Enzymes: Biological Catalysis

Increasing the rate of chemical reactions:

Increase in temp → increase in freq of collisions, forcefulness of collisions → increase in reaction rate

Increasing the rate of chemical reactions:

increase in conc → increase in freq of collisions → increase in reaction rate

Increasing the rate of chemical reactions:

catalyst

• catalyst —substance that accelerates a chemical reaction but is itself unchanged in the process.
• catalyzed reaction has lower activation energy

Increasing the rate of chemical reactions:

enzyme-catalyzed reactions

• don’t proceed at sig rates under physiological conds in absence of enzymes

• enzymes enhance rate of rxns – 10^3-10^20x faster

• affects activation energy for chemical reaction

• speed up both forward and reverse reactions

• enzymes – greek meaning “in yeast” – catalysts present inside cells

• enzymes don’t change position of equilibrium (don’t make thermodynamically non-spontaneous process spontaneous)

General properties of enzymes

high specificity

reaction specificity

coupled reactions

regulated

General properties of enzymes

high specificity

(but variable specificity from enzyme to enzyme) for the reactants (substrates)
• some act on only a single substrate
• some act on a variety of structurally (chemically) related substrates
• stereospecificity – act on only a single stereoisomer

General properties of enzymes

reaction specificity

– generally 100% purity of product – high efficiency (lack of formation of wasteful by-products)
• saves energy
• prevents build-up of potentially toxic metabolic by-products

General properties of enzymes

coupled reactions

– combine, or couple, two reactions that would normally occur separately
• energy gained (released) from one reaction used to drive a second reaction
• coupling the hydrolysis of ATP (to release energy) to second energetically unfavorable reaction

General properties of enzymes

regulated

e.g. phosphorylation/dephosphorylation control of enzyme activity

Rate constant

• at high concentrations of reactants, productive collisions more likely

rate constant

reaction conditions for a chemical rxn require

• collisions between reacting molecules
• collisions with sufficient energy to break the bonds in the reactants
• the breaking of bonds between atoms of the reactants
• the forming of new bonds to give products

Initial velocity

Initial velocity

ES complex – “lock and key”

• enzymes bind substrates transiently – unchanged after reaction (catalyst)
• 1894 – Emil Fischer – proposed that the enzyme is a rigid template (lock) and that the substrate is a matching key
• only specific substrates can fit into a given enzyme
• 1903 - early kinetic studies confirmed that enzyme binds substrate to form enzyme-substrate complex
• ES complexes formed when ligand binds noncovalently in the active site
• substrate reacts transiently with the protein catalyst to form product

• 2 distinct steps:
  1. formation of ES complex
  2. chemical reaction accompanied by dissociation of the product

ES complex – “lock and key”

• overall rate depends on concentrations of enzyme (E) and substrate (S)

• when the amount of enzyme is much less than substrate (substrate [S] is saturating), reaction
  rate has linear dependence on [E]

ES complex – “lock and key”

pseudo first order

• since [S] is saturating (over the course of measurement, conc of S doesn’t limit rxn since all available enzyme binding sites will be occupied, & addition of S has no effect)

• enzyme exists in 2 states, free enzyme, E, and enzyme-substrate complex ES

• if [S] is low, much of enzyme in free form, rate is
  proportional to [S

ES complex – “lock and key”

if [S]>>[E]

• all enzyme will be in ES complex form

• max rate of rxn for enzyme conc & rxn rate can only be increased by increasing amount of ES (which can be increased by increasing [E], maintaining [S]>>[E]

General theory of enzyme action (1913)

• Leonor Michaelis and Maud Menten
• enzyme combines reversibly with substrate to from ES
•ES complex breaks down slower 2nd step to yield free enzyme & rxn product
•slower 2nd reaction limits overall rate of rvn, overall rate of rxn must be proportional to conc of ES
• k1 and k-1 are rate constants governing binding & dissociation of substrate to enzyme
• formation & dissociation of ES complexes are rapid because only non-covalent interactions
• chemical conversion of substrate to product that is rate-limiting (k2 and k-2)

General theory of enzyme action (1913)

enzyme kinetics

• rates dependent on [E]

• in presence of high substrate conc, [S]>>[E], further addition of S will have no effect

• rate of product formation is dependent on [E]

General theory of enzyme action (1913)

slope decreases over time

1) enzyme becomes unstable during rxn
2) degree of saturation of enzyme by substrate decreases as substrate is depleted
3) reverse rxn becomes predominant as product accumulates
4) products of rxn inhibit enzyme
5) any combo of factors above

relationship of reaction velocity and [S]

• plot of initial velocities dependent on [S]

• for most enzymes has shape of rectangular hyperbola recall ligand binding

relationship of reaction velocity and [S]

1. approach to max velocity Vmax as [S] increases & becomes limited by [E] only
2. 0 order (with respect to [S]) at high [S]
3. 1st order (with respect [S]) at low [S]

relationship of reaction velocity and [S]

• curve expressed algebraically by Michaelis Menten equation

• derived from theory of enzyme action & steady- state approx

• where rate-limiting step in enzymatic reactions is
  chemical conversion in ES complex of substrate to product, followed by release of product (P) & generating free enzyme (E)

Michaelis Menten equation

Hill equation

Order of the reaction

Order of the reaction 2

Michaelis-Menten equation, equilibrium model

1) Simple, single step enzymatic reaction
2) assume [S]>[E] (not necessarily saturating), & [S] doesn’t change over time of initial velocity
3) rate limiting step given by k2 (1st order)
4) no chemical changes to substrate in fast reversible substrate binding/dissociation step (formation of ES complex)
5) begin rxn with only enzyme & substrate, consider time frame that deals with initial velocities, contribution of reverse rxn (E + P → S) is negligible

Equations for

Etotal

Es

equilibrium model of the Michaelis-Menten equation with assumptions

1) Simple, single step enzymatic reaction
2) assume [S]>>[E] (but not necessarily saturating) and [S] does not change appreciably over time of initial velocity measurement
3) rate limiting step is given by k2 (1st order); binding and dissociation of substrate to enzyme is relatively fast compared to chemical conversion
4) No chemical changes to substrate takes place in the fast reversible substrate binding/dissociation step (formation of ES complex)
5) begin a reaction with only enzyme and substrate, and consider a time frame that only deals with initial velocities, the contribution of the reverse reaction (E + P → S) is negligible

equilibrium model of the Michaelis-Menten equation with assumptions

Ks

Ks corresponds to substrate conc at ½Vmax (initial velocity directly proportional to binding site occupancy, ½ maximal binding capacity, ½ maximal velocity)

The order of the reaction 𝑣 = 𝑘[𝐴][𝐵] with respect to A is?

0

1

2

3

1

The order of the reaction v=k[B]² with respect to A is?

0

1

2

3

0

The order of the reaction v=k[B]² with respect to B is

0

1

2

3

2

Which enzyme has a higher affinity for substrate?

enzyme 1

enzyme 2

Enzyme 2 because the Ks is lower than Vmax

What is Vo catalyzed by Enzyme 1 at a substrate concentration of 10 mM?

A. 10 μM/min
B. 25 μM/min
C. 50 μM/min
D. 75 μM/min
E. 100 μM/min

C

For the following reaction, why is the term k-2 not included in M-M equation?

A. This reaction never occurs
B. It simplifies the math
C. The M-M equation only
describes the initial reaction rates
D. It is part of the term Ks

C

What statement about enzymes is true?
A. To be effective, they must be present at the same concentrations as reactants
B. They increase the equilibrium constant for the reaction
C. They increase the rate at which substrate is converted to product
D. They are consumed in the reactions that they catalyze

c

What’s the units of Km?

s^-1

g

mol dm^-3

Mol s^-1

mol dm^-3

steady-state kinetics

• G.E. Briggs & Haldane (1925)
• when enzyme mixed with large excess of substrate, there’s initial period where conc of ES builds up
• period of time too short to observe (microseconds)
• reaction quickly reaches steady state where [ES] remains constant
•rate of ES formation = rate of decomposition
• initial velocities, v0 , reflect steady state
• analysis of initial velocities reflect steady state kinetics
• steady-state approx is valid condition for metabolic rxns in cells

steady-state kinetics

Michaelis-Menten equation, steady-state model

1) assume [S]>>[E] (not necessarily saturating) & [S] doesn’t change over time of initial velocity measurement
2) begin rxn with enzyme & substrate, consider time frame deals with initial velocities, contribution of reverse rxn (E + P → S) is negligible
3) rate limiting step is given by kcat (1st order)
4) Apply steady-state approx substrate binding (ES complex formation) fast & reversible & doesn’t involve chemical changes to substrate assumption necessary for equilibrium model but not necessary here:

Formulas

Vo

Etotal

Rate of ES decomposition

Rate of ES formation

Formulas

ES

Km

New Vo

steady-state model of the Michaelis-Menten equation
with assumptions

Vo equation change again

1. [S] remains constant during rxn ([S 0]≈[St]). Using initial velocities & [S 0 ]>[E]total
2. conversion of product back to substrate is negligible
3. steady-state assumption: rate of formation of ES = rate of decomposition of ES

Equilibrium and steady state models (M-M equation)

Rules of Ks and Km

Michaelis constant Km

• substrate conc where Vmax is ½-maximal

• comparing 2 enzymes, 1 with low & 1 with higher Km, enzyme with lower Km will reach max catalytic activity at lower substrate concs

• where k1 (or k-1 ) > k2, Km approx binding affinity of substrate for enzyme (approximately = Ks)

• term that collects rate constants for formation/decomposition of ES complex under steady-state approx

rate-limiting step

What is V max for this enzyme ?
Enzyme concentration 0.1 μM

A. 100 mM/min
B. 1.0 mM/min
C. 0.5 μM/min
D. 50 μM/min
E. 90 μM/min

E

• note that units in A and B are wrong!

What is Km for this enzyme?
Enzyme concentration 0.1 μM

A. 10 μM
B. 1.0 mM
C. 0.5 μM
D. 5 mM
E. 20 mM

B

Km=(1/2)Vmax = 90/2 = 45

What is kcat for this enzyme?
Enzyme concentration 0.1 μM

A. 5.0 x 10^2
B. 1.0/min
C. 5.0 x 10^2/min
D. 9.0 x10^2/min
E. 50/min

D

steady-state vs. equilibrium model

• can determine [E] total & [S]0

• can monitor for prod formation

• not able to detect intermediates (e.g. ES, EP, etc.)

• assumes constant ES complex concs over time & rxn rate limited by 1st order rxn constant

• doesn’t assume which step is limiting rxn rate, thus use of kcat

• doesn’t assume simple single step rxn where binding & release of substrate (ES complex formation) is fast relative to prod formation & release

• cannot give details of individual rxn steps

• provides description of enzyme behavior, but doesn’t describe intermediates

kcat or turnover number

• # of substrates converted to prod in time on 1 enzyme saturated with substrate

• represent single rate constant (simple 1-step case where 1 step is rate limiting) or a combo of several steps that limit reaction rate

• comparing kcat values of diff enzymes is comparison of relative turnover rates

• enzymes with higher kcat “turnover” more substrate into product

• kcat can be calculated if Vmax and enzyme concentration are known

comparing enzymes

• comparing Km’s

• comparing Km’s: lower Km values, then lower conc of substrate needed to reach maximal catalytic activity

• comparing efficiencies of formation of ES complex under steady-state approximation

comparing enzymes

comparing kcat ’s:

• higher kcat values = more turnover per unit of time

• comparing diff (maximal) catalytic efficiencies (when substrate is saturating in conc & all E binding sites are occupied by S)

Vo when S is very small compared to Km

Vo when S is very large compared to Km

Region A

Region B

catalytic proficiencies of some enzymes

• kcat /Km compares diff enzyme activities

• ratio approaches 10^8-10^9 which is limit because of diffusion at physiological conds

• catalytic proficiency expresses increased rxn rate in presence of enzyme

• high catalytic efficiency ([S]>>[E] assumption for M-M kinetics generally true)

Lineweaver Burk equation

fate of glucose in the liver

The structure of XylE bound to D-xylose has an
outward-facing, partly occluded conformation

Homology-based modelling of GLUT1 structure.

Glucose transport 2

Kinetic properties of glucose transporters

GLUT4 activity is regulated by insulin-dependent translocation

• Intracellular pool of GLUT4 in membranous vesicles translocate to the cell membrane when insulin binds to its receptor

• presence of more receptors increases Vmax for glucose uptake (doesn’t affect Km)

• When insulin signal is withdrawn, GLUT4 proteins return to intracellular pool

• GLUT4 is present in muscle & adipose tissue

Fate of glucose in the liver

Hexokinase

Glucokinase

– Phosphoryl group of ATP is transferred to glucose
– Different isoforms – isozymes
• Most have similar affinity for glucose
• Glucokinase – has high affinity for glucose
– Most isozymes are product – inhibited
– Glucose – 6 – P is trapped in cytosol

Glucokinase vs. Hexokinase

apparent Km

• only in simple, single step situations where binding/dissociation of substrate to enzyme is fast relative to 2nd single catalytic step with rapid product release will Km ≈ Ks

• Km combines all rate constants

• treated as apparent dissociation constant that assumes reaction satisfies assumptions of equilibrium model

• may be treated as dissociation constant for all enzyme-bound species

• substrate binding equilibrium (Ks) is only 1 component of Km

• similarly for kcat , combo of all individual rate constants involved in rate-limiting the reaction, & referred as apparent kcat

• Km is always Vo = Vmax /2

enzyme inhibitor

• binds to an enzyme & interferes with its activity

• prevent formation of ES complex, or block chemical reaction that leads to product formation for reversible inhibitors

non-covalent interactions
reversible inhibition, 3 basic types

competitive inhibition
uncompetitive inhibition
noncompetitive (mixed inhibition)

competitive inhibition

• binding of inhibitor prevents binding of substrate

• inhibitor binds only to free enzyme

• when an inhibitor is bound, substrate cannot bind,

• when substrate bound (ES complex formation) inhibitor cannot bind

• S and I are in competition for binding to free enzyme

• more common type

competitive inhibition 2

• keep [E] fixed & vary concs of S and I

• rate of formation of ES dependent on [S]: rate = k1 [E][S]

• rate of formation of EI will be dependent on [I]: rate = ki1 [E][I]

• if [S] is increased, more ES will form, reducing amount of EI

• high [S], can still saturate E and achieve max
  velocity (Vmax)

• presence of inhibitor causes need for more substrate to achieve same initial velocity

• more substrate needed to form ES

• competitive inhibitors raise Km but don’t change Vmax

• Ki is true equilibrium constant if EI is dead end & can only break down by returning to E & I

uncompetitive inhibition

• bind only to ES, not to free enzyme

• if add more substrate, cannot change amount of ESI

• ESI formation dependent on ES

• presence of inhibitor will reduce amount of ES complex & reduce rate

• when susbtrate is saturating (all substrate-binding sites on E are occupied) there will be less active ES complex

• lower Vmax

uncompetitive inhibition 2

• presence of I decrease concentration of ES

• will shift the equilibrium for ES formation to the forward direction

• for the same amount of S, more ES will be formed in the presence of inhibitor because of shift in equilibrium

• will “appear” to increase affinity of E for S

• uncompetitive inhibitors decrease the Km

• ratio of Km /Vmax remains unchanged

noncompetitive (mixed) inhibition

• can bind to E or ES, leading to formation of EI or ESI complexes

• S can bind to E or EI

• apparent decrease in Vmax with no change in Km

noncompetitive (mixed) inhibition 2

• presence of I leads to less ES in for a given [S]

• leading to lower maximum velocity

• because S can bind to either E or EI, no apparent change in affinity as reflected in no change in Km

• most cases of noncompetitive inhibition are actually mixed inhibition where binding of S to EI is affected compared to binding to S

• both Km and Vmax affected

stop

irreversible enzyme inhibitors

• form stable covalent bond with enzyme

• decreases pop of active enzyme

irreversible enzyme inhibitors

allosteric enzymes

doesnt really have a title

• affected by changes in structure mediated by interaction with small molecule regulators

• allosteric protein

• e.g. binding of oxygen to haemoglobin

• don’t exhibit typical M-M kinetics due to cooperative substrate binding

• sigmoidal curve for initial velocities results from transition between T state and R state

• when n=1 (no cooperativity) same as M-M

• greater than 1 indicates positive cooperativity less than 1 indicates negative cooperativity

• n does not represent # binding sites (but cannot exceed the number of binding sites)

allostery

binding of allosteric effector to distinct site that doesn’t overlap normal binding site of substrate, product or transported molecule

allosteric protein

active state: R state, and inactive state: T state (interconvert)

allosteric inhibitor

• binds best to T state at its allosteric site on the protein; stabilizing the T state (inactivity)

• binding of substrate to active site, or allosteric activator to its allosteric site required to dissociate allosteric inhibitor and allow stabilization of R state (active)

allostery and haemoglobin

• In R state (active, or high oxygen binding, oxyhaemoglobin) 2,3 BPG binding site is too small to accommodate allosteric effector

• 2,3 BPG lowers affinity of haemoglobin for oxygen (T state, deoxyhaemoglobin)

• allosteric effector function of 2,3 BPG is necessary to lower binding of oxygen to haemoglobin in tissues to allow for oxygen release

allostery and regulation of enzymatic activity

• glycolysis

• phosphoenolypyruvate (intermediate near end of glycolysis pathway) is an allosteric inhibitor of E. coli phosphofructokinase-1

• if glycolysis pathway is blocked, phosphoenolpyruvate will accumulate and allosterically inhibit phosphofructokinase-1 and shut down production of phosphoenolpyruvate

allostery and regulation of enzymatic activity 2

• ADP allosterically activates phosphofructokinase -1

• overall pathway of glycolysis results in net synthesis of ATP from ADP

• high levels of ADP indicate a need for ATP synthesis, and ADP binds to phosphofructokinase-1 and activates it, turning on the glycolysis pathway

general properties of allosteric enzymes

1. activities of allosteric enzymes are changed by metabolic inhibitors and activators

2. allosteric modulators bind noncovalently to the enzmes/proteins they regulate

3. almost always mutisubunit proteins

4. usually a sigmoidal curve for initial velocity vs. [S] for at least one substrate

general properties of allosteric enzymes

1

1. activities are changed by metabolic inhibitors and activators
- often do not resemble substrates or products

general properties of allosteric enzymes

2

2. allosteric modulators bind noncovalently to enzmes/proteins they regulate
- modulators aren’t altered chemically by enzyme

general properties of allosteric enzymes

3

3. almost always mutisubunit proteins
- not all multisubunit proteins are allosterically regulated

general properties of allosteric enzymes

4

4. usually a sigmoidal curve for initial velocity vs. [S] for at least one substrate
- cooperativity of substrate binding

cooperativity of substrate binding

• addition of allosteric activator lowers Km^app and produces a hyperbolic curve

• addition of allosteric inhibitor raises Km^app

cooperativity of substrate binding 2

• equilibrium between T and R states for enzyme

• equilibrium can be shifted by addition of allosteric regulators or presence of substrate

The graph shows an enzyme-catalyzed reaction without an
inhibitor (control) and with two increasing concentrations of inhibitor (I). Which of the following is true?
A.The inhibitor is a positive modulator.
B. The inhibitor and substrate bind to the same site.
C. The inhibitor causes a drastic reduction in Vmax.
D.The inhibitor binds to the substrate.

b

Explanation:
The graph is typical for competitive inhibition. Here, the
substrate and inhibitor compete for the active site and are
often structural analogs (similar in molecular structure).