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PubMed2006

Different effects of nine clausenamide ennatiomers on liver glutathione biosynthesis and glutathione S-transferase activity in mice.

AIM: To study the effects of nine synthetic clausenamide with different stereo structures on liver glutathione (GSH) biosynthesis and glutathione S-transferase (GST) activity in mice. METHODS: The nine test compounds were racemic mixtures and their ennatiomers of clausenamide, neoclausenamide and epineoclausenamide. Mice were administered clausenamide 250 mg/kg once daily for 3 consecutive days, ig, and were killed 24 h after the last dosing. The mouse liver cytosol GSH and GST were determined with related biochemical methods. RESULTS: Nine clausenamides exhibited different effects on liver GSH and GST. Of nine clausenamides, only (+) and (+/-)clausenamide markedly increased liver cytosol GSH content. The mechanism of increasing liver GSH content of (+)clausenamide is mainly due to stimulating the key limiting enzyme gamma-glutamylcysteine synthetase (gamma-GCS) activity for GSH biosynthesis. The other test clausenamides had no such effect on liver GSH. All of the nine clausenamides induced a significant increase of GST activity. CONCLUSION: The effects of clausenamide ennatiomers on liver GST and GSH varied with the alterations of their spatial structures. (+)Clausenamide stimulated liver GSH biosynthesis through enhancing gamma-GCS activity.

Animals↗
PubMed1992

Complete 15N and 1H NMR assignments for the amino-terminal domain of the phage 434 repressor in the urea-unfolded form.

The amino-terminal domain of the phage 434 repressor consisting of residues 1-69 forms a globular structure of five tightly packed helices, with nearly identical molecular architectures in crystals and in solution. Upon addition of urea to an aqueous solution of this protein, the NMR spectrum of a second form of the protein appears in addition to the native form, and at a urea concentration of 7 M, this urea-unfolded form is the only species observed. At intermediate urea concentrations, the two forms of the protein inter-convert at a rate that allows the observation of the exchange process by NMR. Starting from the previous assignments for the native protein, we obtained nearly complete sequence-specific (1)H and (15)N NMR assignments for the unfolded form of the protein. For most amino acid residues, the (1)H chemical shifts of the urea-unfolded protein are very similar to the random coil values, but some discrete regions of the polypeptide chain were identified that are likely to retain residual nonrandom spatial structure as evidenced by deviations of (1)H chemical shifts and amide proton exchange rates from the expected random coil values.

Amino Acid Sequence↗
PubMed2002

Synthesis, structural evaluation, and estrogen receptor interaction of 2,3-diarylpiperazines.

To develop novel estrogen receptor (ER) ligands, ring-fused derivatives of the hormonally active (1R,2S)/(1S,2R)-1-(2-chloro-4-hydroxyphenyl)-2-(2,6-dichloro-4-hydroxyphenyl)ethylenediamine 4b were synthesized. (2R,3S)/(2S,3R)-2-(2-Chloro-4-hydroxyphenyl)-3-(2,6-dichloro-4-hydroxyphenyl)piperazine 4 induced ligand-dependent gene expression in MCF-7-2a cells, stably transfected with the plasmid ERE(wtc)luc and was therefore used as a lead structure. The influence of the substitution pattern in the aromatic rings (4-OH (1), 2-F,4-OH (2), 2-Cl,4-OH (3), 2,6-Cl2,3-OH (5), and 2,6-Cl2,4-OH (6)) and the effect of N-ethyl chains on the ER binding and activation of gene expression were studied. The synthesis started from the respective methoxy-substituted (1R,2S)/(1S,2R)-configurated 1,2-diarylethylenediamines 6b to 4b, which were reacted with dimethyl oxalate in order to get 5,6-diarylpiperazine-2,3-diones. Reduction with BH3*tetrahydrofuran and ether cleavage with BBr3 yielded the piperazines 1-6. The N-alkylation of the piperazines 1a-3a, which was employed for obtaining compounds 7-11, was succeeded by acetic anhydride followed by reduction and ether cleavage. Nuclear magnetic resonance (NMR) spectroscopical studies revealed a synclinal conformation of the 1,2-diarylethane pharmacophore and a preference of the substituents at the heterocyclic ring for an equatorial position. This spatial structure prevents an interaction with the ER analogously to that of estradiol (E2). Therefore, the piperazines can displace E2 from its binding site only to a very small extent. Only the N-ethyl (8) and N,N'-diethyl (11) derivatives of piperazine 3 showed relative binding affinity values > 0.1% (8, 0.42%, and 11, 0.17%). Nevertheless, ER-mediated gene activation was verified for the piperazines 4 (20%), 6 (73%), 7 (34%), 8 (74%), and 11 (37%) (concentration, 1 microM; E2, 100% activation) on the MCF-7-2a cell line. O-methylation led to completely inactive compounds and showed the necessity of H bridges from the piperazines to the ER for activating gene expression.

Animals↗
PubMed1990

Protein--DNA contacts in the structure of a homeodomain--DNA complex determined by nuclear magnetic resonance spectroscopy in solution.

The 1:1 complex of the mutant Antp(C39----S) homeodomain with a 14 bp DNA fragment corresponding to the BS2 binding site was studied by nuclear magnetic resonance (NMR) spectroscopy in aqueous solution. The complex has a molecular weight of 17,800 and its lifetime is long compared with the NMR chemical shift time scale. Investigations of the three-dimensional structure were based on the use of the fully 15N-labelled protein, two-dimensional homonuclear proton NOESY with 15N(omega 2) half-filter, and heteronuclear three-dimensional NMR experiments. Based on nearly complete sequence-specific resonance assignments, both the protein and the DNA were found to have similar conformations in the free form and in the complex. A sufficient number of intermolecular 1H-1H Overhauser effects (NOE) could be identified to enable a unique docking of the protein on the DNA, which was achieved with the use of an ellipsoid algorithm. In the complex there are intermolecular NOEs between the elongated second helix in the helix-turn-helix motif of the homeodomain and the major groove of the DNA. Additional NOE contacts with the DNA involve the polypeptide loop immediately preceding the helix-turn-helix segment, and Arg5. This latter contact is of special interest, both because Arg5 reaches into the minor groove and because in the free Antp(C39----S) homeodomain no defined spatial structure could be found for the apparently flexible N-terminal segment comprising residues 0-6.

Animals↗
PubMed1997

[1H-15N NMR signal assignment and secondary structure of bacteriorhodopsin (1-231) in solution].

15N-Labeled de-(232-248)-bacteriorhodopsin [BR(1-231)] was solubilized in 1:1 chloroform-methanol solvent mixture that contained 1.0 M 2HCO2N2H4 and mimic membrane medium. Resonances in the 1H-15N heteronuclear multiple-quantum coherence (HMQC) spectrum of BR (1-231) were assigned using the data of two- and three-dimensional NMR experiments. Of 117 cross-peaks present in the 1H-15N HMQC spectrum, 98 were assigned to residues in 1-75 and 193-231 segments of the protein. Almost all cross-peaks that correspond to the 76-192 segment were absent in the HMQC spectrum (except for six cross-peaks from the side chains and 14 cross-peaks from the backbone). Deuterium exchange rates of amide protons and cross-peaks of nuclear Overhauser effect helped to localize helices A (residues 8-30), B (residues 40-65), and G (residues 198-226). The periodicity in the rates of deuterium exchange of NH protons of helices A, B, and G was explained by the compact arrangement of these helices in the protein globule. The broadening of signals from six residues in helix G, which, according to the electron cryomicroscopy model of bacteriorhodopsin, is in contact with the NMR-unobservable bundle of helices CDEF, indicates specific interactions of the helices in BR(1-231). These data suggest that BR(1-231) solubilized in an organic medium has a spatial structure similar to that in the electron cryomicroscopy model of BR.

Amino Acids↗
PubMed1993

Comparing the human and schistosomal hypoxanthine-guanine phosphoribosyltransferases by circular dichroism.

The hypoxanthine-guanine phosphoribosyltransferases (HGPRTases) of human and the parasitic trematode, Schistosoma mansoni, are of biomedical importance. The conformations of these two enzymes were studied by circular dichroism (CD). The schistosomal HGPRTase is estimated to contain 27% alpha-helix and 30% beta-structure. This result is consistent with what is predicted from a tertiary model (Craig, S.P., Cohen, F.E., Yuan, L., McKerrow, J.H. and Wang, C.C. (1991) in Molecular & Immunological Aspects of Parasitism (Wang, C.C., ed.), pp. 122-138, Am. Assoc. Adv. Sci., Washington DC, USA), which proposes that the enzyme is an alpha/beta barrel protein. The human enzyme is estimated to contain 21% alpha-helix and 53% beta-form. The two enzymes are different in their thermostability. The human enzyme remains active after being heated to 85 degrees C for 15 min, while the schistosomal enzyme only retains its activity at temperature below 65 degrees C. The transition temperature (T1/2) of the schistosomal HGPRTase was determined by CD measurement to be 57.5 degrees C. One of the enzyme substrates, phosphoribose pyrophosphate (PRPP), stabilizes the HGPRTases by preventing the human enzyme from unfolding at 85 degrees C and partially protecting the schistosomal enzyme from unfolding at 65 degrees C. It is suggested that the amino-acid substitutions in the human enzyme improve the spatial structure and stability of its alpha-helices, which may lead to an enhanced thermostability.

Amino Acid Sequence↗
PubMed2003

Temporal dynamics of linguistic processes are reorganized in aphasics' cortex: an EEG mapping study.

Brain lesions are known to elicit reorganization of function in representational cortex. Using linguistic function as an example, we show that (a) injury-related reorganization may also be observed in language-related cortex and (b) this reorganization not only appears in cortical space but also in the dynamic flow of activity. The present study investigated cortical reorganization in a group of 10 nonfluent aphasics who demonstrated partial recovery of linguistic functions. Compared with controls, linguistic functions were organized in an atypical manner, both in terms of spatial structures involved and in the time course of the linguistic processes, from word reading to late stages of word encoding in working memory. For this purpose, event-related potentials were recorded in a two-stimulus design comprising phonological and semantic tasks. Subjects were asked to judge whether two words, separated by a 2-s interval, rhymed (phonological task) or were semantically associated. During word reading of the phonological task, controls showed negativity/activation over occipital sites, whereas patients displayed negativity at left-medial orbitofrontal locations anterior to the common sites of lesion. During the subsequent 2-s interval associated with word encoding, the two groups showed a reversed pattern: significant left-right anterior asymmetry prevailed in controls, whereas lateralization was absent in patients. Aphasics displayed maximum positivity/inhibition over the left frontal regions, at the typical site of lesion. Compared with controls, patients exhibited significant disinhibition (decreased positivity) of right frontal areas and greater activation of left temporal sites. These results suggest that the concept of language plasticity should include, in addition to spatial aspects of linguistic reorganization, the reorganized temporal dynamics associated with recovery of impaired functions.

Adult↗
PubMed2006

Single proline residues can dictate the oxidative folding pathways of cysteine-rich peptides.

The cysteine-rich N and C-terminal domains of minicollagen-1 from Hydra nematocysts fold with excesses of oxidized/reduced glutathione (10:1) into globular structures with distinct cystine frameworks despite their identical cysteine sequence pattern. An additional main difference is the cis conformation of a conserved proline residue in the N-terminal and the trans conformation of this residue in the C-terminal domain. Comparative analysis of the oxidative folding revealed for the C-terminal domain a fast and highly cooperative formation of a single disulfide isomer. Conversely, oxidation of the N-terminal domain proceeds mainly via an intermediate that results from the fast quasi-stochastic disulfide formation according to the proximity rule. The rate of conversion of the bead-like isomer into the globular end-product is largely dominated by the trans-to-cis isomerization of the critical proline residue as well assessed by its replacement with (4R)- and (4S)-fluoroproline known to exhibit distinct propensities for the trans and cis conformation, respectively. Independently, whether the trans or cis conformation is favored by these substitutions, both analogues retain sufficient sequence-encoded information to fold almost quantitatively into the identical cystine framework and thus spatial structure of the parent peptide with the critical proline residue as cis isomer, but at rates significantly lower for the (4R) than for the (4S)-fluoroproline analogue. Correspondingly, other sequence-encoded structural elements have to act as a driving force for these unidirectional folding pathways despite the rather simple sequence composition consisting only of aliphatic residues, some proline and only one aromatic residue (tyrosine) in the core parts of the C and N-terminal domains. The two cysteine-rich domains of minicollagen-1 may well represent ideal targets for ab initio structure calculations in order to learn more about the elementary information encoded in such primordial molecules.

Amino Acid Sequence↗
PubMed1997

Stringent structural and sequence requirements of the human herpesvirus 6B lytic-phase origin of DNA replication.

The lytic-phase origin of DNA replication from human herpesvirus 6B (HHV-6B oriLyt) contains two binding sites for the origin-binding protein (OBPH6B), both of which are required for DNA replication and which are separated by an AT-rich spacer. We have tested the functional significance of the structural, spatial and sequence characteristics of this spacer element by constructing a series of mutated origin sequences and analysing their replication efficiency. Changes in the sequence composition of length of the spacer resulted in dramatic decreases in replication efficiency. Furthermore, in contrast to what has been observed for herpes simplex virus type 1 (HSV-1) oriS, insertion of a complete helical turn of DNA into the spacer also resulted in abrogation of origin function. These data suggest that the arrangement of OBP sites in HHV-6B oriLyt is stringently constrained in terms of spacing and intervening sequence.

Base Sequence↗
PubMed1988

[Increased substrate selectivity during transition from Ca2+-activated to K+,EDTA-activated nucleoside triphosphatase activity of heavy meromyosin].

A comparison of kinetic parameters (Km(app) and V) of hydrolysis by heavy meromyosin of natural (ATP and ITP) and modified nucleoside triphosphates showed that in the K+, EDTA-ATPase conformation the enzyme exhibited a higher selectivity towards the structure of the substrate nucleoside moiety than in the case of the Ca2+-stimulated nucleoside triphosphatase activity. In the presence of Ca2+, all the N1- and N6-substituted analogs of ATP as well as ITP, etheno-ATP and the dialdehyde derivative of ATP were hydrolyzed at a high rate irrespective of their markedly decreased affinity for heavy meromyosin. In the presence of K+, EDTA the ATPase activity showed a tendency for a total decrease of the analog affinity for nucleoside triphosphates, i.e., the impossibility of tight binding of the substrate phosphate residues to the protein in the absence of bivalent cations, which was concomitant with an increase in the hydrolysis rate. However, it was found that only in N1-substituted analogs any appreciable changes in the substrate properties were absent. All the other nucleoside triphosphates tested (N6-carboxy-methoxy-ATP, N6-(N'-acetylaminoethoxy)-ATP, etheno-ATP, ITP and the dialdehyde derivative of ATP having a rupture in the ribose ring) lost their ability to be hydrolyzed by heavy meromyosin. The experimental results as well as the literature data are suggestive of differences in the spatial structure of the active center in two different myosin conformations associated with a high catalytic activity, i.e., K+, EDTA-ATPase and Ca2+-ATPase.

Adenosine Triphosphatases↗
PubMed1997

Insensitivity of V1 complex cell responses to small shifts in the retinal image of complex patterns.

An important role for neurons in the early visual system is to convey information about the structure of visual stimuli. However, neuronal responses show substantial variation across presentations of the same stimulus. In awake monkeys, it has been assumed that a great deal of this variation is related to the scatter in eye position (inducing scatter in the retinal position of the stimulus). Here we investigate the implied consequence of this assumption, i.e., that the scatter variation in eye position degrades the decodability of the neural response. We recorded from 50 complex cells in primary visual cortex of fixating monkeys while different complex stimuli were presented. Three types of retinal shifts were considered: natural scatter in the fixation, systematic fixation point shift, and systematic stimulus position shift. The stimulus pattern accounts for >50% of the response variance, always six times that accounted for by the scatter in eye position during fixation. The retinal location of a stimulus had to be shifted by 10-12 min of arc, an amount almost two times larger than the smallest picture element, before the responses changed systematically. Nonetheless, changes of the stimulus at the single pixel level often gave rise to discriminable responses. Thus complex cells convey information about the spatial structure of a stimulus, independent of rigid stimulus displacements on the order of the receptive field size or smaller.

Animals↗
PubMed2006

Molecular basis of substrate specificity in family 1 glycoside hydrolases.

ss-glycosidases are active upon a large range of substrates. Besides this, subtle changes in the substrate structure may result in large modifications on the ss-glycosidase activity. The characterization of the molecular basis of ss-glycosidases substrate preference may contribute to the comprehension of the enzymatic specificity, a fundamental property of biological systems. ss-glycosidases specificity for the monosaccharide of the substrate nonreducing end (glycone) is controlled by a hydrogen bond network involving at least 5 active site amino acid residues and 4 substrate hydroxyls. From these residues, a glutamate, which interacts with hydroxyls 4 and 6, seems to be a key element in the determination of the preference for fucosides, glucosides and galactosides. Apart from this, interactions with the hydroxyl 2 are essential to the ss-glycosidase activity. The active site residues forming these interactions and the pattern of the hydrogen bond network are conserved among all ss-glycosidases. The region of the ss-glycosidase active site that interacts with the moiety (called aglycone) which is bound to the glycone is formed by several subsites (1 to 3). However, the majority of the non-covalent interactions with the aglycone is concentrated in the first one, which presents a variable spatial structure and amino acid composition. This structural variability is in accordance with the high diversity of aglycones recognized by ss-glycosidases. Hydrophobic interactions and hydrogen bonds are formed with the aglycone, but the manner in which they control the ss-glycosidase specificity still remains to be determined.

Amino Acid Sequence↗
PubMedDate not supplied

[Thin layer chromatography of coordinated Ag+-complexes of plant diacylglycerols].

Coordination complexes of unsaturated rac-1,2-diacylglycerols (DAGs) with silver ions were separated by adsorption and reversed-phase TLC (Ag-TLC and Ag-rpTLC, respectively). During the Ag-TLC, the silver ion complexes were shown to be formed by the DAG coordination centers of various structures and only on the adsorbent surface. Separation of the complexes proceeds according to the adsorption mechanism, and there is an inverse exponential functional relationship between the DAG mobility and their double bond number. Meanwhile, during the Ag-rpTLC, the Ag(+)-complexes are formed only with double bonds, only in solution, and at a 1:1 ratio. The complexes are fractionated by partitioning between two liquid phases, and the relationship between the mobility and unsaturation of these complexes is directly proportional. Nevertheless, despite all the differences between the two TLC methods, the polarity of DAGs with a bent configuration of their acyl chains greatly exceeds that of DAGs with the same unsaturation but with the acyl-chain conformation close to extended: it is two to three times greater in Ag-TLC and 30-40% greater in Ag-rpTLC. In addition, the relationship between the mobility and unsaturation of DAG complexes exhibits quantitative rather than qualitative differences in both versions of argentation TLC. Thus, under all conditions of argentation liquid chromatography, the mobility of complexes and, therefore, their polarity are determined not only by their composition (unsaturation), but also by the spatial structure (conformation) of their molecules.

Chromatography, High Pressure Liquid↗
PubMed2006

Assortative mating and differential male mating success in an ash hybrid zone population.

BACKGROUND: The structure and evolution of hybrid zones depend mainly on the relative importance of dispersal and local adaptation, and on the strength of assortative mating. Here, we study the influence of dispersal, temporal isolation, variability in phenotypic traits and parasite attacks on the male mating success of two parental species and hybrids by real-time pollen flow analysis. We focus on a hybrid zone population between the two closely related ash species Fraxinus excelsior L. (common ash) and F. angustifolia Vahl (narrow-leaved ash), which is composed of individuals of the two species and several hybrid types. This population is structured by flowering time: the F. excelsior individuals flower later than the F. angustifolia individuals, and the hybrid types flower in-between. Hybrids are scattered throughout the population, suggesting favorable conditions for their local adaptation. We estimate jointly the best-fitting dispersal kernel, the differences in male fecundity due to variation in phenotypic traits and level of parasite attack, and the strength of assortative mating due to differences in flowering phenology. In addition, we assess the effect of accounting for genotyping error on these estimations. RESULTS: We detected a very high pollen immigration rate and a fat-tailed dispersal kernel, counter-balanced by slight phenological assortative mating and short-distance pollen dispersal. Early intermediate flowering hybrids, which had the highest male mating success, showed optimal sex allocation and increased selfing rates. We detected asymmetry of gene flow, with early flowering trees participating more as pollen donors than late flowering trees. CONCLUSION: This study provides striking evidence that long-distance gene flow alone is not sufficient to counter-act the effects of assortative mating and selfing. Phenological assortative mating and short-distance dispersal can create temporal and spatial structuring that appears to maintain this hybrid population. The asymmetry of gene flow, with higher fertility and increased selfing, can potentially confer a selective advantage to early flowering hybrids in the zone. In the event of climate change, hybridization may provide a means for F. angustifolia to further extend its range at the expense of F. excelsior.

Evolution, Molecular↗
PubMed1989

Aspects of the lognormal function in the analysis of regional population distribution.

"The spatial structure of population within a metropolitan-area-based region is approached via the population density function, in much the same way as has been undertaken for a city or metropolitan area.... The concern in the balance of the paper is with certain properties lognormal form.... Consideration is given first to properties based on density. The population form of the lognormal function is then derived, and properties based on population are examined. Attention is also given to relationships among density-based and population-based properties." The approach is illustrated using data for London, England, for the period 1971-1981.

Demography↗
PubMed2026

Experimental evolution reveals contrasting adaptive landscapes in lab and field environments.

Experimental evolution is widely used to infer microbial responses to environmental change, yet most laboratory studies impose constant, well-mixed conditions that differ fundamentally from fluctuating, spatially structured field environments. We compared genomic evolution in the leaf litter-associated bacterium Curtobacterium strain MMLR14_002 under control and warming treatments in laboratory culture and in a complementary field experiment. Laboratory-derived isolates accumulated more mutations per genome and exhibited stronger locus-level parallelism, with mutations recurring in a small number of coding loci. Field-derived isolates accumulated fewer mutations per genome, and these mutations rarely occurred in the same coding loci across replicate populations. Instead, field isolates exhibited a higher proportion of intergenic mutations, with mutations recurring in the same intergenic regions across independent field deployments. When coding mutations were detected in the field, they were distributed across functionally diffuse targets and more often involved metabolic pathways than the core cellular processes repeatedly targeted during laboratory evolution. Warming itself did not consistently influence mutation accumulation or the genomic distribution of mutations; instead, laboratory and field contexts primarily shaped the accumulation, targets, and repeatability of genomic change. These results suggest that laboratory thermal evolution identifies adaptive routes favored under sustained selection but may overestimate coding-level parallelism under heterogeneous field conditions. Bridging laboratory and field evolution will likely require experimental designs that incorporate temporal variability and spatial heterogeneity characteristic of natural systems.IMPORTANCEA central goal of experimental evolution is to infer how microbes evolve in nature from laboratory studies. Here, we evaluate this assumption by comparing genomic evolution of a leaf litter-associated Curtobacterium strain in laboratory and field warming experiments to identify broad patterns rather than isolate the contribution of any single environmental factor. We find that the strong parallelism at coding loci observed under laboratory conditions is reduced in the field, while mutations recurring in the same intergenic regions across field deployments suggest that parallel evolution in nature may more often involve regulatory noncoding regions rather than coding targets. These results show that environmental context reshapes adaptive landscapes and may limit the parallelism of coding-level genomic responses inferred from homogeneous laboratory conditions.

experimental evolution↗
PubMedDate not supplied

Introduction of wavelet analyses to rainfall/runoffs relationship for a karstic basin: the case of Licq-Atherey karstic system (France).

Karstic systems are highly heterogeneous geological formations characterized by a multiscale temporal and spatial hydrologic behavior with more or less localized temporal and spatial structures. Classical correlation and spectral analyses cannot take into account these properties. Therefore, it is proposed to introduce a new kind of transformation: the wavelet transform. Here we focus particularly on the use of wavelets to study temporal behavior of local precipitation and watershed runoffs from a part of the karstic system. In the first part of the paper, a brief mathematical overview of the continuous Morlet wavelet transform and of the multiresolution analysis is presented. An analogy with spectral analyses allows the introduction of concepts such as wavelet spectrum and cross-spectrum. In the second part, classical methods (spectral and correlation analyses) and wavelet transforms are applied and compared for daily rainfall rates and runoffs measured on a French karstic watershed (Pyrénées) over a period of 30 years. Different characteristic time scales of the rainfall and runoff processes are determined. These time scales are typically on the order of a few days for floods, but they also include significant half-year and one-year components and multi-annual components. The multiresolution cross-analysis also provides a new interpretation of the impulse response of the system. To conclude, wavelet transforms provide a valuable amount of information, which may be now taken into account in both temporal and spatially distributed karst modeling of precipitation and runoff.

Disasters↗
PubMed1997

The evolution of cooperation in a lattice-structured population.

The evolution of cooperation among unrelated individuals is studied in a lattice-structured habitat, where individuals interact locally only with their neighbors. The initial population includes Tit-for-Tat (abbreviated as TFT, indicating a cooperative strategy) and All Defect (AD, a selfish strategy) distributed randomly over the lattice points. Each individual plays the iterated Prisoner's Dilemma game with its nearest neighbors, and its total pay-off determines its instantaneous mortality. After the death of an individual, the site is replaced immediately by a copy of a randomly chosen neighbor. Mathematical analyses based on mean-field approximation, pair approximation, and computer simulation are applied. Models on one and two-dimensional regular square lattices are examined and compared with the complete mixing model. Results are: (1) In the one-dimensional model, TFT players come to form tight clusters. As the probability of iteration w increases, TFTs become more likely to spread. The condition for TFT to increase is predicted accurately by pair approximation but not by mean-field approximation. (2) If w is sufficiently large, TFT can invade and spread in an AD population, which is impossible in the complete mixing model where AD is always ESS. This is also confirmed by the invasion probability analysis. (3) The two-dimensional lattice model behaves somewhat in between the one-dimensional model and the complete mixing model. (4) The spatial structure modifies the condition for the evolution of cooperation in two different ways: it facilitates the evolution of cooperation due to spontaneously formed positive correlation between neighbors, but it also inhibits cooperation because of the advantage of being spiteful by killing neighbors and then replacing them.

Animals↗