Ordering pathway

Lastly, it is appropriate to comment on the relationships between the intermediates seen in photochemical studies and possible reactive intermediates along the reaction coordinates of related thermal transformations. Earlier kinetics studies (] 3) of the reactions of Ru3(CO)i2 with various phosphorous ligands PR3 have found evidence for both first order and second order pathways leading to substitution plus some cluster fragmentation. The first order path was proposed to proceed via reversible CO dissociation to give an intermediate analogous to II. 

The kg value was determined to be about 6.9 x 10" s independent of the nature of L in 50°C decalin (AH - 31.8 kcal mol-1 AS - +20.2 cal mol 1 K l). Competition ratios k.g/ky equal to 3 and 5 were determined for L - P(OPh3)3 and PPI13, respectively under the same conditions. The second order pathway was proposed to occur via nucleophilic attack of L on the cluster, and an intermediate with a formulation the same as II/ was suggested, without supporting evidence of its existence, as a possible initial product of this nucleophilic attack. However, since fragmentation was only a minor side reaction of the substitution reactions with L - PPI13, it is quite unlikely that the photofragmentation and second order thermal substitution reactions occur via a common intermediate. 

Fig. 4. Dependence of obs vs. [H+] for lj demetalation 25°C, 0.1 M KPF6. The solid line is calculated using the best-fit k and k3 values. The broken line shows the first-order pathway dominating at lower [HCIOJ. From Ref. (13).

THE COMBINED EQUILIBRIUM AND STEADY-STATE TREATMENT. There are a number of reasons why a rate equation should be derived by the combined equilibrium and steady-state approach. First, the experimentally observed kinetic patterns necessitate such a treatment. For example, several enzymic reactions have been proposed to proceed by the rapid-equilibrium random mechanism in one direction, but by the ordered pathway in the other. Second, steady-state treatment of complex mechanisms often results in equations that contain many higher-order terms. It is at times necessary to simplify the equation to bring it down to a manageable size and to reveal the basic kinetic properties of the mechanism. 

In contrast to the facile reduction of aqueous V(III) (—0.26 V versus NHE) [23, 24], coordination of anionic polydentate ligands decreases the reduction potential dramatically. The reduction of the seven-coordinate capped-octahedral [23] [V(EDTA)(H20)] complex = —1.440 V versus Cp2Fe/H20) has been studied extensively [25,26]. The redox reaction shows moderately slow electron-transfer kinetics, but is independent of pH in the range from 5.0 to 9.0, with no follow-up reactions, a feature that reflects the substitutional inertness of both oxidation states. In the presence of nitrate ion, reduction of [V(EDTA) (H20)] results in electrocatalytic regeneration of this V(III) complex. The mechanism was found to consist of two second-order pathways - a major pathway due to oxidation of V(II) by nitrate, and a minor pathway which is second order in nitrate. This mechanism is different from the comproportionation observed during... 

This process is referred to as an ordered pathway. An alternative is a random-order pathway, in which the two substrates can bind to the enzyme in either order. Still another scheme is for Si to bind to the enzyme and be converted to... 

Double-reciprocal plots for an ordered pathway. Measurements made at different fixed values of [S2] give a set of lines that intersect to the left of the ordinate. The two values of Km, Vm.ix and ATsl can be obtained by replotting the slopes and intercepts of these lines as functions of 1/[S2]. A random pathway gives similar results, but can be distinguished by making such measurements for the reverse reaction (Pi + P2 — Si + S2) in addition to the forward reaction. 

Fig. 8.22. A diagram of some of the events associated with apoptosis, showing related flow cytometric assays (outlined in bold boxes). Although it is generally agreed that calcium flux and caspase activation are early events following the trigger signal, the events following on from there may be essential steps in an ordered pathway or may be independent and merely symptomatic of apoptosis.

This allows us to diagram the coherence order pathway of an NMR experiment in a very simple way. For example, in an INEPT experiment with intermediate DQC we have... 

Coherence Order Pathway Selection by Phase Cycling... 

Once we have diagramed the desired coherence order pathway, it is easy to add gradients to select that pathway. One simple solution is to use the 3,4,5 relationship of a right triangle 3x3 + 4x4 = 5x5. Put a gradient in the first half of t of relative amplitude G = 5, another in the second half with amplitude G2 = 3, and a third in the refocusing delay with amplitude G3 = 4. As the coherence order p is 5, —3, and —4, respectively, during these three periods, we have a total twist of ... 

Figure 2 Representative ladder diagrams for the possible cascading fifth-order pathways, (a) The sequential cascade pathway, (b) The parallel cascade pathways.

The biological activity of proteins generally depends on a unique three-dimensional conformation, which in turn is inherently linked to its primary sequence. Protein folding, the conversion of the translated polypeptide chain into the native state of a protein, is the critical link between gene sequence and three-dimensional structure. Mechanistically, folding is believed to proceed through a predetermined and ordered pathway, either via kinetic intermediates or by direct transition from the unfolded to the native state [99]. In both cases, local and non-local interactions alike stabilize transient structures along the pathway and funnel the intermediates towards the native state. 

An elegant, general solution for first-order networks has been provided in a classic publication by Wei and Prater [22]. In essence, the mathematics are developed for a reaction system with any number of participants that are all connected with one another by direct first-order pathways. For example, in a system with five participants, each of these can undergo four reactions, for a total of twenty first-order steps. Matrix methods are used to obtain concentration histories in constant-volume batch reactions, and a procedure is described for determination of all rate coefficients from such batch... 

Bindereif A, Green MR. An ordered pathway of snRNP binding during mammalian pre-mRNA splicing complex assembly. 51. 

Figure 1 Ordered pathway of hemoglobin catabolism. Host Hb cleavage is initiated by PfPMI and PfPM2. Hb unfolds, releases heme and exposes other peptide bonds to the falcipains. Resultant protein fragments are degraded even more by falcilysin and transported to the cytosol where they are broken down into needed amino acids. The heme released in the first step aggregates via biomineralization to form HZ.

The general kinetic scheme shown in Scheme 8 has been developed for alkyl migration in [Mn(R)(CO)s] compounds. Thus, two pathways to the final product are avaUable (i) a second-order pathway (AiMn(R)(CO)5][L]) and (ii) a two-step sequence via the coordinatively unsaturated intermediate [Mn(COR)(CO)4]. In polar solvents, this intermediate may exist as a solvated hexacoordinate species, [Mn(COR)-(CO)4(S)] (S = molecule of solvent). In the absence of a suitably polar solvent, the intermediate is thought to adopt a square-based pyramidal conformation (99,100) with the acetyl ligand occupying a basal position, although a 7r-acyl derivative has also been proposed (101,102). 

Catalytic properties and assay of malate dehydrogenase Dehydrogenases probably operate according to an, at least partially, ordered pathway (Banaszak and Bradshaw, 1975) ... 

---