PROTEIN STRUCTURE

To understand how enzymes work, we must consider their structure. Enzymes are proteins which are linear polymers of amino acids. Each amino acid has an amino group, a carboxylic acid group, a hydrogen atom and an R group all surrounding a central carbon atom - the alpha carbon. Proteins contain 20 different amino acids each with different R-groups. In glycine, the simplest amino acid, the R-group is just a hydrogen atom.

Amino acids are linked by peptide bonds formed between the carboxyl group of one amino acid and the amino group of the next.

The twenty amino acids found in proteins show a variety of structures. The wide choice of possible monomers makes proteins very versatile, with a wide range of properties and capabilities. The amino acids may be classified into groups. The major division is between those with hydrophilic (water loving) or hydrophobic (water hating) R-groups. Note that some amino acids can be classified in more than one sub-group.

Hydrophilic

1) Acidic (Hydrophilic and Charged)

aspartic acid glutamic acid

2) Basic (Hydrophilic and Charged)

lysine arginine

histidine (see below) is mildly basic and contains an aromatic ring

3) Hydrophilic but Uncharged - Amides

asparagine glutamine

glycine is often classified as hydrophilic but uncharged although it has no functional group, just a hydrogen atom as its R-group.

4) Hydrophilic but Uncharged - Hydroxyl Containing

serine threonine

tyrosine has a hydroxyl attached to an aromatic ring - it is therefore not very hydrophilic and may even act as a hydrophobic group if it is buried in the middle of a protein.

Hydrophobic

5) Aromatic

phenylalanine and tryptophan are aromatic and hydrophobic

histidine has an aromatic ring (although not a benzene ring) but it is hydrophilic and basic NOT hydrophobic

tyrosine has an aromatic ring (see above)

6) Hydrophobic without Aromatic Rings

alanine valine leucine isoleucine methionine (contains sulfur)

proline (see below) acts as a hydrophobic residue although this is not its major role; its ring is not aromatic

7) Sulfur Containing

cysteine (cystine is cysteine-S-S-cysteine)

methionine also contains sulfur, but it usually acts as an unreactive hydrophobic residue (see above)

8) Imino Acid

proline is, strictly speaking, an imino acid (rather than an amino acid) since it has an -NH- group as part of a ring (rather than an -NH2).

 

Proteins - General Comments

Proteins may be catalytically active (i.e. enzymes) or may act as transport carriers across membranes (e.g. lactose permease) or in aqueous solution (e.g. maltose binding protein). In addition there are structural proteins with no catalytic or binding activities. Simple proteins consist only of amino acids. Conjugated proteins also contain other organic or inorganic components.

Holoenzyme = Apoenzyme + Prosthetic group.

Proteins may consist of one or more polypeptide chains. There are usually an even number of subunits, though frequent exceptions are known. Subunits may be identical or different. They are held together by covalent bonds between cysteine residues ( disulfide bonds) or more often by non-covalent bonds (hydrogen bonds, ion pair attractions, hydrophobic interactions, van der Waals forces).

The average polypeptide chain is 30 to 50,000 in molecular weight. Individual polypeptide chains with MW >100,000 are rare.

Levels of Protein Structure

a) Primary structure: Originally defined as structure due to covalent bonding, i.e. the sequence of amino acids linked by peptide bonds. Today the primary structure of biological macromolecules is considered to be the sequence of the monomers (almost, but not quite, the same thing).

b) Secondary structure: folding of the polypeptide chains due to the formation of hydrogen bonds between the peptide groups which link the amino acids together. The polypeptide chain must be folded around to bring two peptide groups alongside. The hydrogen on the nitrogen of one peptide group is then bound to the oxygen of the other.

There are two major classes of secondary structure, the alpha-helix in which the polypeptide chain is wound in a helix and the beta-sheet in which the polypeptide chain is zig-zagged back and forth.

The alpha-helix has 3.6 amino acids per turn. The pitch (repeat length) is 0.54 nm and the rise per residue is thus about 0.15 nm. The R-groups extend outwards from the tightly packed helical polypeptide backbone. Intrachain H-bonds occur between successive twists of the helix and run parallel to the long axis of the helix. The H-bonds go from the N-atom of one peptide bond to the C=O group of the third amino acid beyond. All peptide groups may form H-bonds in the alpha-helix which is therefore very stable. With L-amino acids a right handed helix is most stable. (You cannot form a stable helix with mixed D- and L- amino acids).

The beta-sheet consists of a polypeptide chain folded back on itself several times. The structure is held together by H-bonds going sideways. The sections of the polypeptide chain which lie side by side are usually antiparallel and all peptide groups can form H-bonds. The R-groups lie alternately above and below the zigzagging plane of the beta-sheet.

A "reverse turn" (also known as a beta-turn or a beta-bend) is where the polypeptide chain turns back upon itself. Beta-sheets have reverse turns at the ends of each segment, but such turns are also found frequently in other places. Proline has a rigid ring structure which causes an approximately 90° change in direction of the polypeptide chain which disrupts most secondary structures. Pro and Gly are found most often in reverse turns.

Different amino acids favor the a alpha-helix, the a beta-sheet or the reverse turn. In particular two bulky residues or two residues with the same charge will not fit side by side into an a-helix. Apart from this most amino-acids fit best into the a-helix (except for Cys, Asp, Gly, Lys, Asn, Pro, Ser, Thr, Val). The amino acids with short polar side chains (Ser, Asp, Asn) or no genuine side chain (Gly, Pro) are usually found in reverse turns or random coils.

c) Tertiary Structure: Results from interactions between the R-groups. Thus a protein may contain several regions of alpha-helix or beta-sheet folded overall into a globular structure. In between regions of secondary structure are found regions of random coil. Most proteins have a well defined tertiary structure (an exception is silk which is totally beta-sheet).

d) Quaternary Structure: Results from assembly of several individual polypeptide chains. Most proteins with MW greater than 50,000 consist of subunits. Multienzyme complexes are aggregates containing several enzyme activities which are successive steps in a metabolic pathway. A good example is pyruvate dehydrogenase of Escherichia coli which includes three enzyme activities:

E1 and E3 are themselves made up of further subunits. Overall there are over 80 polypeptides per particle, with a total MW = 4.8 million. The transacetylase forms a cube in the middle of the complex. The 12 pyruvate decarboxylase molecules lie on the 12 edges of the cube formed by the transacetylase. The 6 lipoate dehydrogenase molecules occupy the 6 faces of the cube. This structure will self assemble spontaneously if the parts are mixed together.

Forces Which Maintain Higher Level Structures

a) Interpeptide hydrogen bonds. Maintain secondary structure.

b) Disulfide bonds between cysteine residues. According to older definitions these would be included in primary structure as they are covalent bonds. However, primary structure is nowadays considered to be the sequence of the amino acids. In practice disulfide bonds help maintain tertiary or quaternary structures. Since disulfides are easily reduced to -SH groups inside cells, they are of little use in stabilizing intracellular proteins. They are mostly used for extracellular proteins which are exposed to air outside cells.

c) Hydrogen bonds between R-groups, involving eg:

-NH in ring of His, Trp

-OH of Ser, Thr, Tyr

-CONH2 of Asn, Gln

d) Ionic bonds (—NH3+ -OOC—) between R-groups of basic and acidic amino acid residues. Relatively few of the possible ionic interactions occur in practice. This is because most polar groups are on the surface of the protein and form hydrogen bonds to the water.

e) Hydrophobic bonds between R-groups. The most important influence on tertiary and quaternary structure. Most proteins fold up so that their polar residues are largely exposed at the surface. The hydrophobic residues are buried inside, away from the water. The internal structure is thus dictated largely by hydrophobic interactions. This is the oil drop model of protein structure. (Note that intrinsic membrane proteins show an inverse conformation).

The strength of hydrophobic bonds increases with temperature, hence many subunit proteins tend to come apart at low temperatures. Formation of hydrophobic bonds is driven mostly by entropy. For example, to dissolve a benzene ring in water - DG = +4 kcal (DH = 0, DS = -14). Exposed hydrocarbon residues exert an organizing effect on surrounding water molecules. Self association of hydrocarbon residues liberates solvent molecules and so the entropy increases.

Denaturation of Proteins

Denaturation is the loss of correct 3-dimensional structure. Only non-covalent bonds are broken during denaturation. When proteins are denatured their enzyme activities no longer work and they often precipitate out of solution - this is what happens when you boil an egg. Heat, extremes of pH, detergents, chaotropic agents and denaturants destroy non-covalent structure and denature proteins.

The detergent sodium dodecyl sulfate (SDS) is widely used to solubilize and denature proteins before running them on polyacrylamide gels to separate them by molecular weight. SDS has a long hydrocarbon tail which winds around the polypeptide backbone. The negatively charged sulfate group sticks out into the water and solubilizes the protein/SDS complex.

Denaturation is also promoted by the reduction of disulfide bonds. In the laboratory, beta-mercaptoethanol (BME; HOCH2CH2SH) is often used to break disulfide bonds.

Chaotropic agents (e.g. thiocyanate, perchlorate) disrupt water structure and so allow hydrophobic groups to dissolve much more readily. This destabilizes proteins which rely on the oil drop model.

Denaturants are a special class of molecules e.g. urea, guanidinium chloride. They have a dual function: a) they help the exposure of hydrophobic groups to the solvent like chaotropes and b) they disrupt the hydrogen bonds which maintain secondary structure. They do this by forming hydrogen bonds themselves with all the groups on the protein which can form hydrogen bonds.

Opposing entropy changes occur during denaturation. Hence it is thermodynamically very complex and not fully understood.

1) protein unfolds thus disorder increases

2) exposure of hydrophobic groups to water which thus becomes more ordered

 

ENZYME MECHANISM (Wood et al., Chapters 7 and 8)

There are two major considerations - substrate specificity and catalytic power. Enzymes must bind the correct substrate and position it correctly relative to catalytically active groups in the active site. Most enzymes are very large relative to their substrates. The actual reaction occurs in the active site, a small region of the enzyme where the substrate is bound.

Lock and Key Model: the enzyme active site fits the substrate exactly. In chymotrypsin almost no detectable structural change occurs upon substrate binding.

Induced Fit Model: the binding of the substrate induces a change in enzyme conformation so that the two fit together better and so that groups in the active site which are required for catalysis are properly positioned. In carboxypeptidase binding of substrate causes a tyrosine (at position 248) to move 12 Angstroms to a position where it is in physical contact with substrate and can play a direct catalytic role. Most enzymes are not rigid but somewhat flexible.

Actually, the active site is often designed to fit the transition state intermediate better than the substrate itself. Consequently the conversion of the substrate to the reaction intermediate is favored because this will bind better.

Specificity May Be Very Strict Or Relatively Broad:

Broad specificity is shown by many degradative enzymes e.g. alkaline phosphatase, which removes phosphates from a wide range of molecules, or carboxypeptidase which snips the C-terminal amino-acid off many polypeptide chains.

Intermediate specificity is most common e.g. alcohol (ethanol) dehydrogenase of E. coli will act on C2, C3, and C4 alcohols; pyruvate dehydrogenase will also use the C4 homolog of pyruvate etc.

Some enzymes are absolutely specific. Aspartase catalyses the interconversion of aspartate and fumarate:

L-Aspartate ==> Fumarate + NH3

It will only use aspartate (not similar amino acids such as glutamate) and only the L-isomer. Nor will it add NH3 to maleate, the cis isomer of fumarate.

Catalytic Power:

Enzymes lower the energy of the transition state by stabilizing the original reaction intermediate or by providing an alternative reaction pathway. Rate increases by enzymes range from 108 to 1020 relative to the uncatalysed, spontaneous reaction (e.g. 109 for alcohol dehydrogenase; 1016 for alkaline phosphatase). Factors involved in enzyme rate increases:

a) Proximity: The enzyme binds the substrate so that the susceptible bond is very close to the catalytic group in the active site. Calculations indicate that the local concentration of substrate in the active site may be as much as 50M whereas its concentration in the cytoplasm may be less than 1mM. Since chemical reaction rates are proportional to the concentrations of the reactants a rate enhancement of up to 106 may be generated by local concentration effects. This effect is counteracted to some extent by the fact that the concentration of enzyme active sites is low (the active site is a small portion of a very large molecule; the total protein concentration in cytoplasm is 1 to 10mM at most).

Compare two versions of the attack of an amide on an ester where both reacting groups are on the same molecule (A) or on separate molecules (B). Reaction (A) proceeds 105 times faster than the bimolecular reaction (B). In fact, B is so slow it cannot be accurately measured.

b) Orientation: Proximity alone is insufficient. The reacting groups must be properly oriented. Orbital steering hypothesis - binding of the substrate(s) to the enzyme aligns the reactive groups so that the relevant molecular orbitals overlap. This increases the probability of forming the transition state. For a typical bimolecular reaction in free solution about 1/100 collisions between molecules of sufficient energy actually leads to a reaction. Thus the maximum effect of orientation would be 100-fold.

Consider the attack on an aryl ester by a carboxylic acid.

Now let's put both reacting groups on the same molecule - i.e. we will link R1 and R2 together. As the five examples show, the relative rate gets greater as the reacting groups are brought closer together. In addition, holding them in the correct orientation also helps. (Ar = methoxyphenyl group.)

c) Covalent Intermediates: Here the strategy is to lower the transition state energy "hump" by taking an alternative reaction pathway.

Uncatalysed: BX + Y ==> BY + X

Catalysed: BX + Enz ==> Enz-B + X

Enz-B + Y ==> Enz + BY

Where B is usually some chemical group such as a phosphate group, acyl group or glycosyl group. Phosphoenzymes usually attach the phosphate to serine or histidine. Serine type - phosphoglucomutase, alkaline phosphatase. Histidine type - glucose 6 phosphatase, phosphotransferase system. Acyl enzymes usually attach the acyl group at an active serine or cysteine residue. Most proteases (eg trypsin, elastase, subtilisin are serine enzymes. Cysteine enzymes include papain (a protease), glyceraldehyde phosphate dehydrogenase and most enzymes using acyl CoA derivatives.

Histidine, serine and cysteine operate by nucleophilic catalysis. Their nucleophilic groups (imidazole ring, OH and SH respectively) are good electron donors the intermediates they form are unstable and react easily with the final acceptors. Since the whole point is that covalent intermediates should rapidly break down to release the reaction product, enzyme covalent intermediates are very difficult to isolate.

d) Acid-Base Catalysis: Specific acid-base catalysis is due to H+ or OH- ions. General acid-base catalysis is due to proton donors or proton acceptors, which donate or remove protons to (or from) the transition state intermediate. Most hydrolytic enzymes use acid/base catalysis.

Concerted acid-base catalysis: Providing both acid and base simultaneously is impossible in free solution, yet enzymes can do this. An acidic group in one part of the active site donates a proton and a basic group in another part of the active site removes a second proton from the reaction intermediate.

Amino acids with extra carboxyl or amino groups can obviously act as acids or bases. In addition, histidine (pK around 7.0) can act as either an acidic or basic catalyst depending on whether or not it is protonated. Also, histidine reacts very fast (protonation/deprotonation of imidazole ring has a reaction half-time of less than 10-10 seconds at neutral pH). Histidine is rarely found in proteins except at catalytic sites.

e) Metal Ion Catalysis: Many enzymes have metal ions at the active site. Sometimes these are used as redox centres, as in cytochromes, nitrate reductase etc. However, often the metal ion does not get reduced or oxidised, but acts to stabilize negative charges on the reaction intermediate. In carboxypeptidase, Zn2+ polarizes the C=O of the peptide bond which is about to be broken. In alcohol dehydrogenase Zn2+ polarizes the C=O group of acetaldehyde, so allowing the hydride ion (H–) to be added to the carbon atom.

f) Bond Distortion: Binding to enzyme distorts the substrate - medieval torture rack model. The active site of the enzyme gives the best fit NOT with the substrate (or product) but with the transition state intermediate. Hence after the substrate is bound it tends to be forced into the shape of the reaction intermediate. Distortion is difficult to demonstrate since the strain is imposed once the substrate has bound to the enzyme. A chemical example is the hydrolysis of organic phosphates:

Lysozyme degrades the sugar chains of peptidoglycan, which have alternating NAG and NAM residues. Lysozyme has an active site (a long narrow cleft) which binds six sugar residues. In vitro, lysozyme can chop up short oligosaccharides, in particular it cuts the hexamer after residue #4.

The X-ray crystallography of lysozyme with this substrate bound is one of the few direct demonstrations of distortion. Sugar #4 is twisted out of its normal chair conformation by the enzyme. The other five sugars are bound in their stable conformations.

Order of reaction:

This is determined by the relationship between the reaction rate and the reactant concentration. To find the order of reaction, vary the concentration of each reactant and plot the 1n (rate) vs 1n (reactant). The order is given by the slope of the resulting straight line. The molecularity of a reaction is the number of molecules reacting and is not necessarily the same as the order of reaction.

First Order Reaction:

The rate of disappearance of A is proportional to [A]

A ===> Product The Rate Equation is: -d[A]/dt = k[A]

Where [A] = concentration of A; t = time; k is the rate constant (first order) with units of sec-1

The integrated rate equation (from 0 to time t) is:

ln [Ao]/[A] = kt where [Ao] refers to zero time

Second Order Reaction:

The rate of disappearance of A is proportional to [A] • [B]

A + B ===> Product The Rate Equation is: -d[A]/dt = k[A] [B]

Where k is the rate constant (second order) with units of in Molar-1 sec-1

Zero Order:

Rate is independent of concentration. Many catalyzed reactions are zero order (with respect to the reactants) and the rate depends on the concentration of the catalyst or some other factor.

Termolecular reactions:

The likelihood that three molecules collide and react simultaneously is extremely low and reactions involving three or more reactants usually proceed via several steps. The observed order of reaction depends on the rate limiting step.

To find the order of reaction, vary the concentration of each reactant and plot 1n (rate) vs 1n (reactant). The order is given by the slope of the straight line resulting. Second order reactions may appear to be first order under extreme conditions. Thus if the concentration of A is high and of B is very low then the rate will be nearly proportional to the concentration of the limiting reactant (i.e. B) - pseudo first order. Many catalyzed reactions are zero order (with respect to the reactants) and the rate depends on the concentration of the catalyst or some other factor. Reactions may be mixed, that is of fractional order - neither pure first nor second order.

Enzyme Reactions and The Michaelis Menten Equation

The general principles of chemical kinetics apply to enzyme reactions, with certain modifications. Saturation is the most distinctive of these. At low substrate concentrations, the rate is approximately proportional to substrate concentration (i.e. the reaction is first order in S). At high substrate concentrations all the active sites are full, i.e. the enzyme is saturated and the maximum velocity is reached. Here the rate is independent of substrate concentration (i.e. zero order in S). In between, the reaction rate is of fractional order. However, the rate still depends on the enzyme concentration, whatever the concentration of substrate.

Michaelis and Menten assumed that the substrate, S, reacts with the enzyme, E, to form a complex, ES, which then breaks down to form free enzyme and the product, P. If k1 and k2 are the rate constants for the first and second steps and k's with negative subscripts refer to the reverse reactions, then:

k1 k2

E + S <============> ES <============> E + P

k-1 k-2

V = initial velocity (rate at which P is formed)

[Ef] = concentration of free enzyme

[E] = total concentration of enzyme

[ES] = concentration of enzyme substrate complex

Since the amount of substrate, S, bound to the enzyme, E, is very small relative to the total concentration of S, we can assume that:

free substrate = total substrate = [S]

Derivation of the Michaelis-Menten Equation

The initial velocity, V, is the rate of breakdown of ES to yield the final product, P:

1) V = k2 [ES]

Unfortunately, neither k2 nor [ES] can be directly measured.

Consider ES. The back reaction P + E Æ ES can be ignored since we are trying to find an equation for V, the initial velocity (at time = 0, [P] = 0). Hence for the rate of formation of ES we have:

2) d[ES] / dt = k1 [Ef] [S] = k1 {[E]-[ES]} [S]

For the breakdown of ES we have:

3) -d[ES] / dt = k-1 [ES] + k2[ES]

We now assume that the reaction has entered a steady state and that the formation of ES balances its breakdown. Consequently:-

4) k1 {[E]-[ES]} [S] = k-1 [ES] + k2 [ES]

Separate out the rate constants and combine them into one expression:

5) k-1 + k2 / k1= Km = [S] {[E]-[ES]} / [ES]

Equation 5 defines Km, the Michaelis constant. Solving for [ES]:

6) [ES] = [E] [S] / {Km + [S]}

From equation (1), [ES] = V/ k2 Substituting this in equation 6 we get:

7) V = k2[E] [S] / {Km + [S]}

Consider the situation when the enzyme is saturated. The maximum initial velocity, Vm, occurs when all of the enzyme has substrate bound and so cannot work any faster i.e. [E] = [ES]. Thus:

8) Vm = k2 [E]

By combining equations 7 and 8 and eliminating k2 we get the Michaelis Menten equation (9). It refers to an enzyme catalyzed reaction with a single substrate. Note that the concentration of enzyme is included in Vm.

9) V = Vm [S] / {Km + [S]}

Vm and Km both vary with the nature of substrate and may vary with pH and temperature. For multisubstrate enzymes each substrate has a characteristic Km and Vm. A few enzymes do not show saturation with substrate, this is because the breakdown of ES is so fast it cannot easily be made rate limiting.

Consider the special case when the initial velocity is half maximal, i.e. when V = Vm/2 Inserting this in the Michaelis Menten equation (9) we get:

10) Vm/2 = Vm [S] / {Km + [S] Hence: 1/2 = S / {Km + [S]}

11) thus: Km + [S] = 2[S] Hence: Km = [S] when V = Vm/2

Thus Km is the substrate concentration for half maximal velocity. Its units are moles/liter and it is independent of the enzyme concentration.

Assumptions used

a) [S] is much greater than [E] so that the amount of S bound by E at any given time is negligible, compared to total [S].

b) Initial velocity allows us to neglect the reverse reaction, P + E ==> ES

c) Steady state for the breakdown and formation of ES.

Definitions and Units

Enzyme unit = moles (or usually micromoles or nanomoles) of product formed/minute under specified conditions of temperature, pH, [S], etc.

Specific activity = enzyme units/mg protein

Total enzymatic activity = specific activity x total amount of protein

= total number of enzyme units

Catalytic constant = Vm per mole of pure enzyme (if the molecular weight of the enzyme is unknown, the catalytic constant is often given per 100,000 g of enzyme)

Turnover number = catalytic constant/number of active sites on enzyme (usually this is the number of subunits making up the final protein).

= Vm per mole of active sites. Turnover numbers range from 100 to over a million.

Affinity & The Substrate Dissociation Constant

Consider the dissociation of the enzyme substrate complex: ES <==> E + S

Ks the equilibrium, or dissociation, constant for enzyme substrate binding is defined as:

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

In most enzymatic reactions k2 is small relative to k-1. In such cases Km and Ks are the same because the definition of Km = { k-1 + k2 }/ k1 approximates to k-1 / k1 = Ks

Since 1/Ks is a measure of the affinity of an enzyme for its substrate, 1/Km is therefore an approximate measure of affinity. When Km is high, affinity is low and vice versa.

Plotting Experimental Data

A) Lineweaver-Burke method (double reciprocal plot)

Take the Michaelis Menten equation: V = Vm[S] / Km + [S]

13) Take the reciprocal of both sides: 1 /V = Km + [S] / Vm[S]

14) Split into separate terms: 1/V = Km / Vm[S] + [S] / Vm[S]

15) Cancel to give: 1/V = Km / Vm x 1/ [S] + 1/Vm

This is the Lineweaver-Burke equation. A plot of 1/V versus 1/[S] gives a straight line. We can therefore obtain Km and Vm accurately from experimentally measured initial rates at different substrate concentrations.

Slope = Km/Vm

Intercept = 1/Vm (on 1/V axis)

Intercept = –1/Km (on 1/[S] axis)

B) Eadie-Hofstee Method

17) Multiply equation 13 by Vm on both sides: Vm /V = {Km + [S]} / [S]

18) Now multiply through by V: Vm = VKm/ [S] + V[S] / [S]

19) Rearrange to give Eadie-Hofstee equation: V = Vm – VKm/ [S]

Plot V versus V/[S]. This plot magnifies departures from linearity which may escape observation on a Lineweaver-Burke plot.

Slope = –Km

Intercept = Vm (on V axis)

Intercept = Vm/Km (on V/[S] axis)

Two Substrate Reactions

These may be tackled by providing a large excess of one substrate and varying the other. Hence a pseudo first order situation is obtained and the Michaelis-Menten equation may be used for the variable substrate and Km and Vm determined.

Temperature and pH

The rate of most enzyme reactions increases about two-fold for every 10°C rise in temperature. However, at high temperatures enzymes are denatured. The temperature optimum is thus a result of two opposing factors.

The pH profile varies greatly from enzyme to enzyme. Since Km varies with pH, such profiles should be derived with saturating substrate concentrations (i.e plot Vm versus pH).

Enzyme Inhibition

Reversible inhibition occurs when analogs of the substrate bind reversibly at the active site so preventing access of the substrate. The substrate and the inhibitor compete for the same binding site, so this is often called competitive inhibition. The extent of inhibition depends both on the relative concentrations and the relative affinities of the substrate and the inhibitor.

Remember that the substrate binds to the active site and then goes via the transition state to the product. The active site is often designed to fit the transition state intermediate better than the substrate itself. Consequently some of the best competitive inhibitors are molecules which mimic the transition state intermediate - "transition state analogs". Proline racemase interconverts the L- and D- isomers of proline by removing an H-atom and replacing it in a different configuration.

The substrate and product are both tetrahedral about the alpha carbon but the transition state is planar. The best competitive inhibitors are flat ring compounds rather than ones which look most like the substrate.

Irreversible inhibition is due to covalent modification of the enzyme, by the inhibitor, usually at the active site. The covalent inhibitor is not usually an analog of the substrate. Suicide inhibitors are substrate analogs which are converted by the enzyme to products which are reactive irreversible inhibitors and which go on to react covalently with the enzyme and kill it. Lethal synthesis occurs when an enzyme converts a substrate analog into an inhibitor which kills the cell by attacking some other target (i.e. the enzyme which makes it is not harmed). Examples of inhibitors will be given when we discuss metabolic reactions.

Allosteric Enzymes

Allosteric enzymes change their shape and properties upon binding a small regulatory molecule (the allosteric effector). Many key enzymes in metabolic sequences exhibit such anomalous kinetic behavior. Such enzymes may be activated or inhibited by the action of small molecules at sites distinct from the active site. These regulatory sites are known as allosteric sites. Typical properties of allosteric enzymes:

1) Do not follow Michaelis-Menten kinetics. Plots of V versus [S] are sigmoid not hyperbolic. This implies multiple, interacting binding sites.

2) Allosteric effectors are usually unrelated chemically to the substrate of the enzyme they control. Often they are the end (or major) products of whole metabolic sequences in which the enzyme is involved.

3) Allosteric effectors may inhibit or activate. Some allosteric enzymes have both an activator and an inhibitor - i.e. two different allosteric sites.

4) Allosteric changes may alter the Km or the Vm or both.

5) All allosteric enzymes have subunits.

In some cases the subunits stay together. When the allosteric effector binds, it changes the shape of the subunit to which it binds. This shape change is then transmitted to the next subunit which, as a bonus, can now bind the allosteric effector more easily). The subunits are said to undergo a concerted shape change.

In other cases, binding of allosteric effectors changes the shape of the subunits and also changes subunit assembly. Only one form of the protein can assemble into a multi-subunit protein.

Note that DNA binding regulatory proteins are also allosteric proteins. They change their shape and their ability to bind to DNA when they bind small regulatory molecules. The principle is the same.