Plekhg4 is a novel Dbl family guanine nucleotide exchange factor protein for rho family GTPases

Mutations in the PLEKHG4 (puratrophin-1) gene are associated with the heritable neurological disorder autosomal dominant spinocerebellar ataxia. However, the biochemical functions of this gene product have not been described. We report here that expression of Plekhg4 in the murine brain is developmentally regulated, with pronounced expression in the newborn midbrain and brainstem that wanes with age and maximal expression in the cerebellar Purkinje neurons in adulthood. We show that Plekhg4 is subject to ubiquitination and proteasomal degradation, and its steady-state expression levels are regulated by the chaperones Hsc70 and Hsp90 and by the ubiquitin ligase CHIP. On the functional level, we demonstrate that Plekhg4 functions as a bona fide guanine nucleotide exchange factor (GEF) that facilitates activation of the small GTPases Rac1, Cdc42, and RhoA. Overexpression of Plekhg4 in NIH3T3 cells induces rearrangements of the actin cytoskeleton, specifically enhanced formation of lamellopodia and fillopodia. These findings indicate that Plekhg4 is an aggregation-prone member of the Dbl family GEFs and that regulation of GTPase signaling is critical for proper cerebellar function.

Lewy body-like α-synuclein aggregates resist degradation and impair macroautophagy

Cytoplasmic α-synuclein (α-syn) aggregates, referred to as Lewy bodies, are pathological hallmarks of a number of neurodegenerative diseases, most notably Parkinson disease. Activation of macroautophagy is suggested to facilitate degradation of certain proteinaceous inclusions, but it is unclear if this pathway is capable of degrading α-syn aggregates. Here, we examined this issue by utilizing cellular models in which intracellular Lewy body-like α-syn inclusions accumulate after internalization of pre-formed α-syn fibrils into α-syn-expressing HEK293 cells or cultured primary neurons. We demonstrate that α-syn inclusions cannot be effectively degraded, even though they co-localize with essential components of both the autophagic and proteasomal protein degradation pathways. The α-syn aggregates persist even after soluble α-syn levels have been substantially reduced, suggesting that once formed, the α-syn inclusions are refractory to clearance. Importantly, we also find that α-syn aggregates impair overall macroautophagy by reducing autophagosome clearance, which may contribute to the increased cell death that is observed in aggregate-bearing cells.

The Aggregation of Brucella abortus Occurs Under Microaerobic Conditions and Promotes Desiccation Tolerance and Biofilm Formation

Brucella abortus causes brucellosis mainly in cattle. The infection is transmitted to humans by ingestion of animal products or direct contact with infected material. While the intracellular lifestyle of Brucella is well characterized, its extracellular survival is poorly understood. In nature, bacterial persistence is associated with biofilms, where aggregated cells are protected from adversity. The inability of Brucella abortus to aggregate under aerobiosis and that fact that the replicative niche of Brucella is characterized by microaerobic conditions prompted us to investigate the capacity of this pathogen to aggregate and grow in biofilms under microaerobiotic conditions. The results show that B. abortus aggregates and produces biofilms. The aggregates tolerate desiccation better than planktonic cells do, adhere and displace even in the absence of the lipopolysaccharide-O antigen, flagella, the transcriptional regulator VjbR, or the enzymes that synthesize, transport, and modify cyclic β (1,2) glucan.

Mechanism of an ATP-independent protein disaggregase: I. structure of a membrane protein aggregate reveals a mechanism of recognition by its chaperone

BACKGROUND

A novel chaperone, cpSRP43, recognizes and disassembles the aggregates formed by its client proteins.

RESULTS

The client proteins of cpSRP43 form stable disc-shaped aggregates with the chaperone recognition motif displayed onthe surface.

CONCLUSION

The surface-exposed motif on the aggregate allows it to be recognized by its chaperone.

SIGNIFICANCE

Understanding the structure and energetics of protein aggregates provides insights into the mechanism of theirDISASSEMBLY.Protein aggregation is detrimental to the maintenance of proper protein homeostasis in all cells. To overcome this problem, cells have evolved a network of molecular chaperones to prevent protein aggregation and even reverse existing protein aggregates. The most extensively studied disaggregase systems are ATP-driven macromolecular machines. Recently, we reported an alternative disaggregase system in which the 38-kDa subunit of chloroplast signal recognition particle (cpSRP43) efficiently reverses the aggregation of its substrates, the light-harvesting chlorophyll a/b-binding (LHC) proteins, in the absence of external energy input. To understand the molecular mechanism of this novel activity, here we used biophysical and biochemical methods to characterize the structure and nature of LHC protein aggregates. We show that LHC proteins form micellar, disc-shaped aggregates that are kinetically stable and detergent-resistant. Despite the nonamyloidal nature, the LHC aggregates have a defined global organization, displaying the chaperone recognition motif on its solvent-accessible surface. These findings suggest an attractive mechanism for recognition of the LHC aggregate by cpSRP43 and provide important constraints to define the capability of this chaperone.

A new approach for aggregation of Paramecium caudatum by nitric oxide

BACKGROUND AND OBJECTIVES

Nitric oxide (NO) plays a role in thermoregulation and growth of protozoa. This work aimed to add the molecule NO in physiology of protozoa in contact with abused narcotic substances.

MATERIALS AND METHODS

A sedative drug, morphine, was infused into a cell chamber containing Paramecia. The cell response to the drug was recorded promptly after drug infusion using a potency protocol provided for the first time at this laboratory. A precursor of NO, L-arginine, was treated jointly with drug to involve the NO system in protozoan performance to drug exposure. Marking of NADPH-diaphorase (NADPH-d) was followed to provide data to explain the mechanisms.

RESULTS

Morphine particularly (0.5 to 60 µg/µ1) aggregated the Paramecia. The infusion of L-arginine (1 to 8 µg/µ1) together with morphine potentiated this effect, though, pre-usage of L-NAME (1 to 8 µg/µ1), a blocker of NO production, reversed the response. Notably the activation of NADPH-d in solely morphine or L-arginine plus morphine samples was revealed. However, the expression of marker was attenuated upon pre-infusion with L-NAME.

CONCLUSION

This study introduces a new approach to involve NO in physiology of aggregation of Paramecia following exposure to the misused sedative drug, morphine.

A Fluorescent Styrylquinoline with Combined Therapeutic and Diagnostic Activities against Alzheimer's and Prion Diseases

(E)-6-Methyl-4'-amino-2-styrylquinoline (3) is a small molecule with the proper features to potentially diagnose, deliver therapy and monitor response to therapy in protein misfolding diseases. These features include compound fluorescent emission in the NIR region and its ability to interact with both Aβ and prion fibrils, staining them with high selectivity. Styrylquinoline 3 also inhibits Aβ self-aggregation in vitro and prion replication in the submicromolar range in a cellular context. Furthermore, it is not toxic and is able to cross the blood brain barrier in vitro (PAMPA test).

Strategies to stabilize compact folding and minimize aggregation of antibody-based fragments

Monoclonal antibodies (mAbs) have proven to be useful for development of new therapeutic drugs and diagnostic techniques. To overcome the difficulties posed by their complex structure and folding, reduce undesired immunogenicity, and improve pharmacokinetic properties, a plethora of different Ab fragments have been developed. These include recombinant Fab and Fv segments that can display improved properties over those of the original mAbs upon which they are based. Antibody (Ab) fragments such as Fabs, scFvs, diabodies, and nanobodies, all contain the variable Ig domains responsible for binding to specific antigenic epitopes, allowing for specific targeting of pathological cells and/or molecules. These fragments can be easier to produce, purify and refold than a full Ab, and due to their smaller size they can be well absorbed and distributed into target tissues. However, the physicochemical and structural properties of the immunoglobulin (Ig) domain, upon which the folding and conformation of all these Ab fragments is based, can limit the stability of Ab-based drugs. The Ig domain is fairly sensitive to unfolding and aggregation when produced out of the structural context of an intact Ab molecule. When unfolded, Ab fragments may lose their specificity as well as establish non-native interactions leading to protein aggregation. Aggregated antibody fragments display altered pharmacokinetic and immunogenic properties that can augment their toxicity. Therefore, much effort has been placed in understanding the factors impacting the stability of Ig folding at two different levels: 1) intrinsically, by studying the effects of the amino acid sequence on Ig folding; 2) extrinsically, by determining the environmental conditions that may influence the stability of Ig folding. In this review we will describe the structure of the Ig domain, and the factors that impact its stability, to set the context for the different approaches currently used to achieve stable recombinant Ig domains when pursuing the development of Ab fragment-based biotechnologies.

Effects of water chemistry on aggregation and soil adsorption of silver nanoparticles

OBJECTIVES

In this study, we investigated the influence of ionic strength and natural organic matter (NOM) on aggregation and soil adsorption of citrate-coated silver nanoparticles (AgNPs).

METHODS

Time-resolved dynamic light scattering measurements and batch adsorption experiments were used to study their aggregation and soil adsorption behaviors, respectively.

RESULTS

The aggregation rate of AgNPs increased with increasing ionic strength and decreasing NOM concentration. At higher ionic strength, the AgNPs were unstable, and thus tended to be adsorbed to the soil, while increased NOM concentration hindered soil adsorption. To understand the varying behaviors of AgNPs depending on the environmental factors, particle zeta potentials were also measured as a function of ionic strength and NOM concentration. The magnitude of particle zeta potential became more negative with decreasing ionic strength and increasing NOM concentration. These results imply that the aggregation and soil adsorption behavior of AgNPs were mainly controlled by electrical double-layer repulsion consistent with the Derjaguin-Landau-Verwey-Overbeek theory.

CONCLUSIONS

This study found that the aggregation and soil adsorption behavior of AgNPs are closely associated with environmental factors such as ionic strength and NOM and suggested that assessing the environmental fate and transport of nanoparticles requires a thorough understanding of particle-particle interaction mechanisms.

Aggregation of Human Eyelid Adipose-derived Stem Cells by Human Body Fluids

Fetal bovine serum (FBS) is the most frequently used serum for the cultivation of mammalian cells. However, since animal-derived materials might not be appropriate due to safety issues, allogeneic human serum (HS) has been used to replace FBS, particularly for the culture of human cells. While there has been a debate about the advantages of HS, its precise effect on human adult stem cells have not been clarified. The present study aimed to investigate the effect of HS on the human eyelid adipose stem cells (HEACs) in vitro. When HEACs were cultivated in a medium containing 10% HS, many cells moved into several spots and aggregated there. The phenomenon was observed as early as 9 days following 10% HS treatment, and 12 days following 5% HS plus 5% FBS treatment. However, the aggregation was never observed when the same cells were cultivated with 10% FBS or bovine serum albumin. To examine whether cell density might affect the aggregation, cells were seeded with different densities on 12-well dish. Until the beginning of aggregation, cells seeded at low densities exhibited the longest culture period of 16 days whereas cells seeded at high densities showed the shortest period of 9 days to form aggregation. The number of cells was 15.1±0.2×10⁴ as the least for the low density group, and 29.3±2.8×10⁴ as the greatest for the high density group. When human cord blood serum or normal bovine serum was examined for the same effect on HEACs, interestingly, cord blood serum induced the aggregation of cells whereas bovine serum treatment has never induced. When cells were cultivated with 10% HS for 9 days, they were obtained and analyzed by RT-PCR. Compared to FBS-cultivated HEACs, HS-cultivated HEACs did not express VIM, and less expressed GATA4, PALLD. On the other hand, HS-cultivated HEACs expressed MAP2 more than FBS-cultivated HEACs. In conclusion, human adult stem cells could move and form aggregates by the treatment with human body fluids.

Application and use of differential scanning calorimetry in studies of thermal fluctuation associated with amyloid fibril formation

The aggregation of proteins into amyloid fibrils is a topic that has attracted great interest because the process is associated with the pathology of numerous human diseases. Despite considerable progress in the elucidation of the structure of amyloid fibrils and the kinetic mechanism of their formation, knowledge on the thermodynamic aspects underlying the formation and stability of amyloid fibrils is limited. In this review, we summarize recent calorimetric studies of amyloid fibril formation, with the goal of obtaining a better understanding of the causal factors that thermally induce proteins to aggregate into amyloid fibrils. Calorimetric data show that differential scanning calorimetry is a useful technique to study the causative factors that thermally trigger the conversion to the amyloid structure and highlight the physics related to the thermal fluctuation of proteins during this conversion.

Infrared spectroscopy of proteins in reverse micelles

Reverse micelles are a versatile model system for the study of crowded microenvironments containing limited water, such as those found in various tissue spaces or endosomes. They also preclude protein aggregation. Reverse micelles are amenable to study by linear and nonlinear infrared spectroscopies, which have demonstrated that the encapsulation of polypeptides and enzymatically active proteins into reverse micelles leads to conformational changes not seen in bulk solution. The potential value of this model system for understanding the folding and kinetic behavior of polypeptides and proteins in biologically important circumstances warrants increased study of reverse micelle systems by infrared spectroscopy. This article is part of a Special Issue entitled: FTIR in membrane proteins and peptide studies.

Cocaine induces a reversible stomatocytosis of red blood cells and increases blood viscosity

Severe side effects of cocaine consumption are vasoocclusive events such as myocardial infarction and stroke. We have hypothesized that cocaine could affect red blood cells (RBCs) and alter the rheological behaviour of blood. Heparinized blood from healthy volunteers was incubated with a final hematocrit of 45% with increasing cocaine concentrations: 0, 10, 100, 1000, and 10'000 μmol/L plasma. Time dependence of the shape change was tested in phosphate buffered saline containing cocaine. RBCs were fixed in 1% glutaraldehyde for morphological analysis. Blood viscosity was measured with a Couette Viscometer (Contraves LS 30) at 37°C and a shear rate of 69.5 s⁻¹. RBC aggregation was assessed with a Myrenne aggregometer. Cocaine induced a dose-dependent stomatocytic shape transformation of RBCs, which was more pronounced in buffer than in plasma (plasma protein binding of the drug). Stomatocytosis occurs when a drug intercalates preferentially in the inner half of the membrane lipid bilayer. It was a time-dependent process with two components, an almost instant shape change occurring within 1 s, followed by a gradual further shape change during 10 min. Stomatocytosis was reversible by resuspension of the RBCs in cocaine-free buffer. This stomatocytic shape change increased whole blood viscosity at high shear rate from 5.69±0.31 mPa.s to 6.39±0.34 mPa.s for control and 10'000 μmol/L cocaine, respectively (p<0.01). RBC aggregation was not affected by the shape change. These effects occurred at a cocaine concentration, which is several-fold above those measured in vivo. Therefore, it is unlikely that hemorheological factors are involved in vascular events after cocaine consumption.

Cellular toxicity of mutant SOD1 protein is linked to an easily soluble, non-aggregated form in vitro

Mutations in superoxide dismutase 1 (SOD1) are found in approximately 20% of patients with familial amyotrophic lateral sclerosis. The propensity of mutant SOD1 to form aggregates in pathologically affected cells (i.e. motor neurons) has implicated these poorly soluble protein aggregates and/or their misfolded soluble precursors as being instrumental to the disease process. We investigated the relative solubility and toxicity of four different mutant SOD1 proteins in a cell-based model system and demonstrate that the mutant, misfolded SOD1 proteins that are the most soluble are also the most toxic. This toxicity was ameliorated by upregulating heat-shock protein chaperones in order to refold the soluble, misfolded protein, regardless of the presence of poorly soluble SOD1. We further demonstrate that increasing the solubility of a SOD1 mutant protein that is both poorly soluble and non-toxic, as compared to other mutant proteins, resulted in remarkably increased toxicity of the mutant SOD1. Again, this increased toxicity was attenuated by upregulating heat-shock protein chaperones in order to refold the soluble, misfolded proteins. These findings implicate easily soluble, misfolded SOD1 as being toxic to the cell and support the hypothesis that reducing solubility of mutant SOD1 proteins through aggregation may occur as a self-protective response in the cell.

Interaction of Water-Soluble CdTe Quantum Dots with Bovine Serum Albumin

Semiconductor nanoparticles (quantum dots) are promising fluorescent markers, but it is very little known about interaction of quantum dots with biological molecules. In this study, interaction of CdTe quantum dots coated with thioglycolic acid (TGA) with bovine serum albumin was investigated. Steady state spectroscopy, atomic force microscopy, electron microscopy and dynamic light scattering methods were used. It was explored how bovine serum albumin affects stability and spectral properties of quantum dots in aqueous media. CdTe-TGA quantum dots in aqueous solution appeared to be not stable and precipitated. Interaction with bovine serum albumin significantly enhanced stability and photoluminescence quantum yield of quantum dots and prevented quantum dots from aggregating.

Assessment of Influence of Magnetic Forces on Aggregation of Zero-valent Iron Nanoparticles

Aggregation of zero-valent nanoparticles in groundwater is influenced by several physical phenomena. The article shortly introduces preceding works in modeling of aggregation of small particles including influence of sedimentation, velocity profile of water, heat fluctuations, and surface electric charge. A brief description of inclusion of magnetic forces into the model of aggregation follows. Rate of influence of the magnetic forces on the aggregation depends on the magnitude of magnetization of the particles, radius of nanoparticles, size of the aggregates, and their concentration in the solution. Presented results show that the magnetic forces have significant influence on aggregation especially of the smallest iron particles.

Inhibition of beta-amyloid(1-40) Peptide Aggregation and Neurotoxicity by Citrate

The accumulation of beta-amyloid (Abeta) aggregates is a characteristic of Alzheimer's disease (AD). Furthermore, these aggregates have neurotoxic effects on cells, and thus, molecules that inhibit Abeta aggregate formation could be valuable therapeutics for AD. It is well known that aggregation of Abeta depends on its hydrophobicity, and thus, in order to increase the hydrophilicity of Abeta, we considered using citrate, an anionic surfactant with three carboxylic acid groups. We hypothesized that citrate could reduce hydrophobicity and increase hydrophilicity of Abeta(1-40) molecules via hydrophilic/electrostatic interactions. We found that citrate significantly inhibited Abeta(1-40) aggregation and significantly protected SH-SY5Y cell line against Abeta(1-40) aggregates-induced neurotoxicity. In details, we examined the effects of citrate on Abeta(1-40) aggregation and on Abeta(1-40) aggregates-induced cytotoxicity, cell viability, and apoptosis. Th-T assays showed that citrate significantly inhibited Abeta(1-40) aggregation in a concentration-dependent manner (Th-T intensity: from 91.3% in 0.01 mM citrate to 82.1% in 1.0 mM citrate vs. 100.0% in Abeta(1-40) alone). In cytotoxicity and viability assays, citrate reduced the toxicity of Abeta(1-40) in a concentration-dependent manner, in which the cytotoxicity decreased from 107.5 to 102.3% as compared with Abeta(1-40) aggregates alone treated cells (127.3%) and the cell viability increased from 84.6 to 93.8% as compared with the Abeta(1-40) aggregates alone treated cells (65.3%). Furthermore, Hoechst 33342 staining showed that citrate (1.0 mM) suppressed Abeta(1-40) aggregates-induced apoptosis in the cells. This study suggests that citrate can inhibit Abeta(1-40) aggregation and protect neurons from the apoptotic effects of Abeta(1-40) aggregates. Accordingly, our findings suggest that citrate administration should be viewed as a novel neuroprotective strategy for AD.

Ordering Transitions in Liquid Crystals Permit Imaging of Spatial and Temporal Patterns Formed by Proteins Penetrating into Lipid-Laden Interfaces

Recent studies have reported that full monolayers of L-α-dilaurylphosphatidylcholine (L-DLPC) and D-α-dipalmitoylphosphatidylcholine (D-DPPC) formed at interfaces between thermotropic liquid crystals (LCs) and aqueous phases lead to homeotropic (perpendicular) orientations of nematic LCs and that specific binding of proteins to these interfaces (such as phospholipase A₂ binding to D-DPPC) can trigger orientational ordering transitions in the liquid crystals. We report on the nonspecific interactions of proteins with aqueous-LC interfaces decorated with partial monolayer coverage of L-DLPC. Whereas nonspecific interactions of four proteins (cytochrome c, bovine serum albumin,immunoglobulins, and neutravidin) do not perturb the ordering of the LC when a full monolayer of L-DLPC is assembled at the aqueous-LC interface, we observe patterned orientational transitions in the LC that reflect penetration of proteins into the interface of the LC with partial monolayer coverage of L-DLPC. The spatial patterns formed by the proteins and lipids at the interface are surprisingly complex, and in some cases the protein domains are found to compartmentalize lipid within the interfaces. These results suggest that phospholipid-decorated interfaces between thermotropic liquid crystals and aqueous phases offer the basis of a simple and versatile tool to study the spatial organization and dynamics ofprotein networks formed at mobile, lipid-decorated interfaces.

Therapeutic Strategies in Huntington's Disease

This article provides an overview of the therapeutic strategies, from ordinary classical drugs to the modern molecular strategy at experimental level, for Huntington's disease. The disease is characterized by choreic movements, psychiatric disorders, striatal atrophy with selective small neuronal loss, and autosomal dominant inheritance. The genetic abnormality is CAG expansion in huntingtin gene. Mutant huntingtin with abnormally long glutamine stretch aggregates and forms intranuclear inclusions. In this review, I summarize the results of previous trials from the following aspects; 1. symptomatic/palliative therapies including drugs, stereotaxic surgery and repetitive transcranial magnetic stimulation, 2. anti-degenerative therapies including anti-excitotoxicity, reversal of mitochondrial dysfunction and anti-apoptosis, 3. restorative/reparative therapies including neural trophic factors and tissue or stem cell transplantation, and 4. molecular targets in specific and radical therapies including inhibition of truncation of huntingtin, inhibition of aggregate formation, normalization of transcriptional dysregulation, enhancement of autophagic clearance of mutant huntingtin, and specific inhibition of huntingtin expression by sRNAi. Although the strategies mentioned in the latter two categories are mostly at laboratory level at present, we are pleased that one can discuss such "therapeutic strategies", a matter absolutely impossible before the causal gene of Huntington's disease was identified more than 10 years ago. It is also true, however, that some of the "therapeutic strategies" mentioned here would be found difficult to implement and abandoned in the future.

Spatial scale of aggregation in three acarine predator species with different degrees of polyphagy

Aggregative responses by the predatory mites, Phytoseiulus persimilis, Typhlodromus occidentalis, and Amblyseius andersoni (Acari: Phytoseiidae), to spatial variation in the density of mobile stages of Tetranychus urticae (Acari: Tetranychidae) were studied over different spatial scales on greenhouse roses. Significant spatial variations in prey numbers per leaflet, per leaf, per branch or per plant were present in all experimental plots. None of the predator species responded to prey numbers per plant, and all searched randomly among plants. Within a plant, the oligophagous P. persimilis searched randomly among branches, but aggregated strongly among leaves within a branch and among leaflets within a leaf. The narrowly polyphagous T. occidentalis searched randomly among leaflets within a leaf and amond leaves within a branch, but aggregated strongly among leaflets or leaves within a plant. The boradly polyphagous A. andersoni searched randomly among leaflets within a leaf, a branch or a plant, and among leaves within a branch or a plant, but distributed themselves more often on branches with lower prey densities. Thus, specialist predators aggregate strongly at lower spatial levels but show random search at higher spatial levels, whereas generalist predators show random search at lower spatial levels but aggregate at higher spatial levels. This is the first empirical evidence demonstrating the relation between the degree of polyphagy and the spatial scale of aggregation. It is also concluded that both the prey patch size (i.e. grain) and predator foraging range (i.e. extent) are important for analyzing spatial scales of predator aggregation. The importance of studying spatial scale of aggregation is also discussed in relation to predator-prey metapopulation dynamics.

Aquatic arthropod communities in Nepenthes pitchers: the role of niche differentiation, aggregation, predation and competition in community organization

The structure and organization of aquatic arthropod communities in Nepenthes ampullaria pitchers were studied at two sites (M in Malacca and K in Kuching) in Malaysia. The communities consisted mainly of aquatic dipteran larvae. Community M was dominated by a filter feeder, Tripteroides tenax, which reached a high density despite a strongly aggregated distribution. Community K had five trophic groups: carrion feeders, filter feeders, detritus feeders, nipping predators and hooking predators, each including multiple species. The summed density of filter feeders in Community K remained much below the level attained by filter feeders in Community M. Niche differentiation within each trophic group with regard to pitcher age and feeding behaviour was not sufficient to allow species coexistence through niche separation alone. Aggregated distributions directly reduced interspecific encounters. Nevertheless, species belonging to the same trophic group commonly shared the same pitcher, because of high occurrence probabilities of dominant species and positive associations between some taxa (due mainly to similar occupancies by pitcher age). Predator coexistence in Community K may have been facilitated by self-limitation of the large predators through intraspecific cannibalism strengthened by aggregation. Prey coexistence, on the other hand, may have relied more on population suppression by predation, especially the selective removal of old instar Tripteroides.

Player Aggregation in Noncooperative Games, II

Conditions are given under which subsets of the players of a noncooperative game can be combined into "aggregate players" without changing the set of equilibrium-point solutions of the game. These conditions are shown to be the weakest possible ones with a certain specified kind of generality. "Approximate" versions of the results are also formulated and proven.

Player Aggregation in Noncooperative Games

A condition is given, under which subsets of the players of a noncooperative game can be combined into "aggregate players" without changing the set of equilibrium-point solutions of the game. The condition is that an individual player's payoff does not depend on the strategy choices of the other players forming the same aggregate player. "Approximate" versions of this result are also formulated and proven.