Biochemistry and Human Nutrition

Module 2. Enzymes

Lesson 8
ENZYME KINETICS

8.1 Introduction

• In the absence of enzyme, the conversion of S to P is slow and uncontrolled. In the presence of a specific enzyme, S is converted swiftly and specifically to product.
• Enzyme is specific; it will not convert A to B or X to Y.
• Enzymes also provide rate acceleration. On comparing the rate of a chemical reaction in solution with the rate of the same reaction with the reactants bound to the enzyme, the enzyme reaction will occur up to 10¹⁴ times faster.
• A unit is the amount of enzyme that will catalyze the conversion of 1 μmol of substrate to product in 1 min under a given set of conditions.
• Units of enzyme can be converted to milligrams of enzyme by a conversion factor called the specific activity. Specific activity is the amount of enzyme activity per milligram of protein (micromoles of product formed per minute per milligram of protein, or units per milligram).
• For a given pure enzyme under a defined set of conditions, the specific activity is a constant; however, different enzymes have different specific activities.
• An enzyme assay is the act of measuring how fast a given (or unknown) amount of enzyme will convert substrate to product—the act of measuring a velocity.
• Velocity (rate, v, activity, d[P]/dt, d[S]/dt) is how fast an enzyme converts substrate to product, the amount of substrate consumed, or product formed per unit time. Units are micromoles per minute (μmol/min) = units.

8.2 The Michaelis-Menten Equation

The primary function of enzymes is to enhance rates of reactions so that they are compatible with the needs of the organism. To understand how enzymes function, we need a kinetic description of their activity. For many enzymes, the rate of catalysis V₀, which is defined as the number of moles of product formed per second, varies with the substrate concentration [S] in a manner shown in Figure 8.1. The rate of catalysis rises linearly as substrate concentration increases and then begins to level off and approach a maximum at higher substrate concentrations. Consider an enzyme that catalyzes the S to P by the following pathway:

Fig. 8.1 Effect of substrate concentration on the initial velocity of an enzyme-catalyzed reaction

The extent of product formation is determined as a function of time for a series of substrate concentrations. As expected, in each case, the amount of product formed increases with time, although eventually a time is reached when there is no net change in the concentration of S or P. The enzyme is still actively converting substrate into product and visa versa, but the reaction equilibrium has been attained. We define V₀ as the rate of increase in product with time when [P] is low; that is, at times close to zero (hence, V₀). Thus, for the graph in Figure, V₀ is determined for each substrate concentration by measuring the rate of product formation at early times before P accumulates .We begins our kinetic examination of enzyme activity with the graph shown in Figure. At a fixed concentration of enzyme, V ₀ is almost linearly proportional to [S] when [S] is small but is nearly independent of [S] when [S] is large. In 1913, Leonor Michaelis and Maud Menten proposed a simple model to account for these kinetic characteristics. The critical feature in their treatment is that a specific ES complex is a necessary intermediate in catalysis. The model proposed, which is the simplest one that accounts for the kinetic properties of many enzymes, is

To simplify matters, we will work under the steady-state assumption. In a steady state, the concentrations of intermediates, in this case [ES], stay the same even if the concentrations of starting materials and products are changing. This occurs when the rates of formation and breakdown of the ES complex are equal. Setting the right-hand sides of equations 3 and 4 equal gives

Now let us examine the numerator of equation 8. The concentration of uncombined substrate [S] is very nearly equal to the total substrate concentration, provided that the concentration of enzyme is much lower than that of substrate. The concentration of uncombined enzyme [E] is equal to the total enzyme concentration [E]T minus the concentration of the ES complex

• At very low substrate concentration, when [S] is much less than K M, V₀ = (V max/K M)[S]; that is, the rate is directly proportional to the substrate concentration.
• At high substrate concentration, when [S] is much greater than K M, V₀ = V max; that is, the rate is maximal, independent of substrate concentration.
• The meaning of K M is evident from equation 15.

When V₀ = V max/2
Then [S] = Km,

• Thus, K M is equal to the substrate concentration at which the reaction rate is half its maximal value.
• K_m is an important characteristic of an enzyme-catalyzed reaction and is significant for its biological function. For most enzymes, K_m lies between 10^-1 and 10^-7 M.

8.3 The Significance of K_m and V_max Values

• The K_m value for an enzyme depends on the particular substrate and on environmental conditions such as pH, temperature, and ionic strength.
• K_m is the concentration of substrate at which half the active sites are filled. Thus, K_m provides a measure of the substrate concentration required for significant catalysis to occur.
• K_m is equal to the dissociation constant of the ES complex if k₂ is much smaller than k_-1 .
• High K_m indicates weak binding; a low K_m indicates strong binding. K_m indicates the affinity of the ES complex only when k_-1 is much greater than k₂.
• The maximal rate, V max, reveals the turnover number of an enzyme, which is the number of substrate molecules converted into product by an enzyme molecule in a unit time when the enzyme is fully saturated with substrate.

8.4 The Double-Reciprocal Plot

The Michaelis-Menten equation can be algebraically transformed into equations that are more useful in plotting experimental data.

This form of the Michaelis-Menten equation is called the Lineweaver-Burk equation. For enzymes obeying the Michaelis-Menten relationship, a plot of 1/V0 versus 1/[S] yields a straight line. This line has a slope of Km/Vmax, an intercept of 1/V_max on the 1/V0 axis, and an intercept of -1/Km on the 1/[S] axis. The double-reciprocal presentation, also called a Lineweaver-Burk plot, has the great advantage of allowing a more accurate determination of Vmax, which can only be approximated from a simple plot of V0 versus [S]. The double-reciprocal plot of enzyme reaction rates is very useful in distinguishing between certain types of enzymatic reaction mechanisms and in analyzing enzyme inhibition.

Fig. 8.2 The double-reciprocal plot