Chapter 10 Enzyme Kinetics, Inhibition, and Control

1st order reaction

A→P

rate: v = k[A]

units: M/s

2nd order reaction

2A→P

• v=k[A]² in M/s

A+B→P

• v=k[A][B] in M/s

Pseudo 1st order

A+B→P when [B] » [A]

• appears first order with respect to substrate A

when [A] » [B}

• appears first order with respect to B

elementary kinetics

simple, 1 step

descriptions of each elementary reaction collectively constitute the mechanistic description of the overall process

reaction order indicates

the number of molecules participating in an elementary reaction

At constant T, the rate of an elementary rxn is proportional to

frequency at which reacting molecules collide

plot of first-order rate equation

ln [A] = -kt + ln[A]_o

half life of first order rate equation

t_1/2= 0.693/k

plot of second order rate equation

1/[A] = kt + 1/[A]_o

half life of second-order rate

t_1/2= 1/k[A]_o

General chemical equation for a simple enzyme-catalyzed reaction

steady state assumption

rate of ES formation equals rate of ES breakdown

keeps [ES] effectively constant

NOT equilibrium

substrate concentration drops and product concentration rises, but [ES] and free [E] remain ~constant

What happens to reaction kinetics when [S] is much larger than [E]?

when substrate concentration is much greater than total enzyme concentration, the enzyme becomes completely saturated with substrate

makes the reaction zero-order with respect to substrate b/c [S] is no longer limiting the rate

what is the rate limiting step when all enzyme is bound as ES? What is the formula for V_max?

when all enzyme is bound as ES, the breakdown of ES into product via k₂ is rate limiting

v_max = k₂[E]_T

pseudo-first-order process dependent on total enzyme concentration

Michaelis-Menten Equation

tells you how fast an enzyme will work based on the substrate you feed it

when you plot velocity vs substrate concentration, it curves upward into a rectangular parabola, flattening at V_max due to saturation

What is K_M?

Michaelis constant

the exact [S] needed to reach ½ of V_max

A low K_M means the enzyme reaches max speed with _____ substrate

little substrate

enzyme has high affinity, grabs substrate tightly

A high K_M means the enzyme reaches max speed with ____ substrate

high substrate concentration

enzyme has low affinity, it holds loosely

K_M is unique for every specific enzyme-substrate pair, but it changes is you…

alter temperature or pH

catalytic constant

k_cat

turnover number!

represents the maximum number of reaction processes that each active site can catalyze per unit of time when enzyme is fully saturate

an intrinsic constant for a given enzyme

catalytic efficiency

k_cat/K_M

measure of efficiency and specificity at low [S]

Low [S] Behavior

[S] « K_M → little ES complex forms → almost all E is in free form

under these conditions, v_o = (k_cat/K_M) [E]_T[S]

Lineweaver-Burk Plot

linearizes kinetic data

X-intercept Lineweaver-Burk plot

-1/K_M

Why does high [S] matter for reliability?

high [S] gives reliable data and accurate K_M values

Low [S] creates tiny v_o readings; when converted into reciprocals for a Lineweaver-Burk plot, tiny experimental errors get heavily magnified

what is considered catalytically perfect?

k_cat/K_M = x 10⁸-10⁹ M^-1s^-1

can steady state kinetics determine reaction mechanism?

No, but it can be used to eliminate proposed mechanisms

Steady state kinetics are incapable of revealing enzyme intermediates

reactions involving 2 substrates and yielding 2 products account for

~60% of known biochemical reactions

most are transfer reactions

also redox reactions in which reducing equivalents are transferred between 2 substrates

Redox examples of bisubstrate reactions

1. Hydrolysis of peptide bond by trypsin = transfer of peptide carbonyl group from peptide N to H₂O

2. Hydride ion is formally transferred from ethanol to NAD⁺ using alcohol dehydrogenase

   

sequential reactions can be

ordered: compulsory order of substrate addition to enzyme

random: no preferential order of substrate addition to enzyme

ordered bisubstrate reaction

substrates are designated by the letters A and B in the order that they add to the enzyme

products are designated by P and Q in the order that they leave the enzyme

random bisubstrate reaction

some dehydrogenases and kinases operate randomly

sequential reactions with no preference for the order of substrate addition

ping pong reaction

double-displacement

group transfer reaction in which 1+ products are released before all substrate have been added

chemical X changes hands twice:

1. it is displaced off substrate A and onto the enzyme

2. it is then displaced off the enzyme and onto substrate B

enzyme inhibitor

something that decreases enzyme activity

enzyme inactivator

irreversibly inhibits enzyme

permanently blocks

competitive inhibition

inhibitor competes with substrate

reduces the amount of free enzyme available for substrate to bind to

modified MM equation for competitive inhibition

α = 1 + [I]/K_I

What is α?

the factor by which you have to increase your substrate concentration to overcome the inhibitor

α = 1 + [I]/K_I

In competitive inhibition, I makes K_M appear

larger

decreases affinity for S

increases K_M^app

takes a much higher substrate concentration to reach 1/2V_max

K_I

equilibrium constant with the inhibitor

a lower K_I means a tighter, more powerful inhibitor

How does competitive inhibition impact V_max

V_max is unchanged

if you dumb enough substrate in, you can still get to max velocity

Alcohol dehydrogenase breaks down methanol in the body into toxic byproducts. Thus, ethanol is given as…

a competitive inhibitor because it competes for the same active site

saves the patient by blocking the toxic buildup

uncompetitive inhibition

inhibitor competes with ES complex

inhibitor binds directly to the enzyme-substrate complex but not to the free enzyme

makes the E appear inactive

uncompetitive inhibition makes V_max appear

makes V_max appear smaller

uncompetitive inhibition makes K_M appear

makes K_M appear lower

mixed inhibition

inhibitor binds to both enzymes and ES complex

bind to a site distinct from the substrate

mixed (noncompetitive) inhibition does what to V_max apparent

mixed/noncompetitive inhibition decreases V_max apparent

modified Michaelis-Menten equation for mixed inhibitor (noncompetitive)

α (affecting K_M)

α’ (affecting V_max)

mixed/noncompetitive inhibition does what to K_M

may increase or decrease K_M^app

Apparent K_M in mixed/noncompetitive inhibition goes down when…

inhibitor binds more tightly to the ES complex than to the free enzyme

K^’_I < K_I

K_M apparent in mixed/noncompetitive inhibition stays the same when

the inhibitor has equal affinity for both

α = α’ & K_I = K’_I

V_max still drops though in pure non-competitive inhibition

Apparent K_M in mixed/noncompetitive inhibition goes up when…

inhibitor binds more tightly to the free enzyme (E) than to the ES complex

K_I < K’_I

On a Lineweaver-Burke plot, uncompetitive enzyme inhibition appears

as parallel lines with the same slope

adding more S does not reverse effect of uncompetitive inhibitor because binding of substrate does not interfere with binding of uncompetitive inhibitor

pure noncompetitive inhibition

binds to both E and ES with equal affinity

Succinate vs malonate with succinate dehydrogenase

Succinate dehydrogenase = citric acid cycle enzyme that converts succinate to fumarate

competitively inhibited by malonate, which resembles structure of succinate, but cannot be dehydrogenated

Oseltamivir (Tamiflu) is hydrolyzed in the liver to yield oseltamivir carboxylate which is a _____ inhibitor of influenza neuraminidase

competitive inhibitor of influenza neuraminidase

Why are TS analogs typically effective inhibitors?

TS analog = stable substance that geometrically and electronically resembles TS of reaction

typically effective because catalysis often relies on enzyme’s ability to bind to and stabilize its reaction TS

Adenosine deaminase

converts nucleoside adenosine to inosine

inosine is the TS analog inhibitor

Mixed inhibition: α > α’

inhibitor binds more tightly to free enzyme than ES

K_I < K’_I

the lines intersect in quadrant II

behavior more similar to competitive inhibitor, K_M increases, V_max drops

Mixed inhibition: α’ > α

inhibitor binds more tightly to the ES complex than free enzyme

K’_I < K_I

lines intersect in quadrant III

leans towards uncompetitive behavior, meaning the apparent K_M actually decreases with dropping V_max

(Pure) Noncompetitive inhibition: α = α’

inhibitor has equal affinity for both free enzyme and ES complex

K_I = K’_I

lines all converge on x-axis at -1/K_M (does not change!)

y-intercepts go up, meaning V_max apparent drops

Why does pure noncompetitive inhibition mirror irreversible inhibitor/inactivator?

it effectively just reduces the amount of active enzyme floating in beaker

y-intercept in mixed inhibition (Lineweaver Burke)

always moves up as you increase inhibitor concentration because V_max always drops in mixed inhibition

Enzyme control

need to coordinate activities

can control

• enzyme concentration: balance between synthesis and degradation

• enzyme activity: allosteric control

Allosteric control

something binds somewhere other than active site, affects binding at another site

ex: feedback inhibition

Aspartate transcarbamoylase (ATCase) catalyzes: carbamoyl phosphate + aspartate → N-carbamoyl aspartate

an example of allostery and feedback inhibition

first step in pyrimidine biosynthesis

ATCase reaction is allosteric thus the graph is

sigmoidal (S-shaped) — demonstrates cooperative binding

Allosteric effectors in ATCase binding

CTP = allosteric inhibitor; binds to the T-state, shifts curve right, makes enzyme less eager to bind aspartate

ATP = allosteric activator; shifts curve to the left, stimulating the enzyme

CTP inhibits ATCase early…

this helps balance cellular nucleotides:

• high ATP stimulates ATCase to make more pyrimidines

• high CTP inhibits ATCase and shifts cell toward purine synthesis

T-state vs R-state of ATCase

ATCase = large heterododecamer made of catalytic and regulatory subunits (2c₃r₃)

T-state: tense, low-activity, tightly bound conformation favored when CTP is bound

R-state: relaxed; high-activity conformation favored when substrates or ATP (allosteric activator) are bound — opens up structure

How does PALA help demonstrate ATCase’s conformational change from T→R

PALA = bisubstrate analog that mimics both ATCase’s substrates stuck together

Because it cannot be chemically converted into product, it acts as a powerful, tight-binding competitive inhibitor that locks enzyme into place

PALA binds tightly to the R-state but it does not bind to the T-state

Binding of PALA to enzyme induces a conformational change that swings 2 domains together such that…

their 2 bound substrates can react to form product

2 main models of allostery

symmetry model

sequential model

symmetry model of allosterism

ligand binds more tightly to the R state than to T, ligand binding with promote the T→R shift

this increases the affinity of the unliganded subunits for the ligand

simultaneous transition, all-or-none (all R or all T)

pre-existing T←→R equilibrium shifted by differential ligand binding

sequential model of allosterism

conformational changes occur sequentially as more ligand-binding sites are occupied

localized conformational shift alters the shape and increases ligand affinity of adjacent subunits through domino effect

allows hybrid T and R subunits

ligand-induced shape change propagates locally to neighbors

In eukaryotes, the most common covalent modification is

phosphorylation and dephosphorylation of the hydroxyl group on Ser, Thr, or Tyr residues

Glycogen phosphorylase catalyzes the…

phosphorolysis of glycogen

the rate limiting step of glycogenolysis

Primary way to switch glycogen phosphorylase from inactive (T) to active (R) is by

attaching a phosphate group to a specific amino acid (Ser14)

using phosphorylase kinase to stick P onto glycogen phosphorylase using ATP (pushes to R state)

phosphoprotein phosphatase removes that phosphate group, turning it back off

Glycogen phosphorylase a vs b

Phosphorylase b: less active (dephosphorylated)

• naturally prefers T form

• it can be nudged into action by AMP (allosteric activator signaling low energy) or shut down by ATP and G6P (allosteric inactivators signaling plenty of energy)

Phosphorylase a: phosphorylated/active

• P group and favors R form

• flood of glucose can act as an inhibitor, forcing it back to T-form to tell the cell, “there is enough glucose, stop breaking down glycogen!”