Enzyme KineticsEnzyme Kinetics

Enzyme Kinetics IAn enzyme-catalyzed reaction of substrate S to An enzyme-catalyzed reaction of substrate S to

product P, can be writtenproduct P, can be written

Actually, the enzyme and substrate must combine and Actually, the enzyme and substrate must combine and E recycled after the reaction is finished, just like any E recycled after the reaction is finished, just like any catalyst.catalyst.

Because the enzyme actually binds the substrate the Because the enzyme actually binds the substrate the reaction can be written as:reaction can be written as:

The simplest reaction is a single substrate going to a The simplest reaction is a single substrate going to a single product.single product.

ES P

E + S k1

k1

ES k2

P + E

Rate or velocity of the reaction depends on the Rate or velocity of the reaction depends on the formation of the ESformation of the ES The P -> ES is ignoredThe P -> ES is ignored The equilibrium constant Keq is based on The equilibrium constant Keq is based on

the idea that the reaction is limited to the the idea that the reaction is limited to the formation of the ES complex and that only formation of the ES complex and that only K1 and K-1 are involved because the K1 and K-1 are involved because the thermodynamics of the reversal of K2 cause thermodynamics of the reversal of K2 cause it to be minimalit to be minimal

How fast an enzyme catalyzes a reaction is it's rate. The How fast an enzyme catalyzes a reaction is it's rate. The rate of the reaction is in the number of moles of rate of the reaction is in the number of moles of product produced per secondproduct produced per second

Keq = k1

K-1

rate (v) =

d[P]

dt = k2 [ES]

The relationship between the concentration of a The relationship between the concentration of a substrate and the rate of an enzymatic reaction substrate and the rate of an enzymatic reaction is described by looking at the is described by looking at the concentration of S concentration of S and vand v When the reaction is first order - the rate is When the reaction is first order - the rate is

dependent on [S]dependent on [S] When the reaction is zero order, there is no When the reaction is zero order, there is no

relationship between v and S relationship between v and S A second order is between 1st and 0 order, A second order is between 1st and 0 order,

where the relationship between V and [S] is where the relationship between V and [S] is not proportional to [S]not proportional to [S]

[ Substrate]

Initial Velocity (Vi or V)

• To study enzymes, first order kinetics must be To study enzymes, first order kinetics must be followed! followed!

• Think of the graph of [S] vs. v in this Think of the graph of [S] vs. v in this way:way:

The velocity increases as the substrate The velocity increases as the substrate concentration is increased up to a point concentration is increased up to a point where the enzyme is "saturated" with where the enzyme is "saturated" with substrate.substrate.

At this point the rate of the reaction (v) At this point the rate of the reaction (v) reaches a maximal value and is reaches a maximal value and is unaffected by further increases in unaffected by further increases in substrate because all of the enzyme substrate because all of the enzyme active site is bound to substrateactive site is bound to substrate

For the most part enzyme reactions are For the most part enzyme reactions are treated as if there is only one substrate treated as if there is only one substrate and one product.and one product. If there are two If there are two substrates, one of them is held at a substrates, one of them is held at a high concentration (0 order) and the high concentration (0 order) and the other substrate is studied at a lower other substrate is studied at a lower concentration so that for concentration so that for that that substrate, it is a first order reactionsubstrate, it is a first order reaction. . This leads us to the M and M equation.This leads us to the M and M equation.

Conditions for Michaelis -MentenConditions for Michaelis -Menten

Two assumptions must be met for the Two assumptions must be met for the Michaelis-Menten equationMichaelis-Menten equation

EquilibriumEquilibrium -the association and -the association and dissociation of the substrate and dissociation of the substrate and enzyme is assumed to be a rapid enzyme is assumed to be a rapid equilibrium and Ks is the equilibrium and Ks is the enzyme:substrate dissociation enzyme:substrate dissociation constant.constant.

Conditions for Michaelis -MentenConditions for Michaelis -Menten

Two assumptions must be met for the Michaelis-Two assumptions must be met for the Michaelis-Menten equationMenten equation

• Steady stateSteady state - the enzyme substrate complex - the enzyme substrate complex ES is at a constant value. That is the ES is ES is at a constant value. That is the ES is formed as fast as the enzyme releases the formed as fast as the enzyme releases the product. For this to happen the concentration product. For this to happen the concentration of substrate has to be much higher than the of substrate has to be much higher than the enzyme concentration. That is why we only enzyme concentration. That is why we only study the initial velocity. Later in the reaction study the initial velocity. Later in the reaction the substrate concentration is relatively lower the substrate concentration is relatively lower and the rate of product starts to be limited by and the rate of product starts to be limited by diffusion and not the mechanism of the enzyme.diffusion and not the mechanism of the enzyme.

Michaelis-Menten Enzyme kineticsMichaelis-Menten Enzyme kinetics• Don't for get the two assumptions - They both Don't for get the two assumptions - They both

lead to the same equation, the michaelis-lead to the same equation, the michaelis-menten equation.menten equation.

• What is this awe inspiring equation?What is this awe inspiring equation? The The Michaelis-Menten kinetic model explains Michaelis-Menten kinetic model explains several aspects of the behavior of many several aspects of the behavior of many enzymes. Each enzyme has a Km value that is enzymes. Each enzyme has a Km value that is characteristic of that enzyme under certain characteristic of that enzyme under certain conditions.conditions.

Graphical model of the representation of the Graphical model of the representation of the M&M eq. M&M eq. – Reaction velocity (V) vs concentration of Reaction velocity (V) vs concentration of

substrate [S]substrate [S]– - as [S] increases, velocity increases and - as [S] increases, velocity increases and

eventually levels off = Veventually levels off = V max max

– 1st order vs zero order rates of reaction - 1st order vs zero order rates of reaction - back to the two assumptionsback to the two assumptions

– There are two important values for each There are two important values for each enzyme that are described by the M&M enzyme that are described by the M&M equation; Vequation; V max max and Km (Michaelis-Menten and Km (Michaelis-Menten constant)constant)

• Graphically, these are shown as 1/2 V Graphically, these are shown as 1/2 V maxmax = Km = Km can not reach real V can not reach real V maxmax so.... so....

Mathematical model of the representation of the M&M Mathematical model of the representation of the M&M eq. -eq. -

For the reaction:For the reaction:

1) The Michaelis constant Km is:1) The Michaelis constant Km is:

Think of what this means in terms of the equilibrium.Think of what this means in terms of the equilibrium.

Large vs. a small KmLarge vs. a small Km

E + S k1

<->

k 1

ES k2

P + E

Km = K-1 + K2

K1

22) When investigating the initial rate (Vo) the ) When investigating the initial rate (Vo) the Michaelis-Menten equation is:Michaelis-Menten equation is:

Graphical representation is a hyperbola. Think of Graphical representation is a hyperbola. Think of the difference between Othe difference between O22 binding of myoglobin binding of myoglobin

and hemoglobin.and hemoglobin. When [S] << Km, the velocity is dependent on [S]When [S] << Km, the velocity is dependent on [S] When [S] >> Km, the initial velocity is When [S] >> Km, the initial velocity is

independent of [S]independent of [S] When [S] = Km, then Vo = 1/2 When [S] = Km, then Vo = 1/2 VV max max

Prove this mathematically and graphicaly.Prove this mathematically and graphicaly.

Vo =Vmax [S]

[S] + Km

• Km is a measure of the affinity of the Km is a measure of the affinity of the enzyme for it's substrate and also enzyme for it's substrate and also informs about the rate of a reaction. informs about the rate of a reaction. The binding constant is appoximated by The binding constant is appoximated by KmKm

• Rules for using the M&M equation:Rules for using the M&M equation:• The reaction must be first order and [S] The reaction must be first order and [S]

>> E (two assumptions)>> E (two assumptions)

Turnover Number - kcatTurnover Number - kcat - the direct measure of - the direct measure of the catalytic production of product. The larger the catalytic production of product. The larger the kcat is, the more rapid the catalytic events at the kcat is, the more rapid the catalytic events at the enzyme's active site must be. The number of the enzyme's active site must be. The number of times a binding and reaction event "turns over"times a binding and reaction event "turns over"

- When the [S] << Km so that most of the When the [S] << Km so that most of the enzyme is in the free state [E]enzyme is in the free state [E]tt = [E] = [E]free free then then V = kcat / Km [E][S]V = kcat / Km [E][S]

- This is a second order rate constant between This is a second order rate constant between the substrate and the free enzyme. This is a the substrate and the free enzyme. This is a good measure of efficiency and specificity.good measure of efficiency and specificity.

- When the kcat/Km is near very high, the When the kcat/Km is near very high, the fastest the enzyme can catalyze a reaction is fastest the enzyme can catalyze a reaction is the diffusion rate of a molecule! the diffusion rate of a molecule!

101088 - 10 - 1099 / M / M .. sec sec

Lineweaver-BurkLineweaver-Burk (double reciprocal (double reciprocal plot)plot)

Vmax and Km are not likely to be Vmax and Km are not likely to be determined by increasing [S] determined by increasing [S]

Instead the [S] vs. Vo data are Instead the [S] vs. Vo data are transformed to a plot of their reciprocal transformed to a plot of their reciprocal of each value.of each value.

1/[S] vs. 1/Vo1/[S] vs. 1/Vo

+

1

Vo=

And this can be simplified to:

Vo =V

max [S]

[S] + Km

Km + [S]

Vmax

[S]

1

Vo= (

Km

Vmax

[S])1 1

Vmax

.

This is the equation for a straight line

Y = mX + b

Y = 1/Vo and X = 1 / [S]

So What?So What? KKmm - relates to affinity ; V - relates to affinity ; Vmaxmax relates to relates to

efficiencyefficiency KKmm tell how much substrate to use in an assay tell how much substrate to use in an assay

If more than one enzyme share the same If more than one enzyme share the same substrate, Ksubstrate, KMM also will determine how to also will determine how to

decide which pathway the substrate will takedecide which pathway the substrate will take

VVmaxmax tells about pathways tells about pathways Rate limiting enzyme in pathwayRate limiting enzyme in pathway KKm m andand VVmaxmax can be used to determine can be used to determine

effectiveness of inhibitors and activators for effectiveness of inhibitors and activators for enzyme studies and clinical applicationsenzyme studies and clinical applications

Enzyme inhibitorsEnzyme inhibitorsCompetitive inhibitionCompetitive inhibition

Inhibitor is similar to Inhibitor is similar to substrate and both bind to substrate and both bind to or near active site. or near active site. compete’ for bindingcompete’ for binding

inhibitor is unreactive - EI inhibitor is unreactive - EI statestate

Lineweaver Burke intersect Lineweaver Burke intersect at the Y axisat the Y axis

Competitive Inhibition

Enzyme inhibitorsEnzyme inhibitors

Noncompetitive inhibitorNoncompetitive inhibitor inhibitor binds distal to inhibitor binds distal to active siteactive site

effects enzyme rate not effects enzyme rate not affinity affinity

binds E in E S or Ebinds E in E S or EReversibleReversibleLineweaver Burke intersect Lineweaver Burke intersect at the Y axisat the Y axis

Noncompetitive Inhibition

Mixed InhibitionMixed Inhibition• Inhibitor binds to enzyme site Inhibitor binds to enzyme site

that involves both S binding that involves both S binding and catalysisand catalysis

• binds E in E S or Ebinds E in E S or E

• Forget the alpha businessForget the alpha business

Mixed Inhibition

Enzyme inhibitorsEnzyme inhibitors

Uncompetitive inhibitorUncompetitive inhibitorbinds covalently in the binds covalently in the transition statetransition state

suicide inhibitorsuicide inhibitorbinds to the ES complexbinds to the ES complex lowers affinity and velocitylowers affinity and velocity lineweaver Burke plots are lineweaver Burke plots are parallelparallel

Uncompetitive Inhibition

Penicillin as a suicide substrate Penicillin as a suicide substrate • - suicide substrates are often un - suicide substrates are often un

competitive inhibitors that decrease the competitive inhibitors that decrease the energy of the transition state and allow energy of the transition state and allow the ES to have lower energy that that of the ES to have lower energy that that of the EP.the EP.

• Bacterial cell wall - extensive cross linking Bacterial cell wall - extensive cross linking of sugars and peptidesof sugars and peptides

• Penicillin (and ampicillin) have a highly Penicillin (and ampicillin) have a highly reactive ß lactam ring which makes a reactive ß lactam ring which makes a peptide bond very reactive.peptide bond very reactive.

Penicillin as a suicide substrate Penicillin as a suicide substrate

• Penicillin mimics the peptide alanine Penicillin mimics the peptide alanine residues and forms a low energy residues and forms a low energy intermediate by covalently reacting with a intermediate by covalently reacting with a serineserine

• In molecular biology, we use this as a tool. In molecular biology, we use this as a tool. Ampicillin will stop E. coli growth. Bacteria Ampicillin will stop E. coli growth. Bacteria that have a gene (plasmid) inserted into that have a gene (plasmid) inserted into the bacteria have ß lactamase. An enzyme the bacteria have ß lactamase. An enzyme that hydrolyses the reactive peptide bond that hydrolyses the reactive peptide bond found in amicillin and penicillinfound in amicillin and penicillin

Competitive Noncompetitive Uncompetitive

Binds active site

inhibition reversed by increasing [S]

Kmapp increases with inhibitor (x axis intercept changes)

no change in 1/V max

Usually analogs of substrate

Transition analog

binds covalentlyES not E free

changes both x and y axis (Km and Vmax)

binds to other than binding site

not reversed by increasing

no effect on S binding (K m) only slows down rate (V)

decreased V maxapp (Y axis intercept)

inhibitor binds both E free and ES complex

Other Types of InhibitorsOther Types of Inhibitors

Allosteric RegulationAllosteric Regulation

• An organism must be able to regulate the An organism must be able to regulate the catalytic activities of its component enzymes catalytic activities of its component enzymes

• coordinate many metabolic processescoordinate many metabolic processes

• Respond to changes in the environmentRespond to changes in the environment

• Growth and differentiation Growth and differentiation

• Both Inhibitors and affectorsBoth Inhibitors and affectors

Allosteric RegulationAllosteric Regulation

• do not follow do not follow Michaelis-Menten Michaelis-Menten kinetics - instead use kinetics - instead use a hill plot for both + a hill plot for both + and – effectsand – effects

• similar to Osimilar to O22 dissociation of dissociation of hemoglobinhemoglobin

Allosteric RegulationAllosteric Regulation

• Two ways:Two ways:

• Control enzyme Control enzyme availabilityavailability

– Synthesis of Synthesis of enzymeenzyme

– DegenerationDegeneration

• Control enzyme activityControl enzyme activity– Alterations which Alterations which

affect the substrate affect the substrate binding affinitybinding affinity

– Turn over numberTurn over number

Allosteric RegulationAllosteric Regulation

• Can cause large changes in enzymatic activityCan cause large changes in enzymatic activity

• Regulated by covalent modificationsRegulated by covalent modifications

• Usually Phosphorylation and de-Usually Phosphorylation and de-Phosphorylation of specific Ser and Tyr Phosphorylation of specific Ser and Tyr residues.residues.

PhosphorylationPhosphorylation

• Phosphorylation is the addition of a phosphate (PO4) Phosphorylation is the addition of a phosphate (PO4) group to a protein or other organic molecule. group to a protein or other organic molecule.

• kinaseskinases (phosphorylation) and (phosphorylation) and phosphatasesphosphatases (dephosphorylation) are involved in this process. Many (dephosphorylation) are involved in this process. Many enzymes and receptors are switched "on" or "off" by enzymes and receptors are switched "on" or "off" by phosphorylation and dephosphorylation. phosphorylation and dephosphorylation.

• Reversible phosphorylation results in a conformational Reversible phosphorylation results in a conformational change in the structure in many enzymes and change in the structure in many enzymes and receptors, causing them to become activated or receptors, causing them to become activated or deactivated. Phosphorylation usually occurs on serine, deactivated. Phosphorylation usually occurs on serine, threonine, and tyrosine residues in eukaryotic proteins threonine, and tyrosine residues in eukaryotic proteins

Phosphorylation regulates Phosphorylation regulates phosphenol-pyruvate (PEP) phosphenol-pyruvate (PEP)

carboxylasecarboxylase• CAM and C4 plants require a CAM and C4 plants require a

separation of the initial carboxylation separation of the initial carboxylation from the following de-carboxylationfrom the following de-carboxylation

• DiuranalDiuranal regulation is usedregulation is used

• IN CAM PLANTS:-IN CAM PLANTS:-

• Phosphorylation of the serine residue Phosphorylation of the serine residue of of phosphenol-pyruvate (PEP) phosphenol-pyruvate (PEP) carboxylase carboxylase (Ser-OP) yields a form of (Ser-OP) yields a form of the enzyme which is active at nightthe enzyme which is active at night

– This is relatively insensitive to malic This is relatively insensitive to malic acidacid

Photophorylation regulates Photophorylation regulates phosphenol-pyruvate phosphenol-pyruvate

(PEP)carboxylase(PEP)carboxylase• During the day:During the day:

• De-Phosphorylation of the serine De-Phosphorylation of the serine (ser-OH) gives a form of the (ser-OH) gives a form of the enzyme which is inhibited by enzyme which is inhibited by malic acidmalic acid

• THIS IS THE OPPOSITE WAY THIS IS THE OPPOSITE WAY AROUND FOR C4 PLANTS!AROUND FOR C4 PLANTS!

PhosphorylationPhosphorylation

• The addition of a phosphate (PO4) molecule to a polar R The addition of a phosphate (PO4) molecule to a polar R group of an amino acid residue can turn a hydrophobic group of an amino acid residue can turn a hydrophobic portion of a protein into a polar and extremely hydrophilic portion of a protein into a polar and extremely hydrophilic portion of molecule. portion of molecule.

• In this way it can introduce a conformational change in the In this way it can introduce a conformational change in the structure of the protein via interaction with other structure of the protein via interaction with other hydrophobic and hydrophilic residues in the protein hydrophobic and hydrophilic residues in the protein

• Examples:Examples:

• Phosphorylation of the cytosolic components of NADPH Phosphorylation of the cytosolic components of NADPH oxidase, plays an important role in the regulation of protein-oxidase, plays an important role in the regulation of protein-protein interactions in the enzyme protein interactions in the enzyme

• Phosphorylation of the enzyme GSK-3 by AKT (Protein kinase Phosphorylation of the enzyme GSK-3 by AKT (Protein kinase B) as part of the insulin signaling pathway B) as part of the insulin signaling pathway

PhosphorylationPhosphorylation

• There are thousands of distinct phosphorylation There are thousands of distinct phosphorylation sites in a given cell since: sites in a given cell since:

• There are thousands of different kinds of There are thousands of different kinds of proteins in any particular cell (such as a proteins in any particular cell (such as a lymphocyte). lymphocyte).

• It is estimated that 1/10th to 1/2 of proteins are It is estimated that 1/10th to 1/2 of proteins are phosphorylated (in some cellular state). phosphorylated (in some cellular state).

• Phosphorylation often occurs on multiple Phosphorylation often occurs on multiple distinct sites on a given protein.distinct sites on a given protein.

Oxidative PhosphorylationOxidative Phosphorylation

Bisubstrate ReactionsBisubstrate Reactions

• So far:So far:

• Simple, single-substrate reactions that obey the Simple, single-substrate reactions that obey the Michaelis-Menten modelMichaelis-Menten model

• However, approx 60% of known biochemical However, approx 60% of known biochemical reactions involve two substrates and yield two reactions involve two substrates and yield two productsproducts

• Either:Either:– transfer reactions – moving a functional group transfer reactions – moving a functional group

from one substrate to the otherfrom one substrate to the other– Oxidation/reduction reaction between substratesOxidation/reduction reaction between substrates

Bisubstrate ReactionsBisubstrate Reactions

• Sequential reactions Sequential reactions

• All substrates must combine All substrates must combine with the enzyme before the with the enzyme before the reaction can occur and reaction can occur and products are releasedproducts are released

• A - leading substrateA - leading substrate• B – following substrateB – following substrate

• P – 1st product leaving P – 1st product leaving enzymeenzyme

• Q – 2Q – 2ndnd product leaving enzyme product leaving enzyme

• ie NAD+ and NADH reactions ie NAD+ and NADH reactions involving dehydrogenasesinvolving dehydrogenases

Bisubstrate ReactionsBisubstrate Reactions• Ping-pong reactions Ping-pong reactions • Group transfer reactions in which Group transfer reactions in which

one or more products are released one or more products are released beforebefore all substrates have been all substrates have been added.added.

• Two stage reaction:Two stage reaction:• A functional group from 1A functional group from 1stst sub (A) sub (A)

is transferred to the 1is transferred to the 1stst product (P) product (P) forming a stable enzyme (F) –forming a stable enzyme (F) –The The PingPing

• The functional group is displaced The functional group is displaced from the enzyme by the 2from the enzyme by the 2ndnd substrate (B) to yield 2substrate (B) to yield 2ndnd product product (Q), regenerating the original form (Q), regenerating the original form of the enzyme (E) – of the enzyme (E) – The PongThe Pong

• ieie many reactions involvingmany reactions involving Trypsin Trypsin