Random-order pathway

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... 

Enzymes often require multiple substrates to complete their catalytic cycle. This may involve combining two compounds into one molecule or transferring atoms or electrons from one substrate to another. The substrates may both bind to an enzyme and react collectively, or each substrate might bind, react, and release sequentially. With two substrates, if both bind to the enzyme, a ternary complex (ES S2) will form (Scheme 4.8). The order of substrate addition may be important (ordered) or not (random order). Cases in which the two substrates react sequentially follow a double-displacement, or ping-pong, mechanism (Scheme 4.9). Enzymes requiring more than two substrates have more complicated complexation pathways. 

C3b is a dangerous protein to have floating around, since it can activate the destructive end of the complement pathway. In order to minimize random damage, two proteins (factors I and H), search out, stick to, and destroy C3b in solution. But if C3b is on the surface of a cell, then another protein (properdin), binds to and protects C3b from degradation so that it can do its job. How does C3b target foreign cells in the absence of antibodies C3b is effective only if it sticks to the surface of a cell. The chemical reaction by which it does so goes faster in the presence of the molecules typically found on the surface of many bacteria and viruses. ... 

Some of the natural extensions of this classical approach include the treatment of mechanisms with multiple intermediate complexes and near-equilibrium conditions (e.g., Peller and Alberty, 1959). Enzyme-catalyzed reactions that involve two substrates and two products are among the most common mechanisms found in biochemistry (about 90% of all enzymatic reactions according to Webb, 1963). It is not surprising, then, that this class of mechanisms also has received a great deal of attention (e.g., Dalziel, 1957,1969 Peller and Alberty, 1959 Bloomfield et al., 1962a,b Cleland, 1963a,b,c). This class includes mechanisms in which reactant molecules enter and exit a single pathway in fixed order and mechanisms with parallel pathways in which reactant molecules enter and exit in a random order (Cleland, 1970). 

The student should be aware that a pathway is essentially a conceptual model developed by biochemists in order to represent the flow of compounds and energy through metabolism. Such models are simply ways of trying to explain experimental data. A potential problem in representing metabolic pathways as in Figure 1.1 is that there is an implication that they are physically and/or topographically organized sequences. This is not necessarily true. With some exceptions (described in Section 1.3), most enzymes are likely to be found free within the cytosol or a compartment of a cell where reactions occur when an enzyme and its substrate meet as a result of their own random motion. Clearly this would be very inefficient were it not for the fact that cells contain many copies of each enzyme and many molecules of each type of substrate. 

In this section, we describe the role of fhe specific membrane environment on proton transport. As we have already seen in previous sections, it is insufficient to consider the membrane as an inert container for water pathways. The membrane conductivity depends on the distribution of water and the coupled dynamics of wafer molecules and protons af multiple scales. In order to rationalize structural effects on proton conductivity, one needs to take into account explicit polymer-water interactions at molecular scale and phenomena at polymer-water interfaces and in wafer-filled pores at mesoscopic scale, as well as the statistical geometry and percolation effects of the phase-segregated random domains of polymer and wafer at the macroscopic scale. 

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. 

Random Bi Bi Ternary Complex Mechanism The random or noncompulsory ordered mechanism is noticeably symmetrical, with two different paths for producing the EAB complex from free enzyme E and its substrates A and B, as well as two different pathways for producing the EPQ complex from free enzyme E and its products P and Q ... 

A two-substrate, two-product enzyme-catalyzed reaction scheme in which both the substrates (A and B) and the products (P and Q) bind and are released in any order. Note that this definition does not imply that there is an equal preference for each order (that is, it is not a requirement that the flux of the reaction sequence in which A binds first has to equal the flux of the reaction sequence in which B binds first). In fact, except for rapid equilibrium schemes, this is rarely true. There usually is a distinct preference for a particular pathway in a random mechanism. A number of kinetic tools and protocols... 

When taken collectively, the overall evidence indicates that hexokinase can both add and release substrates and products in a random mechanism. However, the mechanism cannot be described as rapid equilibrium random. The evidence also indicates that the preferred pathway is the ordered addition of glucose followed by ATP, then the release of ADP followed by glucose-6-P. Danenberg and Cleland have recently attempted to assign relative rate constants to a general random mechanism for hexokinase as shown in Fig. 14 (30). 

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. 

The relative concentration of dicarboxylic acids with respect to aminoacids is higher (by one or two orders of magnitude). As in the case of monocarboxylic acids, every possible isomer seemed to be present, ranging from C2 to C5 molecules. In the case of chiral molecules, the two enantiomers coexisted in nearly equal concentration. Oxalic acid was detected as calcium salt, but the state of the other dicarboxylic acids in the Murchison meteorite remains an open problem 24 >. Dicarboxylic acids, as monocarboxylic acids, seem to be the result of synthetic pathways that give mixtures at random 44-45... 

---