Observing the observer (I): meta-bayesian models of learning and decision-making

In this paper, we present a generic approach that can be used to infer how subjects make optimal decisions under uncertainty. This approach induces a distinction between a subject's perceptual model, which underlies the representation of a hidden "state of affairs" and a response model, which predicts the ensuing behavioural (or neurophysiological) responses to those inputs. We start with the premise that subjects continuously update a probabilistic representation of the causes of their sensory inputs to optimise their behaviour. In addition, subjects have preferences or goals that guide decisions about actions given the above uncertain representation of these hidden causes or state of affairs. From a Bayesian decision theoretic perspective, uncertain representations are so-called "posterior" beliefs, which are influenced by subjective "prior" beliefs. Preferences and goals are encoded through a "loss" (or "utility") function, which measures the cost incurred by making any admissible decision for any given (hidden) state of affair. By assuming that subjects make optimal decisions on the basis of updated (posterior) beliefs and utility (loss) functions, one can evaluate the likelihood of observed behaviour. Critically, this enables one to "observe the observer", i.e. identify (context- or subject-dependent) prior beliefs and utility-functions using psychophysical or neurophysiological measures. In this paper, we describe the main theoretical components of this meta-Bayesian approach (i.e. a Bayesian treatment of Bayesian decision theoretic predictions). In a companion paper ('Observing the observer (II): deciding when to decide'), we describe a concrete implementation of it and demonstrate its utility by applying it to simulated and real reaction time data from an associative learning task.     

Family counts: deciding when to murder among the Icelandic Vikings

In small scale societies, lethal attacks on another individual usually invite revenge by the victim's family. We might expect those who perpetrate such attacks to do so only when their own support network (mainly family) is larger than that of the potential victim so as to minimise the risk of retaliation. Using data from Icelandic family sagas, we show that this prediction holds whether we consider biological kin or affinal kin (in-laws): on average, killers had twice as many relatives as their victims. These findings reinforce the importance of kin as a source of implicit protection even when they are not physically present. The results also support Hughes' (1988) claim that affines are biological kin because of the shared genetic interests they have in the offspring generation.     

Characterization of the binding of Cu(II) and Zn(II) to transthyretin: effects on amyloid formation

Although metal ions can promote amyloid formation from many proteins, their effects on the formation of amyloid from transthyretin have not been previously studied. We therefore screened the effects of Cu(II), Zn(II), Al(III), and Fe(III) on amyloid formation from wild-type (WT) transthyretin as well as its V30M, L55P, and T119M mutants. Cu(II) and Zn(II) promoted amyloid formation from the L55P mutant of transthyretin at pH 6.5 but had little effect on amyloid formation from the other forms of the protein. Zn(II) promoted L55P amyloid formation at pH 7.4 but Cu(II) inhibited it. Cu(II) gave dose-dependent quenching of the tryptophan fluorescence of transthyretin and the fluorescence of 1-anilino-8-naphthalene sulfonate bound to it. Zn(II) gave dose-dependent quenching of the tryptophan but not the 1-anilino-8-naphthalene sulfonate fluorescence. Apparent dissociation constants for Cu(II) and Zn(II) binding at pH 7.4 of approximately 10 nM and approximately 1 microM (approximately 0.4 microM and approximately 5 microM at pH 6.5), respectively, were obtained from the quenching data. Zn(II) enhanced urea-mediated the dissociation of the L55P but not the WT transthyretin tetramer. Cu(II), depending on its concentration, either had no effect or stabilized the WT tetramer but could enhance urea-mediated dissociation of L55P.     

Silver(I), mercury(II), cadmium(II), and zinc(II) target exposed enzymic iron-sulfur clusters when they toxify Escherichia coli

The toxicity of soft metals is of broad interest to microbiologists, both because such metals influence the community structures in natural environments and because several metals are used as antimicrobial agents. Their potency roughly parallels their thiophilicity, suggesting that their primary biological targets are likely to be enzymes that contain key sulfhydryl moieties. A recent study determined that copper poisons Escherichia coli in part by attacking the exposed [4Fe-4S] clusters of dehydratases. The present investigation sought to test whether other soft metals also target these enzymes. In vitro experiments revealed that low-micromolar concentrations of Ag(I) and Hg(II) directly inactivated purified fumarase A, a member of the dehydratase family. The enzyme was also poisoned by higher levels of Cd(II) and Zn(II), but it was unaffected by even millimolar concentrations of Mn(II), Co(II), Ni(II), and Pb(II). Electron paramagnetic resonance analysis and measurements of released iron confirmed that damage was associated with destruction of the [4Fe-4S] cluster, and indeed, the reconstruction of the cluster fully restored activity. Growth studies were then performed to test whether dehydratase damage might underlie toxicity in vivo. Barely toxic doses of Ag(I), Hg(II), Cd(II), and Zn(II) inactivated all tested members of the [4Fe-4S] dehydratase family. Again, activity was recovered when the clusters were rebuilt. The metals did not diminish the activities of other sampled enzymes, including NADH dehydrogenase I, an iron-sulfur protein whose clusters are shielded by polypeptide. Thus, the data indicate that dehydratases are damaged by the concentrations of metals that initiate bacteriostasis.     

Cobalt(II) and zinc(II) binding to a ferredoxin maquette

We have examined the Co(II) and Zn(II) affinity of the prototype ferredoxin maquette ligand, NH(2)-KLCEGG.CIACGAC.GGW-CONH2 (IAA), which was originally designed to bind a [4Fe-4S] cluster. UV-Vis spectroscopy demonstrates tight 1:1 complex formation between Co(II) and IAA. The intensity of the S-->Co(II) charge transfer bands at 304 and 340 nm and the ligand field bands between 630 and 728 nm indicate Co(II) coordination by the four cysteine thiolates of IAA in a pseudo-tetrahedral geometry. A dissociation constant value of 5.3 microM was determined for the Co(II)-IAA complex at pH 6.5. Zn(II) readily displaces Co(II) from IAA as evinced by loss of the Co(II) spectral features. The dissociation constant for Zn(II), 20 pM at pH 6.5, was determined be competition experiments with Co(II)-IAA. These results demonstrate that the ferredoxin maquette ligand is an excellent ligand for Zn(II).     

Synthesis and properties of trinuclear polypyridyl complexes Ru(II)-Co(II)-Ru(II) and Ru(II)-Co(III)-Ru(II): Their photoinduced interconversion

The trinuclear [{Ru^II(bpy)₂(bpy-terpy)}₂Co^II]⁶⁺ complex (1⁶⁺) in which a Co(II)-bis-terpyridine-like centre is covalently linked to two Ru(II)-tris-bipyridine-like moieties by a bridging bipyridine-terpyridine ligand has been synthesised and characterised. Its electrochemical, photophysical and photochemical properties have been investigated in CH₃CN. The cyclic voltammetry exhibits two successive reversible oxidation processes, corresponding to the Co^III/Co^II and Ru^III/Ru^II redox couples at E_1/2 = −0.06 and 0.91 V vs Ag/Ag⁺ 10 mM, respectively. The one-electron oxidized form of the complex, [{Ru^II(bpy)₂(bpy-terpy)}₂Co^III]⁷⁺ (1⁷⁺) obtained after exhaustive electrolysis carried out at 0.2 V is fully stable. 1⁶⁺ and 1⁷⁺ are only poorly luminescent, indicating that the covalent linkage of the Ru(II)-tris-bipyridine centre to the cobalt subunit leads to a strong quenching of the Ru^II excited state by an intramolecular process. Luminescence lifetime experiments carried out at different temperatures indicate that the transfer is more efficient for 1⁷⁺ compare to 1⁶⁺ due to lower activation energy. Continuous irradiation of 1⁷⁺ performed at 405 nm in the presence of P(Ph)₃ acting as sacrificial electron donor leads to its quantitative reduction into 1⁶⁺, whereas similar experiment starting from 1⁶⁺ with a sulfonium salt as sacrificial electron acceptor converts 1⁶⁺ into 1⁷⁺ with a slower rate and a maximum yield of 80%. These photoinduced electron transfers were followed by UV-Visible spectroscopy and compared with those obtained with a simple mixture of both mononuclear parent complexes i.e. [Ru^II(bpy)₃]²⁺ and [Co^II(tolyl-terpy)₂]²⁺ or [Co^III(tolyl-terpy)₂]³⁺ (tolyl-terpy = 4′-(4-methylphenyl)-2,2′:6′,2′′-terpyridine).     

Binding of zinc(II) and copper(II) to the full-length Alzheimer's amyloid-beta peptide

There is evidence that binding of metal ions like Zn2+ and Cu2+ to amyloid beta-peptides (Abeta) may contribute to the pathogenesis of Alzheimer's disease. Cu2+ and Zn2+ form complexes with Abeta peptides in vitro; however, the published metal-binding affinities of Abeta vary in an enormously large range. We studied the interactions of Cu2+ and Zn2+ with monomeric Abeta(40) under different conditions using intrinsic Abeta fluorescence and metal-selective fluorescent dyes. We showed that Cu(2+) forms a stable and soluble 1 : 1 complex with Abeta(40), however, buffer compounds act as competitive copper-binding ligands and affect the apparent K(D). Buffer-independent conditional K(D) for Cu(II)-Abeta(40) complex at pH 7.4 is equal to 0.035 micromol/L. Interaction of Abeta(40) with Zn2+ is more complicated as partial aggregation of the peptide occurs during zinc titration experiment and in the same time period (within 30 min) the initial Zn-Abeta(40) complex (K(D) = 60 micromol/L) undergoes a transition to a more tight complex with K(D) approximately 2 micromol/L. Competition of Abeta(40) with ion-selective fluorescent dyes Phen Green and Zincon showed that the K(D) values determined from intrinsic fluorescence of Abeta correspond to the binding of the first Cu2+ and Zn2+ ions to the peptide with the highest affinity. Interaction of both Zn2+ and Cu2+ ions with Abeta peptides may occur in brain areas affected by Alzheimer's disease and Zn2+-induced transition in the peptide structure might contribute to amyloid plaque formation.     

Individual recognition in crayfish (Cherax dispar): the roles of strength and experience in deciding aggressive encounters

The outcomes of agonistic interactions modulate access to resources and thereby affect fitness. Success in agonistic encounters may depend on intrinsic physical and physiological performance, and on social experience. Here we test the hypothesis that previous experience will override physical strength in determining the outcome of fights in the freshwater crayfish Cherax dispar. Between unfamiliar opponents, greater chelae closing force significantly increases the chances of winning. However, even when the chelae of the original winners were disabled, the winners kept on winning against the same opponents after 30min and 24h. This winner effect disappeared when previous winners encountered unfamiliar individuals. Similarly, a previous loss did not affect the outcomes of subsequent encounters with unknown crayfish. We suggest that this prolonged recognition of individuals and their relative fighting ability is a mechanism that can reduce the number of agonistic encounters experienced by individuals.     

Interaction of Nickel(II) with histones: in vitro binding of nickel(II) to the core histone tetramer

The absorption spectra of Ni(II) bound to the core histone tetramer, (H3-H4)2, of chicken erythrocytes in 500 mM NaCl + 100 mM phosphate (pH 7.4) were recorded. A charge transfer band was seen at 317 nm, characteristic of a bond between Ni(II) and the sulfur atom of Cys-110 of histone H3. The conditional affinity constants for Ni(II) binding at pH 7.4 for low and high Ni(II) saturation (log Kc = 4.26 +/- 0.02 and 5.26 +/- 0.11 M-1, respectively) were calculated from spectrophotometric titrations with the use of this band. The binding of Ni(II) to (H3-H4)2 is proposed to involve the Cys-110 and His-113 of different H3 molecules within the tetramer. The competition between histones and low-molecular-weight chelators for Ni(II) in the cell nucleus, histidine and glutathione, is discussed on the basis of the above results, indicating that histone H3 is very likely to bind Ni(II) dissolved intracellularly from phagocytosed particulate nickel compounds.     

Observations of rotation within the F(o)F(1)-ATP synthase: deciding between rotation of the F(o)c subunit ring and artifact

Annexin-I (ANX-I) is a 37-kDa protein with a calcium-dependent phospholipid-binding property. Previously we have observed the inhibition of cytosolic phospholipase A2 (cPLA2) by ANX-I in the studies using purified recombinant ANX-I, and proposed a specific interaction model for the mechanism of cPLA2 inhibition by ANX-I [Kim et al. (1994) FEBS Lett. 343, 251-255]. Here we have studied the role of ANX-I in the cPLA2 signaling pathway by transient transfection assay. The stimulation of Rat2 fibroblast cells with phorbol 12-myristate 13-acetate (PMA) induced the c-fos serum response element (SRE). The SRE stimulation by PMA was dramatically reduced by (1) pretreatment with a cPLA2-specific inhibitor, arachidonyltrifluoromethyl ketone, or (2) co-transfection with antisense cPLA2 oligonucleotide, indicating that the SRE activation was through cPLA2 activation. Co-transfection with an ANX-I expression vector also reduced the SRE stimulation by PMA, suggesting the inhibition of cPLA2 by ANX-I. The active domain of ANX-I was mapped using various deletion mutants. ANX-I(1-113) and ANX-I(34-346) were fully active, whereas ANX-I(114-346) abolished the activity. Therefore the activity was in the amino acid 34 to 113 region, which corresponds to the conserved domain I of ANX-I.     

The binding of Mg(II) and Ni(II) to synthetic polynucleotides

Equilibria and kinetics of the interactions of Mg2+ and Ni2+ with poly(U), poly(C) and poly(I) have been investigated at 25 degrees C, an ionic strength of 0.1 M, and pH 7.0 or 6.0. Analogous studies involving poly(A) were reported earlier. All binding equilibria were studied by means of the (usually small) absorbance changes in the ultraviolet range. This technique yields apparent binding constants which are fairly large for the interaction of Ni2+ with poly(A) (K = 0.9 X 10(4) M-1) and poly(I) (K approximately equal to 2 X 10(4) M-1) but considerably lower for the corresponding Mg2+ systems, Mg2+-poly(A) (K = 2 X 10(3) M-1) and Mg2+-poly(I) (K = 280 M-1). Each of the two pyrimidine nucleotides binds both metal ions with about the same strength (K approximately equal to 65 M-1 for poly(U) and K near 600 M-1 for poly(C]. In the case of poly(C) the spectral changes deviate from those expected for a simple binding equilibrium. In addition, the binding of Ni2+ to the four polynucleotides was measured by using murexide as an indicator of the concentration of free Ni2+. The results obtained by this technique agree or are at least consistent with those derived from the ultraviolet spectra. Complications are encountered in the binding studies involving poly(I), particularly at higher metal ion concentrations, obviously due to the formation of aggregated poly(I) species. Kinetic studies of the binding processes were carried out by the temperature-jump relaxation technique. Measurable relaxation effects of time constants greater than 5 microseconds were observed only in the systems Ni2+-poly(A) and Ni2+-poly(I). Such not-too-fast reaction effects are expected for processes which include inner-sphere substitution steps at Mg2+ or Ni2+. The relaxation process in Ni2+-poly(I) is characterized by (at least) four time constants. Obviously, the complicated kinetics again include reactions of aggregated poly(I). The absence of detectable relaxation effects in all other systems (except Mg2+-poly(I), the kinetics of which was not investigated) indicates that inner-sphere coordination of the metal ions to specific sites of the polynucleotides (site binding) does not occur to a significant extent. Rather, the metal ions are bound in these systems mainly by electrostatic forces, forming a mobile cloud. The differences in binding strength which are nevertheless observed are attributed to differences in the conformation of the polynucleotides which result in different charge densities.     

The binding of copper(II) and zinc(II) to oxidized glutathione

1H and 13C NMR studies of Zn(II) binding to oxidized glutathione (GSSG) in aqueous solution over the pH range 4-11 show that it forms a complex with a 1:1 Zn:GSSG stoichiometry. At pH values between 6 and 11 the metal ligands are the COO- and NH2 groups of the glutamate residues. Below pH 5 the glycine end of the molecule also binds to the metal ions. EPR and visible absorption spectra of Cu(II) GSSG solutions suggest that similar complexes are formed with Cu(II). The solid products obtained from these solutions are shown by analysis and EPR to be primarily binuclear with Cu2GSSG stoichiometry, although the structures depend on the pH and stoichiometry of the solution from which they were obtained.     

Influence of copper(II) and magnesium(II) ions on the ciprofloxacin binding to DNA

The influence of magnesium(II) and copper(II) ions on the binding of ciprofloxacin to double stranded calf thymus DNA was studied by fluorescence emission spectroscopy, ultraviolet- and circular dichroism (CD) spectroscopy. The interaction of ciprofloxacin and copper(II) ions was followed by strong fluorescence quenching which was almost unaffected by the presence of DNA. On the other hand, only a slight decrease in fluorescence emission intensity, which was enhanced in the presence of DNA, was observed for ciprofloxacin interaction with magnesium(II) ions. Furthermore, magnesium(II) ions increase the thermal stability of the DNA, while, in the presence of ciprofloxacin, the degree of stabilisation is smaller. In contrast, copper(II) ions destabilise double helical DNA to heat, while ciprofloxacin slightly affects only the second transition of the biphasic melting curve of calf thymus DNA. Magnesium(II) ions at 25 degrees C induce conformational transitions of DNA at concentrations of 1.5 mM and 2.5 M, as monitored by CD. On the other hand copper(II) ions induce only one conformational transition, at a concentration of 12.7 microM. At higher concentrations of copper(II) ions (c>700 microM) DNA starts to precipitate. Significant changes in the CD spectra of DNA were observed after addition of ciprofloxacin to a solution containing DNA and copper(II) ions, but not to DNA and magnesium(II) ions. Based on our spectroscopic results, we propose that copper(II) ions are not directly involved into ciprofloxacin binding to DNA via phosphate groups as it has been suggested for magnesium(II) ions.