kinetics tutorial

7/29/2019 Kinetics tutorial

1/14

1

Biochemistry 230

Receptor Binding

Tracy Handel

[email protected]

3246 PSB

Oct 28, 2008 Receptors have two major properties: Binding and Transduction

Binding: To a first approximation, obeys laws of thermodynamics.

Typically stereoselective, saturable, reversible.

Transduction: The second property of a receptor is that the binding of

an agonist must be transduced into some kind of functional response

(biological or physiological).

Different receptor types are linked to effector systems either directly or

through simple or more-complex intermediate signal amplification

systems. Some examples are:

Ligand-gated ion channels nicotinic Ach receptorsSingle-transmembrane receptors RTKs like insulin or EGF receptors7-transmembrane GPCRs opioid receptors

Soluble steroid hormones estrogen receptor

Drews, J. Drug discovery:A historical perspective. Science287(2000)1960-1964.

Drug Receptors

Basic Binding Equilibrium Plotting methods Competitive and non-competitive

relationships

Agonism and Antagonism Receptor Theory

Spare receptors


2/14

2

kon = # of binding events/time (Rate of association) =[ligand] [receptor] kon = M

-1 min-1

koff= # of dissociation events/time (Rate ofdissociation) = [ligand receptor] koff= min

-1

Binding occurs when ligand and receptor collide withthe proper orientation and energy.

Interaction is reversible. Rate of formation [L] + [R] or dissociation [LR]

depends solely on the number of receptors, the

concentration of ligand, and the rate constants konand koff.

kon/k1

[ligand] + [receptor] [ligand receptor]

koff/k2

Basic Binding Equilibrium

At equilibrium, the rate of formation equals that ofdissociation so that:

[L] [R] kon = [LR] koff

KD = koff/kon = [L][R]

[LR]*this ratio is the equilibrium dissociation constant or KD.

G= -RTlnK

Basic Binding Equilibrium

KD is expressed in molar units (M/L) and expresses theaffinity of a drug for a particular receptor.KD is an inverse measure of receptor affinity.KD = [L] which produces 50% receptor occupancy

BasIC Binding Equation

P + L P-Lkon

koff

Kd=

[P][L]

[PL]

[P]o= [P]+ [PL]

[P]o [PL]= [P]

[PL]=[P]o[L]o

[L]o +Kd

Kd= [L]

o

[P]

[PL]

If [L]o >> [P]o , [L]o = [L]

Kd=L

o

Po[ ] PL[ ][ ][ ]PL[ ]

=

LoPo[ ]

PL[ ]

Lo

[PL]

[P]o

=

[L]o

[L]o+K

d

Fraction Bound Protein =

[PL]

[P]o

Know this

Know thismeasure this

Calculate this


3/14

3

Receptor Fractional Occupancy (F.O)

F.O. =

Use the following numbers:

[L] = KD= 50% F.O.

[L] = 0.5 KD = 33% F.O.

[L] = 10x KD = 90.9%+ F.O.

[L] = 0= 0% F.O.

100

50

0

Ligand Concentration

FractionalOccupancy

[PL]

[P]o=

[L]o

[L]o +Kd

The amount of drug bound at any time issolely determined by:

the number of receptors the concentration of ligand added the affinity of the drug for its receptor.

Binding of drug to receptor is essentially the same asdrug to enzyme as defined by theMichelis-Menten

equation.

BINDING VS KINETIC EQUATIONS

[PL]

[P]o

[L]o

Nonlinear Plots

Kd

[PL]

[P]o

[L]o

Semilog Plots

0 5 100

0.5

1

1010.1

Kd

0

0.5

1

Can compare Ligands

with Many log differences

in affinity on SemiLog Plots

1/[PL]/[Po]

1/[L]

-1/Kd

Double Reciprocal Plot (linearization)

[PL]

[P]o

=

[L]o

[L]o+K

dLike

Lineweaver-Burke Plot for

Enzyme Kinetics!


4/14

4

Classical Scatchard Plot (Another Linearization)

Kd =

[P][L]

[PL]

[PL] =[P][L]

Kd

=

[P]o [PL]( )[L]K

d

[PL]

[L]=

[P]o

Kd

[PL]

Kd

[PL]

[L]

[PL]

Bound

Free

Bound

1

Kd

Scatchard with n Independent, Equivalent Binding Sites

[PL]

[P]o= n

[L]

[L]+Kd

[PL]/[P]o

[L]=

n

Kd

[PL]/[P]o

Kd

# of sites

[PL]/[P]o

[L]

[PL]/[P]o

1

Kd

n

fraction bound

free

fraction bound

Multiple Site Binding Models

P + 2L P-L2

[PL2]

[P]o

[L]o

Both Sites

First Site (High Affinity)

Second Site (Low Affinity)

Independent, nonequivalent binding sites

Bound

Free

Free

Both Sites

Nonlinearity in the Scatchard plot is also observed withmixture of different receptor subtypes

Biphasic scatchard plot seenwhen Kds for two sites differ by10-fold or more

Cooperativity in Ligand Binding

P + nL P-LnKd

Y =[L]

n

[L]n+Kd

n = 1: noncooperativity

n < 1: negative cooperativity

n > 1: positive cooperativity

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

Nonlinear Plot

N = 2

N = 1

N = 0.5

Y

SemiLog Plot

Y


5/14

5

Receptor occupancy =[RL]

[Rtotal]

[L]

[L] + K=

Ligand concentration

Cant Always Measure Direct Binding When Studying Receptors.

Often Measure Some Response that is a Function of Agonist

Binding to Receptor. Efficacy term Defines Response with Binding

/max

[L]Receptor response =

[]

[max] [L] + K=

= 1 for simplicityfor now

DERIVATION OF COMPETITIVE INHIBITION

Competitive Inhibition

I BINDS AT SAME SPOT AS L

[RL]

[Rtotal]=

[L]

[L] + K[I]

KI1 +

[L]

[L] +K=

Max Bound/Max Response unchanged. Can always overcome inhibition

with more agonistPARALLEL SHIFTS

/max =

K K K

0 = [I] < [I] < [I]

/max

1/[L]

-1/Kd

Double Reciprocal Plot of Competitive Inhibition

-I

+I

-1/K

[PL]/[Po]

/max

1

1


6/14

6

The Schild plot

Linearization of Competitive Binding Data

[I]

KI[A] = [A] 1 +

[I]

KI= 1 +

[A]

[A]= Dose ratio = K

Dose ratio 1 = [I] / KI

log(Dose ratio - 1) = log([I]) log(KI)

y = x - b

A and A: concentration of

agonist in the absence and

presence of I, respectively

required to get

the same response /max

K

When Does ratio =2 then I= Ki (because log 1=0)

[A] [A] [A]

/max

The Schild plot

log(doseratio1)

-log([I])

-log(KI)

Noncompetititve Inhibition

Inhibitor binds at different site

than agonist, does not affect Kd,

but LRI and RI are non-functional

so reduces /max. Binding of agonist

and inhibitor dont affect each other

0 = [I] < [I] < [I] < [I]

Kd

/max

max

' = 1

1+[I]

Ki

max

= 1

1+[I]

Ki

[L]

[L]+KD

when [I]=Ki

max

= 0.5


7/14

7

[PL]/[Po]

1/[L]

-1/Kd

Double Reciprocal Plot of NonCompetitive Inhibition

-I

+I

/max

1

1

Competitive antagonists

.

Bind to the same site as theendogenous ligand or agonist.

Can be over come! Their presence produces a right-ward

shift in both the binding and dose-response curves.

No change in max. Similar dose-response curve shapes

indicates the presence of a

competitive agonist (competing forthe same binding sites).

A = agonist aloneB = antagonist (one concentration)

A+B = agonist + antagonist

surmountableKi

Kd response

Non-competitive antagonis

Does not prevent formation of the DRcomplex, but impairs the conformation

change which triggers a response.

Bind to a site different than the agonistbinding site

Cannot be overcome by adding moreagonist

max is reduced but EC50 (Kd) remains thesame.

Dose-response curves will havedifferent shapes indicating different

binding sites.

response

Ki Ki

Kd

Kd


8/14

8

Not every ligand is radiolabeledWhatto do?????

Some Practical Issues

Competition binding assays

Allows one to determine a rough estimate of anunlabeled ligands affinity for a receptor.

Introduction into the incubation mixture of a non-radioactive drug (e.g. drug B) that also binds to R will

result in less of R being available for binding with D*,

thus reducing the amount of [D*R] that forms. This

second drug essentially competes with D* foroccupation of R. Increasing concentrations of B result

in decreasing amounts of [D * R] being formed.

Method: Single concentration of labeled ligand Multiple (log-scale) concentrations of the unlabeled/

competing ligand.

Competition binding assays The concentration of inhibitor which displaces 50% of the

radiolabeled ligand is known as the IC50for that drug.

IC50 cannot be viewed as the KD of the inhibitor because it isjust an estimate.

Ki = the equilibrium inhibitor dissociation constant. It is the concentration of the competing ligand that would

bind to 50% of sites in the absence of the radioligand.

Ki can only be determined after the IC50 is known. Uses the equation of Cheng and Prusoff.

Ki

= IC50

1 + [radiolabeled ligand]

Kd (radiolabeled ligand)

Example: Find Ki of morphine in a preparation with3H-diprenorphine.

IC50

= 100 nM Ki= 25 nM

[L] = 3 nM (labeled)KD = 1 nM (of labeled L)


9/14

9

Drug dose-effect relationships

(Receptor=Effector)Drug

ReceptorDrug Effector2nd Messenger

Examples:

Enzymes observed effect: enzyme activity Ion channels observed effect: ion conductivity

Examples:

Enzymes observed effect: some physiological / clinicalreadout (acetylsalicylic acid / cyclo-oxygenase / pain relief)

Alpha-adrenergic receptor IP3 Ca++ increasedmuscle contraction

Drug dose-effect relationships

Receptor = effector

Occupancy

Effect

log [Drug]

Receptor

occupancy

(%)

Observed

effect (%)

Downstream Receptor Activation: What Can Measure Upon

GPCR Activation

GTPS binding (the most direct measure of GPCR activation;

detect with radioactive GTP35S) non-hydrolyzeable analogue

cAMP Levels (Direct Detection, or couple to a reporter gene

(GFP) linked through CREB)

Calcium Flux (detect with Calcium Sensitive Dyes)

Phosphorylation of Proteins (detect with Antibodies)

Production of New Proteins (detect with Antibodies)

Internalization of Receptor (visualize with GFP-fusions)

Migration......other


10/14

10

( )[ ][ ]

[ ][ ]

+=

==

LK

Lf

R

LRfSf

Dt

max

The Response of a Receptor Involves an Occupation Term and

an Efficacy Term Affinity: The tenacity by which a drug binds to its

receptor.

Efficacy: Relative maximal effect of a drug Full agonist = 1 (*equal to the endogenous

ligand)

Antagonist = 0 Partial agonist = 0~1 (*produces less than the

maximal response, but with maximal binding to

receptors.)

Potency: ability of a drug to cause a measuredfunctional change. Related to affinity but related tofunctional readout rather than binding.

DEFINITIONS

Agonist alone

antagonist or

inverse agonist

alone

Log10 [Ligand]

/max

Definitions: Agonist, Inverse Agonist, Antagonist

Response of a Receptor with No Basal Activity

Definitions: Constitutively Active Receptors

Simple Two State Model of Receptor Activation. The bottom shows aconstitutively active receptor

R R* response

R R* response

L + R LR* response

A lot of mutations dispersed throughout receptors cause increased constitutiveactivity

Most GPCRs have some basal activity


11/14

11

Definitions: Constitutive Activity, Agonist Inverse Agonist, Antagonist

Full

agonist

alone

Inverse

agonist

antagonist alone

Log10 [Ligand]

/max

constitutive

activity

of receptor

alone

Response of a Receptor with Constitutive Activity

Definitions

Drug potency and efficacy

log [Drug]

Observedeffect

Efficacy:

effect at

saturating

concentration

potency: 1 / EC50EC50

Red more Potent than Blue, Blue has higher efficacy

( )[ ][ ]

[ ][ ]

+=

==

LK

Lf

R

LRfSf

Dt

max

67

Need to Understand the Physical Basis for Efficacy

Effector

enzymes

channels

. . .

Odorants,

Tastes

Generic GPCR Signaling

Small Molecules

Peptides

Nucleosides, nucleotides

Amino acids, amines, Ach

Lipid derived (PGs, LTs,LPA, S1P, ...)

Proteins

TSH, LH, FSH, hCG

Thrombin

VIP, Glucagon, PTH

C5a, chemokines

Adapted from Bockaert J & Pin JP

EMBO J18:1723-29 [1999]

G-protein

Response: All kinds of changes in the cell


12/14

12

Structure of rhodopsin (top, in the

membrane) and the approximate

orientation of a heterotrimeric G

protein (bottom). The subunits are

highligted as follows: G (purple),

GDP (red), G (green), G

(yellow).

Coupling of a GPCR to Heterotrimeric G Proteins: A

Docked Model Based on Rhodopsin Structure and a G protein Complex

DRYBox is on IC Loop 2*

*

Extracellular View of Helices

in Rhodopsin (based on structure)

Extracellular View of -adrenergic rece

with bound epinephrine/adrenaline(cartoon from Gomperts text on Signal Transduction)

Proposed Conformational Changes Upon Agonist Binding

Ligand Binding on EC side

causes inward movement

of helices on EC side

and outward movement on

IC side

Data suggest that

TM VI and VII move

away from TMIII, opening

up IC side of GPCR and

exposing the DRY box

to G proteins

View from IC side

Flourescent Label Here

Why??


13/14

13

Effect of Agonists and Partial Agonists on 2AR

Fluorescence Intensity (Conformation) and GTP S

binding (Activation)

Detection of a ConformationalTransition that Tracks with Activation

Efficacy:

ISO & EPI: full agonists

SAL & DOB: partial agonists

Alprenolol is an antagonis

Swaminath JBC 2004

Sequential Binding...

biphasic: fast and slow;

slow dependent on

presence of chiral -

hydroxy

Conformational Changes in B2AR detected by Fluorescence

biphasic: slow dependent

on chirality of-hydroxy

Nepi: full

Dop: partial

Swaminath JBC 2004

Sequential Binding...

Conformational Changes in B2AR detected by Fluorescence

biphasic: slow dependent

on presence of chiral -

hydroxy; magnitude and

rate dependent on alkyl

substituent

fast rate dependent on

catechol hydroxyls

Cat: weak partial ag

Dop: partial ag

Funtionally, slower conformational changes ~~ correlate with

efficient agonist induced receptor activation/internalization

G-protein activation &

internalization

G-protein activation

G-protein activation &

small internalization


14/14

14

Agonist binding to B2AR

Lock and Key Model: Bindi

Preformed Site

Sequential Binding Model

Different Conformations and

Rates of Conformational

Change Influence Signaling

Response

all have

same

Kd

Kd ~ 100-fold

lower

Understanding Efficacy in B2AR

( )[ ][ ]

[ ][ ]

+=

==

LK

LfR

LRfSf

Dt

max

kinetics tutorial

Documents