R and T forms

Two different enzymatically active forms of PFK could be identified which may be considered the R and T form in the framework of the symmetry model. The R form possesses a high affinity for the substrate fructose-6-P, the T form binds fructose-6-P with lower affinity. Upon binding of the inhibitor phosphoenolpyruvate, PFK converts to the T form. The enzyme is foimd in the R form upon binding the substrates (ATP or fructose-6-P) or the activator (ADP). There exist high resolution crystal structures of both forms. 

The structural differences between the R- and T-form are strongest at the interface between the dimers and impact heavily the binding site for fructose-6-P. At the binding site for the second substrate, ATP, there are only minor structural differences between the two conformations. Overall, the transition from R- to T-form is accompanied by a rotation of the two dimers aroimd the small interface the large contact surface within a dimer remains relatively imchanged. 

Figure 7.8 Equilibria among the R and T forms of hemoglobins ar-chains are represented by circles, /3-chains by squares. The clamps represent electrostatic interactions. >-< represents 2,3-diphosphoglycerate. a, b, c and d represent electrostatic linkages that are broken or formed in the processes of interconversion between the reversible tight to relaxed conformation.

The shape of the saturation curve defined by Eq. (9.59) depends on the values of L and c. If L = 0, then the T form of the protein does not exist and Y = XR[X]/(1 + XR[X]). This defines a hyperbolic binding function. Similarly if L = Y = XT[X]/(1 + XT[X]). Thus, deviations from hyperbolic binding occur only if both R and T forms exist otherwise the situation described for the Adair equation in Example 9.13 applies since binding is independent and identical at each site. 

An interesiing special case occurs when two resis-lances. R, and /t,. form a parallel circuit. T Iio fraction of the current in R, is given by... 

If a substrate were to have equal affinities for the R and T forms, the forms would be indistinguishable kinetically and the system would behave as if all the enzyme were present in a single form. Thus, Michaelis-Menten kinetics would apply, and a plot of the reaction velocity versus the substrate concentration would be hyperbolic. 

Finally, the relative concentrations of the R and T forms are determined by the value of the equilibrium... 

Let us assume that the R- and T-forms of an enzyme consisting of four protomers are in an equilibrium which lies completely on the side of the T-form ... 

FIGURE 15.12 71 versus [S] curves for an allosteric V system. The V system fits the model of Moiiod, Wyman, and Chaiigeux, given the following conditions (1) R and T have the affinity for the substrate, S. (2) The effectors A and I have different affinities for R and T and thus can shift the relative T/R distribution. (That is, A and I change the apparent value of L.) Assume as before that A binds only to the R state and I binds only to the T state. (3) R and T differ in their catalytic ability. Assume that R is the enzymatically active form, whereas T is inactive. Because A perturbs the T/R equilibrium in favor of more R, A increases the apparent Vmax- I favors transition to the inactive T state. 

This is a member of an interesting class of compounds which are chiral, without actually containing a defined chiral centre. They are chiral because their mirror images are non-superimposable. In the case of this molecule, there is no rotation about the bond between the two naphthol rings because of the steric interaction between the two hydroxyl groups, d and T forms can be isolated and are perfectly stable (Optical purity determination by H NMR, D. R Reynolds, J. C. Hollerton and S. A. Richards, in Analytical Applications of Spectroscopy, edited by C. S. Creaser and A. M. C. Davies, 1988, p346). 

Later, Kuppermann and Belford (1962a, b) initiated computer-based numerical solution of (7.1), giving the space-time variation of the species concentrations from these, the survival probability at a given time may be obtained by numerical integration over space. Since then, this method has been vigorously followed by others. John (1952) has discussed the convergence requirement for the discretized form of (7.1), which must be used in computers this turns out to be AT/(Ap)2normalized forms of r and t. Often, Ar/(Ap)2 = 1/6 is used to ensure better convergence. Of course, any procedure requires a reaction scheme, values of diffusion and rate coefficients, and a statement about initial number of species and their distribution in space (vide infra). 

Thermodynamics imposes restrictions on both the rate r and the form of the rate law representing it. Thus, at given (T, P), for a system reacting spontaneously (but not at equilibrium),... 

One application in liquid chromatography which does alter the separation process is the use of a specific series of derivatives to enable the separation of chiral (optical isomers) forms of alcohols, amines and amino acids using reverse-phase separation. FLEC is available in the two chiral forms (+)-l-(9-fluorenyl) ethyl chloroformate and (—)-l-(9-fluorenyl) ethyl chlorofor-mate (Figure 3.12). Reaction of two stereoisomers of a test compound (e.g. T+ and T—) with a single isomer of the derivatizing reagent (e.g. R+) will result in the formation of two types of product, T+R+ and T—R+. It is possible to separate these two compounds by reverse-phase chromatography. 

Koshland s model also assumes two states, R and T, but of each subunit. The binding of one ligand causes only one subunit to switch completely but induces a slight change in a neighbouring subunit which can now bind another ligand molecule easily. Because each subunit changes in turn, hybrid forms of R and T conformations are possible. 

The problem in the above example is to perform an enantiocontrolled electrophilic substitution in the a-position of a carboxylic acid derivative 1. To this end, chiral auxiliary 2, readily available in both (R) and (5) form from phenylalanine, is attached to the acid chloride 1 by amide formation. The amide 3 is converted into the (T )-enolatc 4, with the chelate ring forming... 

If the incident field component is perpendicular to the plane of incidence, all the expressions for reflected, transmitted, and absorbed light are identical in form with those in the preceding paragraph we need merely substitute R and T for / n and 7j(. 

Three important parameters enter the model calculations the mass loss rate M, the stellar radius R and the temperature parameter T . The fit of the helium line profiles of HD 50896 requires a final wind velocity of 1700 km/s. Hence, we now calculate a small grid of models in the appropriate range of R and T and with the specially adapted v. The mass-loss rate is kept at log (M/(M /yr)) = -4.4 as an arbitrary choice. The results are presented in the form of contour lines in the log T, -log R,-plane. Those of the contours which match the observed equivalent widths or peak intensities are extracted and yield a "fit diagram". We obtain a well-defined intersection region centered about R = 2.6 R, T = 60 kK (hereafter quoted as "model B"). °... 

Control in allosteric enzymes may take two extreme forms.4 In K (= binding) systems, the ones discussed so far, the substrate and the effector molecules have different affinities for the R and T states. The binding of an effector alters the affinity of the enzyme for the substrate, and vice versa. The R and the T states can have the same intrinsic value of cat, and activity is modulated by changes in affinity for the substrate. In V (= rate) systems, the substrate has the same affinity for both states, but one state has a much higher value of kCM. The effector molecule binds preferentially to one of the two states, and so modulates activity by changing the equilibrium position between the two. As the substrate binds... 

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