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Many reactions that occur in food systems in which intact or macerated foodstuffs are constituents are catalyzed by enzymes originating in the plant or animal tissue. Enzymes are biocatalysts primarily consisting of proteins that bind substrates stereospecifically so that the activation energy barrier to the reaction is decreased. Although enzymes are ubiquitous in biological systems, two of the more important with regard to food systems are hydrolases (enzymes that catalyze hydrolysis of compound molecules such as esters, proteins, complex carbohydrates, etc.) and oxidoreductases (enzymes that catalyze oxidation or reduction reactions such as peroxidase and lipoxygenase).

Since enzymes are so important in food processing as biocatalysts for both beneficial use (e.g., rennin in cheese-making) and food deterioration and decrease in quality (e.g., starch hydrolases), the kinetics of enzyme-catalyzed reactions have been widely studied. Furthermore, since most enzymes are very substrate specific, the kinetics of enzyme-catalyzed reactions can be easily determined qualitatively and quantitatively. For our purposes, we shall consider enzyme kinetics in general.

B. Michaelis – Menten Analysis

Michaelis and Menten (1913) proposed the theory of enzyme-substrate complex formation to describe enzyme kinetics. This is depicted in the following reaction scheme:

where E is the enzyme, S the substrate, ES the enzyme-substrate complex, and P the product. The rate constants for the forward and reverse reactions are k₁, k₂and k₂₁, k₂₂, respectively. Both reactions are reversible in the general case.

From this description, when the substrate concentration is very small, the forward reaction to form ES is first-order in S. At very large substrate concentration, the forward reaction is zero order in S since the reaction rate is only dependent on the concentration of enzyme. This is characteristic of enzyme-catalyzed reactions in foods. Figure 2.4 illustrates the dependence of initial velocity of the reaction on substrate concentration.

Michaelis and Menten (1913) applied steady-state kinetic analysis to Eq.

(32) and derived the following equation to describe the velocity of an enzyme-catalyzed reaction as depicted in Fig. 2.4

v ¼2dS dt ¼dP

dt ¼ Vmax½
S

Kmþ S½
ð33Þ

where v is the velocity, Vmaxis the maximum velocity when enzyme is saturated with substrate, Km½¼ ðk₂₁þ k2Þ/k1
is the substrate concentration at which v ¼ 0.5V_max, and [S] is the substrate concentration at time t. In this analysis, k₂₂ is assumed to be zero. To eliminate complications that can arise when substrate concentration decreases or product concentration increases, most kinetic studies on enzymes are completed at very small conversion ratio ([S]_t/[S]₀# 0.05), i.e., ,5% conversion).

Determination of K_m and V_max may be conveniently determined by linearizing Eq. (33). The resulting plot is called a Lineweaver-Burk plot (Lineweaver and Burk, 1934). Taking the reciprocal of both sides of Eq. (33) results in

1 v¼ 1

Vmax

þ Km

Vmax½
S ð34Þ

F^IGURE2.4 Enzyme-catalyzed reaction.

Thus a plot of 1/v versus 1/ S½
results in a straight line with intercept 1/V_maxand slope K_m/V_max.

One mechanism for inactivating or controlling the activity of enzymes is the use of inhibitors. An inhibitor is a compound that interacts with the enzyme reducing the activity of the enzyme. Inhibitors have found widespread use in treatment of microbially caused diseases. The inhibitor may compete competitively with substrates or cofactors for binding to active sites or the inhibitor may form a covalent bond with active site groups. Inhibitors are also used to control enzyme activity in plant and animal tissue after harvest. Other chemical and physical means of controlling enzyme activity include chelation or sequestration of metal cofactors, elevated temperatures for short periods (e.g., blanching), shifting the pH outside the range for enzyme activity, treatment with high pressure, and use of shear forces. Several of these treatments are covered elsewhere in this book.

Reversible inhibitors are distinguished from irreversible inhibitors by forming complexes with the enzyme that can be reversed by displacing the equilibrium by dialysis or gel filtration. Irreversible inhibitors, on the other hand, slowly form covalent bonds with enzyme, enzyme-substrate or enzyme-product complexes. Reversible inhibitors are identified by the nature of their interaction with the enzyme and consequently by their effect on the intercept and slope of a Lineweaver-Burk plot. The intercept and slope for three types of reversible inhibitors are given in Table 2.4.

Competitive inhibition occurs when the inhibitor binds reversibly with the enzyme competing with the substrate for active sites. Noncompetitive inhibition is observed when the inhibitor does not compete with the substrate for binding with enzyme but rather both inhibitor and substrate can bind to the enzyme simultaneously. Uncompetitive inhibition occurs when the inhibitor can only

TABLE2.4 Slope and Intercept Values for Lineweaver-Burk Inhibitors^a

Type of inhibition Slope y intercept x intercept

None _V^Km

Noncompetitive 1 þ_K^Io

i

aIo¼ concentration of inhibitor; Ki¼ dissociation constant of inhibitor-enzyme complex.

Source: Whitaker (1996).

bind to the enzyme-substrate or one or more of the intermediate complexes.

Finally, a more complex reversible inhibition occurs when the inhibitor binds to multi-subunit enzymes. Kinetically, this can be analyzed to produce the number of subunits to which the inhibitor can bind. Whitaker (1996) gives an analysis of the kinetics. Irreversible inhibitors, those that form covalent bonds with the enzyme or its substrate complexes, can be treated kinetically through rate equations and not through Lineweaver-Burk or Michaelis-Menton analysis.

The effect of temperature on enzyme activity and inactivation is generally treated by the Arrhenius equation. At temperatures well below that where protein denaturation occurs, the Arrhenius activation energy for the enzyme-catalyzed reaction is less than that for nonenzyme-catalyzed conversion. At higher temperatures at which enzyme inactivation can occur, the Arrhenius activation energy for enzyme inactivation is very large, as illustrated in Table 2.3. Large activation energy is indirect evidence that numerous hydrogen bonds must be broken to permanently alter the structure and destroy the active site of the enzyme. It has been demonstrated that some enzymes have heat-stable isozymes, proteins that perform the same function as the enzyme but are marginally different in conformation. For these isozymes, the Arrhenius activation energy for inactivation is usually much smaller than the heat-labile isozymes (i.e., less temperatures sensitive) indicating that perhaps only a few hydrogen bonds need to be broken to eliminate enzyme activity or perhaps one covalent bond such as a disulfide bond.

VIII. SUMMARY

To design food-processing operations and predict shelf life of foods it is essential to have quantitative data on rates of reaction and their dependence on macro- and microenvironmental variables. The literature is replete with studies on reactions important in foods. Unfortunately, control of process variables and quality of the data are not uniformly good. Consequently, when using literature values it is important to examine the original reference to make your own assessment of quality of the data. Points to observe include were the important variables identified, was the study properly conducted, were conditions consistent with those is your system (e.g., pH, presence of catalysts, temperature)? Were a sufficient number of half-lives traversed in the concentration range so that accurate rate constants could be determined? Did the concentration range cover that in which you are interested? For temperature dependence determination, were an adequate number of temperatures (generally more than four) used and does the temperature range cover your process conditions? As we shall see in later chapters these are important points to consider if food process operations are to be properly designed.

REFERENCES

Benson SW. The Foundations of Chemical Kinetics. New York: McGraw-Hill, 1960.

Hill CG Jr. An Introduction to Chemical Engineering Kinetics and Reactor Design. New York: McGraw-Hill, 1977, pp. 34 – 37.

Lineweaver H and Burk D. Determination of enzyme dissociation constants. J Am Chem Soc 56:658 – 666, 1934.

Michaelis L and Menton MI. Kinetics of invertase action. Biochem Z 49:333 – 369, 1913.

Thijssen HAC and Kerkhof DJAM, Effect of temperature-moisture content history during processing on food quality. In Hoyem T and Kvale O, eds. Physical, Chemical and Biological Changes in Foods Caused by Thermal Processing. London: Applied Science Publishing, 1977, pp. 10 – 30.

Whitaker JR. Enzymes, In Fennema OR, eds. Food Chemistry. 3rd ed. New York:

Marcel Dekker, 1996, Chapter 7, pp. 431 – 530.

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