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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.
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: Karsten.Rippe@kip.uni-heidelberg.de
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 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 In the end it is nothing but equilibrium binding and kinetics Karsten Rippe, Biochemistry II Lecture
Binding of Glycerol-Phosphate to triose phosphate isomerase(we need energy...)
Antibody HyHEL-10 in complex with Hen Egg White Lyzoyme (we need to protect ourselves ...)
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 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 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 forbinding 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
KD 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 • 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 • 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 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 orpartial 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 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 µ of a substance is 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
Titration of a macromolecule D 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)
Analysis of binding of RNAP·s54 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 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 tomonitor 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 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 degree of binding n n for one binding site n for two binding sites n for n binding sites (Adair equation)
Binding to a single binding site: Deriving an expressionfor 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 determinethe 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”.
Binding to a single binding site. Titration of DNA with aprotein 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 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 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 andmacroscopic 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 ligandsto 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 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 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 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 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 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 • 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)