Bio385 - SG3 Kinetics

BIO 385 |  Kinetics R E A D I N G A S S I G N M E N T LPoB8 6.3– pgs 188-197 (Sec 6.3 up to “ Enzymes are Subject to…”) P R E P A R A T I O N & P O N D E R I N G 1. What is the basic model for the enzyme cycle? Which key kinetic parameter is associated with each stage? The basic model for the enzyme cycle is often described using the Michaelis-Menten equation, which provides a simplified representation of enzyme-substrate interactions. The enzyme cycle typically involves several stages, and key kinetic parameters associated with each stage are as follows: 1. **Substrate Binding (E + S ⇌ ES)**: - **Association Rate Constant (k1)**: This parameter represents the rate at which the substrate (S) binds to the enzyme (E) to form the enzyme-substrate complex (ES). - **Dissociation Rate Constant (k-1)**: This parameter represents the rate at which the ES complex dissociates back into free enzyme (E) and substrate (S). 2. **Enzyme-Substrate Complex Conversion (ES → E + P)**: - **Catalytic Rate Constant (k2)**: This parameter represents the rate at which the ES complex converts into products (P) while releasing the enzyme (E). The overall rate of the enzymatic reaction (the reaction velocity, V) can be described using the Michaelis-Menten equation: Where: - V is the reaction velocity. - [E] 0 is the initial concentration of the enzyme. - [S] is the concentration of the substrate. In this equation, the Michaelis constant K m is defined as , and it represents the 1 3

BIO 385 |  substrate concentration at which the reaction velocity is half of its maximum (Vmax). So, in summary, the key kinetic parameters associated with the enzyme cycle are: - **k1**: The association rate constant for substrate binding. - **k-1**: The dissociation rate constant for the ES complex. - **k2**: The catalytic rate constant for product formation. - **Km**: The Michaelis constant, which relates to the substrate concentration at half of the maximum reaction velocity. These parameters are crucial for understanding the kinetics of enzyme-catalyzed reactions and for designing experiments to characterize enzyme behavior. 2. Describe five basic enzyme parameters, how their values are determined experimentally, and what those values mean. 1. **Turnover Number (Kcat)**: - **Determination**: Kcat is determined experimentally by measuring the maximum rate of product formation (Vmax) and dividing it by the total enzyme concentration ([E]). - **Meaning**: Kcat represents the number of substrate molecules converted to product per enzyme molecule per unit of time. It provides a measure of the enzyme's catalytic efficiency. 2. **Michaelis Constant (Km)**: - **Determination**: Km is experimentally determined by measuring the initial reaction velocity (V) at various substrate concentrations ([S]) and analyzing the data using the Michaelis-Menten equation. - **Meaning**: Km is a measure of the affinity of the enzyme for its substrate. A lower Km indicates higher substrate affinity, while a higher Km suggests lower affinity. Km is also the substrate concentration at which the reaction velocity is half of its maximum (Vmax). 3. **Catalytic Efficiency (Kcat/Km)**: - **Determination**: Catalytic efficiency is calculated by dividing Kcat by Km. - **Meaning**: Catalytic efficiency provides a comprehensive measure of an enzyme's performance. Enzymes with high catalytic efficiency have both a high turnover number (Kcat) and a low Michaelis constant (Km), indicating they work efficiently even at low substrate concentrations. 4. **Vmax (Maximum Reaction Velocity)**: - **Determination**: Vmax is determined experimentally by measuring the initial reaction velocity at saturating substrate concentrations (where [S] >> Km). - **Meaning**: Vmax represents the maximum rate at which the enzyme can convert substrate into product under optimal conditions (i.e., when the enzyme is fully saturated with substrate). 5. **Inhibition Constants (Ki)**: - **Determination**: Ki values are determined experimentally by measuring enzyme activity in the presence of different concentrations of inhibitors and analyzing the data using 2

BIO 385 |  dissociation (k -1 ). - The total enzyme concentration ([E] 0 ) is approximately equal to the free enzyme concentration ([E]). Under these conditions, you can approximate (Kd) using (Km) as follows: **Potential Danger of the Approximation:** The danger of this approximation lies in the fact that it assumes simplified conditions that may not hold true in all cases. The assumptions mentioned above may not be valid for all enzyme- substrate systems, especially when more complex kinetic behaviors or multiple substrate binding sites are involved. Using Km as an approximation for Kd can lead to inaccuracies and misinterpretation of binding affinities, especially in situations where enzyme-substrate interactions deviate significantly from simple Michaelis-Menten kinetics. V O C A B U L A R Y You should have both a formal and working definition of the following terms. Many of these are found in the book or in the outline below. Pre-Steady State Steady State Initial Velocity (V 0 ) Maximum Velocity (V max ) Reaction progress plot Rate limiting step Michaelis Menton plot Line Weaver Burke Plot Rate constants Michaelis Constant (K m ) Turn over number Specificity Constant pH Activity Profile Bisubstrate reaction Ternary Complex Cleland Nomenclature O U T L I N E I. Steady State Kinetics A. Initial Velocity (V 0 ) – the rate of product formation overtime at a given substate concentration. 1. Determined from a graph of product formation vs time. 2. Initial slope is linear and referred to as “steady state”, only 2-3% of substrate converted to product 3. Slope gradually flattens because substrate starts to become more and more scarce. 4. Changes based on amount of substrate a. Hard to determine the V 0 for low substrate concentrations because the substrate is consumed so quickly B. Michaelis-Menton Plots 4

BIO 385 |  1. Plot of Initial Velocity (see above) Vs Substrate Concentrations a. Shape of Rectangular Hyperbola (linear positive slope that flattens at an upper limit) b. Upper limit represents Vmax (maximum enzyme velocity, given infinite substrate) 2. The M-M formula V 0 = V max [ S ] K m + [ S ] C. Deriving the Michaelis Menton Formula – important to note the assumptions 1. Rate Constants and Reaction Rates Refresher D. What are the Kinetic Parameters and what are they used for? 1. Dissociation constant 2. K cat (Turnover number) 3. Specificity constant 4. Michaelis Constant (K m ) – a. Experimentally found as the substrate concentration that produces ½ V max on M-M plot b. Equals Km = (k -1 +k 2 )/k 1 Combination of several rates constants 5. Maximum Velocity (V max ) II. Enzyme Reactions that Catalyze two or more Reactants 1. Tertiary Complex – complex that involves E, S1, and S2 a. Ordered – order matters. S1 must bind first then S2 b. Random – Either substrate can bind first 2. Ping Pong (double displacement) mechanism – S1 binds then leaves, Then S2 binds and leaves 3. Cleland Nomeclature 4. Lineweaver Burke plots (Double Reciprocal) a. One line = Substrate 1 is varied while substrate 2 is held at a constant. b. Lines created for several S2 concentrations c. Intersecting lines indicates tertiary complex d. Parallel lines indicates Ping Pong 5

BIO 385 |  3. (LPoB8 6-14). Graphical Analysis of Vmax and Km. A kinetic study of intestinal Peptidase using glycylglycine as the substrate produced the experimental data shown in the table. The peptidase catalyzes this reaction: 4. (LPoB8 6-17) 5. (LPoB8 6-25) 6. 7. 7