Positive states

In be complexes bci complexes of mitochondria and bacteria and b f complexes of chloroplasts), the catalytic domain of the Rieske protein corresponding to the isolated water-soluble fragments that have been crystallized is anchored to the rest of the complex (in particular, cytochrome b) by a long (37 residues in bovine heart bci complex) transmembrane helix acting as a membrane anchor (41, 42). The great length of the transmembrane helix is due to the fact that the helix stretches across the bci complex dimer and that the catalytic domain of the Rieske protein is swapped between the monomers, that is, the transmembrane helix interacts with one monomer and the catalytic domain with the other monomer. The connection between the membrane anchor and the catalytic domain is formed by a 12-residue flexible linker that allows for movement of the catalytic domain during the turnover of the enzyme (Fig. 8a see Section VII). Three different positional states of the catalytic domain of the Rieske protein have been observed in different crystal forms (Fig. 8b) (41, 42) ... 

A ci positional state where the exposed NeH group of His 161 which is a ligand of the Rieske cluster forms a hydrogen bond with a propionate group of heme Ci (42)... 

A 6 positional state that is stabilized by the interaction of His 161 with a molecule of the inhibitor stigmatellin bound in the quinone binding pocket (41), which is supposed to mimic the hydrogen bonding pattern of the reaction intermediate, semiqui-none (43)... 

In addition to this large movement of the Rieske protein, small but nevertheless significant conformational differences within the functional domain are observed. The structure of the functional domain of the Rieske subunit in the PGi22 crystal form showing the ci positional state is the same as that of the water soluble fragment... 

Fig. 8. (a) Structure of the full-length Rieske protein from bovine heart mitochondrial bci complex. The catalytic domain is connected to the transmembrane helix by a flexible linker, (b) Superposition of the three positional states of the catalytic domain of the Rieske protein observed in different crystal forms. The ci state is shown in white, the intermediate state in gray, and the b state in black. Cytochrome b consists of eight transmembrane helices and contains two heme centers, heme and Sh-Cytochrome c i has a water-soluble catalytic domain containing heme c i and is anchored by a C-terminal transmembrane helix. The heme groups are shown as wireframes, the iron atoms as well as the Rieske cluster in the three states as space-filling representations. 

When the second-site revertants were segregated from the original mutations, the bci complexes carrying a single mutation in the linker region of the Rieske protein had steady-state activities of 70-100% of wild-type levels and cytochrome b reduction rates that were approximately half that of the wild type. In all these mutants, the redox potential of the Rieske cluster was increased by about 70 mV compared to the wild type (51). Since the mutations are in residues that are in the flexible linker, at least 27 A away from the cluster, it is extremely unlikely that any of the mutations would have a direct effect on the redox potential of the cluster that would be observed in the water-soluble fragments. However, the mutations in the flexible linker will affect the mobility of the Rieske protein. Therefore, the effect of the mutations described is due to the interaction between the positional state of the Rieske protein and its electrochemical properties (i.e., the redox potential of the cluster). 

The bifurcation of the electron pathways is aided by the mobility of the catalytic domain of the Rieske protein. Three positional states of the catalytic domain of the Rieske protein have been observed in different crystal forms of the 6ci complex (Fig. 8b see Section III,B,5) (41, 42). In each single positional state, the Rieske protein is unable to perform all electron transfer reactions occuring during turnover ... 

In the ci positional state, fast electron transfer from the Rieske protein to cytochrome Ci will he facilitated hy the close interaction and by the hydrogen bond between His 161 of the Rieske protein and a propionate group of heme Ci, but the Rieske cluster is far away from the quinone binding site. 

In the b positional state, The Rieske cluster can interact with quinone bound in the reaction pocket, but the distance to heme Ci is too large (>30 A) to allow fast electron transfer. 

Therefore, the Rieske protein has to switch between the positional states during turnover. The following reaction scheme combines the movement of the catalytic domain of the Rieske protein with the redox-dependent stabilization of the intermediate semiquinone (Fig. 19) (42) ... 

The interaction with the deprotonated hydroquinone (QH ) will move the Rieske protein toward the b positional state (C). 

After the electron transfer (step 3), the resulting semiquinone is tightly hound to the reduced Rieske cluster in the b positional state (D) in this state, the semiquinone intermediate will he stabilized (116). 

After the second electron transfer from semiquinone to heme 6l (step 4), the interaction between the Rieske cluster and the resulting quinone is weakened so that the reduced Rieske protein can now occupy the preferred ci positional state (E), which allows rapid electron transfer from the Rieske cluster to heme Ci (step 5). 

How is the mobility of the Rieske cluster within the bci complex and the switch between different positional states related to (and controlled by) the electrostatic properties of the Rieske cluster ... 

Its stability then decreases progressively until we reach curium where aqueous solutions containing the tetra-positive state must be complexed by ligands such as fluoride or phosphotungstate. Even then, they oxidize water and revert to cur-ium(lll). The expected drop in I4 between curium and berkelium provides Bk" (aq) with a stability similar to that of Ce (aq), but the decrease in stability is then renewed, and beyond californium, the +4 oxidation state has not yet been prepared [2, 10, 15]. 

TVrithes and reduced supercoiling force constant (Wr and KsdNi, with N the loop size) were calculated from Fig. 6(b) and (d), and (a) and (c), respectively, using the theory as described in the text. K /Ni values were 12, 11.5 and 11 in closed negative , open , and closed positive states, respectively, but a unique value of 12 was used to fit experimental data points in Fig. 5. 

Until recently, the theory did not allow the configuration of the positive state to be described, due to entry/exit DNAs interpenetration upon application of the positive constraint to the loop. A recent development [63] takes the DNA impenetrability into account and deals with the resulting DNA self-contacts, which were allowed to slide freely, following the needs of the energy minimization process. 

These results raise the prospect of dynamics of nucleosomes in linker histone-free chromatin, that is, of a thermal fluctuation of nucleosomes between closed negative , open , and closed positive states identified in the minicircle system. If this equilibrium exists, an extra supercoiling constraint applied to the fiber should displace it in one direction or the other depending on the sign of that constraint, and this displacement should be reversible upon its removal. 

By representing the operator containing the potential energy in position state space and the one containing the kinetic energy in momentum space, one obtains the following phase space discretized path integral representation ... 

Reflection may also be prompted by more positive states, for example, by an experience of successfully completing a task which previously was thought impossible, (p. 19)... 

J is said to be bounded below, and the largest possible value of c is called the lower bound of J. In what follows all quadratic forms are assumed to be bounded below, even if it is not positively stated. 

Pr+ positive state of remanent polarization of the dynamically measured hysteresis loop... 

Prrei+ positive state of relaxed remanent polarization, relaxed for one second in the Pr+ state. Equal to the positive state of remanent polarization of the quasi statically measured loop (see Section 3.3.4)... 

E.g. sharp momentum and position states. At least one of such a conjugate pair is dictated by Heisenberg s principle to be statistically uncertain. 

The results in this chapter make clear that a chiral outcome, the enhancement off j particular enantiomer, can arise by coherently encoding quantum interference infqjS mation in the laser excitation of a racemic mixture. The fact that the initial stall displays a broken symmetry and that the excited state has states that are eith jj symmetric or antisymmetric with respect to ah allows for the creation of a si position state that does not have these symmetry properties. Radiatively couplingfhf states in the superposition then allows for the transition probabilities from L and fi t differ, allowing for depletion of the desired enantiomer. 

The differences in the nature of the soluble species derived from the positive oxidation states of these elements help to explain the irregular trend in the oxidation potentials going from the tripositive to the penta-positive states. For acid solutions ... 

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