Mutarotation equations

By application of first-order, kinetic equations, B. Anderson and Degn claimed that an equilibrated (25°) aqueous solution of D-fructose contains 31.56% of jS-D-fructofuranose and 68.44% of -D-fructopyranose. N.m.r. studies, however, showed that, at equilibrium, a solution of D-fructose contains /3-D-fructopyranose, -D-fructofuranose, a-D-fructofuranose, and a trace of a-D-fructopyranose the distribution of these isomers was shown by gas-liquid chromatography to be 76,19.5, and 4%, respectively. Based on Anderson and Degn s result, Shallenberger reasoned that, as 0.68 X 1.8 = 1.22 (which approximates the reported sweetness of mutarotated D-fructose ), the furanose form(s) must possess very little sweetness. 

In equation 8.2-6a, the slope of -1 with respect to pH refers to specific hydrogen-ion catalysis (type B, below) and the slope of + 1 refers to specific hydroxyl-ion catalysis (Q if k0 predominates, the slope is 0 (A). Various possible cases are represented schematically in Figure 8.5 (after Wilkinson, 1980, p. 151). In case (a), all three types are evident B at low pH, A at intermediate pH, and C at high pH an example is the mutarotation of glucose. Cases (b), (c), and (d) have corresponding interpretations involving two types in each case examples are, respectively, the hydrolysis of ethyl orthoacetate, of P -lactones, and of y-lactones. Cases (e) and (f) involve only one type each examples are, respectively, the depolymerization of diacetone alcohol, and the inversion of various sugars. 

Further experiments by Brown and particularly Henri were made with invertase. At that time the pH of the reactions was not controlled, mutarotation did not proceed to completion, and it is no longer possible to identify how much enzyme was used (Segal, 1959). Nevertheless, in a critical review of kinetic studies with invertase, Henri concluded (1903) that the rate of reaction was proportional to the amount of enzyme. He also stated that the equilibrium of the enzyme-catalyzed reaction was unaffected by the presence of the catalyst, whose concentration remained unchanged even after 10 hours of activity. When the concentration of the substrate [S] was sufficiently high the velocity became independent of [S]. Henri derived an equation relating the observed initial velocity of the reaction, Vq, to the initial concentration of the substrate, [S0], the equilibrium constant for the formation of an enzyme-substrate complex, Ks, and the rate of formation of the products, ky... 

The rates of mutarotation of glucose, in the presence of 0 to 0.238M imidazole and of 0 to 0.230M benzimidazole at 25°, have been measured the rate constant data are given in Table I. Linear plots of the observed rate constants for glucose vs. the molarity of imidazole or benzimidazole (Im or BIm) are obtained. The straight lines follow the equations... 

It is easy to see from Equation 8 why —NH3+ ion does not catalyze the mutarotation The positively charged ion cannot extract the proton from the hydroxyl group on carbon 1. When no NaOH is added, in the presence of 0.0114M Cd(N03)2, the rate constant of mutarotation is 0.0122, practically the same as in the absence of the metal. This is as expected, since no glucosamine complex is present. 

Mutarotation has been shown to be a first-order reaction, the velocity constant being independent of reaction time and concentration of reactants. The rate of mutarotation increases 2.8 times with a 10°C rise in temperature. By applying the law of mass action, equations have been developed to measure the rate of the reversible reaction between the a and (3 forms of lactose. If a dilute lactose solution at constant temperature contain a moles of a and b moles of /3, then the amount of (3 formed (x) per unit of time is... 

Equations similar to those for mutarotation have been derived, expressing the relationship between the solubility behavior of the two forms of lactose and the equilibrium or rate constants (Hudson 1904). The constants derived by both mutarotation and solubility methods are in agreement. The solubility equations have been used to develop procedures for measuring a- and /3-lactose in dry milk (Roetman 1981). 

As a solution of one anomer was allowed to mutarotate, an increasing amount of the second anomer became evident until finally the usual equilibrium mixture was obtained (see Figure 2). By determining the peak areas, the percent of each anomer present at any given time interval could be calculated. Since the equation for the mutarotation coefficient, k, can be expressed in the form of Equation 1, the coefficient can be determined... 

Although the crystalline forms of a- and /3-D-glucose are quite stable, in solution each form slowly changes into an equilibrium mixture of both. The process can be observed as a decrease in the optical rotation of the a anomer (+112°) or an increase for the /3 anomer (+18.7°) to the equilibrium value of 52.5°. The phenomenon is known as mutarotation and commonly is observed for reducing sugars. Both acids and bases catalyze mutarotation the mechanism, Equation 20-1, is virtually the same as described for acid- and base-catalyzed hemiacetal and hemiketal equilibria of aldehydes and ketones (see Section 15-4E) ... 

A possibility that was proposed quite early for the glucose mutarotation, and that could conceivably be of importance for other reactions, is simultaneous catalysis by an acid and a base. It will be recalled from Section 8.1 that hydration requires addition of a proton at one site and removal of a proton from another. If both these processes were to occur in one step, either by means of separate acid and base molecules acting together or by action of a single molecule containing both an acidic and a basic center, we would designate the process as a concerted acid and base catalysis (Equation 8.39).60 Swain found that the rate of... 

The velocity of the reaction is greatly accelerated by acid or base. The rate is at a minimum for pyranose-pyranose interconversions in the pH range 2.5 to 6.5. Both acids and bases accelerate mutarotation rate, with bases being more effective. This was expressed by Hudson (1907) in the following equation ... 

The enhanced reactivity of chelated amino acid esters towards attack by other nucleophiles has been used to advantage in the sequential synthesis of small peptides equation (4l).225 Formation of the amide bond takes only seconds to minutes at room temperature in DMSO as solvent, and the peptide can be easily recovered by reducing the metal to the Co" state. Recent studies have shown that the A and A diastereoisomeric reactants are selective in their couplings to (2 ) and (S) amino acid esters and that mutarotation at the asymmetric centre of the chelated ester reactant varies from 0-6%.226 Isied and coworkers have described the use of the Co(NH3)3+ as a C-terminal protecting group for the sequential synthesis of peptides (equation 42).227 This procedure has advantages over other methods in some cases. 

Mutarotation at S is also reported to be catalyzed by light,1041 possibly via an O-bound sulfenate intermediate (equation 162). Adamson and coworkers report that photodecomposition to Co j is the final outcome.1049 For sulfinate complexes donor S to O isomerization occurs1020,1049 and red O-bound (N,0)[Co(cyst02)(en)2](C104)2-H20 has been isolated.1029 This process (equation 163 hv 350-450 nm) is thermally reversible (r1/2 600h, r.t.) but which O atom is involved, axial or equatorial, is not known. The O-bound form is now asymmetric, and some specificity might be expected. 

The last equation is essentially the same as that used earlier by Urech, Trey, Levy, Lowry, and Simon. The early workers expressed the mutootation constants by use of the logarithmic base 10 and the time in minutes this custom has been largely maintained by carbohydrate chemists, although, in other fields, the use of natural logarithms and measurement of time in seconds are more common. In the present article, unless stated otherwise, mutarotation constants are expressed in minutes with logarithms to the base 10, and are calculated from the equation ... 

The mutarotations of the first group, designated simple mutarota-tions, can be expressed by equation 5, the exponential form of equation ... 

The proportions of the three constituents calculated from the measurements of optical rotation difiFered widely from those calculated from the measurements of dilatation and refractivity. Inasmuch as the experimental data could not be represented satisfactorily by the equations derived for the three-component system, these workers concluded that the reaction system involves more than three components. Subsequently, the following reaction system came to be widely used as a working hypothesis for the interpretation of mutarotation reactions. 

We now believe that this scheme needs to be revised by including several acyclic transition states, as will be discussed in Part II. Determination of the separate rate-constants for the reactions is not possible, but an empirical equation (7), developed by Lowry and Smith, is convenient for recording and comparing mutarotation data. Here,... 

Table VI (see p. 53) gives a summary of mutarotation measurements made by the authors for a group of sugars under comparable conditions. The mutarotation constants are expressed to the base 10. If it is desired to use the natural logarithmic base, equation 7 is changed only by replacement of the base 10 by the base e, by multiplying exponents mi and m2 by 2.3026.

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