Oligonucleotide analogues containing a C3′-NH-C(O)-CH<Subscript>2</Subscript>-C5′ amide internucleotide bond

A dinucleotide containing a C3′-NH-C(O)-CH₂-C5′ amide internucleotide bond was synthesized by the interaction of 3′-deoxy-3′-amino-5′-O-(tert-butyldimethylsilyl)thymidine with 3′-O-benzyl-2′-O-tert-butyldimethylsilyl-5′-deoxy-5′-carboxymethylribosylthymine, which was obtained from 2′-O-acetyl-3′-O-benzyl-5′-deoxy-5′-ethoxycarbonylmethylribosylthymine through the methanolysis of the acetyl group followed by silylation of liberated hydroxyl and ester saponification. After standard manipulation with protecting groups, the dinucleotide was converted into 3′-O(2-cyanoethyl-N,N-diisopropylphosphoramidite), which was used for the synthesis of modified oligonucleotides on an automated synthesizer. The melting curves of the duplexes formed by modified and complementary natural oligonucleotides were registered, and the melting temperatures and thermodynamic parameters of the duplex formation were calculated. The introduction of a single modified bond into the oligonucleotide led to an insignificant decrease in the melting temperature of these duplexes as compared to unmodified ones.     

What can we learn about the lipid vesicle structure from the small-angle neutron scattering experiment?

Small-angle neutron scattering (SANS) on the unilamellar vesicle (ULV) populations (diameter 500 and 1,000 Å) in D₂O was used to characterize lipid vesicles from dimyristoylphosphatidylcholine (DMPC) at three phases: gel L_β′, ripple P_β′ and liquid L_α. Parameters of vesicle populations and internal structure of the DMPC bilayer were characterized on the basis of the separated form factor (SFF) model. Vesicle shape changes from nearly spherical in the L_α phase to elliptical in the P_β′ and L_β′ phases. This is true for vesicles prepared via extrusion through pores with the diameter 500 Å. Parameters of the internal bilayer structure (thickness of the membrane and the hydrophobic core, hydration and the surface area of the lipid molecule) were determined on the basis of the hydrophobic–hydrophilic (HH) approximation of neutron scattering length density across the bilayer ρ(x) and of the step function (SF) approximation of ρ(x). DMPC membrane thickness in the L_α phase (T=30°C) demonstrates a dependence on the membrane curvature for extruded vesicles. Prepared via extrusion through 500 Å diameter pores, vesicle population in the L_α phase has the following characteristics: average value of minor semi-axis 266±2 Å, ellipse eccentricity 1.11±0.02, polydispersity 26%, thickness of the membrane 48.9±0.2 Å and of the hydrophobic core 19.9±0.4 Å, surface area 60.7±0.5 Ų and number of water molecules 12.8±0.3 per DMPC molecule. Vesicles prepared via extrusion through pores with the diameter 1,000 Å have polydispersity of 48% and membrane thickness of 45.5±0.6 Å in the L_α phase. SF approximation was used to describe the DMPC membrane structure in L_β′ (T=10°C) and P_β′ (T=20°C) phases. Extruded DMPC vesicles in D₂O have membrane thickness of 49.6±0.5 Å in the L_β′ phase and 48.3±0.6 Å in the P_β′ phase. The dependence of the DMPC membrane thickness on temperature was restored from the SANS experiment.     

Mechanosensitive ion channels in chara: influence of water channel inhibitors, HgCl2 and ZnCl2, on generation of receptor potential

Characean internodal cells generate receptor potential (ΔE _m) in response to mechanical stimuli. Upon a long-lasting stimulus, the cells generated ΔE _m at the moment of both compression and decompression, and the amplitude of ΔE _m at the moment of decompression, (ΔE _m)_E, was larger than that at compression. The long-lasting stimulus caused a membrane deformation (ΔD _m) having two components, a rapid one, (ΔD _m)_rapid, at the moment of compression and a slower one, (ΔD _m)_slow, during the long-lasting compression. We assumed that (ΔD _m)_slow might have some causal relation with the larger ΔE _m at (ΔE _m)_E. We treated internodal cells with either HgCl₂ or ZnCl₂, water channel inhibitors, to decrease (ΔD _m)_slow. Both inhibitors attenuated (ΔD _m)_slow during compression. Cells treated with HgCl₂ generated smaller (ΔE _m)_E compared to nontreated cells. On the other hand, cells treated with ZnCl₂ never attenuated (ΔE _m)_E but, rather, amplified it. Thus, the amplitude of (ΔD _m)_slow did not always show tight correlation with the amplitude of (ΔE _m)_E. Furthermore, when a constant deformation was applied to an internodal cell in a medium with higher or lower osmotic value, a cell having higher turgor always showed a larger (ΔE _m)_E. Thus, we concluded that changes in tension at the membrane may be the most important factor to induce activation of mechanosensitive Ca²⁺ channel.     

Use of principal component analysis in interpretation of deoxyribonucleic acid relatedness

Principal component analysis (PCA) of published DNA-relatedness data showed the usefulness of this method in displaying relationships among closely related bacteria. Very similar ordinations were obtained when relative binding ratios (RBR) at 60°C or 75°C or ΔT _m values were used to form the data matrix. A curvilinear relationship and a (quasi) linear relationship were found, respectively, between 75°C and 60°C RBR and ΔT _m and 60°C RBR. These statistical relationships explain the similarity of PCA results using either measurement (60°C RBR, 75°C RBR, or ΔT _m). Use of PCA is suggested to delineate groups within a complex set of DNA-relatedness data. The level of ΔT _m within groups and between groups should help decide whether these groups are genospecies.     

Photoinhibition of colonial and unicellular <Emphasis Type="Italic">Microcystis</Emphasis> cells in a summer bloom in Lake Taihu

To evaluate the photoinhibition of colonial and unicellular cells of Microcystis aeruginosa under natural conditions, the maximum and effective quantum yields of photosystem II were measured from variable chlorophyll a fluorescence in samples from Lake Taihu during a summer bloom from June 19 to 21, 2006. Diurnal changes in the photoinhibition of Microcystis cells incubated immediately below the surface in clear bottles for 30 min and in situ samples under natural conditions were measured. At solar noon during the three days, the mean values of maximum quantum yield (F _v/F _m) and effective quantum yield (ΔF/F _m′) for unicellular cells (F _v/F _m = 0.15, ΔF/F _m′ = 0.10) were lower than those for colonial cells (F _v/F _m = 0.25, ΔF/F _m′ = 0.15). For in situ samples, the values of F _v/F _m and ΔF/F _m′ for colonial cells at solar noon on the three days (F _v/F _m 0.30, 0.25, 0.29; ΔF/F _m′ 0.24, 0.21, 0.22) were also higher than those of unicellular cells (F _v/F _m 0.26, 0.18, 0.25; ΔF/F _m′ 0.15, 0.11, 0.14). The results indicate that colony formation has a protective effect on Microcystis cells by reducing the occurrence of photoinhibition under high light intensities.     

A Water Mediated Electrostatic Interaction Gives Thermal Stability to the “Tail” Region of the GrpE Protein from <Emphasis Type="Italic">E. coli</Emphasis>

The GrpE protein from E. coli is a homodimer with an unusual structure of two long paired α-helices from each monomer interacting in a parallel arrangement to form a “tail” at the N-terminal end. Using site-directed mutagenesis, we show that there is a key electrostatic interaction involving R57 (mediated by a water molecule) that provides thermal stability to this “tail” region. The R57A mutant showed a drop in T _m of 8.5°C and a smaller ΔH _u (unfolding) compared to wild-type for the first unfolding transition, but no significant decrease in dimer stability as shown through equilibrium analytical ultracentrifugation studies. Another mutant (E94A) at the dimer interface showed a decrease in ΔH _u but no drop in T _m for the second unfolding transition and a slight increase in dimer stability.     

Oligonucleotide analogs with peptide internucleotide linkages

Oligonucleotide analogs containing one or a few glycine, L-, and D-alanine or L-and D-phenylalanine residues instead of phosphodiesterinternucleotide linkages were synthesized. The stability of the duplexes formed by modified oligonucleotides and their wildtype complements was studied. Oligonucleotides with D-alanine residues in internucleotide linkages form duplexes more stable than native ones (ΔT(m) +0.2 °C per modification), whereas other modifications destabilize the duplexes.     

A model of photosystem II for the analysis of fast fluorescence rise in plant leaves

The polyphasic patterns of fluorescence induction rise in pea leaves in vivo and after the treatment with ionophores have been studied using a Plant Efficiency Analyzer. To analyze in detail photosystem II (PS II) electron transfer processes, an extended PS II model was applied, which included the sums of exponential functions to specify explicitly the light-driven formation of the transmembrane electric potential (ΔΨ(t)) as well as pH in the lumen (pH_L(t)) and stroma (pH_S(t)). PS II model parameters and numerical coefficients in ΔΨ(t), pH_L(t), and pH_S(t) were evaluated to fit fluorescence induction data for different experimental conditions: leaf in vivo or after ionophore treatment at low or high light intensity. The model imitated changes in the pattern of fluorescence induction rise due to the elimination of transmembrane potential in the presence of ionophores, when ΔΨ = 0 and pH_L(t), pH_S(t) changed to small extent relative to control values in vivo, with maximum ΔΨ(t) ∼ 90 mV and ΔΨ(t) ∼ 40 mV for the stationary state at ΔpH ≅ 1.8. As the light intensity was increased from 300 to 1200 μmol m⁻² s⁻¹, the heat dissipation rate constants increased threefold for nonradiative recombination of P680⁺Phe⁻ and by ∼30% for P680⁺Q_A⁻. The parameters ΔΨ, pH_S and pH_L were analyzed as factors of PS II redox state populations and fluorescence yield. The kinetic mechanism of fluorescence quenching is discussed, which is related with light-induced lumen acidification, when ⁺Q_A⁻ and P680⁺ recombination probability increases to regulate the Q_A reduction.     

Understanding the Influence of State/Phase Transitions on Ice Recrystallization in Atlantic Salmon (Salmo salar) During Frozen Storage

Temperature fluctuations during storage and distribution of frozen foods lead to ice recrystallization and microstructural modifications that can affect food quality. Low temperature transitions may occur in frozen foods due to temperature fluctuations, resulting in less viscous and partially melted food matrices. This study systematically investigated the influence of state/phase transitions and temperature fluctuations on ice recrystallization during the frozen storage of salmon fillets. Using a modulated differential scanning calorimeter, we identified the characteristics glass transition temperature (T _g ′) of −27 °C and the onset temperature for ice crystal melting (T _m ′) of −17 °C in salmon. The temperature of salmon fillets in sealed plastic trays was lowered to −35 °C in a freezer to achieve the glassy state. The temperature (T) of frozen salmon fillets in sealed plastic trays was modulated to achieve a rubbery state (T > T _m ′), a partially freeze-concentrated state (T _g ′ < T < T _m ′) and a glassy state (T < T _g ′). We performed temperature modulation experiments by exposing packaged salmon to room temperature twice a day for 2 to 26 min during 4 weeks of storage. We also analyzed ice crystal morphology using environmental scanning electron microscopy and X-ray computed tomography techniques to observe the pore distribution after sublimation of ice crystals. Melt–refreeze and isomass rounding mechanisms of ice recrystallization were noticed in the frozen salmon subjected to temperature modulations. Results show that ice crystal growth occurred even in the glassy state of frozen salmon during storage, with or without temperature fluctuations. Ice crystal size in frozen salmon was greater in the rubbery state (T > T _m ′) due to the increased mobility of unfrozen water compared to the glassy state. The morphological/geometric parameters of ice crystals in frozen salmon stored for 1 month differed significantly from those in 0-day storage. These findings are important to the frozen food industry because they can help optimize storage and distribution conditions and minimize quality loss of frozen salmon due to recrystallization.     

Enhancing the Stability of Oligonucleotide Duplexes. The Effect of Adding 1-(2"-Deoxy-β-D-ribofuranosyl)-5-nitroindole

We studied the properties of DNA duplexes containing 5-nitroindole (N) in one of the chains. We synthesized 8-membered oligos with N at the 5" or at the 3" end: 5"-d(NXGACCGTC)-3" or 5"-d(GACCGTCXN)-3", where X is one of the four natural bases, making all four kinds of oligos with and without N. We also prepared 11-membered oligos complementary to the above octanucleotides: 5"-d(TGACGGTCYZT)-3" and 5"-d(TZYGACGGTCT)-3", where Y and Z are A, G, C, or T. The stability of duplexes obtained with these oligos was assessed by melting, and the thermodynamic parameters H, S, and T _m were calculated. Comparison of the melting curves for modified and nonmodified duplexes demonstrated that the presence of N at the 5" end of one chain raises the T _m by 6.6° on average; if N is at the 3" end of the same chain, the T _m increases by about 3°.     

Susceptibility behaviour and specific heat anomaly in single crystals of alanine and valine

Magnetization of single crystals ofD-,L-alanine andD-valine were measured as a function of temperature using the SQUID magnetometer. An obvious lambda transition at 270 ± 1 K was shown in the specific heat measurement of alanine and valine enantiomers by differential scanning calorimetry (DSC). Magnetic transition temperature seems coincident with that of lambda transition. Temperature dependence of the X-ray powder diffraction forD-valine showed no crystal lattice change under the temperature cooling down from 293 K to 123 K. We propose that the difference of theX T curve between theD-alanine andL-alanine is attributable to the variation of intramolecular geometry of chirality density in the presence of an external magnetic field. The chirality characteristics of alanine and valine enantiomers by the specific heat and susceptibility behaviour are discussed.     

Characterisation of <Emphasis Type="SmallCaps">l</Emphasis>-alanine and glycine absorption across the gut of an ancient vertebrate

This study utilised an in vitro technique to characterise absorption of two amino acids across the intestinal epithelium of Pacific hagfish, Eptatretus stoutii. Uptake of l-alanine and glycine conformed to Michaelis–Menten kinetics. An uptake affinity (K _m; substrate concentration required to attain a 50% uptake saturation) of 7.0 mM and an uptake capacity (J _max) of 83 nmol cm⁻² h⁻¹ were described for l-alanine. The K _m and J _max for glycine were 2.2 mM and 11.9 nmol cm⁻² h⁻¹, respectively. Evidence suggested that the pathways of l-alanine and glycine absorption were shared, and sodium dependent. Further analysis indicated that glycine uptake was independent of luminal pH and proline, but a component of uptake was significantly impaired by 100-fold excesses of threonine or asparagine. The presence of a short-term (24 h) exposure to waterborne glycine, similar in nature to that which may be expected to occur when feeding inside an animal carcass, had no significant impact on gastrointestinal glycine uptake. This may indicate a lack of cross talk between absorptive epithelia. These results are the first published data to describe gastrointestinal uptake of an organic nutrient in the oldest extant vertebrate and may provide potential insight into the evolution of nutrient transport systems.     

Improving the thermostability and activity of Melanocarpus albomyces cellobiohydrolase Cel7B

Two different types of approach were taken to improve the hydrolytic activity towards crystalline cellulose at elevated temperatures of Melanocarpus albomyces Cel7B (Ma Cel7B), a single-module GH-7 family cellobiohydrolase. Structure-guided protein engineering was used to introduce an additional tenth disulphide bridge to the Ma Cel7B catalytic module. In addition, a fusion protein was constructed by linking a cellulose-binding module (CBM) and a linker from the Trichoderma reesei Cel7A to the C terminus of Ma Cel7B. Both approaches proved successful. The disulphide bridge mutation G4C/M70C located near the N terminus, close to the entrance of the active site tunnel of Ma Cel7B, led to improved thermostability (ΔT _m = 2.5°C). By adding the earlier found thermostability-increasing mutation S290T (ΔT _m = 1.5°C) together with the disulphide bridge mutation, the unfolding temperature was increased by 4°C (mutant G4C/M70C/S290T) compared to that of the wild-type enzyme, thus showing an additive effect on thermostability. Both disulphide mutants had increased activity towards microcrystalline cellulose (Avicel) at 75°C, apparently solely because of their improved thermostability. The addition of a CBM also improved the thermostability (ΔT _m = 2.5°C) and caused a clear (sevenfold) increase in the hydrolysis activity of Ma Cel7B towards Avicel at 70°C.     

The effect of divalent cations on the catalytic activity of the human plasma 3′-exonuclease

The 3′-exonuclease from human plasma is a soluble form of nucleotide pyrophosphatase/phosphodiesterase 1 (NPP1) (EC 3.1.4.1/EC 3.6.1.9). Here, the possibility of divalent cation influence for the 3′-exonuclease activity was investigated using the phosphorothioate congener of oligonucleotide containing all phosphorothioate internucleotide linkages of the [R_P]-configuration ([R_P-PS]-d[T₁₂]) as the substrate for this enzyme. It was found that the 3′-exonuclease is a metalloenzyme, i.e. its phosphodiesterase activity was completely abolished at 0.8 mM concentration EDTA and, in turn, it was restored in the presence of Mg²⁺ or Mn²⁺ ions. In addition, Mg²⁺ can be replaced effectively by Ca²⁺, Mn²⁺, or Co²⁺, but not by Ni²⁺ and Cd²⁺ during the hydrolysis of the phosphorothioate substrate in human plasma. In addition, the mechanism is postulated, by which a single internucleotide phosphorothioate bond of the S_P-configuration at the 3′-end of unmodified phosphodiesters (PO-oligos), or their phosporothioate analogs (PS-oligos) protects these compounds against degradation in blood.     

Enzymatic and Hybridization Properties of Oligonucleotide Analogues Containing Novel Phosphotriester Internucleotide Linkage

Abstract

Enhanced cellular uptake, stable and discriminating hybridization and increased stability in biological media are of particular interest for oligonucleotides of potential therapeutic application. Additionally, toxicity or immunogenicity of the oligonucleotide analogues and their biodegradation products should be minimized by minimal alteration of the biological structure and effort and cost of bulk production should be as low as possible by using a standard automated synthesis protocol. Oligonucleotide phosphotriesters with oligoethyleneglycol substituents show promise to ideally combine all these advantages. Here we describe the hybridization properties and the stability of modified oligonucleotides containing triester internucleotide linkages substituted with α,ω-dihydroxy-(3,6-dioxa)-octan-1-yl group (“triethyleneglycol triester linkages”) towards enzymatic degradation. The triester linkages are stable towards exo- and endonucleases. Regardless of number and position of triester linkages, the modified oligonucleotides showed practically no decrease of T_m in hybridization studies with complementary biological oligonucleotides. In further enzymatic studies the modified oligonucleotides were highly stable towards nucleases in human blood serum.     

Assessing photosynthetic efficiency in an experimental mangrove canopy using remote sensing and chlorophyll fluorescence

This study examined the ability of the photochemical reflectance index (PRI) to track changes in effective quantum yield (Δ F/F _m ′), non-photochemical quenching (NPQ), and the xanthophyll cycle de-epoxidation (DPS) in an experimental mangrove canopy. PRI was correlated with (Δ F/F _m ′) and NPQ over the 4-week measurement period and over the diurnal cycle. The normalised difference vegetation index (NDVI) was not correlated with any aspect of photochemical efficiency measured using chlorophyll fluorescence or xanthophyll pigments. This study demonstrated that photochemical adjustments were responsible for controlling the flow of energy through the photosynthetic apparatus in this mangrove forest canopy rather than canopy structural or chlorophyll adjustments.     

Seasonal variations in biomass, abundance and composition of zooplankton in the subarctic waters north of Iceland

The seasonal variations in biomass, abundance and species composition of zooplankton in relation to hydrography and chlorophyll a were studied in the subarctic waters north of Iceland. The sampling was carried out at approximately monthly intervals from February 1993 to February 1994 at eight stations arranged along a transect extending from 66°16′N–18°50′W to 68°00′N–18°50′W. The mean temperature at 50 m depth showed a clear seasonal pattern, with lowest water temperatures in February (∼1.1°C) and the highest in July (∼5.4°C). The spring growth of the phytoplankton began in late March and culminated during mid-April (∼7.0 mg Chl a m⁻³). Both the biomass and the abundance of total zooplankton were low during the winter and peaked once during the summer in late May (∼4 g m⁻² and ∼38,000 individuals m⁻²). A total of 42 species and taxonomic groups were identified in the samples. Eight taxa contributed ∼90% of the total zooplankton number. Of these Calanus finmarchicus was by far the most abundant species (∼60% of the total zooplankton). Less important groups were ophiuroid larvae (∼9%), Pseudocalanus spp. (∼8%), Metridia longa (∼4%), C. hyperboreus (∼3%), Acartia longiremis (∼2%), chaetognaths (∼2%) and euphausiid larvae (∼2%). The dominant copepods showed two main patterns in seasonal abundance: C. finmarchicus, C. hyperboreus and C. glacialis had one annual peak in numbers in late May, while Pseudocalanus spp., M. longa and A. longiremis showed two maxima during the summer (July) and autumn (October/November). Ophiuroid larvae and chaetognaths (mainly Sagitta elegans) peaked during the middle of July, while the number of euphausiid eggs and larvae was greatest from May to July. The succession in population structure of C. finmarchicus indicated its main spawning to be in April and May, coincident with the phytoplankton spring bloom. A minor spawning was also observed sometime between August and October. However, the offspring from this second spawning contributed only insignificantly to the overwintering stock of C. finmarchicus. Received: 12 September 1997 / Accepted: 1 March 1998     

Irradiance influences tea leaf (<Emphasis Type="Italic">Camellia sinensis</Emphasis> L.) photosynthesis and transpiration

Rates of net photosynthesis (P _N) and transpiration (E), and leaf temperature (T_L) of maintenance leaves of tea under plucking were affected by photosynthetic photon flux densities (PPFD) of 200–2 200 μmol m⁻² s⁻¹. P _N gradually increased with the increase of PPFD from 200 to 1 200 μmol m⁻² s⁻¹ and thereafter sharply declined. Maximum P _N was 13.95 μmol m⁻² s⁻¹ at 1 200 μmol m⁻² s⁻¹ PPFD. There was no significant variation of P _N among PPFD at 1 400–1 800 μmol m⁻² s⁻¹. Significant drop of P _N occurred at 2 000 μmol m⁻² s⁻¹. PPFD at 2 200 μmol m⁻² s⁻¹ reduced photosynthesis to 6.92 μmol m⁻² s⁻¹. PPFD had a strong correlation with T_L and E. Both T_L and E linearly increased from 200 to 2 200 μmol m⁻² s⁻¹ PPFD. T_L and E were highly correlated. The optimum T_L for maximum P _N was 26.0 °C after which P _N declined significantly. E had a positive correlation with P _N.     

Glutathione and Vitamin B12 Cooperate in Stabilization of a B12 Trafficking Chaperone Protein

The protein bCblC (bCblCpro) is a bovine homolog of a human B₁₂ trafficking chaperone that is responsible for the processing of vitamin B₁₂ and its escorted delivery in intracellular B₁₂ metabolism. In this study, we found that bCblCpro is highly thermolabile with a T _m = 42.0 ± 0.2 °C as shown for the human homolog, suggesting thermal regulation of these proteins. Binding of the reduced form of glutathione (GSH) that is a predominant cellular thiol increased the T _m of bCblCpro from 42 °C to ~45 °C (ΔT _{m max} = 3.1 ± 0.2 °C and AC₅₀ = 2.1 ± 0.5 mM). Binding of vitamin B₁₂ and its derivatives also stabilized bCblCpro increasing the T _m to a different extent and vitamin B₁₂ (cyanocobalamin, CNCbl) was the least efficient (ΔT _{m max} = 4.3 ± 0.3 °C and AC₅₀ = 291 ± 36 μM). However, the stabilizing effect of CNCbl was significantly greater for GSH-bound bCblCpro (ΔT _{m max} = 12.8 ± 0.6 °C and AC₅₀ = 9.3 ± 1.6 μM) than for GSH-free bCblCpro. In addition, the stabilizing effect of GSH was also greater for CNCbl-bound bCblCpro (ΔT _{m max} = 9.3 ± 0.3 °C and AC₅₀ = 57.0 ± 6.8 μM). Limited proteolysis revealed that thermal stabilization of bCblCpro is derived from conformational changes of the protein induced by binding of the ligands. The results in this study indicate that GSH cooperates with vitamin B₁₂ in thermal stabilization of bCblCpro and is a positive regulator of the protein.     

Contributions to the theory of organismic sets: Leadership

The theory of organismic sets (Bull. Math. Biophysics,31, 159–189, 1969) is applied to the theory of leadership in human society. The ability of making decisions, required for leadership, is a product of the activities of the cells of the cerebral cortex, which are elements of the subsetS ₀₂ of the organismic set “man” (loc. cit.). Products of the activities of the elements of an organismic set do not need to be of a material nature. Such things as thoughts, feelings, attitudes, etc., are also products of the activitiesa ₁ of the elements. An individual can makeall necessary decisions for adaptation in a changing environment, when his subsetS ₀₂ contains as a proper subset a set {a ₁₂ ^′ ∼ ⊂S ₀₂ of activities. It is shown that such individuals are rare. If none exist, then the one who possesses a subset {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ of higher cardinalityc _m than any other individual, will be the leader. The possibility is discussed that fromN individualsN′ 〈N possess subsets {a ₁₂ ^* ∼ ⊂ {a ₁₂ ^′ ∼ all of the same cardinalityc _m but differing in the type of their elements, thus resulting in several leaders. It is then discussed what determines which of theN −N′ individuals will choose a particular oneN′ individuals as leader. Cooperation and competition between leaders is discussed.