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The Michaelis-Menten (M-M) equation is the starting point for all of classical enzyme kinetics. M & M came up with a simple chemical scheme involving enzyme (E), substrate (S) and the consequent product (P).

Draw a reaction progress graph. Assume a starting concentration of [S] = 10 μM and the total enzyme concentration [E]T = 1 μM, Be sure to include [P] as a function of time as well, and any intermediates included in part (a). Using you graph indicate how to estimate the initial velocity of the reaction, v0. You may assume the reaction proceeds completely to products.

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Related questions

A 5 00μl reaction co ntaining 0.5 pmol of an enzyme following Michaelis – Menten kinetics with saturating substrate concentration is studied . For this enzyme k1 = 1 x 10 9 M - 1 s - 1 , k - 1 = 2 x 10 3 s - 1 , and k2 = 1 x 10 5 s - 1 .

a . What is the Vmax for the enzyme considering that it has only one substrate binding site ? b. What are the values of Km and Ks? Is this a rapid equilibrium enzyme or does it follow steady state kinetics? Explain why .

c . What is the substrate concentration needed to achieve half maximal velocity? Explain the basis for your answer.

d . If the substrate concentration in part c is doubled , how many fold will the initial velocity increase?

e . What is the Km i f the concentration of the enzyme is doubled? f . What is the efficiency of this enzyme?

g. Would this enzyme be considered a perfect enzyme? Explain.

h . If 0.25 pmol of an irreversible or classic non - competitive inhibitor is added before starting the reaction. What is the resulting Km for the enzyme?

describe the definitions of substrate, enzyme active site and its general characteristics, and apoand

holo-enzymes.

· describe the fact that enzyme catalysis is specific in terms of the type of reaction and the exact

substrate structure.

· Explain the difference in the “lock-and-key’ model and the induced fit model of enzyme

substrate interaction.

· describe that reaction rate constant thus reaction rate is dependent on the activation energy.

· describe the relationship between the energy of the transition state and the activation energy.

· describe the relative binding affinity of a substrate and its transition state to the enzyme.

· Explain how enzymes speed up reaction rate, i.e., how do enzymes lower the activation

energy. Note: Factors other than preferential stabilization of transition state also contribute to increased

reaction rate. They include 1) enzymes placing one substrate (reactant) next to the other substrate (reactant)

so that the reaction is no longer dependent on the collision rate of the two substrates; 2) enzymes sequester the

substrate(s), minimizing solvent competition thus speeding up the reaction; 3) in enzyme complexes with each

enzyme catalyzing one step in a multi-step reaction sequence, the product of one reaction is fed to the active site

of another enzyme for the next step without the product diffusing away from the enzyme complex thereby

increasing reaction rate.

· describe the Michaelis-Menten equation relating the initial velocity to total substrate

concentration.

· describe the assumptions that went into the derivation of the Michaelis-Menten equation. ([E]

is constant, steady state assumption, etc)

· describe the relationship between Vmax and kcat and the fact that kcat is a constant for a given

enzyme and substrate at a given temperature and solution condition; whereas Vmax can differ

for a given enzyme and substrate at a given temperature and solution condition, depending

on the enzyme concentration.

· describe the definition of Kd (equilibrium dissociation constant for ES into E and S).

· describe the relationship between Kd and the affinity of substrate for the enzyme, i.e., the

higher the Kd, the weaker the binding between E and S.

· describe the relationship between Kd and Km, i.e., in general, the higher the Kd, the higher theKm.

· Use the Michaelis-Menten equation and the relationship between Vmax and kcat to do

calculations.

· describe the other names for the catalytic rate constant, kcat (i.e., the turn over number; also

called krelease) and why it is so called (kcat reports on per unit time per enzyme molecule the

number of product molecules formed/released, thus the name turnover number or krelease).

· Determine Vmax and Km using both the Michaelis-Menten plot (initial velocity versus [S]) and

the Lineweaver-Burk Plot (the double reciprocal plot), given the data of initial velocity and

[S].

· Draw the Michaelis-Menten plot AND the double reciprocal plot (Lineweaver Burk), given

the Vmax and Km values.

· describe the fact that the term kcat/Km is the best parameter for measuring the catalytic

capability (efficiency) of an enzyme.

· describe the existence of irreversible enzyme inhibition and the general mechanisms of

irreversible inhibition.

· describe the different types of reversible inhibitions, namely the competitive, uncompetitive,

and mixed inhibitions (noncompetitive inhibition is a special case in which the inhibitor

binds E and ES with equal affinity therefore α is equal to α’ – Km is not affected).

· Describe each type of inhibition in terms of inhibitor binding site (active site or other than

the active site), how the inhibitor affects vmax and Km and the quantitative relationship of

each parameter with and without the inhibitor present and their relationship with [I] and KI

or KI

’

.

· Show the characteristics of each type of inhibition on a Michaelis-Menten plot (initial

velocity versus total substrate concentration), i.e. draw the curves with and without the

competitive inhibitor.

· Show the characteristics of each type of inhibition on a double reciprocal plot (LineweaverBurk

Plot) by drawing the lines with and without the competitive inhibitor.

· Given the Michaelis-Menten or double reciprocal plot with and without the inhibitor,

determine the type of inhibitor.

· describe the fact that transition state analogs are potent inhibitors.

· Explain why transition state analogs are potent inhibitors.

· describe that not all enzymes obey Michaelis-Menten kinetics.

· describe situations when an enzyme will not obey Michaelis-Menten kinetics (when the enzyme

catalyzes reactions with multiple substrates or when the enzyme is allosteric, i.e. binding of

the substrate at one active site affects the other active site(s) for the same substrate).

· Name the four types of catalytic mechanisms. (electrostatic catalysis, general/specific acid

base catalysis, metal ion catalysis, covalent catalysis)

· Contrast acid/base catalysis to general acid/base catalysis, i.e., comment on their similarity

and difference.

· Name the eight common general acid/base pairs in proteins and write the formula of the

acid and base form for each pair (hint: consider the eight amino acids that have ionizable

side chains…)

· describe the meaning of covalent catalysis.

· describe the reaction catalyzed by chymotrypsin and the three catalytic residues in

chymotrypsin.

· Draw the interactions among the three catalytic residues (catalytic triad).

· State the catalytic role of each of the catalytic residues and how they accomplish that.

· describe the steps in the formation of the acyl-enzyme intermediate, and the substrate and

products in this first part of the chymotrypsin mechanism.

· Draw the transition state structure for the formation of the acyl-enzyme intermediate and

indicate by drawing how it is preferentially stabilized.

· describe the steps in the regeneration of chymotrypsin (deacylation), the substrates and

product of this second part of the chymotrypsin mechanism.

· Draw the transition state for deacylation and explain how it is preferentially bound to or

stabilized by the enzyme.

· Explain what general acid and base catalysis refers to and what groups act as the general acid

and base in the chymotrypsin mechanism.

· Explain what covalent catalysis refers to in the chymotrypsin mechanism.

· Explain the basis for the substrate specificity of chymotrypsin (consider the composition of

the active site – chymotrypsin specifically cleaves peptide bonds adjacent to aromatic

residues)

· Explain the term “serine protease”. Answer: these are proteases (enzymes that

hydrolyze peptide bonds) that have serine as a catalytic residue (that acts as a

nucleophile, which can attack the carbonyl carbon of the peptide bond).

· Key features of Hexokinase, enolase and lysozyme mechanisms that were discussed in class

(specific methods of catalysis utilized by these enzymes; general description of overall

catalytic transformation)

· describe the four regulatory strategies of enzyme catalysis

· describe the definition of feedback inhibition (mechanism of cellular regulation that regards an

enzyme that catalyzes the production of a given substance that then inhibits the cell when

concentration of that substance has reached an appropriate level – this balances/regulates

amount of product provided with amount needed)

· describe the most common type of covalent modification and the types of enzymes

responsible for the addition and removal of the chemical group in this covalent

modification.

· Explain the general mechanism of phosphorylation in regulating enzyme activity.

· describe the general naming scheme for active and inactive proteases.

· describe that protease inhibitors exist to inhibit protease.

· describe that enzymes are regulated through covalent and non-covalent processes.

· Noncovalent regulation

o Describe noncovalent modification in general terms. Elaborate on the relation

among enzyme activity, allostery, effector molecules (small molecules) and control

proteins.

o Concerning allosteric regulation, some enzymes have multiple active sites for the

same substrate and the binding of the substrate increases the activity of the enzyme

by stabilizing the R (more active) state over the T (relatively inactive) state. (Lecture

13: “Noncovalent Modification: Allosteric Regulators”)

ß Draw a curve for the initial reaction velocity versus substrate concentration.

ß describe and explain the specific shape of the v0 vs. [S] plot.

ß Draw on the same graph above a v0 vs. [S] curve for the enzyme in the

absence of allostery. and how th i.e., in the absence of conformational change

upon substrate binding. Comment on the shape of this curve.

ß Comment on the benefit of allosteric activation.

ß When an inhibitor is present for such an allosteric enzyme, the v0 versus [S]

plot will shift. Draw a v0 vs. [S] curve with and without the inhibitor.

ß When an activator is present for such an allosteric enzyme, the v0 versus [S]

plot will shift. Draw a v0 vs. [S] curve with and without the inhibitor.

ß When an activator is present for such an allosteric enzyme, the v0 versus.

ß describe the relationship between feedback inhibition and allosteric regulation

and the reason behind the term “feedback inhibition”.

· Covalent regulation

o describe the most common covalent modification, the enzymes that catalyze the

modification and the removal of that modification, respectively and the amino acid

residues that tend to be the site of this modification.

o Write the structure of the added group bonded to those residues and the reaction for

this covalent modification.

o Rationalize the effectiveness of phosphorylation on altering the activity of an

enzyme.

o describe the mechanism of chymotrypsinogen activation to chymotrypsin (cleavage of

zymogen by trypsin).

Enzyme Kinetics Simulation Experiment

Adapted from Junker, M. J. Chem. Educ. 2010, 87, 294-295.

Objective:

To simulate the working of enzymes in the catalysis of biochemical reactions.

Materials:

Bolts (15) and nuts to match, purchased at a hardware store or found in your basement. If you don’t have any nuts and bolts, use anything made of two parts that can be taken apart. For example, red and blue paper clips, large and small paper clips, baby food jars and lids. Use your imagination. In addition, you will need something to glue the two pieces together. You will also need a device to time yourself, a watch with a second hand or a stop watch.

Background Information and Theory:

Read pp. 655-672 in Seager and Slabaugh. Most of the metabolic reactions in Chapters 23 and 24 are catalyzed by enzymes. Enzymes work by lowering the activation energy for biochemical reactions. The first step is for the substrate (S), the reactant to react with the enzyme (E) to form the Enzyme-Substrate Complex (ES):

E + S ES. The second step is for the enzyme to convert the substrate into the product(s). In this case there will be two products, P1 and P2: ES P1 + P2. In this simulation the substrate will be the nut and bolt screwed together. You will be the enzyme. As the enzyme, it will be your job to find the substrate and unscrew the nut from the bolt. The nut will be P1 and the bolt will be P2. The simulation will simulate the case where the substrate concentration is less than saturation. (Figure 20.6, p. 663), below maximum velocity). It will also simulate saturating the substrate concentration. (Figure 20.6, p. 663, at maximum velocity). Competitive Inhibition, (p. 668) and non-competitive inhibition (p. 669) will be simulated as well.

Procedure:

Enzyme Kinetics When Substrate Concentration is Less Than Saturation

Screw the 15 nuts on to the 15 bolts. Scatter the bolts randomly around the room you are in. Start the timer and gather and unscrew as many nuts as possible in 30 seconds. Record the number of bolts unscrewed on the table/report sheet in Doc Sharing. (I have also placed the table following the write-up on the main page, here. Divide the number of bolts unscrewed by the time (0.5 minutes) to get the rate of the reaction.

Enzyme Kinetics When Substrate is at Saturation

Reattach the 15 nuts to the bolts. Put all the nut/bolt combinations in front of you on the table. Start the timer and unscrew as many nuts as possible in 30 seconds. Record the number of bolts unscrewed on the report sheet. Divide the number of bolts unscrewed by the time (0.5 minutes) to get the reaction rate.

Enzyme Kinetics With Competitive Inhibition

Reattach the nuts to the bolts. Glue 10 of the nuts to the bolts, so they can’t be removed. Place the nut/bolt combinations in a pile. Unscrew as many of the nuts as possible in 30 seconds. Count the number of unscrewed nuts. Don’t try to muscle the glued ones. They can’t be removed. Count the number of nuts unscrewed. Record this number in the table. Also record the reaction rate by dividing by the time (0.5 minutes)

Enzyme Kinetics With Non-Competitive Inhibition

Reattach the nuts to the bolts. Place the nut/bolt combinations in front of you on the table. Have someone tie your hands behind your back, or mentally tie your hands behind your back. Start the timer and see how many nuts you can remove from the bolts. Record the numbers of nuts removed, and divide by time (0.5 minutes) to get the reaction rate.

Fill out table below.

Condition

Number of Bolts Unscrewed

Time (minutes)

Reaction rate (bolts per minute)

Comment

Scattered bolts

Non-saturated substrate

Pile of Bolts

Saturated Substrate

Some Bolts Glued

Competitive Inhibiter

Arms tied

Non-Competitive Inhibitor

Answer these questions:

How well do you think this simulation represents enzyme kinetics? Did it help you understand kinetics better? Can you think of anything that could be added to improve the simulation?

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