Biochemistry ii binding of ligands to a macromolecule or the secret of life itself
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Biochemistry II: Binding of ligands to a macromolecule (or the secret of life itself...). http://www.dkfz.de/kompl_genome/rippe/pdf-files/Rippe_Futura_97.pdf Principles of physical biochemistry, van Holde, Johnson & Ho, 1998. Slides available at http://www.dkfz.de/Macromol/lecture/index.html.

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Biochemistry ii binding of ligands to a macromolecule or the secret of life itself l.jpg
Biochemistry II: Binding of ligands to a macromolecule(or the secret of life itself...)

  • http://www.dkfz.de/kompl_genome/rippe/pdf-files/Rippe_Futura_97.pdf

  • Principles of physical biochemistry, van Holde, Johnson & Ho, 1998.

  • Slides available at http://www.dkfz.de/Macromol/lecture/index.html

Karsten Rippe

Kirchoff-Institut für Physik

Molekulare Biophysik

Im Neuenheimer Feld 227

Tel: 54-9270

e-mail: [email protected]


The secret of life part i l.jpg
The secret of life, part I

“The secret of life is molecular recognition; the ability of one molecule to "recognize" another through weak bonding interactions.”

Linus Pauling at the 25th anniversary of the Institute of Molecular Biology at the University of Oregon


The secret of life part ii l.jpg
The secret of life, part II

A new breakthrough in biochemical research... and paradise is to be mine! It was strange the way it happened... suddenly you get a break... and whole pieces seem to fit into place... and that's how I discovered the secret to life... itself!

Frank’n Further in the Rocky Horror Picture Show


The secret of life part iii l.jpg
The secret of life, part III

In the end it is nothing but equilibrium binding

and kinetics

Karsten Rippe, Biochemistry II Lecture






X ray crystal structure of the tbp promoter dna complex transcription starts here l.jpg
X-ray crystal structure of the TBP-promoter DNA complex(transcription starts here...)

Nikolov, D. B. & Burley, S. K. (1997). RNA polymerase II transcription initiation: a structural view. PNAS94, 15-22.



Biochemistry ii binding of ligands to a macromolecule l.jpg
Biochemistry II: Binding ofligands 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


The mass equation law for binding of a protein p to its dna d l.jpg
The mass equation law for binding of a protein P to its DNA D

binding of the first proteins with the dissociation constant K1

Dfree, concentration free DNA; Pfree, concentration free protein


What is the meaning of the dissociation constant for binding of a single ligand to its site l.jpg
What is the meaning of the dissociation constant for Dbinding of a single ligand to its site?

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 sit concentration ismuch lower than KD)

3.Almost all binding sites are saturated if the ligand concentration is 10 x KD

4.The dissociatin constant KD is related to Gibbs free energy ∆G by the relation ∆G = - R TKD


K d values in biological systems l.jpg
K DD values in biological systems

Movovalent 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

Trypsin inhibitor to pancreatic trypsin protease KD 0.01 pM

Antibody-antigen interaction have KD 0.1 mM to 0.0001 pM


What is g the thermodynamics of a system l.jpg
What is ∆G? The thermodynamics of a system D

  • 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


Some fundamentals of solution thermodynamics l.jpg
Some fundamentals of solution thermodynamics D

  • At constant pressure P and constant temperature T the system is described by the Gibbs free energy:

  • H is the enthalpy or heat content of the system, S is the entropy of the system

  • a reaction occurs spontaneously only if ∆G < 0

  • at equilibrium ∆G = 0

  • for ∆G > 0 the input of energy is required to drive the reaction


The problem l.jpg
the problem D

In general we can not assume that the total free energy G of a solution consisting of N different components is simply the sum of the free energys of the single components.


Why is it necessary to use partial specific or partial molar quantities l.jpg
Why is it necessary to use partial specific or Dpartial molar quantities?

the problem: In general we can not assume that the total volume V of a solution consisting of N different components is simply the sum of the volume of the single components. For example this is the case for mixing the same volumes of ethanol and water.

the solution: use of partial specific or partial molar quantities

partial specific volume

= increase of volume upon addition of mass

partial molar volume

= increase of volume upon addition of mol particles


Increase of the solution volume upon adding solute l.jpg
Increase of the solution volume upon adding solute D

slope at indicated concentration =

real solutions

volumes additive

Volume of solution

slope =

volume of

pure solvent

Solute added (moles)

The total volume of the solution is the

sum of the partial molar volumes:


The chemical potential of a substance is the partial molar gibbs free energy l.jpg
The chemical potential µ of a substance is D the partial molar Gibbs free energy

for an ideal solution it is:

Ci is the concentration in mol per liter

is the chemical potential of a substance at 1 mol/l



G of an reaction in equilibrium l.jpg
∆G D of an reaction in equilibrium


Titration of a macromolecule d with n binding sites for the ligand p which is added to the solution l.jpg
Titration of a macromolecule DD with n binding sitesfor the ligand P which is added to the solution

n binding sites

occupied

n

degree of binding n

∆Xmax

∆X

0

free ligand Pfree (M)


Slide24 l.jpg
Analysis of binding of RNAP· Ds54 to a promoter DNA sequenceby measurements of fluorescence anisotropy

Rho

Rho

RNAP·s54

+

free DNA with a fluorophore

with high rotational diffusion

-> low fluorescence anisotropy rmin

promoter DNA

Kd

RNAP-DNA complex

with low rotational diffusion

-> high fluorescence anisotropy rmax

RNAP·s54-DNA-Komplex


How to measure binding of a protein to dna one possibility is to use fluorescence anisotropy l.jpg
How to measure binding of a protein to DNA? DOne possibility is to use fluorescence anisotropy

z

vertical

excitation

filter/mono-

chromator

polarisator

sample

x

Definition of fluorescence

anisotropy r

polarisator

I

I

I

I

filter/monochromator

^

y

The anisotropy r reflects the rotational diffusion of a fluorescent species

measured fluorescence

emission intensity


Measurements of fluorescence anisotropy to monitor binding of rnap s 54 to different promoters l.jpg
Measurements of fluorescence anisotropy to Dmonitor binding of RNAP·s54 to different promoters

q = 0.5

q = 0.5

Ptot = KD

Ptot = KD

Vogel, S., Schulz A. & Rippe, K.


Example binding of a protein p to a dna fragment d with one or two binding sites l.jpg
Example: binding of a protein DP to a DNA-fragment D with one or two binding sites

binding of the first proteins with

the dissociation constant K1

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

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

binding of the second proteins with

the dissociation constant K2

alternative expression


Definition of the degree of binding n l.jpg
Definition of the degree of binding Dn

degree of binding n

n for one binding site

n for two binding sites

n for n binding sites (Adair equation)


Slide29 l.jpg
Binding to a single binding site: Deriving an expression Dfor the degree of binding n or the fraction saturation q

from the Adair equation we obtain:

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


Stoichiometric titration to determine the number of binding sites l.jpg
Stoichiometric titration to determine Dthe number of binding sites

1

KD = 10-14(M)

equivalence point

1 protein per DNA

0.8

n or q

Dtot = 10-10(M)

0.6

KD = 10-13(M)

0.4

0.2

KD = 10-12(M)

0

0

1·10 -10

2·10 -10

Ptot (M)

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”.


Slide31 l.jpg
Binding to a single binding site. Titration of DNA with a Dprotein for the determination of the dissociation constant KD

1

0.8

KD = 10-9(M)

n or q

0.6

n or q = 0.5

0.4

KD = 10-9(M)

Ptot = KD

Dtot = 10-10(M)

0.2

0

-9

-9

-9

-9

-8

0

2

10

4

10

6

10

8

10

1

10

Ptot (M)


Increasing complexity of binding l.jpg
Increasing complexity of binding D

all binding sites are

equivalent and independent

simple

cooperativity

heterogeneity

all binding sites are

equivalent and not independent

all binding sites are

independent but not equivalent

difficult

heterogeneity

cooperativity

all binding sites are

not equivalent and not independent

very

difficult


Binding to n identical binding sites l.jpg
Binding to Dn identical binding sites

binding to a single binding site

binding to n independent and

identical binding sites

strong cooperative binding to n identical binding sites

approximation for cooperative binding to

n identical binding sites, aH HiIl coefficient


Difference between microscopic and macroscopic dissociation constant l.jpg
Difference between microscopic and Dmacroscopic dissociation constant

microscopic binding

macroscopic binding

Dfree

kD

kD

2 possibilities for the formation of DP

DP

2 possibilities for the dissociation of DP2

kD

kD

DP2


Cooperativity the binding of multiple ligands to a macromolecule is not independent l.jpg
Cooperativity: the binding of multiple ligands Dto a macromolecule is not independent

2

independent binding

microscopic binding constant

kD = 10-9(M)

macroscopic binding constants

K1 = 5·10-10(M); K2 = 2·10-9(M)

1.5

n2

1

cooperative binding

microscopic binding constant

kD = 10-9(M)

macroscopic binding constants

K1 = 5·10-10(M); K2 = 2·10-10(M)

0.5

0

-9

-9

-9

-9

-8

0

2

10

4

10

6

10

8

10

1

10

P free (M)


Logarithmic representation of a binding curve l.jpg
Logarithmic representation of a binding curve D

2

independent binding

microscopic binding constant

kD = 10-9(M)

macroscopic binding constants

K1 = 5·10-10(M); K2 = 2·10-9(M)

1.5

n2

1

cooperative binding

microscopic binding constant

kD = 10-9(M)

macroscopic binding constants

K1 = 5·10-10(M); K2 = 2·10-10(M)

0.5

0

-11

-10

-9

-8

-7

10

10

10

10

10

P free (M)

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

  • Logarithmic representation since the chemical potential µ is proportional to the logarithm of the concentration.


Visualisation of binding data scatchard plot l.jpg
Visualisation of binding data - Scatchard plot D

independent binding

microscopic binding constant

kD = 10-9(M)

macroscopic binding constants

K1 = 5·10-10(M); K2 = 2·10-9(M)

9

3

10

intercept = n/kD

n/ P frei

9

2

10

slope = - 1/kD

cooperative binding

microscopic binding constant

kD = 10-9(M)

macroscopic binding constants

K1 = 5·10-10(M); K2 = 2·10-10(M)

9

1

10

intercept = n

0

0

0.5

1

1.5

2

n


Visualisation of binding data hill plot l.jpg
Visualisation of binding data - Hill plot D

2

1.5

strong

binding

limit

1

slope a H=1.5

0.5

log[n/ (2–n)]= log[q/ (1–q)]

0

-0.5

weak

binding

limit

-1

K2/2

2·K1

-1.5

-2

-11

-10

-9

-8

10

10

10

10

log (P free)



The monod wyman changeau mwc model for cooperative binding l.jpg
The Monod-Wyman-Changeau (MWC) Dmodel for cooperative binding

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

P

T0

T1

T2

T3

T4

+P

T conformation (all binding sites

are weak)

+P

+P

+P

kT

kT

kT

kT

L0

L1

L2

L3

L4

+P

+P

+P

+P

R conformation (all binding sites are strong)

kR

kR

kR

kR

R0

R1

R2

R3

R4

• 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


The koshland nemethy filmer knf model for cooperative binding l.jpg
The Koshland-Nemethy-Filmer (KNF) Dmodel for cooperative binding

P

b-conformation

(induced by ligand binding)

a-conformation

(facilitated binding)

a-conformation

+P

+P

P

P

k2

k1

+P

k’2

P

P

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

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

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

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

• subunits can adopt a mixture of a-b confomations.


Summary l.jpg
Summary D

  • Thermodynamic relation between ∆G und KD

  • Stoichiometry of binding

  • 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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