ENZYME KINETICSV

Kelompok Bioproses Kelas C :

1. Gapenda Sari Kaban (13-066)

2. Evan Kurniawan (13-067)

3. Vivian (13-073)

4. Yudi Faradey P (13-081)

5. Alexander (13-089)

6. Andre Prasetia W (13-090)

7. Trecy Kartika (13-093)

8. Maria Paula S (13-094)

ENZYME ASSAY

The analysis for enzyme activity.

The results obtained from enzyme assays are not in weight of enzyme, but units of catalytic activity.

One unit of enzyme activity

= the amount of enzyme which will catalyze the formation of 1 mol product per minute under specified conditions

Enzyme assays must be carried out under conditions that are optimal for activity, with the pH, temperature and concentration of reagents used in a predetermined manner.

Enzyme assays must be made under initial velocity conditions.

velocity v = rate of disappearance of a substrate, or rate of formation of a product (more precise)

Why initial velocity?

(1) The possibility of back-reaction

(2) Denaturation of the enzyme

(3) Product inhibition

(4) Decrease of substrate concentration below the saturation level (can be avoided with substrate concentration > 4 KM)

The assay should always be tested to show that the velocity v is proportional to the amount of enzyme added.

[Example] For the determination of the enzymatic activity of alcohol oxidase (AO) from yeast, the following coupled reactions are utilized:

where DH2 is a dye precursor, D is the dye, and HP is the enzyme horseradish peroxidase. The dye is monitored by means of a spectrophotometer at a wavelength of 405 nm. The standard curve of the absorbance versus concentration of H2O2 was found to be:

A sample of clarified yeast cell lysate assayed for AO activity by this method gave a rate of change of A405 of 0.082/min after a dilution of 1:40,000. Calculate the AO concentration in units per mL, where 1 unit (U) is equal to the amount of enzyme producing 1 mol of H2O2 per minute under the conditions of the assay.

Solution:

or

AO activity in the assay

AO activity in the clarified cell lysate = 40000 2.175 U/L = 87 U/mL#

[Example] To measure the amount of glucoamylase in a crude enzyme preparation, 1 mL of the crude enzyme preparation containing 8 mg protein is added to 9 mL of a 4.44% starch solution. One unit of activity of glucoamylase is defined as the amount of enzyme which produced a mol of glucose per min in a 4% starch solution at pH 4.5 and 60C. Initial rate experiments show that the reaction produces 0.6 mol of glucose/mL-min. What is the specific activity of the crude enzyme preparation?

Solution:

#

MICHAELIS-MENTEN KINETICS

Assumptions for the Michaelis-Menten kinetics:

(1) The ES complex is established rather rapidly.

(2) The rate of the reverse reaction of the second step is negligible.

It often holds only when product accumulation is negligible at the beginning of the reaction.

Approaches used in developing the rate expression: (1) rapid-equilibrium approach, and (2) quasi-steady-state approach.

A. Rapid-Equilibrium Approach

[E] and [ES] are in equilibrium (it implies that k2 << k1).

(the Michaelis-Menten constant)

[E] and [ES] are difficult to measure.

[E]t = initial amount of enzyme

where Vmax = maximum reaction velocity = k2[E]t

B. Quasi-Steady-State Approach (Briggs-Haldane Analysis)

[E] and [ES] remain constant.

In the equilibrium approach,

v1 = v1

In the steady-state approach,

v1 = v1 + v2

where Vmax = k2[E]t and

(Note: in the equilibrium approach.)

* The steady-state assumption is satisfactory as long as [S]/[E]t > 103.

DETERMINATION OF Km AND Vmax

v: initial rate (to avoid product inhibition effect)

* Note: keep [S] < 0.05[S]0 when determining the reaction rate.

A. Lineweaver-Burk Plot:

x-axis intercept:

B. Hanes-Woolf Plot C. Eadie-Hofstee Plot

vKm + v[S] = Vmax[S]

v[S] = Vmax[S] vKm

Comments on the methods used to determine Km and Vmax:

[S]: controlled by the investigator, quite precisely

v: subject to more or less experimental error

Various linear transformations do not provide equally accurate estimates of the parameters.

(1) Plot (Lineweaver-Burk plot)

* Put considerable emphasis on rate values obtained at low [S].

Small v Large

Important in determining the position of the fitted line.

* Larger errors are expected for smaller v’s.

* Least reliable, in general.

(2) Plot v.s. [S] (Hanes-Woolf plot)

* Give less variation in accuracy over the practical range of [S].

* Put considerable emphasis on small v.

(3) Plot v v.s.

* Place equal emphasis on all points (v appears on both sides).

* Show some degree of inevitable correction.

* Best linear transformation when the error of v is large.

[Example] The following data has been obtained for two different initial enzyme concentrations for an enzyme-catalyzed reaction.

v at [E]t = 0.015 g/L(g/L-min)

[S](g/L)

v at [E]t = 0.00875 g/L(g/L-min)

1.14 20.0 0.67

0.87 10.0 0.51

0.70 6.7 0.41

0.59 5.0 0.34

0.50 4.0 0.29

0.44 3.3

0.39 2.9

0.35 2.5

Find Km and k2.

Solution:

(Hanes-Woolf plot)

From the plot of [E]t = 0.015 g/L,

Vmax = k2[E]t = 1/0.6 = 1.67 g/L-min; Km = 9.2 g/L.

From the plot of [E]t = 0.00875 g/L,

Vmax = k2[E]t = 1.0 g/L-min; Km = 10 g/L.

#

INTEGRATED MICHAELIS-MENTEN EQUATION—BATCH KINETICS

or

Slope = 1/Km; intercept = Vmax/Km.

Note: (1) Reaction may be product inhibition. (2) Reaction conditions may change. (pH change) (3) Reaction may approach an equilibrium position. (S P)

Michaelis-Menten assumptions and reaction scheme are invalid.

[Example] An enzyme reaction follows the Michaelis-Menten kinetic, with Km = 0.03 mol/L and Vmax = 13 mol L1 min1. An incoming substrate has a concentration of 10 mol/L and a flow rate of 10 L/h. (a) What should be the size of a steady-state continuous stirred-tank reactor for a 95% conversion? Assume that the enzyme concentration in the reactor is constant. (b) What should be the size of the reactor if you employ a plug-flow reactor?

Solution:

(a) Continuous stirred-tank reactor

Material balance on the substrate:

{Rate of input} {Rate of output} = {rate of disappearance}

[S]0 = 10 mol/L; [S] = 0.5 mol/L (for a 95% conversion)

Vreactor = 0.13 L

(b) Plug-flow reactor

= 0.74 min

#

ENZYME INHIBITION

Enzyme inhibitions may be irreversible or reversible.

* Irreversible inhibitors (such as heavy metals) form a stable complex with enzyme and reduce enzyme activity.

May be reversed only by using chelating agents (such as EDTA and citrate).

* Reversible enzyme inhibitions: competitive, noncompetitive, and uncompetitive.

Competitive Inhibition

or

where Vmax = k2[E]t

* Vmax is unaffected by competitive inhibitors, but the apparent Km is increased.

* A higher level of [S] is required to attain a given reaction rate.

* The degree of inhibition is reduced as substrate concentration increases.

Clinical Application of Differential Enzyme Inhibition. Human blood serum contains a class of enzymes known as acid phosphatases, which hydrolyze biological phosphate esters under slightly acidic conditions (pH 5.0):

Acid phosphatases are produced by erythrocytes, the liver, kidney, spleen, and prostate gland (前列腺；攝護腺). From the clinical standpoint, the enzyme from the prostate gland is most important because an increased concentration in the blood is frequently an indication of cancer of the prostate gland. The phosphatase from the prostate gland is strongly inhibited by the tartrate ion, while acid phosphatases from other tissues are not. How can this information be used to develop a specific procedure for measuring the activity of the acid phosphatase of the prostate gland in human blood serum?

Answer: Measure the total acid phosphatase activity in the presence and absence of tartrate ion.

Treatment of Methanol Poisoning. Methanol (wood alcohol), a commercial solvent once used as an automotive antifreeze, is very toxic and may cause death if a person swallows as little as 30 mL. The extreme toxicity is due not to the methanol itself but to its metabolic product, formaldehyde. Methanol is rapidly oxidized to formaldehyde by the action of the liver enzyme alcohol dehydrogenase:

Part of the medical treatment for methanol poisoning is to give the patient ethanol (ethyl alcohol), either by mouth or intravenously (靜脈注射), in amounts that would cause intoxication in a normal individual. Explain why this treatment is effective.

Answer: Ethanol competes with methanol for the active site of alcohol dehydrogenase.

Noncompetitive Inhibition

* The apparent Vmax is decreased by noncompetitive inhibitors; Km is unaffected.

* The degree of inhibition is not a function of the substrate concentration.

Uncompetitive Inhibition

* An uncompetitive inhibitor decreases Vmax and Km to the same extent.

* Inhibition is increased as substrate concentration increases.

[S]

v

Determination of the type of inhibition:

Lineweaver-Burk equation:

y-axis intercept ; x-axis intercept

Vmax is unaffected but Km is increased.

Competitive inhibition.

Km is unaffected but Vmax is decreased.

Noncompetitive inhibition.

Both Vmax and Km are varied.

Uncompetitive inhibition.

VI

Kelompok Bioproses C;

1. Khairull Fahmi

2. Mhd.Reza Rahmadhan

3. Ariel Seumupa

4. Devi Sahara

5. Afdal Supi

6. M. Zulfadli

7. Christina Eka

8. Florentina Pandiangan

[Example] The hydrolysis of urea by urease is an only partially understood reaction and shows inhibition. Data for the hydrolysis of the reaction are given as follows.

[S] = 0.2 M [S] = 0.02 M

1/v [I] 1/v [I]

0.22 0 0.68 0

0.33 0.0012 1.02 0.0012

0.51 0.0027 1.50 0.0022

0.76 0.0044 1.83 0.0032

0.88 0.0061 2.04 0.0037

1.10 0.0080 2.72 0.0044

1.15 0.0093 3.46 0.0059

where v = mol/L-min and [I] is inhibitor molar concentration. Determine the kinetic parameters (Km and KI).

Solution:

(Lineweaver-Burk plot)

Using the data of [I] = 0, 0.0012, 0.0044, and 0.006 M,

1/Km = 13, or Km = 7.77 102 M; 1/Vmax = 0.2, or Vmax = 5.0 mol/L-min.

The reaction belongs to a noncompetitive inhibition.

For [I] = 0.0012 M and [S] = 0.2 M, v = 3 mol/L-min.

KI = 6.0 103 M.

Remarks: or

[I] 0 0.0012 0.0044 0.0060Vmax,app 5 4 2 1.33

1 1.25 2.5 3.76

or KI = 2.2 103 M

#

[I] 103, M

0 1 2 3 4 5 6 70.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

appmax,

max

V

V

[Problem] The steady-state kinetics of an enzyme is studied in the absence and presence of an inhibitor (inhibitor A). The initial rate is given as a function of substrate concentration in the table below.

[S] (mmol L1)v (mmol L1 min1)

No inhibitor Inhibitor A1.25 1.72 0.981.67 2.04 1.172.50 2.63 1.475.00 3.33 1.9610.0 4.17 2.38

(a) What kind of inhibition is involved? (b) Determine Vmax and Km in the absence and presence of inhibitor.

Solution:

Eadie-Hofstee plot:

Plot v versus , slope = Km, intercept = Vmax.

(●) In the absence of inhibitor, Km = 2.5 mmol L1, Vmax = 5.0 mmol L1 min1.

(○) With inhibitor, Km, app = 2.5 mmol L1, Vmax, app = 3.0 mmol L1 min1.

It is of noncompetitive inhibition.#

KINETICS FOR REVERSIBLE REACTIONS

By steady-state approximation,

or

ALLOSTERIC ENZYME KINETICS

Some enzymes have more than one substrate binding site. The binding of one substrate to the enzyme facilitates binding of other substrate molecules.

* Determination of kinetic parameters:

SUBSTRATE INHIBITION

“The enzyme, which is probably oligomeric, has multiple binding sites for substrate.”

ES2 does not react further.

Remarks:

(1) At low [S], the term involving [S]2 can be neglected, and inhibition effect is not observed.

(2) At high [S], inhibition is dominant.

(3) The substrate concentration resulting in the maximum reaction rate, [S]max, can be determined by setting dv/d[S] = 0.

BISUBSTRATE REACTIONS: SINGLE-DISPLACEMENT REACTIONS

Direct transfer of an atom or a functional group from one of the substrate to the other.

where Vmax = k5[E]t

BISUBSTRATE REACTIONS: DOUBLE-DISPLACEMENT (OR PING-PONG) REACTIONS

AX donates X to the enzyme. A must then leave before B, the acceptor of X, is bound.

Occurs when coenzymes are involved.

EFFECT OF TEMPERATURE ON ENZYME ACTIVITY

Enzymes have an optimal temperature for their activities.

* For many proteins, denaturation begins to occur at 45 to 50C and is severe at 55C.

* In nearly all cases, inactivation becomes virtually instantaneous at temperature well below 100C.

* Thermophilic bacteria contain heat-stable enzymes.

A crystalline -amylase from Bacillus stearothermophilus can retain 90% of activity after 1 h at 90C.

The effect of temperature on enzyme activity may be due to several different causes:

(1) The actual velocity of breakdown of the enzyme-substrate complex

(2) The stability of enzyme

(3) Change of the affinity of the enzyme for substrate (Km), activators, or inhibitors

(4) Change of the rate-limiting step

(5) Change of the oxygen solubility

(6) Change in the pH of the buffer used

Both catalytic and denaturation reactions can be represented by the Arrhenius equation:

where k = reaction rate constant, A = Arrhenius constant, E = activation energy, R = gas-law constant, and T = absolute temperature.

For enzyme-catalyzed reactions, Ea = 420 kcal/mol (with most values about 11 kcal/mol); for enzyme deactivation, Ed = 40130 kcal/mol (with most values about 70 kcal/mol).

* A rise in temperature from 3040C,

1.8-fold increase in the rate of catalysis (for Ea = 11 kcal/mol), while 41-fold increase in the rate of denaturation (for Ed = 70 kcal/mol).

The temperature range of Arrhenius relationship is quite limited.

EFFECT OF pH ON ENZYME ACTIVITY

Proteins possess many ionizable groups.

pH change will affect the catalytic site and conformation of the enzyme.

In general, enzymes are active only over a limited pH range, and in most cases a definite optimal pH is observed.

The optimal pH may be due to:

(1) A true reversible effect of pH on Vmax

(2) A change in the enzyme/substrate affinity

(3) A change in the stability of the enzyme

Enzymes may become irreversibly denatured at the extremes of pH.

The optimal pH is a function of other parameters such as temperature, substrate concentration, and buffer solution.

pH dependence of the reaction rate for ionizing enzymes:

[E]t = [E] + [EH] + [EH2+] + [EHS]

Rate expression for the case of ionizing substrate:

[E]t = [E] + [ESH+]

Theoretical prediction of the pH optimum of enzymes requires knowledge of the active site characteristics.

This is very difficult to obtain.

The pH optimum is usually determined experimentally.

VII

Kelompok bioprocess kelas C :

1. Gewa Handika (13-082)

2. Sy. Nadiratuzzahrah (13-083)

3. Yayang Afandy (13-084)

4. Muhammad Ridha (13-085)

5. Finnya Angkie Winoto (13-087)

6. Irsa Septiawan (13-100)

7. M. Faizul Hisham (13-103)

8. Salwa Jody Gustia (13-104)

EFFECT OF BUFFER ON ENZYME REACTION

A buffer system consists of a weak acid (the proton donor) and its conjugate base (the proton acceptor).

* Buffering action:

or

where Ka = acid’s dissociation constant

If the concentrations of the buffer components (i.e., [HA] and [A]) are made equal, the solution will be buffered at a pH corresponding to logKa.

* Titration curves of weak acids:

If the concentrations of the buffer components are higher than added acid (or base), the buffer ratio (and so the pH) will change little.

Two examples of preparation of buffers:

The choice of buffer system is a very important parameter in enzyme reactions.

* The nature of the buffer system may influence the enzyme reaction.

* The nature of the buffer may play an important role in enzyme stabilization.

It is commonly observed that carboxylic and sulfonic acid buffers stabilize enzymes.

Tris buffer has been known to cause a significant number of problems.

* Ionic strength may have a strong effect on enzyme stability and activity.

* Buffers may influence the thermodynamics of the catalyzed reaction.

The true product of the urease reaction is ammonium carbamate, which is decomposed by a subsequent buffer-mediated proton transfer.

EFFECT OF ENZYME CONCENTRATION ON REACTION RATE

In most cases, any two molecules of enzyme function independently, i.e., v [E]t.

Other proportionalities are due to:

(1) Inhibitors are present in the assay solution.

(2) Insufficient amount of coenzyme added.

(3) The enzyme reaction is not the rate-limiting step.

Instead, it is the diffusion of macromolecular substrate.

* Examples:

Lipases act on triglycerides (macromolecular substrate)

v [E]t1/2

Lipases act on benzyl ethyl ester (small substrate)

v [E]t

Deviations from linearity with enzyme concentration:

A: normal cases.

B: insufficient substrate to saturate the enzyme at high [E]t.

C: an inhibitor for which the enzyme has high affinity is present in the substrate solution.

D: an inhibitory substrate is present in the enzyme solution.

ENZYME DEACTIVATION

Protein structure is stabilized by weak forces.

Forces that maintaining protein structure: hydrogen bonding, ionic attractions, hydrophobic interactions, and S-S linkages.

Native protein structure is only marginally stable.

Stages of protein unfolding:

N = native conformation

A* = critically activated state

ID = incompletely disordered conformation

RC = random coil (fully denatured state)

There are many factors that can cause reduction in enzyme activity.

It is not the individual factors but their combinations that determine rates of enzyme deactivation.

The protein denaturants can be classified into physical, chemical, and biological denaturants.

(1) Physical denaturant

Heat

Target: hydrogen bonds

Driving force: increase of denatured conformations due to increased thermal movement and decreased solvent structure; irreversible covalent modification (e.g., disulfide interchange)

End product: highly disordered conformation; aggregates

Cold

Target: hydrophobic bonds; solvated groups

Driving force: altered solvent structure; dehydration

End product: aggregates; inactive monomers

Mechanical forces

Target: solvated groups; void volume

Driving force: changes in solvation and void volume; shearing

End product: highly disordered conformation; inactive monomers

Radiation

Target: functional groups (e.g., cySH, peptide bonds)

Driving force: decrease of structure-forming interactions after photo-oxidation or attack by radicals

End product: highly disordered conformation; aggregates

(2) Chemical denaturant

Acids

Target: buried uncharged groups (e.g., his, peptide bonds)

Driving force: decrease of structure-forming ionic interactions

End product: random coil

Alkali

Target: buried uncharged groups [e.g., tyr, cySH, (cyS)2]

Driving force: decrease of structure-forming ionic interactions

End product: random coil

Organic H-bond-formers

Target: hydrogen bonds

Driving force: decrease of structure-forming H bonds between water and native conformation

End product: random coil

Salts

Target: polar and nonpolar groups

Driving force: salting in/salting out bias of polar and nonpolar groups in solvent

End product: highly disordered conformation

Solvents

Target: nonpolar groups

Driving force: solvation of nonpolar groups

End product: highly disordered conformation; peptide-chains with large helical regions

Surfactants

Target: hydrophobic domains (all surfactants) and charged groups (ionic surfactants only)

Driving force: formation of partially unfolded structures including micelle-like regions

End product: incompletely disordered conformation; large helical regions

Oxidants

Target: functional groups (e.g., cySH, met, try, and others)

Driving force: decrease of structure-forming and/or functional interactions

End product: inactivated enzyme; sometimes disordered structure

Heavy metals

Target: functional groups (e.g., cySH, his, and others)

Driving force: masking of groups pertinent to structure or function

End product: inactivated enzyme

Chelating agents

Target: cations important for structure or function

Driving force: ligand substitution or cation removal

End product: inactivated enzyme

(3) Biological denaturant

Proteases

Target: peptide bonds

Driving force: hydrolysis of peptide bonds

End product: oligopeptides, amino acids

The simplest model of enzyme deactivation is irreversible first order kinetics.

EN = native enzyme; ED = denatured enzyme.

* Obtaining the enzyme deactivation data:

Expose the enzyme to denaturing conditions for some time interval in the absence of substrate, and then making an initial rate activity assay after returning the enzyme solution to the standard conditions.

* Data for the deactivation of ATPase under several different conditions are consistent with ln([EN]/[E]0) = kdt.

Decay of enzyme activity with time does not always follow the first-order model.

* The profile of luciferase deactivation contains two different linear regions.

A model that fits the data of luciferase deactivation is:

I.C.: t = 0, [EN] = [E]0 and [ED1] = 0

* Loss of activity in protease solution includes deactivation and autodigestion.

* Irreversible enzyme deactivation by a poison:

EN + poison ED

Combination of deactivation model with catalytic reaction sequence:

* ENS is not subjected to deactivation.

or

STRATEGIES FOR ENZYME STABILIZATION

Native enzymes are subject to inactivation by chemical, physical, and biological factors, and the inactivation can occur either in storage or during use.

Physical factors that inactivate enzymes: shear force, surface tension

* Shear denaturation could be correlated as a function combining shear rate and exposure time.

* Data of surface tension: 80 dyne/cm for air-water interface; 1 dyne/cm for plasma membrane of the cell.

Need surfactants to lower the air-liquid surface tension in the operation of foam fractionation.

Methods for enzyme stabilization:

(1) Addition of stabilizing compounds

Substrate

The active site of an enzyme may be its least stable region.

* -Amylase is stabilized by addition of starch.

* Glucose isomerase is stabilized against heat damage by addition of glucose.

Organic solvents

There are many cases that addition of organic solvents cause denaturation at high concentrations but afford considerable stabilization at low concentrations.

A possible rationale: prevention of hydrogen bond rupture.

Salts

Cations such as Ca, Cu, Fe, Mn, Mo, and Zn have an effect on the stability and activity of metalloenzymes.

* Calcium helps to stabilize the tertiary structure of -amylase of Bacillus caldolyticus.

Ca2+ can serve as a stabilizing bridge analogous to a disulfide bond.

Polymer additives

Natural or synthetic polymers such as gelatin, albumin, or polyethylene glycols can increase the heat stability of enzymes.

(2) Chemical modification of enzymes

Crosslinking with bifunctional reagents such as glutaraldehyde

To limit access by proteases and may also serve to lock the protein into an active configuration.

Adding polyamino acid side chains to the R-groups of certain amino acid residues

Use acylation or alkylation to introduce other substituents.

(3) Immobilization of enzymes

Immobilized enzymes are often more stable than enzymes in solution

Examples of enzyme stabilization:

* Glucoamylase

Methods: addition of substrate analogs, glucose, gluconolactone

Effect: enhanced thermal stability

* Lactate dehydrogenase

Methods: addition of substrate lactate or effector fructose-diphosphate

Effect: greater thermal stability

Note: the enzyme is destabilized by addition of pyruvate substrate.

* -Amylase

Method: addition of 5070% sorbitol

Effect: better storage and thermal stability

* -Amylase (Bacillus caldolyticus)

Method: addition of Ca2+

Effect: greatly enhanced thermal stability

* Chymotrypsin

Method: addition of 5090% glycerol

Effect: improved resistance to proteolysis

* -Galactosidase

Methods: addition of 510% ethanol or 2-propanol

Effect: increased heat stability

Note: similar levels of methanol, n-propanol destabilize the enzyme.

* Trypsin

Method: addition of polyalanyl (~10 units long) to protein’s amino groups

Effect: more proteolysis, heat deactivation resistance

* Asparaginase

Methods: succinyl substituents added using the acid anhydride

Effect: increased protease resistance

* Glycogen phosphorylase

Methods: butyl or propyl substituents added using the aldehyde and NaBH4

Effect: enhanced thermal stability

* Papain

Method: cross-linked using glutaraldehyde

Effect: better thermal stability

Comments on methods for enzyme stabilization:

(1) The influence of a particular chemical or strategy on one enzyme’s stability cannot always be extrapolated to other enzymes.

(2) The stabilizing effect depends often on a particular combination of solution composition and temperature.