Enzym e kinetics · chem ical reactions The Gibbs free energy change G (also called either the free energy or Gibbs energy) ... the reaction is spontaneous. If the free energy of

Enzyme kinetics

• Enzyme kinetics is the study of the chemical reactions that are catalysed by enzymes, with the quantitative measurement of the rates of enzyme-catalyzed reactions and the systematic study of factors that affect these rates.

• Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in metabolism , how its activity is controlled, and how a drug or an agonist might inhibit the enzyme.

• Applied enzyme kinetics represents the principal tool by which scientists identify and characterize therapeutic agents that selectively inhibit the rates of specific enzyme-catalyzed processes.

• Enzyme kinetics thus plays a central and critical role in drug discovery and comparative pharmacodynamics, as well as in elucidating the mode of action of drugs.

Changes in free energy determine the direction & equilibrium state of chemical reactions

• The Gibbs free energy change G (also called either the free energy or Gibbs energy) describes both the direction in which a chemical reaction will tend to proceed and the concentrations of reactants and products that will be present at equilibrium.

• ∆G for a chemical reaction equals the sum of the free energies of formation of the reaction products ∆Gp minus the sum of the free energies of formation of the substrates ∆Gs.

• If the free energy of formation of the products is lower than that of the substrates, the signs of ∆G-' will be negative, and a chemical reaction said to be exergonic and the reaction is spontaneous.

• If the free energy of formation of the products is higher than that of the substrates, the signs of ∆G+ will be posative, and a chemical reaction said to be endergonic and the reaction is nonspontaneous.

• If ∆G0 the reaction has achieved the equilibiruim and is said to be neither spontaneous nor non spontaneous . The rate of the forwored reaction equil the rate of the reverse reaction.

Factors affecting reaction velocity

• Enzymes can be isolated from cells, and their properties studied in a test tube (that is, in vitro).

• Different enzymes show different responses to changes in :

• substrate concentration.

• temperature.

• pH .

• Enzymic responses to these factors give us valuable clues as to how enzymes function in living cells.

A. Temperature Increase of velocity with temperature:

The reaction velocity increases with temperature until a peak velocity is reached (Figure 5.7). This increase is the result of the increased number of molecules having sufficient energy to pass over the energy barrier and form the products of the reaction.

Decrease of velocity with higher temperature: heat energy

can also increase the kinetic energy of the enzyme to a point that exceeds the energy barrier for disrupting the noncovalent interactions that maintain its three-dimensional structure. The polypeptide chain then begins to unfold, or denature, with an accompanying loss of catalytic activity.

Enzymes from humans generally exhibit stability at temperatures up to 45–55°C.

The Q10, or temperature coefficient, is the factor by which the rate of a biologic process increases for a 10°C increase in temperature. For the temperatures over which enzymes are stable, the rates of most biologic processes typically double for a 10°C rise in temperature (Q10 = 2).

B. Hydrogen Ion (pH )Concentration • 1. Effect of pH on the ionization of the active site:

The catalytic process usually requires that the enzyme and substrate have specific chemical groups in either an ionized or unionized state in order to interact. For example, catalytic activity may require that an amino group of the enzyme be in the protonated form (-NH3+).At alkaline pH this group is deprotonated, and the rate of the reaction, therefore, declines.

• Effect of pH on enzyme denaturation: Extremes of pH can also lead to denaturation of the enzyme, because the structure of the catalytically active protein molecule depends on the ionic character of the amino acid side chains.

• The pH at which maximal enzyme activity is achieved is different for different enzymes, and often reflects the [H+] at which the enzyme functions in the body.

• For example, pepsin, a digestive enzyme' in the stomach, is maximally active at pH 2, whereas other enzymes, designed to work at neutral pH, are denatured by such an acidic environment (Figure 5.8).

Substrate concentration affects reaction rate • For a typical enzyme, as substrate concentration is increased, the initial

velocity (vo or vi) increases until it reaches a maximum value Maximal velocity (Vmax).

• Initial velocity: This means that the rate of the reaction is measured as soon as enzyme and substrate are mixed. At that time, the concentration of product is very small and, therefore ,the rate of the back reaction from P to S can be ignored.

1. When further increases in substrate concentration do not further increase vo, the enzyme is said to be "saturated" with substrate (all the enzyme is present as the ES complex. Since no free enzyme remains available for forming ES,

further increases in [S] cannot increase the rate of the reaction. Under these saturating conditions, vo depends solely on the rapidity with which product dissociates from the enzyme so that it may combine with more substrate.

Most enzymes show Michaelis-Menten kinetics, in which the plot of initial reaction velocity, vo, against substrate concentration [S], is hyperbolic.

In contrast, allosteric enzymes frequently show a sigmoidal curve .

Maximal velocity: is the number of substrate molecules converted to product per unit time; velocity is usually expressed as μmol (Figure 5.6).

Rate constant and reaction ordered

• Rate constant (k) measures how rapidly a reaction occurs

• Rate (v, velocity) = (rate constant) (concentration of reactants)

v= k1 [A]

• 1st order reaction (rate dependent on concentration of 1 reactant)

v= k-1[B][C]

• 2nd order rxn (rate dependent on concentration of 2 reactants)

• Zero order rxn (rate is independent of reactant concentration)

Michaelis - Menten equation Reaction model:

In this model, the enzyme reversibly combines with its substrate to form an ES complex that subsequently breaks down to product, regenerating the free enzyme. The model, involving one substrate molecule, is represented below:

where S is the substrate ,E is the enzyme, ES is the enzyme-substrate complex, P is the product k1, k-1 and k2 are rate constants

• The Michaelis-Menten equation describes how reaction velocity varies with substrate concentration:

Where v0 =initial reaction velocity , Vmax = maximal velocity , Km = Michaelis constant = (k-1+ k2)/k1

[S] = substrate concentration

Michaelis-Menten equation • Relative concentrations of E and S: The concentration of substrate ([S]) is much

greater than the concentration of enzyme ([E]), so that the percentage of total substrate bound by the enzyme at any one time is small.

Steady-state assumption: [ES] does not change with time

(the steady-state assumption : the rate of formation of ES is equal to that of the breakdown of ES) (to E + S and to E + P). In general, an intermediate is said to be in steady-state when its rate of synthesis is equal to its rate of degradation.

Rate of ES formation

Rate of ES degradation

Therefore………if the rate of ES formation equals the rate of ES breakdown

1) k1[E][S] = [ES](k-1+ k2)

2) (k-1+ k2) / k1 = [E][S] / [ES]

3) (k-1+ k2) / k1 = Km (Michaelis constant)

• Initial velocity: This means that the rate of the reaction is measured as soon as enzyme and substrate are mixed. At that time, the concentration of product is very small and, therefore ,the rate of the back reaction from P to S can be ignored.

What does Km mean

1. Km = [S] at ½ Vmax

2. Km is a combination of rate constants describing the formation and breakdown of the ES complex

3. Km is usually a little higher than the physiological [S]

4. is characteristic of an enzyme and its particular substrate, and reflects the affinity of the enzyme for that substrate.

5. Km is numerically equal to the substrate concentration at which the reaction velocity is equal to ½ Vmax. Km does not vary with the concentration of enzyme.

6. Small Km A numerically small (low) Km reflects a high affinity of the enzyme for substrate, because a low concentration of substrate is needed to half-saturate the enzyme—that is, reach a velocity that is ½ Vmax (Figure 5.9).

• Large Km A numerically large (high) Km reflects a low affinity of enzyme for substrate because a high concentration of substrate is needed to half-saturate the enzyme.

7. Relationship of velocity to enzyme concentration: The rate of the reaction is directly proportional to the enzyme concentration at all substrate concentrations. For example, if the enzyme concentration is halved, the initial rate of the reaction (v0), as well as that of Vmax, are reduced to one half that of the original.

Order of reaction: When [S] is much less than Km, the velocity of the reaction is approximately proportional to the substrate concentration .The rate of reaction is then said to be first order with respect to substrate.

When [S] is much greater than Km the velocity is constant and equal to Vmax. The rate of reaction is then independent of substrate concentration, and is said to be zero order with respect to substrate concentration .

What does kcat mean? • Catalytic constant, kcat :Vmax divided by the number active sites

Kcat = Vmax /St).

1. kcat is the 1st order rate constant describing ES E+P

2. Also known as the turnover # because it describes the number of reactions a molecule of enzyme can catalyze per second under optimal condition.

3. Most enzyme have kcat values between 102 and 103 s-1

4. For simple reactions k2 = kcat , for multistep reactions kcat = rate limiting step

• Specific activity : Vmax divided by the protein concentration.

Suppose that we have a mixture of an enzyme that contain [E] total= 0.1 µ .at this concentrate(when all active site are filled)the maximal rate of the reaction is 60000 µ /s

Kcat= 60000 µ/ s = 600000 S-1

0.1 µ

Taking reciprocal of turnover number give us the time it takes to convert one substrate into product 1 = 1 = 1.67 X 10-6 S

Kcat 60000

Lineweaver-Burke plot • it is not always possible to determine when Vmax has been achieved, because of the gradual upward slope of the hyperbolic curve at high substrate concentrations. However, if 1/Vo is plotted versus 1/[S], a straight line is obtained .This plot, the Lineweaver-Burke plot (also called a double-reciprocal plot) can be used to calculate :

1. Km (relates to affinity) and Vmax (relates to efficiency)

2. Km how much substrate to use in an assay, if more than one

Enzyme share the same S , Km is also determine how to decide

Which pathway the S will take.

3. Vmax tells about pathways

4. Km & Vmax can be used to determine effectiveness of inhibitors

And activators for enzyme estudies and clinical application.

The equation describing the Lineweaver-Burke plot is:

x axis is equal to -1/Km, and y axis is equal to 1/Vmax.

• Inhibition of enzyme activity

• Any substance that can diminish the velocity of an enzyme-catalyzed reaction is called an inhibitor.

• Reversible inhibitors

bind to enzymes through non covalent bonds. Dilution of the enzyme-inhibitor complex results in dissociation of the reversibly bound inhibitor, and recovery of enzyme activity.

• Irreversible inhibition occurs when an inhibited enzyme does not regain activity on dilution of the enzyme-inhibitor complex.

• The two most commonly encountered types of inhibition are

A. Competitive

B. Noncompetitive.

Inhibition of enzyme activity A. Competitive inhibition

The inhibitor binds reversibly to the same site that the substrate would normally occupy .

Inhibitor block the substrate from binding (competes with the substrate for that site).

• Can not have substrate and inhibitor bind at same.

• Reduce enzyme affinity for the substrate

• Km increases (x intercept change)

Vmax does not change: adding more substrate can overcome the inhibitor

Inhibition of enzyme activity • Statin drugs as examples of competitive inhibitors:

• This group of antihyperlipidemic agents competitively inhibits the first step in cholesterol synthesis. This reaction is catalyzed by Hydroxymethylglutaryl Co A reductase {HMG Co A reductase .

• Statin drugs, such as atorvastatin (Lipitor) and simvastatin (Zocor)1 are structural analogs of the natural substrate for this enzyme,

and compete effectively to inhibit HMG CoA reductase. By doing

so,they inhibit de novo cholesterol synthesis , thereby lowering plasma cholesterol levels .

Noncompetitive inhibition

Inhibition of enzyme activity (Noncompetitive inhibition ) inhibitor and substrate bind at different sites on the enzyme

The inhibitor Inhibit enzyme by changing its conformation.

Enzyme can have both the substrate and inhibitor bond at the same time.

• ESI complex can form

• Not reduced affinity for substrate.

• Km stays same(not change x intercept is same).

• ESI compolex cannot make a product.

Vmax is decreased (y intercept change). Noncompetitive inhibition cannot be overcome by increasing the concentration of substrate.

Inhibition of enzyme activity

• Examples of noncompetitive inhibitors: Some inhibitors act by forming covalent bonds with specific groups of enzymes. For example, lead forms covalent bonds with the sulfhydryl side chains of cysteine in proteins. The binding of the heavy metal shows noncompetitive inhibition.

• Ferrochelatase, an enzyme that catalyzes the insertion of Fe2+ into protoporphyrin (a precursor of heme, is an example of an enzyme sensitive to inhibition by lead.

• Other examples of noncompetitive inhibition are certain insecticides, whose neurotoxic effects are a result of their irreversible binding at the catalytic site of the enzyme acetylcholinesterase.

• For example :β-lactam antibiotics, such as penicillin and amoxicillin, act by inhibiting enzymes involved in bacterial cell wall synthesis. Drugs may also act by inhibiting extracellular reactions.

• angiotensin-converting enzyme (ACE) inhibitors. They lower blood pressure by blocking the enzyme that cleaves angiotensin I to form the potent vasoconstrictor, angiotensin II.

These drugs, which include captopril, enalapril, and lisinopril, cause vasodilation and a resultant reduction in blood pressure.

Regulation of enzyme activity Most enzymes catalyzed reactions involved two or more substrate ("Bi-Bi" reactions).

1. Sequential or Single-Displacement Reactions

both substrates must combine with the enzyme to form a ternary complex before catalysis can proceed (Figure 8–13).

A - leading substrate

B- following substrate

P- 1st product leaving enzyme

Q- 2nd product leaving enzyme

NAD and NADH reactions involving

Dehydrogenases.

An ordered Bi-Bi reaction, characteristic of many NAD(P)H-dependent oxidoreductases

Regulation of enzyme activity 2. Sequential Bi-Bi reactions can be further distinguished on the basis of whether the two substrates add in a random or in a compulsory order.

• Random-order reactions,

either substrate A or substrate B may combine first with the enzyme to form an EA or an EB complex (Figure 8–13).

• Compulsory-order reactions,

A must first combine with E before B can combine with the EA complex. One explanation for a compulsory-order mechanism is that the addition of A induces a conformational change in the enzyme that aligns residues that recognize and bind B.

.

A random Bi-Bi reaction, characteristic of many kinases and some dehydrogenases.

Regulation of enzyme activity 3.Ping-Pong Reactions

• The term "ping-pong" applies to mechanisms in which one or more products are released from the enzyme before all the substrates have been added. Ping-pong reactions involve covalent catalysis and a transient, modified form of the enzyme. Ping-pong Bi-Bi reactions are double displacement reactions. The group undergoing transfer is first displaced from substrate A by the enzyme to form product P and a modified form of the enzyme (F)ping. The subsequent group transfer from F to the second substrate B, forming product Q and regenerating E pong .

A ping-pong reaction, characteristic of amino transferases and serine proteases.

Regulation of enzyme activity Allosteric binding sites

• Allosteric enzymes are regulated by molecules called effectors (also modifiers) that bind non covalently at a site other than the active site.

• Effectors that inhibit enzyme activity are termed negative effectors, whereas those that increase enzyme activity are called positive effectors.

1.Homotropic effectors: When the substrate itself serves as an effector. In such a case, the presence of a substrate molecule at one site on the enzyme enhances the catalytic properties of the other substrate binding sites that is, their binding sites exhibit cooperativity.

2. Heterotropic effectors: The effector may be different from the

substrate. For example the feedback inhibition shown in Figure 5.17.

The enzyme that converts A to B has an allosteric site that binds the end-

product, E. If the concentration of E increases, the initial enzyme in the

pathway is inhibited. for example, the glycolytic enzyme phosphofructo

kinase allosterically inhibited by citrate, which is not a substrate for the

enzyme]

Regulation of enzymes

• Regulation of enzymes by modification

• Many enzymes may be regulated by covalent modification, most frequently by the addition or removal of phosphate groups from specific serine, threonine, or tyrosine residues of the enzyme. Protein phosphorylation is recognized as one of the primary ways in which cellular processes are regulated.

• Induction and repression of enzyme synthesis cells can also regulate the amount of enzyme by altering the rate of enzyme synthesis. The increased (induction) or decreased (repression) of enzyme synthesis leads to an alteration in the total population of active sites. [Note: The efficiency of existing enzyme molecules is not affected.]