binding of ligands to a macromolecule ligand binding.pdf · binding of ligands to a macromolecule...

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Binding of ligands to a macromolecule

“The secret of life is molecular recognition; the

ability of one molecule to "recognize" another through

weak bonding interactions.”

Linus Pauling

Binding of dioxygen to hemoglobin

Complex of the HIV protease the inhibitor SD146(drugs)

Binding of ligands to a macromolecule

• General description of ligand binding

– the esssentials

– thermodynamics

– Adair equation

• Simple equilibrium binding

– stoichiometric titration

– equilibrium binding/dissociation constant

• Complex equilibrium binding

– cooperativity

– Scatchard plot and Hill Plot

– MWC and KNF model for cooperative binding

Binding Basics

Imagine a simple binding reaction between a protein P and a ligand A:

The association constant KA is

PAAP AP

PAKA

and the dissociation constant KD is

.

Rearranging equation (1), we see that APKPA A

A

D KPA

APK

1

2

Let ν represent the moles of bound ligand per mole of protein:

[P] and [A] represent unbound protein and ligand respectively

[P]total and [A]total represent the total protein and ligand in the system

PAP

PA

P

PA

total

AKAPKPA AA

AK

AK

APKP

APK

PAP

PA

A

A

A

A

1

AK

A

D

In many experimental procedures you measure ν and [A] at a range of ligand concentrations, which allows you to estimate KD (and from it, ΔG0

binding)

[A] is the concentration of unbound ligand, which is not the same as [A]total.

Certain binding experiments involve measuring the concentration of boundligand ([PA]) instead.

In this case, you can easily calculate [A]:

AK

A

D

[A] = [A]total – [PA]

It may also be that [A] ≈ [A]total. This is true when [A] >> [P].

• Biological systems can be usually described as having constant pressure P and constant temperature T

– the system is free to exchange heat with the surrounding to remain at a constant temperature

– it can expand or contract in volume to remain at atmospheric pressure

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

[A] (uM)

AK

A

D

A

D KPA

APK

1

1. KD is a concentration and has units of mol per liter

2. KD gives the concentration of ligand that saturates 50% of the

sites (when the total site concentration is much lower than KD)

3. Almost all binding sites are saturated if the ligand concentration is

10 x KD

4. The dissociation constant KD is related to Gibbs free energy ∆G

by the relation ∆G = - R T ln KD

KD values in biological systems

Monovalent ions binding to proteins or DNA have KD 0.1 mM to 10 mM

Allosteric activators of enzymes e. g. NAD have KD 0.1 µM to 0.1 mM

Site specific binding to DNA KD 1 nM to 1 pM

T i i hibit t ti t i t K 0 01 MTrypsin inhibitor to pancreatic trypsin protease KD 0.01 pM

Antibody-antigen interaction have KD 0.1 mM to 0.0001 pM

By using a logarithmic scale for the x-axis, as shown below for the same binding data, the data get more spread out at low [A] and form a characteristic S-shaped curve. The best results are obtained if binding data over several orders of magnitude in [A] can be collected.

1

1.2

0

0.2

0.4

0.6

0.8

0.01 0.1 1 10 100

[A] (uM)

Scatchard Plots

One can “linearize” binding data using the so-called Scatchard plot. Starting with equation

and multiplying both sides by 1 + Ka[A] yields:

AK

AK

A

A

1

ν + ν KA [A] = KA [A]

Dividing through by [A] gives

which rearranges into the following form:

aa KKA

AA KK

A

3

Multiple binding sites

N identical and independent

1.2

If instead we have multiple identical binding sites

then it is possible to show that the appropriate form of the Scatchard equation is

nPAnAP

aa KnK

A

y = -x + 1

R2 = 1

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2

v

v/[A

] (x

10E

6

A plot of ν / [A] versus ν should give a straight line for a binding reaction with identical sites. The slope of this plot is –Ka and the y-intercept is nKa.

n

iiPAi

PAPAPA

1][

...]3[3]2[2][

For n sites on the macromolecule:

Concentration of bound ligand

Concentration of macromolecule [ [ ] [ ] [ ]]PA PA PA PA Concentration of macromolecule 0

[ [ ] [ ] [ ] ...2 3

[ ]0

]PA PA PA PA

nPAi

i

n

iiPA

iPAn

ii

v

0

1

SINGLE SITE

P + A PA APPA

BindingK

PAAP

onDissociatiK

PAP

PAv

A

BK

AB

K

APB

KP

APB

Kv

1

KB

MULTIPLE SITESMULTIPLE SITES

P + A PAPA + A PA2

PA2 + A PA3

ADAIR equation

n

i

iAiK

n

i

iAiiK

n

i

iAPiK

n

i

iAPiiK

v

0

1

0

1

Increasing complexity of binding

all binding sites areequivalent and independent

cooperativity heterogeneity

simple

all binding sites areequivalent and not independent

cooperativityheterogeneity

all binding sites arenot equivalent and not independent

all binding sites areindependent but not equivalent

difficult

verydifficult

Experimental Measurements of Binding

Equilibrium dialysis:

AT = total amount of substrateAB = total amount of BOUND substrateA = total amount of UNBOUND substrate

TE

BAvoccupiedsitesaverage ..#.

Detect physical change on bindingABi = change in measured quantity ABT = total change in measured quantity

fraction of occupied sites =

BTABiA

nv

BAATA

4

Example: binding of a protein P to a DNA-fragment D with one or two binding sites

Dfree Pfree

DP K1Dfree Pfree

DPbinding of the first protein withthe dissociation constant K1

Dfree, concentration free DNA; Pfree, concentration free protein;

DP, complex with one protein; DP2, complex with two proteins;

binding constant KB1

dissociation constant KD

DPPfree

DP2 K2

DPPfree

DP2

binding of the second protein withthe dissociation constant K2

D2Pfree

DP2 K 2* DfreePfree

2

DP2

K 2* K1K2 alternative expression

Stoichiometric titration to determinethe number of binding sites

or

0.6

0.8

1

equivalence point1 protein per DNA

Dtot = 10-10 (M)

KD = 10-14 (M)

K = 10-13 (M)

n

for n =1

To a solution of DNA strands with a single binding site small amounts of protein P are added. Since the binding affinity of the protein is high (low KD value as compared to the total DNA concentration) practically every protein binds as long as there are free binding sites on the DNA. This is termed “stoichiometric binding” or a “stoichiometric titration”.

0

0.2

0.4

0 1·10 -10

Ptot (M)

2·10 -10

KD = 10 13 (M)

KD = 10-12 (M)

for n 1

Myoglobin (Mb) & Hemoglobin (Hb)Myoglobin (Mb) & Hemoglobin (Hb)

Proteins involved in STORAGE (Mb) and TRANSPORT (Hb) of oxygen (O2)

pO2 : partial pressure of oxygen

100

0

20

40

60

80

Lungs Capillaries Active Muscle

pO

2

• Function: to transport O2 from lungs to tissue via blood.

• O2 in tissue required to drive oxidation of metabolic fuels to get energy from food.

Myoglobin & Hemoglobin

• Mb has higher affinity for O2 than Hb, so increases transport – gives O2 higher solubility in tissues so diffuses faster.

Heme: a prosthetic group made of a hydrophobic porphyrin ring. Fe2+ is complexed in the porphyrin ring by two main chain His residues.

The organic portion of the heme molecule is Protoporphyrin IX, a circular system of covalently connected pyrrole groups (which contribute the


nitrogens coordinating the iron)

The framework has as appendages four methyl, two vinyl and two propionate groups

· Heme differs from Protoporphyrin IX only in the addition of the iron

· The heme complex is inserted into the protein with the propionate groups


the propionate groups protruding into the solvent

· The functioning portion of the heme is a tetracoordinated, divalent (Fe+2) iron

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Myoglobin

Single polypeptide chainBinds oxygen in a hyperbolic fashion.Each oxygen binds independently.

• 153 aa, (first protein structure to be solved by Xray crystallography by John Kendrew 1959)

• 8 helices (A-H), 44x44x25 Å

• Role: O2 transport into muscle – needed because muscle uses O2 faster than other tissues.

• O2 has low solubility in blood (10-4 M).

• 4 polypeptide chains (2 alpha and 2 beta) in a quaternary structure.

• Each polypeptide has a heme and can bind O

Hemoglobin

heme and can bind O2

(4 molecules total).

• Binds oxygen in a sigmoid fashion. Each oxygen binds in a cooperative fashion.

Protein Ligand Binding

represents the fraction or percent of the protein that has the ligand “L” bound to it.

Extrapolation to the x axis from the point on the curve that represents 50% occupancy gives the dissociation constant.

The curve is hyperbolic: equation Y = x / (x + z)

Y fraction of ligand bound; x ligand concentration

z represents the dissociation constant (Kd) or the inverse of the association constant (Ka).

Concentration of oxygen in peripheral tissues is a small fraction of that in the lungs

When oxygen-laden h l bi h th

Protein Ligand Binding

hemoglobin reaches the peripheral tissues, the partial pressure of oxygen falls sufficiently that the equilibrium for oxygen binding is shifted toward release p50: the pO2 where 50%

of the heme sites are filled (have bound O2)

Required Binding curve for an O2 transport protein

efficient in binding – inefficient in unloading

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inefficient in binding – efficient in unloading


efficient in binding – efficient in unloading


High Affinity at High O2

effective loading

Low Affinity at Low O2

effective unloading

O2 binding

The functions of myoglobin and hemoglobin are to bind oxygen when its concentration or partial pressure is relatively high, and then release it where it is needed, meaning where its concentration or partial pressure is relatively low.

Oxygen Binding Curve for MyoglobinOxygen Binding Curve for Myoglobin

Th t f t th

AHyperbolic

Curve

Theta refers to the fraction of available sites occupied by O2

Free oxygen is expressed as the partial pressure, PO2

Low P50 means high affinity

Hemoglobin - Transport Protein

Heme binds O2 REVERSIBLY

CO binds to heme more strongly than O2 highly toxic

Hemoglobin has two states:

Oxy-Hemoglobin (4 O2 Bound)

Deoxy-hemoglobin (No O2 Bound)

-Either Fully Loaded or Fully Unloaded

- exhibits cooperative binding (allosteric affect) - the uptake of one ligand influences the affinities of the remaining unfilled binding sites

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myoglobin

NT

SA

TU

RA

TIO

N

Hemoglobin Binds O2 CooperativelyHemoglobin Binds O2 Cooperatively

hemoglobin

OXYGEN PRESSURE

PE

RC

EN

Weak binding- zero O2

molecules bound Strong binding- 4 O2

molecules bound

O2 binding to Myoglobin

• Reversible binding Mb + O2 MbO2

• Kd = [Mb][O2]/[MbO2] (Dissociation constant).

• Fraction Saturation ( or Y, or YO2) % occupied sites Y = [MbO ]/([Mb]+[MbO ])Y = [MbO2]/([Mb]+[MbO2])

= [O2]/(K+[O2])• Partial pressure: express [O2] as

concentration of gas, so Y = pO2/(K+pO2)

• K = pO2 at Y = 0.5. Define as p50 or [O2]1/2

log(Y/1-Y) = h log[S] – logKD

KD = dissociation constant Y = fraction of enzyme with substrate bound Y/1-Y = the fraction of binding sites which are occupied for an enzyme binding substrate.

Th

Hill equation

Three cases:1) If h = 1 then the enzyme exhibits no cooperativity2) If h = n then the enzyme exhibits perfect cooperative behaviour. In this case only enzyme fully bound to substrate or completely unbound would be present. This is never seen in reality. 3) If 1<h<n then the enzyme exhibits a degree of cooperativity. e.g. hemoglobin, h is about 3.

Hill plot

Hill plotBohr Effect

Exchange of oxygen for carbon dioxide and protons

8

In peripheral tissues, metabolism creates carbon dioxide and lowers the pH - the reduced pH promotes oxygen release by

pH effect

decreasing the affinity of hemoglobin for oxygen.

BPG also regulates Hb binding to O2

• Bisphosphoglycerate (BPG) synthesized by red blood cells.

• Binds tightly to deoxy weakly to oxy.

• Binds tightly to deoxy weakly to oxy. • Binds in channel/cavity between subunits. • Cavity in oxy is too small, so BPG can’t bind. • Facilitates release of O2 in capillaries.

Roles of BPG in Hb function

• Useful because it can be adjusted more rapidly than Hb levels.

• Responsible for high altitude adaptation –pcells make more BPG so Hb can unload more O2 in capillaries.

P A PA AP

PAKA

A

D KPA

APK

1

Kinetics of macromolecule ligand binding

APKPA A

Let ν represent the moles of bound ligand per mole of protein:

[P] and [A] represent unbound protein and ligand respectively

[P]total and [A]total represent the total protein and ligand in the system

PAP

PA

P

PA

total

AKAPKPA AA

AK

AK

APKP

APK

PAP

PA

A

A

A

A

1

AK

A

D

In many experimental procedures you measure ν and [A] at a range of ligand concentrations, which allows you to estimate KD (and from it, ΔG0

binding)

n

iiPAi

PAPAPA

1][

...]3[3]2[2][

For n sites on the macromolecule:

Concentration of bound ligand

Concentration of macromolecule [ [ ] [ ] [ ]]PA PA PA PA Concentration of macromolecule 0

[ [ ] [ ] [ ] ...2 3

[ ]0

]PA PA PA PA

nPAi

i

n

iiPA

iPAn

ii

v

0

1

9

Binding to a single binding site. Titration of DNA with aprotein for the determination of the dissociation constant KD

or

0.6

0.8

1

or = 0.5

KD = 10-9 (M)1

Pfree

PfreeKD

1 Pfree

PfreeKD

Ptot

Ptot KD

if Pfree Ptot

Ptot (M)

0

0.2

0.4

0 2 10-9

4 10-9

6 10-9

8 10-9

1 10-8

Ptot = KD Dtot = 10-10 (M)KD = 10-9 (M)

1 Ptot

Ptot KD

Binding to a single binding site: Deriving an expressionfor the degree of binding or the fraction saturation

KD Dfree Pfree

DPDfree Pfree

DP

1K

PfreeP

from the Adair equation we obtain:

1 KD

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KD

Pfree

1 Pfree

KDPfree

1Dtot Ptot KD DtotPtotKD 24DtotPtot

2Dtot

Pfree Ptot 1Dtot

Often the concentration Pfree can not be determined but the total concentration of added protein Ptot is known.

SPECIAL PLOTS

vnkAv

plot eqn y-axis x-axis

result meaning

Scatchard v v/[A] Straight line

Non-cooperativen equivalent sites read n from y

N

S AskAsksn

v11

N

S AskAsksn

v11

vn

vlog Alog

intercept

Scatchard N kinds of sites v v/[A] Curved line

Non-cooperativeN inequivalent sites read n1 from y intercept

Hill N kinds of sites Sigmoid Read k1 and k2 from 2 slopes; low[A] gives strong sites, higher [A] gives weaker sitesCooperative/non-cooperative

Multiple independent binding sitesMultiple independent binding sites

ii

n

AA

BABnA

binding site i in Bi

dd

d

n

i

i

dii

KKnA

AKAn

AKABtA

//]/[

])[/(][

])[/(][]/[][

1

fraction of occupied sites i

moles of bound ligand

per mole of protein

Scatchard plotScatchard plot

Different ways to plot the binding data

• Direct plot: vs [L]

• Logarithmic plot: vs log[L]

• Recipricol plot: 1/ vs 1/[L] (linear line)

• Scatchard plot: /[L] vs [L] (linear line)

PlottingPlottingbindingbinding

datadata

Fraction bound

Free ligand

10

The Scatchard plotThe Scatchard plot

KdAKdA

AKdA

)/][1/()/]([

])[/(][

KdKdA

KdKdA

KdAKdA

KdAKdA

//1]/[

/1/]/[

/][/][

)/][1/()/]([

Cooperativity: the binding of multiple ligandsto a macromolecule is not independent

2

1

1.5

2 independent bindingmicroscopic binding constantkD = 10-9 (M)

macroscopic binding constantsK1 = 5·10-10 (M); K2 = 2·10-9 (M)

P free (M)

0

0.5

0 2 10-9 4 10-9 6 10-9 8 10-9 1 10-8

Adair equation: 2 K2Pfree2Pfree

2

K1K2K2 PfreePfree2

cooperative bindingmicroscopic binding constantkD = 10-9 (M)


Logarithmic representation of a binding curve

1

1.5

2

2

independent bindingmicroscopic binding constantkD = 10-9 (M)


P free (M)

0

0.5

10-11 10-10 10-9 10-8 10-7

Determine dissociation constants over a ligand concentration of at least three orders of magnitudes



Visualisation of binding data - Scatchard plotP

frei

2 109

3 109

intercept = n/kD

slope 1/k

independent bindingmicroscopic binding constantkD = 10-9 (M)


P

0

1 109

0 0.5 1 1.5 2

slope = - 1/kD

intercept = n

n nPfree

kDPfree

n

Pfree

n

kD

n

kD



on

off

P A PA

k

k

Microscopic and macroscopic binding constantsMicroscopic and macroscopic binding constants

ff


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Procedure – Monitor titration of E with L at a suitable wavelength where the absorbance change is large.

At any given wavelength the total absorbance is the sum of the absorbance contribution from each species.

At any point in the titration, at ligand concentration [Lx]

Assume all species except P and PAn are negligible,i.e. there is strong cooperativity, therefore: Measurements

Techniques?

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Isothermal Titration Calorimetry

• Pros• Works in solution• Measures natural part

of binding reaction:

• Cons• Requires H > ± 3-5

kcal/mol for precise determinations

• Most often requiresof binding reaction: G = H – TS G = –RT ln(K)

• Determines the thermodynamics the of binding reaction

• Automatic titration –setup and leave

• Most often requires macromolecule concentrations in the range 1 µM – 1 mM

• Consumes “large” amounts of material

• Insensitive to very tight or very weak binding

• Slow – 2-3 hours per run

ITC Alternatives• Surface Plasmon Resonance

• Requires attachment of molecules to chip• Can give on and off rates

• Intrinsic Fluorescencei i i * id ( ) l• Requires sensitive* Trp or Tyr residue(s) close to

binding site• Interfering agents such as BSA must be absent• Titrating in the ligand can give an increased signal by

itself• Works in solution• Potentially much more sensitive

ITC Instrument

• Small instrument –requires less than 3 ft of bench space

• Completely computerized• Completely computerized operation

• Must be located in room with constant temperature

• No user-serviceable parts except syringe

ITC Instrument II

• Two coin-shaped cells in adiabatic chamber kept at exactly the same temperature – T < 0.001º CT d• Temperature measured EXTREMELY precise –0.00001º C

• Sample can be heated fast, but cooling is slow: Sample should be colder than the experimental temperature when loaded

ITC Instrument III

• Reference cell contains water – nothing is added

• Sample cell contains macromolecule in buffer solutionsolution

• Ligand in syringe is added in computer-controlled injections

• Solution is stirred with the paddle-shaped tip of the needle to ensure rapid mixing of components

ITC Measurements

• When an injection is made, heat will be generated or absorbed by the molecules reacting (exothermic or endothermic reactions)

• Heat input in sample cell adjusted to keep T constant• Heat input in sample cell adjusted to keep T constant

• Exothermic reaction will result in negative peaks (less heat is needed while the reaction proceeds)

• Endothermic reactions will result in positive peaks (more heat is needed while the reaction proceeds)

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ITC Measurements II

• The heat input is integrated over time until the it returns to the baseline value

• The heat generated/absorbed after any given injection is a function of amount of ligand in that injection, total amount of ligand injected until that point of the experiment, concentration of the molecule in the cell, number of ,binding sites, binding constant and H of the reaction

• The observed heat change per injection (dq/dLT) is fitted to the theoretical binding curve, rather than the “standard” binding curve that plots total change versus total added ligand.

•

ITC Data Fitting I

• The standard binding curves

ITC Data Fitting II

• The ITC binding curves

• From Andersen et al. (2001), Biochem. 40; 15408-17

Measuring binding

• This binding curve resembles the traditional binding curve– Kd = 12.6 µM

– H = -5.7 kcal/mol

– G = -6.8 kcal/mol

– S = 3.6 cal/mol/K

Binding modes in DNA

• Intercalation: a flat heteroaromatic ring is inserted between two base pairs of DNA (lengthening and unwinding)

• Groove binders: most drugs bind to the DNA minor groove (prefer AT sequence)

• Covalently attached drugs.

Major groove

3′ end 5′ end

Three-dimensional structure of deoxyribonucleic acid (DNA)

N H 2H 2N

N

B r

Minor groove

Sugar-phosphate backbone

5′ end3′ end

Base pair

Ethidium bromide

Hoechst 33258

NH3C

H

HN

NH

HN

NH

OH

14

Drug Action Mode of Binding

Hoechst 33258 Antitumor Minor groove

Netropsin Antitumor, Antiviral Minor groove

Pentamidine Active against Pneumocystis Carinii

Minor groove

Berenil Antitrypanosomal Minor groove

Distamycin Antitumor, Antiviral Minor groove

Drug action and mode of binding of some DNA binding drugs.

SN7167 Antitumor, Antiviral Minor groove

Nogalamycin Antitumor Intercalation

Menogaril Antitumor Intercalation

Mithramycin Anticancer antibiotic Minor groove

Plicamycin Anticancer antibiotic Minor groove

Chromomycin A3 Anticancer antibiotic Minor groove

cis -Platin Anticancer antibiotic Covalent cross-linking

Daunomycin Anticancer antibiotic Intercalation

Adriamycin Antitumor antibiotic Intercalation

Measurement

Displacement studies

Noncovalent DNA probes.

Binding of Ethidium-Bromide to Transfer RNA

Ethidium bromide can intercalate into nucleic acid structuresIt binds well to both DNA and RNA

Enzyme cofactors NADH, FAD and pyridoxal/pyridoxamine are fluorescent.

15

Extrinsic probes.Protein labeling reagents.

Covalently attached drugs

87

DNA-binding proteins often fit into the major groove of the double helix

Double-stranded DNA has two phosphate groups every 3.4 Angstroms along itslength. These negatively charged ions aggregate around the DNA.

1) Direct interaction with negatively charged phosphates.2) Screening by mobile ion “atmosphere”

we will let be the effect fraction of each phosphate charge neutralized by Na+

ions in solution.

Nonideality in Protein/DNA interactions

When a protein binds to DNA it displaces some sodium:

P + DNA P•DNA + n [Na+]

We generally define a protein/DNA equilbrium constant as

K= [P•DNA]/[P][DNA]But there is an extra term now:

K= [P•DNA][Na+]n/[P][DNA]

The Monod-Wyman-Changeau (MWC)model for cooperative binding

+P

T0 T1 T2

L0 L1 L2

kT

+P

kT

T conformation (all binding sites

are weak)

P P P P P

P

P P

P P

+P

kT

+P

kT

T3 T4

L3 L4

R0 R1 R2

+P

kR

+P

kR

R conformation (all binding sites

are strong)

• in the absence of ligand P the the T conformation is favored

• the ligand affinity to the R form is higher, i. e. the dissociation constant kR< kT.

• all subunits are present in the same confomation

• binding of each ligand changes the T<->R equilibrium towards the R-Form

P P P P P

P P

P P

P

+P

kR

+P

kRR3 R4

(Monod, Wyman & Changeaux)Allosteric protein an oligomer of protein subunits that are symmetrically related; Protomers can exist in two conformations (designated T[ense]: low affinity for substrate, & R[elaxed]: high affinity for substrate) that are in equilibrium whether or not ligand is bound; Ligand can bind to protomers in either conformation, but conformational change alters affinity for the ligand;conformational change alters affinity for the ligand; The molecular symmetry of the protein is conserved during conformational change: the protomers must therefore change in a concerted manner.

positive effectors bind to R (circles) and shift equilibrium to right, negative effectors bind to T (squares) and shift equilibrium to left.

16

The Koshland-Nemethy-Filmer (KNF)model for cooperative binding

+P

k1

+P

k2

-conformation-conformation(induced by ligand binding)

P PP

-conformation(facilitated binding)

k1 2

• Binding of ligand P induces a conformation change in the subunit to which it binds

from the into the -conformation (“induced fit”).

• The bound ligand P facilitates the binding of P to a nearby subunit

in the -conformation (red), i. e. the dissociation constant k2 < k’2.

• subunits can adopt a mixture of confomations.

+P

P

P

k’2

• Thermodynamic relation between ∆G und KD

• Stoichiometry of binding

• Determination of the dissociation constant for simple systems

Summary

• Determination of the dissociation constant for simple systems

• Adair equation for a general description of binding

• Binding to n binding sites

• Visualisation of binding curves by Scatchard and Hill plots

• Cooperativity of binding (MWC and KNF model)

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