What is enzyme catalysis? A catalyst is a substance that accelerates a chemical reaction without itself undergoing any net change

How do enzymes work? Free energy

Thermodynamics of catalysis  G =  H - T  S  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 a result of an enzyme having a higher affinity for the transition 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)* k non k cat KsKs K TS = [E][S]*/[ES]* = [(k cat /K m )/k non ] -1 For Triosephosphate isomerase K TS = , and K m = Thus, this enzyme binds the transition state eight orders of magnitude more 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 k 2 E + S ES E + P k1k1 k-1k-1 k2k2 v = d[P]/dt = k 2 [ES] (1) If we could measure v and [ES] then we could determine k 2, 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.

K s = k -1 /k 1 = [E][S]/[ES] E + S ES E + P k1k1 k-1k-1 k2k2 From this equation: Under certain circumstances (if k -1 >>k 2 ), E and S are in equilibrium with ES, with an equilibrium dissociation constant K s. 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: k 1 [E][S] = k -1 [[ES] + k 2 [ES] Rearrange to give [ES] = (k 1 /k -1 +k 2 )[E][S] Define a constant K m = (k -1 +k 2 / k 1 ) K m [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: K m [ES] = [E] t [S] – [ES][S]

Transfer second term on right side to left side to get: [ES](K m + [S]) = [E] t [S] Rearrange to [ES] = [E] t [S]/(K m + [S]) Using equation 1 we can finally solve for v, velocity v = k 2 [E] t [S]/(K m + [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] v = change in product change in time Increasing [substrate] At high substrate concentrations, the reaction reaches a maximum velocity V max, because the enzyme molecules are saturated; every enzyme is occupied by substrate and carrying out the catalytic step [S] = K m

From these relationships, consider the following: What is K m and what does it mean? K m is a ratio of rate constants: K m = (k -1 +k 2 / k 1 ) Thus in our catalyzed reaction, if k 2 is much smaller than k -1, K m = k -1 /k 1 = K s, the equilibrium constant for [ES] formation. In this case, a large K m means k -1 >>k 1, thus the enzyme binds the substrate very weakly. However, in a separate instance a large k 2 can have a similar effect on K m. Thus, what is the utility of K m ?

The most useful way to think of K m is reflected in the plot Of a reaction that follows the Michaelis-Menten equation In this plot, K m is numerically equal to the substrate concentration At which the reaction velocity equals half of its maximum value. Where [S] = K m, the Michaelis-Menton equation simplifies to v = V max /2 Thus, an enzyme with a high K m requires a higher substrate concentration to achieve a given reaction velocity than an enzyme with a low K m.

In considering Vmax mathematically, by making [S] much Larger than Km the Michaelis-Menten equation simplifies to: V max = k 2 [E] t Thus, another way of writing the Michaelis-Menten rate equation Is: v = V max [S] / (K m + [S]) Typically, all of this is an oversimplification, and enzyme-mediated catalysis looks more like: E + S ES EP E + P k1k1 k-1k-1 k2k2 k3k3

In this more complex system, k 2 must be replaced with a more general constant, called k cat v = k cat [E] t [S]/ (K m + [S]) In the two step reaction we considered first, k cat = k 2. For more complex reactions, k cat is a combination of rate constants for all reactions between ES and E + P. k cat is a rate constant that reflects the maximum number of molecules of substrate that could be converted to product each second per active site. Because the maximum rate is obtained at high [S], when all the active sites are occupied with substrate, k cat (the turnover number) is a measure of how rapidly an enzyme can operate once the active site is filled. k cat = V max /[E] t

Under physiological conditions, enzymes usually do not operate under saturating substrate conditions. Typically, the ratio of [S] to K m is in the range of When K m >> [S], the Michaelis-Menten equation simplifies to: v = k cat /K m ([E] t [S]) The ratio k cat /K m is referred to as the specificity constant which indicates how well an enzyme can work at low [S]. The upper limit of k cat /K m is in the range of 10 8 to 10 9 due to limits of diffusion theory.

Lineweaver-Burk plots are convenient for determination of K m and k cat

Lineweaver-Burk plots result from taking a double reciprocal of the Michaelis-Menten equation. v = V max [S] / (K m + [S]) 1/v = K m /(V max [S]) + 1/V max Plotting 1/v on the y-axis and 1/[S] on the x-axis (both known quantities) The slope is equal to K m /V max, the y-intercept is 1/V max And the x-intercept is –1/K m

Kinetics of enzymes with multiple substrates OrderedPing-Pong Useful web site:

Enzyme Inhibition Competitive Non-competitive

Enzyme inhibition Uncompetitive

Substrate binding influences rates of activity Cooperativity Hysteresis

Regulation of an enzyme’s activity via post-translational mechanisms Modifications Activation by proteolysis Phosphorylation Adenylylation Disulfide reduction

Regulation of an enzyme’s activity via post-translational mechanisms Allostery Phosphofructokinase Aspartate carbamoyl transferase Glycogen phosphorylase Calmodulin

Investigating the structure-function relationship of 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 amino acids to form covalent complexes N-ethylmaleimide (NEM) reacts with free cysteines reagent which modifies H, Y or K residues = DEPC, diethyl pyrocarbonate reagent which modifies H, Y or W residues = NBS, N-Bromosuccinimide reagent which modifies H or carboxyl = Woodward's K; N-ethyl-5-phenylisoxazolium 3'sulfonate reagents which modify lysine or primary amino acid residues = Succinic anhydride; TNBS, 2,4,6-trinitrobenzenesulfonic acid) reagent which modifies Y residues = N-acetylimidazole reagent which modifies SER residues = PMSF, Phenylmethyl sulfonamide reagent which modifies R residues = phenylglyoxal

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-conservative at most positions important for structure, but non-conservative at most positions important for catalysis Cysteine scanning mutagenesis – puts a functional group at positions throughout the protein sequence

FASEB J 1998 Oct;12(13): 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 a way of measuring intra and intermolecular distances