What is enzyme catalysis?

A catalyst is a substancethat accelerates a chemicalreaction without itself undergoing any net change

How do enzymes work?

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Thermodynamics of catalysis

G = H - TS

G = Gibbs Free energy

H = Change in heat (energy)of formation

S = Degree of randomness

How do enzymes work?

Transition state vs. Ground State theory

As Pauling among others suggested is catalysis aresult of an enzyme having a higher affinity for thetransition state

Do enzymes accelerate catalysis by putting substrates in close proximity?

OR

Still to this day a topic of debate, but presently it seems to be a little of both

Affinity for the Transition state

E + S E + (S)*

E + S ES (ES)*

knon

kcat

Ks

KTS

KTS = [E][S]*/[ES]* = [(kcat/Km)/knon]-1

For Triosephosphate isomerase KTS = 10-12, and Km = 10-4

Thus, this enzyme binds the transition state eight orders of magnitudemore strongly than the substrate.

Recognition of transition state effects have led to developments in analogs and catalytic antibodies

Specific catalytic mechanisms

General acid-base catalysis Covalent catalysis Metal Ion catalysis (nucleophile, electrophile)

-Carbonic Anhydrase-Serine proteases-Phosphoryl transfer

Most Enzymes use combinations of these mechanisms

Establishing a relationship between catalytic mechanism and substrate specificity

What happens when you mix enzyme and substrate…

First order reaction

Reactant (R) Product (P)

v = -d[R]/dt = d[P]/dt

Molecular parameters from reaction rates

Assume the conversion of ES to E + P is non-reversible, then the rate of product formation or reaction velocity is dependent solely on [ES] and k2

E + S ES E + Pk1

k-1

k2

v = d[P]/dt = k2[ES] (1)

If we could measure v and [ES] then we could determine k2, however[ES] is not usually measurable. We can measure substrate (or product)concentrations and the total concentration of enzyme [E]t.

[E]t = [E] + [ES] = free enzyme + enzyme in complex with substrate (2)

Thus, we want to express the rate, v, in terms of substrate concentration[S], and total enzyme concentration [E]t.

Ks = k-1/k1 = [E][S]/[ES]

E + S ES E + Pk1

k-1

k2

From this equation:

Under certain circumstances (if k-1 >>k2), E and S are in equilibrium with ES, with an equilibrium dissociation constant Ks.

However, this assumption is not always valid, thus it is of more general use to introduce the concept of the steady state.

In steady state, the rates of formation and breakdown of [ES] are equal:

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

Rearrange to give [ES] = (k1/k-1+k2)[E][S]

Define a constant Km = (k-1+k2/ k1)

Km[ES] = [E][S] (3)

Recall we want to get a formula with measurable quantities [S] and [E]t

Rearrange equation 2 (solve for [E]) and plug into 3 to get:

Km[ES] = [E]t[S] – [ES][S]

Transfer second term on right side to left side to get:

[ES](Km + [S]) = [E]t[S]

Rearrange to

[ES] = [E]t[S]/(Km + [S])

Using equation 1 we can finally solve for v, velocity

v = k2[E]t[S]/(Km + [S]) (4)

This formula is referred to as the Michaelis-Menten equation

Consider a graph that we can construct from the measurable quantities v and [S]

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Increasing [substrate]

At high substrate concentrations, the reaction reaches a maximumvelocity Vmax, because the enzyme molecules are saturated; everyenzyme is occupied by substrate and carrying out the catalytic step

[S] = Km

From these relationships, consider the following:

What is Km and what does it mean?

Km is a ratio of rate constants:

Km = (k-1+k2/ k1)

Thus in our catalyzed reaction, if k2 is much smaller than k-1, Km= k-1/k1 = Ks, the equilibrium constant for [ES] formation.In this case, a large Km means k-1 >>k1, thus the enzyme bindsthe substrate very weakly. However, in a separate instancea large k2 can have a similar effect on Km.

Thus, what is the utility of Km?

The most useful way to think of Km is reflected in the plotOf a reaction that follows the Michaelis-Menten equation

In this plot, Km is numerically equal to the substrate concentration At which the reaction velocity equals half of its maximum value.

Where [S] = Km, the Michaelis-Menton equation simplifies to

v = Vmax/2

Thus, an enzyme with a high Km requires a higher substrate concentration to achieve a given reaction velocity than anenzyme with a low Km.

In considering Vmax mathematically, by making [S] muchLarger than Km the Michaelis-Menten equation simplifies to:

Vmax = k2[E]t

Thus, another way of writing the Michaelis-Menten rate equationIs:

v = Vmax[S] / (Km + [S])

Typically, all of this is an oversimplification, and enzyme-mediatedcatalysis looks more like:

E + S ES EP E + P k1

k-1

k2k3

In this more complex system, k2 must be replaced with a more general constant, called kcat

v = kcat [E]t [S]/ (Km + [S])

In the two step reaction we considered first, kcat = k2. Formore complex reactions, kcat is a combination of rate constants for all reactions between ES and E + P.kcat is a rate constant that reflects the maximum number of

molecules of substrate that could be converted to producteach second per active site. Because the maximum rate isobtained at high [S], when all the active sites are occupied with substrate, kcat (the turnover number) is a measure of howrapidly an enzyme can operate once the active site is filled.

kcat = Vmax/[E]t

Under physiological conditions, enzymes usually do notoperate under saturating substrate conditions. Typically, theratio of [S] to Km is in the range of 0.01-1.0.

When Km >> [S], the Michaelis-Menten equation simplifies to:

v = kcat/Km ([E]t[S])

The ratio kcat/Km is referred to as the specificity constantwhich indicates how well an enzyme can work at low [S].

The upper limit of kcat/Km is in the range of 108 to 109 dueto limits of diffusion theory.

Lineweaver-Burk plots are convenient for determination of Km and kcat

Lineweaver-Burk plots result from taking a double reciprocalof the Michaelis-Menten equation.

v = Vmax[S] / (Km + [S])

1/v = Km/(Vmax[S]) + 1/Vmax

Plotting 1/v on the y-axis and 1/[S] on the x-axis (both known quantities)

The slope is equal to Km/Vmax, the y-intercept is 1/Vmax

And the x-intercept is –1/Km

Kinetics of enzymes with multiple substrates

Ordered Ping-Pong

http://www.curvefit.com/index.htmUseful web site:

Enzyme Inhibition

Competitive Non-competitive

Enzyme inhibition

Uncompetitive

Substrate binding influences rates of activity

Cooperativity Hysteresis

Regulation of an enzyme’s activityvia post-translational mechanisms

Modifications

Activation by proteolysis

Phosphorylation

Adenylylation

Disulfide reduction

Regulation of an enzyme’s activityvia post-translational mechanisms

Allostery

Phosphofructokinase

Aspartate carbamoyl transferase

Glycogen phosphorylase

Calmodulin

Investigating the structure-function relationshipof proteins

Chemical Modification

Site-directed mutagenesis

Fluorescent labeling

Protein structure determination

One is not enough! Need to use combinations of these methods!

Certain chemicals can react with specific aminoacids to form covalent complexes

N-ethylmaleimide (NEM) reacts with free cysteines

reagent which modifies H, Y or K residues = DEPC, diethyl pyrocarbonatereagent which modifies H, Y or W residues = NBS, N-Bromosuccinimidereagent which modifies H or carboxyl = Woodward's K; N-ethyl-5-phenylisoxazolium 3'sulfonatereagents which modify lysine or primary amino acid residues = Succinic anhydride; TNBS, 2,4,6-trinitrobenzenesulfonic acid)reagent which modifies Y residues = N-acetylimidazolereagent which modifies SER residues = PMSF, Phenylmethyl sulfonamidereagent which modifies R residues = phenylglyoxal

http://www.stratagene.com/manuals/200516.pdf

Amino acids that are close together have been observed to be similar in properties in proteins

Dayhoff matrix

Scanning mutagenesis

Alanine scanning mutagenesis - considered semi-conservativeat most positions important for structure, but non-conservativeat most positions important for catalysis

Cysteine scanning mutagenesis – puts a functional group atpositions throughout the protein sequence

FASEB J 1998 Oct;12(13):1281-99 Cys-scanning mutagenesis: a novel approach to structure function relationships in polytopic membrane proteins. Frillingos S, Sahin-Toth M, Wu J, Kaback HR

Example of scanning mutagenesis (lactose permease)

417 amino acid residues

Fluorescent labeling allows you to examine the conformation of the protein

N-(1-pyrene)maleimide

Fluorescence resonance energy transfer (FRET) is away of measuring intra and intermolecular distances