Stage II The ES complex dissociates to yield the fi nal prod-uct (P). Formation of the ES complex is faster than the subsequent transformation to the product.
E S ES (Stage I, fast) (1)
ES P E (Stage II, slow) (2)
As a result, any newly added substrate does not undergo conversion to the product immediately, though it rapidly forms an enzymes-substrate complex. A part of it may even dissociate to form the substrate again, by reversal of the fi rst reaction. Thus, the overall reaction velocity does not show a proportionate rise with the sub-strate concentration.
Max imum value is attained when the enzyme is fully purifi ed.
Turnover number of enzyme: This refers to the number of substrate molecules transformed per unit time by a sin-gle enzyme molecule (or by a sinsin-gle catalytic site), when the enzyme concentration alone is the rate-limiting fac-tor. For example, carbonic anhydrase has a turnover num-ber of 36,000,000. A high turnover numnum-ber enables this enzymes to catalyze an otherwise slow and unfavourable reaction, that involves reversible hydration of dissolved carbon dioxide to form carbonic acid.
CO2 (d) H2O Carbonic anhydrase H2CO3
Turnover numbers of some of the enzymes are given in Table 6.4.
V. Enzyme Kinetics
Enzymes are the most effi cient catalysts known: they increase the rate of a reaction without themselves under-going a change, and without changing the equilibrium of the catalyzed reaction. Rates of enzymatic reactions are infl uenced by a variety of factors, such as concentration of substrates, products, inhibitors, temperature and pH levels. Study of these parameters is important because it provides a great deal of information on nature of a par-ticular enzyme and the biochemical pathways involved.
This is called enzyme kinetics.
Effects of various factors on enzyme activity are deter-mined by the in vitro studies. These studies are conducted by isolating the enzyme from the cell, and then estimat-ing its activity when these factors are varied.
A. Effect of Substrate Concentration
Rate of an enzyme-catalyzed reaction increases with increase in the substrate concentration (Fig. 6.3). As the concentra-tion of the substrate molecules is gradually raised, more and more enzyme active sites are occupied by these mol-ecules. Consequently, substrate transformation increases, refl ecting enhanced enzyme activity.
Table 6.4. Turnover number of some enzymes (at 25°–37°C)
Enzyme Turnover number
Carbonic anhydrase 36,000,000
b-Amylase 11,00,000
Phosphoglucomutase 1,240
Fumarase 800
Fig. 6.3. The relationship between substrate concentration [S]
and reaction velocity (V).
S V
C. Effect of pH
The pH dependence of an enzyme protein is depicted in Fig. 6.5. The activity of a given enzyme is maximum at a specifi c pH which is the optimum pH of the enzyme.
Why does the pH exert such a signifi cant infl uence on the catalytic properties of the enzyme? The reason that the catalytic process requires the enzyme active site and the corresponding substrate molecule to be in appropriate state of ionization. For example, if carboxyl group of some specifi c residue on the active site is in the anionic (ve) form, the corresponding portion of the substrate should be in the cationic (ve) form. Forces of attraction develop between the opposite charges, which permit optimization of the enzyme-substrate interaction. The pH value at which such a state exists corresponds to the optimum pH of the enzyme. The enzyme-substrate interaction being optimum at this pH, the activity of the enzyme reaches a peak (Fig. 6.5). Extremes of pH decreases the enzyme activity by causing denaturation of the enzyme protein.
Each enzyme has its characteristic optimum pH, cor-responding to its maximum activity (Table 6.5). This has been depicted in Figure 6.5 also. The pH values of tissues and body fl uids are tightly regulated. Deviations of more than 0.5 pH unit from the normal blood pH of 7.4 cause protein denaturation, and so rapidly fatal. The cytoplasm of most cells has a pH value between 6.5 and 7.0; the mitochondrial matrix has pH value between 7.5 and 8.0, At lower substrate concentration, the reaction velocity almost
shows a proportional rise with the substrate concentration.
At higher substrate concentration, the reaction velocity does not increase as proportionately, but rather approaches a (fi xed) maximum reaction velocity.
Note: In case of allosteric enzymes, a sigmoid curve is obtained when the reaction velocity is plotted against the substrate concentration.
B. Effect of Temperature
Increase in temperature increases the energy content of the reactant molecules, so that more of them are able to cross the activation energy barrier and form the reaction prod-ucts. As a result, the reaction velocity rises. Increase in the reaction velocity continues till it reaches a peak (or maxi-mum) value. The temperature at which the reaction velocity is maximum is called the optimum temperature (Fig. 6.4).
Further increase in temperature beyond the optimum temperature causes a fall in the reaction velocity. This is because at high temperature (typically somewhere between 42°C and 70°C ) the enzymes get irreversibly denaturated. This explains why an optimum curve is obtained under ordinary assay conditions, that declines steeply at high temperatures.
The temperature dependence of enzymatic reactions explains the fact that metabolic rate increases during fever. Presumably, it is also responsible for the inability of the human body to tolerate body temperatures greater than 42°C. Moreover, protein denaturation is a time-dependent process, and an enzyme that survives the tem-perature of 45°C or more for some minutes may well denature gradually in the course of several hours.
Fig. 6.4. Temperature dependence of enzyme. V reaction velocity. Peak reaction velocity is reached at optimum temper-ature, and falls on increasing/or decreasing the temperature.
Temperature (°C)
20 30 40 50
10 V
Fig. 6.5. pH dependence of some enzymes (V reaction velocity. Each of the three enzymes has its characteristic opti-mum pH, corresponding to its maxiopti-mum activity).
pH Pepsin
Lysozyme Arginase
2 V
4 6 8 10
Table 6.5. Optimum pH values of some enzymes
Enzyme Optimum pH
Pepsin 1.5
Lysozyme 4.8
Trypsin 7.7
Fumarase 7.8
Arginase 9.7
concentration builds up and the substrate concentration falls, the reaction keeps getting slower and eventually stops at equilibrium (Fig. 6.7). Since it is impossible to consider this “changing” reaction rate, only the initial-reaction-rate (Vo) is taken into account.
The relation between Vo and the substrate concentrate [S] is given by Michaelis–Menten equation:
max o
m
V [S]
V K [S]
Vo initial reaction rate; Vmax maximum reaction rate;
Km Michaelis constant; [S] Substrate concentration.
The equation predicates a hyperbolic curve of Vo against [S].
Vo is measured at different substrate concentrations by incubating different amounts of the substrate with enzyme. The rate of disappearance of the substrate or the rate of appearance of the product during the fi rst few min-utes of the reaction only is taken into account.
Vmax is the maximum velocity that can be reached by increasing the substrate concentration (Fig. 6.8). For any particular set of conditions it is a constant. It indicates a saturation state at which most enzyme active sites are occupied by the substrate molecules, and the reaction rate is no longer limited by substrate availability.
and the lysosomes are mildly acidic with pH values between 4.5 and 5.5. Lysosomal enzymes generally have pH optima in this (acidic) range.
D. Effect of Enzyme Concentration
Within reasonable limits, the rate of enzyme-catalyzed reaction increases linearly with enzyme concentration (Fig. 6.6). This is because the number of available substrate binding sites increase with the increase in enzyme concen-tration. For example, if the enzyme concentration is dou-bled, number of substrate binding sites is also doudou-bled, and the rate of the reaction will increase twofold. This relationship holds good at all substrate concentrations.
The rate of enzymatic reaction increases with increasing temperature (typically doubling with every 10°C rise), pH, substrate concentration and concentration of enzyme.
VI. Michaelis–Menten Kinetic Theory of Enzyme Action
Michaelis–Menten model accounts for the kinetic prop-erties of some enzymes. It helps to describe many enzy-matic reactions under the following assumptions:
The reaction has only one substrate
The substrate concentration is much higher than that of the enzyme
Only the initial reaction velocity (Vo) is measured.
Why is it necessary to consider only the initial reaction rate?
At the beginning of the reaction the substrate alone, is present and the unoccupied active-sites of the enzyme molecule are free to bind them. Therefore, the substrate is rapidly converted to the product. As the product
Fig. 6.6. Effect of enzyme concentration on enzyme activity (V reaction rate).
V
Enzyme concentration
V0
Product formed (μmol)
Time (min) x
y
Fig. 6.7. The reaction velocity showing a progressive fall as the reaction proceeds; (x) represents the reaction rate at initial phase of the reaction, and (y) represents reaction rate at equilibrium.
Fig. 6.8. The Michaelis–Menten model predicts a hyperbolic curve of the initial reaction velocity (V
o) against the substrate concentration. K
m is the substrate concentration at half the maximum velocity (V
max).
Vmax
½ Vmax
Km Reaction velocity (V0)
Substrate concentration (S)
With increasing substrate concentration, the reaction rate rises till a constant peak value (Vmax) is reached.
Nearly all enzyme active sites are occupied by the sub-strate at this stage and further increase in subsub-strate con-centration has no effect on the reaction rate. The rate of reaction at this stage is in zero order with respect to the substrate. It implies that the reaction rate is independent of the substrate concentration (Fig. 6.3).
Note: Derivation of the Michaelis–Menten equation is higher-level learning, hence omitted here.
Lineweaver–Burk plot: The slope of the Michaelis–
Menten curve is gradual and upwards giving it a hyper-bolic shape. From this shape, it is not possible to estimate the exact value of Vmax. However, if reciprocal of these parameters:
0
1 1
and
V [S] are plotted against each other, a straight line is obtained (Fig. 6.9). From this line it is possible to determine the exact value of Vmax. This plot, known as double reciprocal plot or the Lineweaver–Burk plot, can be used to determine the exact value of Km. It is also used to determine the mechanism of action of enzyme inhibitors, discussed later.
The equation describing the double reciprocal plot is
m
0 max max
1 K 1
V V [S]V
It is reciprocal of Michaelis–Menten equation. The intercept on the x-axis equals
m [S] is the substrate concentration at the initial phase of the reaction. This changes as the reaction proceeds, so the experimental data are taken, in the fi rst few minutes of the reaction.
Km is a special rate constant called the Michaelis constant. It is defi ned as the substrate concentration at which the reaction rate is half-maximal (Fig. 6.8). At this instance the enzyme is half-saturated with its substrate.
Km has a characteristic value for a given enzyme-substrate pair. In case of the enzyme which acts on more than one substrate, the value of Km is different for each of them. For example, Km of the enzyme hexokinase for fructose is 1.5 mM, whereas for glucose it is 0.05 mM (Table 6.6).
Km refl ects binding affi nity: The Michaelis–Menten con-stant refl ects the binding affi nity of the enzyme for its substrate.
If affi nity is more, less substrate is required to saturate the enzyme, so that Vmax is reached at a relatively low sub-strate concentration. Consequently, the subsub-strate concen-tration corresponding to the half Vmax (i.e. Km) is relatively low. For this reason, high enzyme-substrate affi nity implies a low Km value, and conversely, low-affi nity implies high Km. Higher Km of glucose for glucokinase (10 mM) than that for hexokinase (0.05 mM) for example, indicates that hexoki-nase binds glucose with higher affi nity than glucokihexoki-nase.
The Michaelis–Menten equation describes the relationship between initial reaction velocity and substrate concen-tration under steady state conditions. The Michaelis con-stant Km, defi ned as the substrate concentration at which the reaction velocity is half maximal, is related to the affi nity of the enzyme for the substrate.
The following inferences can be drawn from the Michaelis–Menten kinetics.
Order of reaction: When the substrate concentration is relatively low (far below Km), most of the enzyme active sites are free. An increase in substrate concentration at this stage results in rapid occupancy of the available sites.
Therefore, the reaction rate is related almost linearly, with the substrate concentration, and the reaction shows fi rst order kinetics (Fig. 6.8).
Fig. 6.9.
0
1
V against 1
[S]. The straight line represents the Lineweaver-Burk transformation of the Michaelis–Menten equation.
Enzyme Substrate Km (mM)
Hexokinase ATP 0.4
Glucose 0.05
Fructose 1.5
Glucokinase Glucose 10
b-Galactosidase D-Lactose 40
In sequential reactions all substrates interact together at the enzyme active site. In double displacement they interact with the enzyme one by one.
VII. Inhibition of Enzyme Activity
Enzyme inhibitor is a substance that is capable of dimin-ishing velocity of the enzyme-catalyzed reaction. Two types of inhibitors are recognized: reversible and irrevers-ible. Inhibition by the reversible inhibitor can be reversed, so that the enzyme activity is recovered.
Inhibition by the irreversible inhibitor, on the other hand, cannot be reversed.
Enzyme activities can be inhibited specifi cally in rever-sible (competitive, non-competitive and uncompetitive) and irreversible manner.
A. Reversible Inhibition
The reversible inhibitor (I) acts by forming a loose, dis-sociable complex (EI) with the corresponding enzyme
E I EI
Catalytic activity of the complex (EI) is lower than that of the enzyme alone. Therefore, the substrate trans-formation decreases after addition of the inhibitor. The reversible inhibition may be competitive, non-competitive, and uncompetitive.
Following formation of the EI complex, the reaction may still obey Michaelis–Menten kinetics but with altered Km and Vmax values that vary with the inhibitor concentration.
If the inhibitor acts only on the apparent Km, it is a competitive inhibitor;
if the inhibitor affects only the apparent Vmax, it is a non-competitive inhibitor; and
if the inhibitor affects both the constants, it is an uncompetitive inhibitor.