-mediated electron transfer were apparent. Based on the stability of these proteins, examined by circular dichroism, we propose that the electron transfer pathway can be perturbed not only by the removal of aromatic residues, but also through changes in solvation near the cluster.

Modelling Lipid Competition Dynamics in Heterogeneous Protocell Populations

Recent experimental work in the field of synthetic protocell biology has shown that prebiotic vesicles are able to 'steal' lipids from each other. This phenomenon is driven purely by asymmetries in the physical state or composition of the vesicle membranes, and, when lipid resource is limited, translates directly into competition amongst the vesicles. Such a scenario is interesting from an origins of life perspective because a rudimentary form of cell-level selection emerges. To sharpen intuition about possible mechanisms underlying this behaviour, experimental work must be complemented with theoretical modelling. The aim of this paper is to provide a coarse-grain mathematical model of protocell lipid competition. Our model is capable of reproducing, often quantitatively, results from core experimental papers that reported distinct types vesicle competition. Additionally, we make some predictions untested in the lab, and develop a general numerical method for quickly solving the equilibrium point of a model vesicle population.

Development of the heterogeneous catalysts for the production of levulinic acid from furfuryl alcohol

207 p.