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# Chapter 19 : Enzymatic Activity

Category: Microbial Genetics and Molecular Biology

Enzymatic Activity, Page 1 of 2

< Previous page | Next page > /docserver/preview/fulltext/10.1128/9781555817497/9781555812232_Chap19-1.gif /docserver/preview/fulltext/10.1128/9781555817497/9781555812232_Chap19-2.gif**Abstract:**

This chapter provides a brief description of the most important principles and approaches used in enzyme activity measurements. In addition, the discussion presents practical information useful to investigators who seek to design enzyme assays for performing meaningful and accurate evaluations of catalytic activities. Many investigators refer to compounds such adenosine 5'-phosphotransferase (ATP), NAD+, and CoA as cellular coenzymes, since they are regenerated by other enzyme systems within the cell, even though they are modified during the specific enzyme reaction. The great majority of enzyme assays are conducted on cell free preparations. This approach allows for careful control of substrate and cofactor concentrations, reaction conditions such as pH and ionic strength, and the use of coupled assays where desired. The following discussion covers only the most basic elements of enzyme kinetics; yet, this information should be adequate for the characterization of most enzymes of microbiological interest. Comparison of concentration versus-substrates plots for enzymes exhibiting Michaelis-Menten kinetics, substrate inhibition, or cooperative behavior. Any microbial enzyme activity of interest can be investigated by using the information provided, which summarize various types of enzyme preparations, high light practical considerations for the design and optimization of an enzyme assay, and detail basic approaches for obtaining and analyzing of enzyme kinetic data.

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

## Figures

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

Comparison of progress curves for enzymes that are stable, activated, or inactivated during the assay. For the favorable situation of a stable enzyme (●), the concentration of product formed per unit of time increases in a linear fashion (shown here as v = 5 µM/min). For a particular enzyme, the activity may increase during the assay to reach a steady-state level (▲). This situation is observed for some coupled enzyme systems, or it may be associated with enzyme disaggregation, dissociation of a slow-binding inhibitor, or other type of activation that occurs under assay conditions. Progress curve data for an enzyme exhibiting activation can be fit to equation 12 (with v 0 = 0) to obtain the final rate (v f) and the apparent first-order rate constant for establishment of equilibrium (k app). In the opposite situation (■), the rate of product formation may decrease over time and eventually result in complete enzyme inactivation. Progress curve data for such a labile enzyme can be fit to equation 1 to obtain the initial rate and the inactivation rate constant (v o = 5 µM/min and k inact = 0.1 min-1 for the situation shown). Attempts to estimate v o by taking the tangent to the first few points of such data generally result in an underestimation of the true value. By proper choice of assay conditions (inclusion of reductant, addition or removal of metal chelators, change in ionic strength, provision of glycerol or other additives, etc.), it may be possible to sufficiently enhance the stability of an enzyme so that a linear response is obtained, thus facilitating further characterization.

##### FIGURE 1

Comparison of progress curves for enzymes that are stable, activated, or inactivated during the assay. For the favorable situation of a stable enzyme (●), the concentration of product formed per unit of time increases in a linear fashion (shown here as v = 5 µM/min). For a particular enzyme, the activity may increase during the assay to reach a steady-state level (▲). This situation is observed for some coupled enzyme systems, or it may be associated with enzyme disaggregation, dissociation of a slow-binding inhibitor, or other type of activation that occurs under assay conditions. Progress curve data for an enzyme exhibiting activation can be fit to equation 12 (with v 0 = 0) to obtain the final rate (v f) and the apparent first-order rate constant for establishment of equilibrium (k app). In the opposite situation (■), the rate of product formation may decrease over time and eventually result in complete enzyme inactivation. Progress curve data for such a labile enzyme can be fit to equation 1 to obtain the initial rate and the inactivation rate constant (v o = 5 µM/min and k inact = 0.1 min-1 for the situation shown). Attempts to estimate v o by taking the tangent to the first few points of such data generally result in an underestimation of the true value. By proper choice of assay conditions (inclusion of reductant, addition or removal of metal chelators, change in ionic strength, provision of glycerol or other additives, etc.), it may be possible to sufficiently enhance the stability of an enzyme so that a linear response is obtained, thus facilitating further characterization.

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

Comparison of v-versus-[S] plots for enzymes exhibiting Michaelis-Menten kinetics, substrate inhibition, or cooperative behavior. A single-substrate enzyme following Michaelis-Menten kinetics will yield data forming a rectangular hyperbola that can be fit to equation 5 (●). For the example shown, V max = 100 µmol/min/mg and K m = 5 µM. An enzyme exhibiting the same values of V max and K m, but inhibited by excess substrate (with K i = 25 µM), gives rise to a plot (■) that shows an increase in rate at low concentrations of increasing substrate followed by a decreasing rate at higher [S]. Data such as these should be fit to equation 9 (in particular, they should not be truncated to include only the initial phase). Significantly, the largest observed v (53 μmol/min/mg for the case shown) can be significantly smaller than V max. Positive cooperativity typically results in sigmoidal plots (▲); however, a nonsigmoidal plot with a sharper bend alternatively can arise from negative cooperativity. The data associated with positive cooperativity can be fit to equation 10 to calculate V max, [S]0.5 (the substrate concentration when v = 1/2 V max), and the Hill coefficient, h (100 µmol/min/mg, 5 µM, and 2, respectively, for the data shown).

##### FIGURE 2

Comparison of v-versus-[S] plots for enzymes exhibiting Michaelis-Menten kinetics, substrate inhibition, or cooperative behavior. A single-substrate enzyme following Michaelis-Menten kinetics will yield data forming a rectangular hyperbola that can be fit to equation 5 (●). For the example shown, V max = 100 µmol/min/mg and K m = 5 µM. An enzyme exhibiting the same values of V max and K m, but inhibited by excess substrate (with K i = 25 µM), gives rise to a plot (■) that shows an increase in rate at low concentrations of increasing substrate followed by a decreasing rate at higher [S]. Data such as these should be fit to equation 9 (in particular, they should not be truncated to include only the initial phase). Significantly, the largest observed v (53 μmol/min/mg for the case shown) can be significantly smaller than V max. Positive cooperativity typically results in sigmoidal plots (▲); however, a nonsigmoidal plot with a sharper bend alternatively can arise from negative cooperativity. The data associated with positive cooperativity can be fit to equation 10 to calculate V max, [S]0.5 (the substrate concentration when v = 1/2 V max), and the Hill coefficient, h (100 µmol/min/mg, 5 µM, and 2, respectively, for the data shown).

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

Progress curve comparison of slow-binding versus rapid-equilibrium inhibitors. An uninhibited enzyme is shown to form product at a rate of 5 µM/min (●). In the presence of a slow-binding inhibitor (■), the rate decreases from v 0 to v f with an apparent first-order rate constant k app (5 µM/min, 1 µM/min, and 0.2 min-1, respectively, for the data shown). These data can be analyzed by using equation 12. For comparison, the plot associated with a rapid-equilibrium inhibitor (▲) exhibits no time-dependent decrease in enzyme rate (here shown as 1 µM/min).

##### FIGURE 3

Progress curve comparison of slow-binding versus rapid-equilibrium inhibitors. An uninhibited enzyme is shown to form product at a rate of 5 µM/min (●). In the presence of a slow-binding inhibitor (■), the rate decreases from v 0 to v f with an apparent first-order rate constant k app (5 µM/min, 1 µM/min, and 0.2 min-1, respectively, for the data shown). These data can be analyzed by using equation 12. For comparison, the plot associated with a rapid-equilibrium inhibitor (▲) exhibits no time-dependent decrease in enzyme rate (here shown as 1 µM/min).

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

Double-reciprocal plots illustrating three patterns of inhibition. (A) Kinetic analysis of a single-substrate reaction in the presence of a rapid-equilibrium competitive inhibitor yields a series of lines intersecting on the y axis. These data can be fit to equation 17. (B) Noncompetitive inhibitors result in lines intersecting to the left of the y axis at a point above, below, or on the x axis (as shown), depending on the relative values of K i E and K i ES. These data can be fit to equation 18. (C) Uncompetitive inhibition can give rise to a series of parallel lines that can be fit to equation 19. This type of inhibition is seldom encountered with single-substrate enzymes, and an alternative model involving pseudouncompetitive inhibition ( 33 ) should be considered. For the plots shown, V max = 100 µmol/min/mg, K m = 5 µM, K ic, K i E, K i ES, and K iu were each set to 2 µM, and [I] = 0 (⬤), 1 (♦), 2 (■), and 3 (▲) µM.

##### FIGURE 4

Double-reciprocal plots illustrating three patterns of inhibition. (A) Kinetic analysis of a single-substrate reaction in the presence of a rapid-equilibrium competitive inhibitor yields a series of lines intersecting on the y axis. These data can be fit to equation 17. (B) Noncompetitive inhibitors result in lines intersecting to the left of the y axis at a point above, below, or on the x axis (as shown), depending on the relative values of K i E and K i ES. These data can be fit to equation 18. (C) Uncompetitive inhibition can give rise to a series of parallel lines that can be fit to equation 19. This type of inhibition is seldom encountered with single-substrate enzymes, and an alternative model involving pseudouncompetitive inhibition ( 33 ) should be considered. For the plots shown, V max = 100 µmol/min/mg, K m = 5 µM, K ic, K i E, K i ES, and K iu were each set to 2 µM, and [I] = 0 (⬤), 1 (♦), 2 (■), and 3 (▲) µM.

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

Double-reciprocal plot of kinetic data for a substituted enzyme mechanism. A plot of 1/v-versus-1/[A] is illustrated for a bisubstrate enzyme reaction (V max = 100 µmol/min/mg, K mA = 100 µM, and K mB = 5 µM) at [B] = 0.5 (●), 1 (♦), 2 (◼), and 4 (▲) µM. The data are fit to equation 23.

##### FIGURE 5

Double-reciprocal plot of kinetic data for a substituted enzyme mechanism. A plot of 1/v-versus-1/[A] is illustrated for a bisubstrate enzyme reaction (V max = 100 µmol/min/mg, K mA = 100 µM, and K mB = 5 µM) at [B] = 0.5 (●), 1 (♦), 2 (◼), and 4 (▲) µM. The data are fit to equation 23.

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

Double-reciprocal plot of kinetic data for a sequential enzyme mechanism. A plot of 1/v-versus-1/[A] is illustrated for a bisubstrate nonsubstituted enzyme reaction. Inspection of such a plot cannot distinguish between ordered-binding and random-binding reactions, because either mechanism yields lines that intersect to the left of the y axis (this point may lie above, on, or below the x axis, depending on the specific kinetic parameters). Product inhibition studies should be carried out (Table 1) to discern whether the data fit to equation 29 or 31. The data shown are for an enzyme operating by an ordered-binding mechanism with V max = 100 µmol/min/mg, K mA = 100 µM, K mB = 5 µM, and K iA = 20 µM, at [B] = 0.5 (●), 1 (♦), 2 (◼), and 4 (▲) µM.

##### FIGURE 6

Double-reciprocal plot of kinetic data for a sequential enzyme mechanism. A plot of 1/v-versus-1/[A] is illustrated for a bisubstrate nonsubstituted enzyme reaction. Inspection of such a plot cannot distinguish between ordered-binding and random-binding reactions, because either mechanism yields lines that intersect to the left of the y axis (this point may lie above, on, or below the x axis, depending on the specific kinetic parameters). Product inhibition studies should be carried out (Table 1) to discern whether the data fit to equation 29 or 31. The data shown are for an enzyme operating by an ordered-binding mechanism with V max = 100 µmol/min/mg, K mA = 100 µM, K mB = 5 µM, and K iA = 20 µM, at [B] = 0.5 (●), 1 (♦), 2 (◼), and 4 (▲) µM.

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

## References

## Tables

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19

Product inhibition patterns for two common types of bisubstrate reactions a

a Patterns are described for double-reciprocal plots of 1/v versus 1/[variable substrate] for varied concentrations of product at the stated [fixed substrate].

b Fixed substrate concentration range: U, unsaturated; S, saturated.

c C, competitive; NC, noncompetitive; U, uncompetitive; none, not inhibitory.

d Convergence point is not necessarily on the horizontal axis but is always to the left of the vertical 1/v axis.

e In this mechanism, assignments of A and B are arbitrary, as are P and Q. The patterns stated apply only if there are no dead-end complexes, such as EAP or EBQ

##### TABLE 1

Product inhibition patterns for two common types of bisubstrate reactions a

a Patterns are described for double-reciprocal plots of 1/v versus 1/[variable substrate] for varied concentrations of product at the stated [fixed substrate].

b Fixed substrate concentration range: U, unsaturated; S, saturated.

c C, competitive; NC, noncompetitive; U, uncompetitive; none, not inhibitory.

d Convergence point is not necessarily on the horizontal axis but is always to the left of the vertical 1/v axis.

e In this mechanism, assignments of A and B are arbitrary, as are P and Q. The patterns stated apply only if there are no dead-end complexes, such as EAP or EBQ

**Citation:**

**Hausinger R, Phillips A.**2007. Enzymatic Activity, p 504-526.

*In*Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed),

*Methods for General and Molecular Microbiology, Third Edition*. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch19