The Rate of Enzymatic Reactions

Quick recap • The rate of Chemical Reactions → Rises linearly as the substrate concentration [S] increases. The rate of Enzymatic Reactions → Rises rapidly with the substrate concentration [S] initially and then begins to level off (when the enzyme is saturated) and approaches a maximum (Vmax) at higher substrate concentrations where the enzyme is over saturated (Plateau). • When the substrates' concentration is very high: The rate of the reaction depends on the catalytic activity of the enzyme, not on the concentration of the substrate. The only way to change the rate at this point is to change the [E]. When the substrates' concentration is low: The rate of the reaction is almost linearly proportional to the substrates' concentration. • Turnover Number: is the number of substrate molecules converted (Turned over) into product by a single enzyme molecule in a unit time when the enzyme is fully saturated with substrate. The Michaelis-Menten Equation 1) What happens if the [S] is very low relative to Km? The enzymatic reaction rate (Vo) would be low. 2) What happens if the [S] is very high relative to Km? Km would almost be negligible → 𝑉𝑜 = 𝑉𝑚𝑎𝑥 3) What happens if [S] = Km? 1 𝑉𝑜 = 𝑉𝑚𝑎𝑥 Quick mafs ;) 2 1|Page Note: Very low values are only negligible in addition and subtraction. However, it is not in multiplication and division since even low values can have a huge impact. From the previous 3rd question, we notice that the KM is actually the substrate concentration [S] at which Vo is half maximal (Vmax). The Michaelis constant (KM) Steady State Approximation, is a chemical equation derived by Michaelis and Menten. It included that the substrate enzyme complex (ES) is used up as soon as it has formed, thus the concentration of the ES does not change. In other words, the rate of ES formation = the rate of its dissociation. The derivation of the Michaelis-Menten Equation is not required. K1 → Rate constant of the formation reaction of ES K -1 → Rate constant of the degradation reaction of ES K2 → Rate constant of the formation of E + P Taking these constants into consideration, Michaelis and Menten came up with KM. Dissociation Constants Association Constants 2|Page KM up until now can indicate the following: 1) The substrate concentration [S] at which Vo is half maximal (Vmax). 2) The affinity of an enzyme to a substrate "discussed below". 3) The substrate concentration [S] when 50% of the enzymes' active sites are bound with the substrate. 4) Related to the rate of dissociation of the substrate from the enzyme, to the formation of the enzyme-substrate complex. Rule: The lower the KM value of an enzyme towards a substrate is, the higher the affinity to the same substrate is. It's only an indication for affinity but not an accurate measure of it. For further explanation, imagine these two situations: 1) 200 molecules of a substrate + 10 molecules of an enzyme After a while, we notice that 5 out of the 10 enzyme molecules are bound to the substrate (which is 50% of enzymes' active sites) → KM 1 = 200 2) 50 molecules of a substrate + 10 molecules of an enzyme Here we used the same enzyme but a different substrate (which has a different affinity). After a while, we notice that 5 out of the 10 enzyme molecules are bound to the substrate → KM 2= 50 Conclusion: The 2 nd substrate had more affinity because the number of molecules required to fill half of the active sites on the enzyme was fewer. Notice that KM 2 < KM 1 ➔ KM is a measure of affinity and it is inversely proportional to it. It is the same concept when we mentioned that myoglobin has more affinity than hemoglobin, since myoglobin requires 2 Torr only of O2 to be 50% bound while hemoglobin requires 25 Torr. The KM values of enzymes range widely mostly between 10-1 and 10-7 M Each substrate/enzyme combination has a unique KM value. If the enzyme binds to another substrate generating different products, then KM (Vmax too) will be different. Examine the table in the next page. 3|Page • Catalases' KM = 25 mMol It means that 25 mMol H2O2 is needed to fill 50% of the enzyme active sites. Also it means that 25 mMol is required to reach 1/2 Vmax. • Hexokinase, which phosphorylates hexoses sugars has different KM values for each different substrate (each give different products). • Which substrate has the highest affinity to Hexokinase? Glucose, because it has the lowest KM value, so you need only 0.05mM of Glucose to reach half Vmax. • Which substrate has the lowest affinity to Hexokinase? Fructose, because it has the highest KM value so you need lots of it to reach half Vmax. Please note that the enzymes' concentration [E] in the previous comparisons is constant. The binding ability differs betweent different substrates, but does the Vmax differ when it's the same enzyme? No, Vmax only reflects the catalytic activity of the enzyme, it does not depend on the substrate. However, KM differs since it depends on the substrate. A reaction is catalyzed by an enzyme with 2 different substrates, S (high affinity) and S′ (low affinity). Vmax is the same (depends on the enzyme), but KM (depends on the substrate) differs. S′ has a higher KM because it has a lower affinity. Please see the last page for further explanation. 4|Page Example: A biochemist obtains the following set of data for an enzyme that is known to follow Michaelis-Menten kinetics. Approximately, what is the Vmax and KM of this enzyme? Vmax is the value when the velocity changes are very minimal. Vmax is approximately 700. KM is the substrates' concentration at which Vo is half maximal. ➔ Vo = 700 1/2 Vo ≈ 350 KM = [S] = 8 Dissociation constant (KD) KM describes the affinity of enzyme for the substrate, but it’s not an accurate measure of affinity. KD (dissociation constant) is the actual measure of the affinity. Which constants do you think are related to the affinity? K2 is related to the kinetic activity of the enzyme to form products. However, K1 and K -1 are related to the formation and dissociation of [ES]. ➔ 𝐾𝐷 = 𝐾−1 𝐾1 Vmax and enzyme concentration The reaction’s rate depends on the ability of the substrate to find an active site on the enzyme. So by increasing the enzymes' concentration, the rate of the reaction is increased. KM, affinity and the catalytic power of the enzyme are NOT altered because it is the same substrate. 5|Page As you can see in the graph above, the concentration of the enzyme was doubled which caused a proportional increase in the reaction rate (Vmax is doubled). The KM, however, is unchanged. Kcat • Kcat (also known as K2) is the turnover number, which is the number of substrate molecules converted into product per unit time of a fully saturated enzyme. • It describes how quickly an enzyme acts (how fast the ES complex proceeds to E + P, check the equation). • In other words, the maximal rate, Vmax, reveals the Kcat of an enzyme if the total concentration of active sites [E]T is known, using the following equation: 𝑽𝒎𝒂𝒙 𝑲𝒄𝒂𝒕 = [𝑬]𝒕𝒐𝒕𝒂𝒍 • Kcat means, the number of reactions that can happen per second per one catalytic molecule. • Each enzyme has its own Kcat. Example: Catalase’s Kcat = 40 *106 ➔ 40 *106 molecules of H2O2 are converted to H2O and O2 by one catalase molecule within one second. Note that Kcat is directly proportional to the efficiency of the enzyme. 6|Page Questions 1) An enzyme has a molecular weight of 50,000 g/mol. 10 μg was used of the enzyme in an experiment and the results show that the enzyme at best converts 9.6 μmol of the substrate per min at 25˚C. The turnover number (Kcat) for the enzyme is: MW = 50,000 g/mol Weight = 10-5g ➔ [E]T = 10−5 𝑔 50,000 𝑔/𝑚𝑜𝑙 = 2 * 10-10 Vo = 9.6 * 10-6 mol per min = 1.6 * 10-7 s-1 𝑲𝒄𝒂𝒕 = 𝑽𝒎𝒂𝒙 [𝑬]𝒕𝒐𝒕𝒂𝒍 = 𝟏.𝟔 ∗ 𝟏𝟎−𝟕 𝟐∗𝟏𝟎−𝟏𝟎 = 𝟖𝟎𝟎/𝒔 2) Calculate the Kcat for a 10-6 M solution of carbonic anhydrase which catalyzes the formation of 0.6 M H2CO3 per second when it is fully saturated with substrate. 𝑲𝒄𝒂𝒕 = 𝑽𝒎𝒂𝒙 𝟎. 𝟔 5 -1 = -6= 𝟔 ∗ 𝟏𝟎 𝒔 [𝑬]𝒕𝒐𝒕𝒂𝒍 𝟏𝟎 5 Kcat calculates the number of reactions that occur per unit of time. So to know how long each reaction takes, we divide the rate by K2. Example: From the previous calculation we know that 6 *10 5 reactions occur per second which is Kcat (equals K2), so each catalyzed reaction takes place in a time equal to 𝟏 𝑲𝟐 , which is 1.7 μs for the carbonic anhydrase. Note: The turnover numbers of most enzymes with their physiological substrates fall in the range from 1 to 10 4 per second. 7|Page Vmax does not change: Same Enzyme, different substrates (Glucose/ATP), same products (Glucose 6phosphate). → Same chemical reaction Vmax changes: Same Enzyme, different substrates (Glucose/Fructose), different products (Glucose 6- phosphate/ Fructose 6- phosphate). → Different chemical reaction 8|Page