Enzymes

Contents

Enzymes

Enzymes are simply biological catalysts, made (mostly) of protein. A well known example is catalase, which catalyses the degradation of hydrogen peroxide (H2O2). Like all catalysts, enzymes work by reducing the energy of activation. They are often even better at this than industrial inorganic catalysts at increasing the rate of reaction.

Catalyst

∆G‡ (kJ mol−1)

Uncatalysed

75.2

Platinum

48.9

Catalase

23.0

In an enzyme-catalysed reaction, the non-enzyme reactants are called substrates.

E + S ⇌ ES → E + P

Enzyme + Substrate ⇌ Enzyme-substrate (transition) complex → Enzyme + Product

Enzymes are classified based on what they do to their substrates, according to the Enzyme Commission (EC) classification

  1. Oxidoreductases transfer electrons (often as hydride ions H−).
  2. Transferases transfer chemical groups between molecules.
  3. Hydrolases add or remove H2O from molecules.
  4. Lyases manipulate double bonds by elimination reactions.
  5. Isomerases transfer chemical groups within molecules.
  6. Ligases condense C-{S/N/C/O} bonds using energy from ATP.

EC 3.1.1.7. is acetylcholine esterase:

The active site of an enzyme is the cleft on the surface of an enzyme where the catalysis takes place. Its 3D shape is very specific, and very selective in what it binds to. Consequently, an enzyme only catalyses one (or a very few related) reaction(s). Several models of the active site have been proposed over the years.

The lock and key hypothesis states that the substrates fits into the active site like a key fits into a lock. Although this gives some idea of how the enzyme and substrate interact (showing that the enzyme and substrate require a particular orientation to react), it disagrees with experiment, which shows that the active site and substrate are rarely a perfect fit for one another.

The enzyme and substrate fit tightly and rigidly like a lock and key.

The induced fit hypothesis states that the substrates fits into the active site by deforming it somewhat. Neither enzyme nor substrate are viewed as 'fixed': both change shape somewhat to accommodate each other. In fact, the active site is often complementary in shape to the transition state, which means the substrate is put under stress when it bind to the enzyme. This promotes reaction to form products.

In general, the active site is complementary in shape to the transition complex.

By binding the substrates in a particular orientation, the entropy of the system is decreased, and given that the binding is spontaneous (i.e. ∆G is negative) this means that ∆H = ∆G + T∆S is very negative (exothermic). Much of that enthalpy (energy) is available to reduce the activation energy of the reaction. Most enzymes achieve a rate enhancement of the order of 1 billion by these means.

The rate of reaction is increased by proximity.

Because enzymes bind substrates in particular orientations, they can increase the ROR simply by proximity effects. The reaction with linked molecules is 105 times quicker than the free reaction, because the groups are on the same molecule. This can be increased to 108 times quicker if the groups are also held rigid.

To understand how enzymes bind substrates, we will look at the example of acetylcholine esterase (AChE). AChE is an enzyme in the synapses of nerves that degrades the neurotransmitter acetylcholine (ACh).

Acetylcholine + water → acetic acid + choline

Enzymes can bind substrates by any sort of chemical bond. Different sorts of bonding may lead to different sorts of catalysis.

AChE binds its substrate by dipole/ionic interactions between charged and polar groups on the molecule. During the catalytic cycle, part of the substrate is also bound covalently.

Cofactors

Most enzymes use their amino-acid side chains to bind and manipulate substrates, like fingers; however, some use additional tools, called cofactors. These may be further subdivided into:

Many vitamins are metabolically altered to become soluble coenzymes. This includes:

ATP - click for Jmol version
ATP

Two very important coenzymes are ATP (top) and NADH (bottom).

ATP, ADP and AMP serve as universal energy currency and carry energy using 'high energy' phosphate bonds. They are derived from nucleic acids in food.

NADH - click for Jmol version
NADH

NAD(P)H and NAD(P) serve as universal redox currency, carrying reducing power as hydride ions (H−). They are derived from vitamin B3 (niacin/nicotinic acid).

Coenzymes are continuously recycled, so they can be present at much lower concentrations than substrates. The reason for this is that coenzymes are expensive to synthesise for the cell (and for Sigma Aldrich too).

Prosthetic groups differ from cofactors in being tightly (often covalently) bound to a particular enzyme molecule. A example is haem, which is found in cytochromes and haemoglobin, and carries oxygen and/or electrons.

Haem.
Haem

Iron-sulfur clusters also carry electrons, and are found in ferredoxin, an important intermediate in photosynthesis.

4Fe-4S cluster.
Iron-sulfur clusters

Many of the minerals needed by your body are also used in enzymes as metal ion cofactors. Iron and copper are frequently used to bind and carry electrons, for example in cytochrome oxidase. Zinc helps bind NADH in alcohol dehydrogenase, and is important in binding carbon dioxide in the enzyme carbonic anhydrase. Some nonmetals are also important: selenium replaces sulfur in one of the cysteines of glutathione peroxidase.

Enzyme kinetics

Enzyme kinetics are just a special case of the kinetics that we have already discussed. Enzymes are biological catalysts, which are chemicals that increase the rate at which equilibrium is achieved without themselves being permanently transformed by the reaction. Note that although they change k, they do not change Keq: they alter the rate of equilibrium achievement, not the actual equilibrium point.

Enzyme catalysis rates are affected by three important factors:

Enzymes catalyse reactions by reducing the activation energy and by altering the steric constant in the Arrhenius equation. The former they do by decreasing the energy of the transition state, often by increasing the number of transition states, so dividing the big mountain of the uncatalysed activation energy with a few smaller foot-hills between several intermediate states. The latter they do by ensuring that substrates interact with one another in the correct orientation by binding them in a specific orientation to the active site.

We shall return to our example of AChE to understand how the rate of an enzyme-catalysed reaction varies with concentrations of substrates.

Acetylcholine (ACh) + water + esterase → acetic acid + choline + esterase

At a given pH and temperature, the rate of hydrolysis of ACh depends on

We shall look at each of these in turn.

The rate of an enzyme-catalysed reaction is first order w.r.t. enzyme concentration, i.e. with unlimited substrate, the ROR increases linearly with the concentration of enzyme.

For water, reaction kinetics are usually (pseudo)zeroeth order. This is because the concentration of water in most biological systems is so high that it is not possible to lower or raise it significantly. Lowering the water concentration would require adding enormous quantities of solutes to the system, whose effect on the reaction would likely be more significant than the change in water concentration. We can generally ignore the concentration of water when looking at the kinetics of hydrolytic enzymes.

Pseudozeroeth order kinetics.

The rate of reaction does something complicated with most other substrates. At low concentrations (relative to the amount of enzyme present), initial reaction rates (V) increase linearly with [S]. At high substrate concentrations, they appear zeroeth order, i.e. it doesn't matter how much extra substrate you add, you can't get them to run any faster.

Michaelis-Menten kinetics are parabolic w.r.t. substrate concentration.

This effect is due to the saturation of the enzyme with substrate: there are only a limited number of active sites available for the substrate to be degraded at. Very high substrate concentrations overwhelm the enzyme: all active sites are occupied, and the addition of further substrate does not increase the reaction rate.

Saturation kinetics.
At low [S], V is first order w.r.t. [S]: nearly a straight line [S] < 4. That is to say, it is pseudo-first order w.r.t. [S]. At saturating [S] > 6, it becomes zeroeth order (rate not dependent on [S]), as active sites run out. (In fact, it becomes pseudo-first order w.r.t. enzyme concentration if the substrate is present in massive excess).

         k1     k 3

E + S ⇌ ES ⇌ E + P

         k2     k 4

k1 and k3 are forwards rate constants; k2 and k4 are backwards rate constants for the formation of the enzyme-substrate (ES) complex, and for the formation of product (P) respectively.

When we first mix enzyme and substrate, it will take a little while before the reaction gets going. For the purposes of analysing the kinetics, we assume a steady state, where the rate of product formation is constant.

The steady state is reached just after the reaction starts, when the concentration of the ES complex reaches a constant value.

Leonor Michaelis and Maud Menten assumed k4 is negligible (which is sometimes is). Briggs and Haldane corrected this and their formulation of enzyme kinetics is more useful, but a bit more complex. The derivation below is that of Michaelis and Menten.

The rate of formation of the enzyme-substrate complex ES is:

k1[E][S] + k4[E][P]

However, if we assume k3 ≫ k4,i.e. that the equilibrium favours product hugely over the transition complex, we can ignore the term with k4 in it, and simplify this to:

k1[E][S]

The rate of removal of ES is:

k2[ES] + k3[ES]

At the steady state, the rate of making ES is exactly equal to the rate of removing ES, as we saw from the straight line on the graph, so mathematically:

k1[E][S] = k2[ES] + k3[ES]

If we rearrange this to get all the rate constants on one side and all the concentration terms on the other, we can define a constant called Km, which is the Michaelis constant:

Km = ( k2 + k3 ) ⁄ k1 = [E] [S] ⁄ [ES]

We can't measure [E] (free enzyme) or [ES] easily, but we do know the total enzyme concentration ([E]T), as that is what we will have added when we made up our enzyme solution.

[E] = [E]T − [ES]

If we substitute this into our definition of Km and rearrange it, we get:

[ES] = [E]T[S] ⁄ ([S]+Km)

The overall (initial) reaction rate V is:

V = k3[ES]

This follows from our definition of what a reaction rate is. If we substitute this into the last result, we get:

V = k3[E]T[S] ⁄ ( [S] + Km )

When the enzyme is saturated, [ES] = [E]T, so we can define a maximum velocity, Vm:

Vm = k3[E]T

And this gives us our final result:

V = Vm [S] ⁄ Km + [S]

The assumptions of the model are listed below. There are essentially only three, although they can be subdivided:

  1. k3 ≫ k4, i.e. the degradation of ES to products and enzyme is essentially irreversible. This is a reasonable assumption to make if we are measuring initial rates of reaction, because there will be no product present at this point, and therefore no backwards reaction.
  2. Steady state, i.e. the rate of product formation is constant. This is generally true just milliseconds after mixing enzyme and substrate. This can be shown to be a reasonable assumption by actually measuring product accumulation over time and checking that this is linear. Related to this is the assumption that substrate concentration does not change markedly during the reaction. This is reasonable if we measure the rate of reaction over just a short period, and if there is a large amount of available substrate (compared to the enzyme). In any case, if substrate were not available in reasonable excess, product accumulation would not be linear.
  3. The only species present in the reaction are E, S, P and ES, i.e. there is no co-operativity, product-inhibition, substrate-inhibition, or allosteric effects, and the enzyme is catalytic and not destroyed by the reaction. Furthermore, there should be no competing pathway leading from S to P (i.e. no uncatalysed reaction). This is often not the case, and many enzymes have kinetics that are more complex than the Michaelis-Menten equation.

Km is the substrate concentration giving ½ Vm.

Vm (or Vmax) is the maximum rate at which a certain mass of enzyme can work.

Vm is the velocity at unlimited substrate concentrations.
Fast enzymes have high Vm.

Km is ( k2 + k3 ) ⁄ k1. If k3 ≪ k1, then Km is the ratio of [E][S] to [ES], i.e. Keq for the dissociation of the ES complex. A 'good' enzyme will have a low Km because this means it has a high affinity for its substrate.

An efficient enzyme has a low Km.
Efficient enzymes have low Km.

There are other kinetic parameters important in enzymology:

A concept related to both the speed and efficiency of an enzyme is it specificity. A good enzyme is specific to its substrate: it can find its substrate even if it's only present at low concentrations. Therefore its Km is low. A good enzyme also degrades its substrates rapidly when it finds them. Therefore its Vm and the turnover number are high. The specificity constant is defined to account for both of these, and gives a figure that expresses how 'good' and enzyme is. It equals kcat ⁄ Km. At room temperature, there is an upper limit to the specificity constant of 5 × 109 mol−1 L s−1. If an enzyme is this good, it means every collision between E and S is successful and yields product, rather than dissociating back into E + S (as evidence by a very low Km, which is the dissociation constant for the ES complex back into E + S). Furthermore the ES state is sufficiently short-lived that substrate molecules never attempt (and fail) to bind to an already-occupied active site. That is, the turnover rate of ES to E + P is faster than the collision rate between enzyme and substrate, so there is never a 'queue' of substrate 'waiting' for an active site to become free. Consequently, only the rate of diffusion of substrate into the active site limits the rate of reaction. This situation is called diffusion limitation, in which essentially all collisions between substrate and enzyme are productive (lead to product formation). There are a few enzymes that approach this thermodynamic perfection:

Enzyme inhibitors

Enzymes can be readily inhibited by certain compounds. Investigating the kinetics of inhibition is important in understanding how pesticides, drugs and many other useful chemicals work in biological systems. But first, a brief digression…

To estimate the maximal velocity and Michaelis constant, we could draw a simple plot of V against [S] is correct, and try to read off these values from the graph. However, in practice, this is extremely difficult, and in fact, a simple V vs. [S] plot is completely unhelpful if you want to estimate these kinetic parameters. Instead, we use a Lineweaver-Burk plot ('double reciprocal plot'), from which is much easier to estimate these values.

V = Vm [S] ⁄ ( Km + [S])

If we take reciprocals of both sides, we get:

1 ⁄ V = ( Km ⁄ Vm) × ( 1 ⁄ [S] ) + ( 1 ⁄ Vm )

Y = m X + c

This is the equation of a straight line, and we can very easily calculate values of Vm and Km from a plot of 1 ⁄ V vs. 1 ⁄ [S].

The Lineweaver-Burk plot linearises the otherwise unhelpful Michaelis-Menten plot.

Km and Vm can be determined from the graph from a simple bit of arithmetic on the intercepts and slopes.

Inhibitors interfere with the working of enzymes. Although extremes of temperature or pH will cook or pickle an enzyme (denature it), this is not what we mean by inhibition. Inhibition is the effect of a particular chemical species on the catalysis of an enzyme. Inhibitors are used by many metabolic pathways, for feedback inhibition of products on early stages of the pathway to modulate enzyme activity. The inhibition of enzymes used by viruses and cancer cells can be therapeutic, and many medicines are enzyme inhibitors. The deliberate inhibition of enzymes can cause accumulation of reactants upstream of a metabolic step. There are many sorts of inhibitor, but they can be broadly categorised at reversible or irreversible.

Irreversible inhibitors bind to the enzyme and destroy the active site, or otherwise screw the protein. Suicide inhibitors, a special class of such inhibitors, are activated by the normal catalytic activity of the enzyme, but form an intermediate that binds to and destroys the active site. Irreversible inhibitors bind tightly (often covalently) to the enzyme and cannot be removed by dialysis. They include such things as nerve gases (Sarin, DIPF, Tabun) and insecticides (Malathion).

Iodoacetamide.
Iodoacetamide is the archetypal enzyme inhibitor: it indiscriminately binds to and deactivates cysteine residues.

Suicide inhibitors generally look like the substrate, but attack the enzyme when activated. 5-fluorouracil (which is converted in the body to 5F-dUMP) is a suicide inhibitor of thymidylate synthase, and prevents DNA synthesis in cancerous cells.

Fluorouracil is a mutagenic base analogue.

Because suicide inhibitors bind to the active site, the can be used to find what amino acids are present there. Malathion and other organophosphates are suicide inhibitors of insect AChE, so are widely used as insecticides.

Reversible inhibitors come in many forms: we will look at two important subtypes: competitive and non-competitive inhibitors. Competitive inhibitors bind reversibly to the active site. They are often substrate analogues, like those used to elucidate the Krebs cycle: malonate inhibits succinate dehydrogenase.

Succinate.
Succinic acid.

Malonate.
Malonic acid.

In competitive inhibition, both inhibitor and substrate can bind to enzyme and form two independent complexes. Only ES degrades to products: EI is considered a 'dead-end'. Because the inhibitor binds, to the active site, the substrate cannot (and vice versa), so there cannot be an ternary ESI complex.

Competitive inhibitors can form ES complexes.

Ki = [E] [I] ⁄ [EI]

Ki is the dissociation constant for EI, like Km is the dissociation constant for ES.

Competitive inhibition increases the apparent Km.

The Km appears to be increased to Kmapp by a competitive inhibitor. Ki can be calculated from the slope on Lineweaver-Burk plot:

Competitive inhibition increases the apparent Km.

m = Km ( 1 + [I] ⁄ Ki ) ⁄ Vm.

Calculation of Ki requires us to know the true value of Km, so we also need to run a control experiment to work this out. In fact, in the lab, we'd probably use the inhibitor at several concentrations, and work out Km and Ki from this.

Upshot: Competitive inhibitors compete for the active site with the substrate, and these these unproductive bindings increase the apparent Km; however, at infinite [S], all bindings will produce ES, not EI, so Vm is unaffected.

Non-competitive inhibitors reversibly to somewhere other than the active site: they change the protein conformation allosterically, and reduce the rate at which the enzyme turns over product. They have no effect on Km as the active-site of uninhibited enzyme molecules will only encounter substrate, and no unproductive binding will occur. They do however reduce the apparent Vm; consequently the apparent Vm will be reduced, since the protein is no longer as enzymatically competent. Such inhibitors are generally not substrate analogues.

Because the inhibitor can bind independently of the substrate, an ESI complex can also form. Both ESI and EI are dead-ends.

Noncompetitive inhibitors can form ESI and EI complexes.

Ki = [E] [I] ⁄ [EI]

Kis = [ES] [I] ⁄ [ESI]

The maths is very complex, and we won't go into it. However, note that there are two inhibitor constants; one each for the dissociations of ESI and EI.

Noncompetitive inhibition reduces the apparent Vm.

Vm appears to be decreased to Vmapp by a non-competitive inhibitor. Kis can be determined from the slope and Ki can be determined from the Y-intercept on a Lineweaver-Burk plot:

Noncompetitive inhibition reduces the apparent Vm.

m = Km ( 1 + [I] ⁄ Ki) ⁄ Vm

c = ( 1 + [I] ⁄ Kis ) ⁄ Vm

Again, the true values of Km and Vm are required for these calculations, and need to be determined from an uninhibited assay.

Upshot: non-competitive inhibitors bind somewhere other than the active site, and these bindings reduce the speed at which the enzyme runs, reducing the apparent Vm. Km is unaffected, because for a non-competitive inhibitor, Ki = Kis, and if you run the maths, this results in no apparent change to Km.

Mixed and uncompetitive inhibitions are also possible, with effects on both Kmand Vm. Although the Lineweaver-Burk plot is a convenient way of calculating the inhibitor parameters, it is prone to errors caused by the undue weighting given to very small concentrations of substrate. Other plots (such as Briggs-Haldane plots) and numerical methods (Levenberg-Marquart non-linear regression) may be more appropriate for critical work.

Enzyme regulation

Metabolism involves the tight integration of many complex pathways. The regulation of these pathways is mostly achieved by the regulation of enzymes. This is particularly important in major metabolic pathways (glycolysis, Krebs, urea cycle, gluconeogenesis, etc.), which impact important (and energetically expensive) pathways. Enzymes are frequently regulated, in contrast to inorganic catalysts, which generally cannot be regulated. Enzymes that are regulated usually stand at crossroads of metabolic pathways, and have a small kcat (they are slow), so they rarely run quickly enough to catalyse their reactions to equilibrium: Q (mass action ratio, [products] ⁄ [reactants] ) ≪ Keq. They often work in pairs, catalysing slightly different reactions in the forwards and backwards directions.

PFK and FBP are important enzymes in glycolysis and gluconeogenesis.

Phosphofructokinase is often claimed to be the gatekeeper to glycolysis: it is the step that (more-or-less) irrevocably commits fructose-6-phosphate to conversion to pyruvate (and hence to Krebs). Although this may be over-egging the pudding, it is certainly highly regulated and requires ATP. Fructose-1,6-bis-phosphatase appears to catalyse the backwards reaction, but this is not quite correct: it converts fructose-1,6-bis-phosphate to fructose-6-phosphate, but by dephosphorylation: it does not regenerate ATP. This two-enzyme system allows glycolysis and gluconeogenesis to be tightly regulated.

The rate at which regulation can be effectively achieved varies greatly, from hours to microseconds. In approximate order of speed, enzymes may be regulated by:

  1. Regulation by genetic expression of enzyme (slowest). There is always competition in a cell between the processes of protein synthesis and protein destruction. By altering these rates, one can alter the whole cell catalytic rate. However, it is rather slow, although proteins with a high turnover rate will respond more quickly.
  2. Compartmentation of substrate and enzyme. Enzymes can also be compartmentalised, like the hydrolytic enzymes found in the lysosome, but the release of these suicide enzymes during apoptosis is rather more of an on/off switch than a true regulation.
  3. Activation of a zymogen. Some enzymes are secreted as inactive precursors, called zymogens. Trypsin and pepsin are two such examples: a portion of the zymogen must be cleaved off to form the active enzyme. Again, an on/off switch more than a tight, variable regulation.
  4. Reversible phosphorylation or adenylation. Enzymes can be phosphorylated on their tyrosine, threonine or serine residues. This is a very common regulatory strategy, and a common end-product of a signal cascade.
  5. Competitive product inhibition and allosteric regulation (fastest). Many enzymes are inhibited by either their products, or by other chemicals, often those from further down a metabolic pathway. Such enzymes may be 'gatekeepers' to a specific branch of metabolism, and they usually catalyse a true equilibrium reaction, i.e. one that doesn't go to completion (note this is not exactly the same reaction in the forward and backwards directions, so we are not defying the law that states enzymes do not alter the equilibrium point).

We will be looking principally at the last three ways.

In negative feedback, the later or final products of a metabolic sequence feed-back negatively on early steps, e.g. in Krebs cycle, the final product of a metabolic sequence feeds-back negatively on early steps.

Negative feedback damps down reactions earlier in a metabolic sequence.

In positive feedforward, earlier reactants in a metabolic sequence feed-forward positively on later steps. If a precursor is accumulating, it makes sense to speed up downstream reactions to use it up, e.g. fructose-1,6-bisphosphate activates pyruvate kinase in glycolysis. A combination of feedback and feedforward is used to regulate enzyme activity.

Positive feedforward turns up reactions later in a metabolic pathway.

Metabolism involves the complex integration of many feedback and feedforward loops.

Integration involves many feedback and feedforward loops.

However, there is a problem here: it is unlikely that D, A and F are similar to B, so they cannot inhibit by simple competition, and how on earth can an inhibitor positively regulate a reaction anyway? So what happens instead?

The regulation of enzymes by metabolites leads to the concept of allosteric regulation. Allosteric means 'other structure'. Allosteric modulators can bind at a site other than the active site in question and cause activation or inhibition. These modulators can include the substrate itself, which binds at another active site in a multi-subunit enzyme. In fact, allosterically modulated enzymes almost always have a complex quaternary structure (multiple subunits) and exhibit non-Michaelis-Menten kinetics.

The enzyme phosphofructokinase (PFK) is regulated by:

Therefore ATP and citrate are allosteric inhibitors; and ADP and AMP are allosteric activators.

Allosteric kinetics are sigmoid: the enzyme becomes more specific at higher substrate concentrations.

Why the sigmoid shape? Allosteric enzymes are multi-subunit enzymes, each with an active site. They show a cooperative response to substrates as well as to modulators, and their affinity for substrate increases with increasing substrate concentration. This means that V increases rapidly over a small range of [S] values, then plateaus off rapidly.

Haemoglobin is a four subunit protein (although it is not an enzyme) that binds oxygen, and is often used as a model for allosteric regulation because it is a good model for cooperation in the binding of multiple ligands. Myoglobin is a closely related monomeric protein. The % saturation with oxygen is equivalent to the saturation of the active site of an enzyme: myoglobin shows normal saturation kinetics; but haemoglobin shows sigmoid kinetics.

Myoglobin shows hyperbolic kinetics, haemoglobin shows sigmoid kinetics.

Binding constant, Kb = [Hb(O2)n+1] ⁄ [Hb(O2)n] [O2].

Equilibrium constant

Equation

Value

Kb1

[Hb(O2)] ⁄ [Hb][O2]

0.024

Kb2

[Hb(O2)2] ⁄ [Hb(O2)][O2]

0.074

Kb3

[Hb(O2)3] ⁄ [Hb(O2)2][O2]

0.083

Kb4

[Hb(O2)4] ⁄ [Hb(O2)3 ][O2]

7.4

O2 molecules bind sequentially to Hb with binding constants Kb1 to Kb4, and you can see that each O2 binds more tightly than the last. The differences in Kb cannot be explained on the basis that each subunit has a different binding constant: if this was the case the subunit with the highest Kb would bind first, in practice it binds last.

Haemoglobin saturation shows sigmoid kinetics w.r.t. oxygen concentration.

Oxygen binds to the most difficult site first. This alters the conformation of the protein so the next subunit binds oxygen more easily. This process is then repeated for the other two subunits. This change in conformation caused by the progressive binding of a ligand is known as cooperativity and leads to sigmoid kinetics. The binding of one ligand (substrate or modulator) changes the conformation of the protein. This can increase or decrease the affinity for further ligands. There are two models for this cooperativity:

Both models recognise that subunits change their conformation and alter the binding constant (Kb) for ligands. The low affinity form is known as tense (T). The high affinity form is relaxed (R), and these exist in equilibrium with each other.

In the sequential model, each binding of substrate increases the affinity of the other active sites.

In the sequential model, each substrate binding event increases the affinity of the other subunits.

In the concerted model, the first binding of substrate increases the affinity of the other active sites, but further bindings have no effect. This doesn't contradict the haemoglobin/oxygen binding constants presented earlier, as the increased affinities at ever increasing oxygen concentrations could be due to the increased proportion of relaxed form, rather than to individual increases in each protein molecule.

In the concerted model, only the first substrate binding event increases the affinity.

The currently accepted model for allosteric inhibitors and activators is based on the concerted model. Inhibitors lock all subunits in the tense form, whereas activators locks all subunits in the relaxed form.

In allosteric inhibition, the inhibitor locks the enzyme in the tense conformation. Binding of substrate (when sufficiently little inhibitor is present) locks the enzyme in the relaxed form.

Allosteric inhibitors lock the enzyme in the tense form.

In allosteric activation, the activator locks the enzyme in the relaxed conformation.

Allosteric activators lock the enzyme in the relaxed state.

There is some vocabulary you should know for cooperativity:

A typical allosteric inhibitor therefore cooperates in a heterotropic, negative fashion.

Phosphorylation is another very common way of regulating enzymes, especially in signalling cascades. It requires ATP. A frequently quoted example is glycogen phosphorylase, an enzyme that phosphorylates glycogen, and is itself most active when phosphorylated. Phosphorylation of glycogen phosphorylase is reversible and controlled by the phosphorylase kinase and a phosphatase. (kinases add phosphate groups to proteins, phosphatases remove them). The phosphorylase kinase is itself regulated by phosphorylation. I hope your brain is not bleeding.

Glycogen phosphorylase is activated by phosphorylation.

The regulation is rather complex:

Glycogen phosphorylase is activated by phosphorylation.

Protein kinases like glycogen-phosphorylase kinase act on specific amino-acid sequences, called consensus sequences. Protein-kinase-a acts on the serine/threonine residue in the sequence X-arg-arg/lys-X-ser/thr-asx. Cyclin-dependent-kinase-2 acts on the same residues in the sequence X-ser/thr-pro-X-lys/arg. Only the alcoholic amino acids serine, threonine and tyrosine can be phosphorylated.

Zymogens are the final way of regulating enzymes we will look at. Zymogens are inactive enzyme precursors. They are activated by external means, and undergo cleavage to produce an active enzyme. Digestive enzymes are mostly regulated in this way, because we don't want them to digest the cell that synthesises them! e.g. Pepsin is activated by H+ in the stomach. Trypsin and chymotrypsin follow a more complex scheme.

Chymotrypsin is activated by covalent modification.

Test yourself

  1. How do enzymes bind their substrates? Suggest a mechanism by which polysaccharides could be bound to lysozyme.
  2. Classify the following as prosthetic groups, coenzymes and metal ions. What do they do?
    • ATP in hexokinase.
    • FeS Riske cluster in ferredoxin.
    • Coenzyme-A in citrate synthase.
    • Haem in haemoglobin.
    • NAD+ in alcohol dehydrogenase.
    • Vanadium (III) in nitrogenase (converts nitrogen to ammonia).
  3. What is meant by 'saturation kinetics'?
  4. Explain the kinetic significance of Km and Vm. What do they mean in practical terms?
  5. If Vm is 30 mM s−1, [E]T is 1 mg L−1, and Mr is 20 kDa, what is kcat?
  6. Diisopropyl phosphofluoridate (DIPF) is an inhibitor of acetylcholine esterase.

    DIPF inhibition.

    What sort of inhibitor is it? What uses could it have?
  7. Acid phosphatase is inhibited by inorganic phosphate.

    Phosphate inhibition of phosphatase.

    What sort of inhibitor is it?
  8. How and why is PFK regulated?
  9. Why is trypsin regulated using the zymogen strategy?

Answers

Bibliography

Peer Review.
This page has been peer reviewed by 2 people. Thanks to Prof Marc Wilkins for his feedback.