Biochemistry II: Binding of ligands to a macromolecule (or the secret of life itself...) Karsten Rippe Kirchoff-Institut für Physik Molekulare Biophysik Im Neuenheimer Feld 227 Tel: Principles of physical biochemistry, van Holde, Johnson & Ho, Slides available at

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 dioxygen to hemoglobin (we need air...)

Binding of Glycerol-Phosphate to triose phosphate isomerase (we need energy...)

Complex of the HIV protease the inhibitor SD146 (we need drugs...)

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. PNAS 94,

Structure of the tryptophan repressor with DNA (what is this good for?)

Biochemistry II: 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

The mass equation law for binding of a protein P to its DNA D binding of the first proteins with the dissociation constant K 1 D free, concentration free DNA; P free, concentration free protein

What is the meaning of the dissociation constant for binding of a single ligand to its site? 2. K D gives the concentration of ligand that saturates 50% of the sites (when the total sit concentration ismuch lower than K D ) 3. Almost all binding sites are saturated if the ligand concentration is 10 x K D 1. K D is a concentration and has units of mol per liter 4. The dissociatin constant K D is related to Gibbs free energy ∆G by the relation ∆G = - R T K D

K D values in biological systems Allosteric activators of enzymes e. g. NAD have K D 0.1 µM to 0.1 mM Site specific binding to DNA K D 1 nM to 1 pM Movovalent ions binding to proteins or DNA have K D 0.1 mM to 10 mM Trypsin inhibitor to pancreatic trypsin protease K D 0.01 pM Antibody-antigen interaction have K D 0.1 mM to 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 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 At constant pressure P and constant temperature T the system is described by the Gibbs free energy:

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 or partial 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. partial specific volume = increase of volume upon addition of mass partial molar volume = increase of volume upon addition of mol particles the solution: use of partial specific or partial molar quantities

Increase of the solution volume upon adding solute Solute added (moles) Volume of solution real solutions volumes additive slope = volume of pure solvent slope at indicated concentration = 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: C i is the concentration in mol per liter is the chemical potential of a substance at 1 mol/l

Changes of the Gibbs free energy ∆G of an reaction

∆G of an reaction in equilibrium

Titration of a macromolecule D with n binding sites for the ligand P which is added to the solution free ligand P free (M) degree of binding n n binding sites occupied ∆ X max ∆X∆X 0

Analysis of binding of RNAP·  54 to a promoter DNA sequence by measurements of fluorescence anisotropy Rho + RNAP·  54 promoter DNA RNAP·  54 -DNA-Komplex KdKd free DNA with a fluorophore with high rotational diffusion -> low fluorescence anisotropy r min RNAP-DNA complex with low rotational diffusion -> high fluorescence anisotropy r max

How to measure binding of a protein to DNA? One possibility is to use fluorescence anisotropy z y x sample I  vertical excitation filter/mono- chromator polarisator I II filter/monochromator polarisator measured fluorescence emission intensity Definition of fluorescence anisotropy r The anisotropy r reflects the rotational diffusion of a fluorescent species

Measurements of fluorescence anisotropy to monitor binding of RNAP·  54 to different promoters Vogel, S., Schulz A. & Rippe, K. P tot = K D  = 0.5 P tot = K D

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 K 1 D free, concentration free DNA; P free, concentration free protein; DP, complex with one protein; DP 2, complex with two proteins; binding of the second proteins with the dissociation constant K 2 alternative expression

Definition of the degree of binding for n binding sites (Adair equation) degree of binding  for one binding site for two binding sites

Binding to a single binding site: Deriving an expression for the degree of binding or the fraction saturation  from the Adair equation we obtain: Often the concentration P free can not be determined but the total concentration of added protein P tot is known.

Stoichiometric titration to determine the number of binding sites 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 K D 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”. or  · P tot (M) equivalence point 1 protein per DNA 2· D tot = (M) K D = (M) K D = (M) K D = (M)

Binding to a single binding site. Titration of DNA with a protein for the determination of the dissociation constant K D P tot (M) or  P tot = K D or  = 0.5 D tot = (M) K D = (M)

Increasing complexity of binding all binding sites are equivalent and independent cooperativityheterogeneity all binding sites are equivalent and not independent cooperativityheterogeneity all binding sites are not equivalent and not independent all binding sites are independent but not equivalent simple difficult 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,  H HiIl coefficient

Difference between microscopic and macroscopic dissociation constant kDkD kDkD kDkD kDkD D free DP DP 2 microscopic bindingmacroscopic binding 2 possibilities for the formation of DP 2 possibilities for the dissociation of DP 2

Cooperativity: the binding of multiple ligands to a macromolecule is not independent 2 P free (M) independent binding microscopic binding constant k D = (M) macroscopic binding constants K 1 = 5· (M); K 2 = 2·10 -9 (M) cooperative binding microscopic binding constant k D = (M) macroscopic binding constants K 1 = 5· (M); K 2 = 2· (M)

Logarithmic representation of a binding curve 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. independent binding microscopic binding constant k D = (M) macroscopic binding constants K 1 = 5· (M); K 2 = 2·10 -9 (M) cooperative binding microscopic binding constant k D = (M) macroscopic binding constants K 1 = 5· (M); K 2 = 2· (M)

Visualisation of binding data - Scatchard plot independent binding microscopic binding constant k D = (M) macroscopic binding constants K 1 = 5· (M); K 2 = 2·10 -9 (M) cooperative binding microscopic binding constant k D = (M) macroscopic binding constants K 1 = 5· (M); K 2 = 2· (M)

Visualisation of binding data - Hill plot

Binding of dioxygen to hemoglobin

The Monod-Wyman-Changeau (MWC) model for cooperative binding +P T0T0 T1T1 T2T2 R0R0 R1R1 R2R2 L0L0 L1L1 L2L2 kTkT kRkR kRkR kTkT T conformation (all binding sites are weak) 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 k R < k T. all subunits are present in the same confomation binding of each ligand changes the T R equilibrium towards the R-Form P PPPP P PP PP +P kTkT kTkT T3T3 T4T4 P P P P P P P P P P L3L3 L4L4 kRkR kRkR R3R3 R4R4

The Koshland-Nemethy-Filmer (KNF) model for cooperative binding +P k1k1 k2k2 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 k 2 < k’ 2. subunits can adopt a mixture of  confomations.  -conformation  -conformation (induced by ligand binding) +P P P k’ 2 P P P  -conformation (facilitated binding)

Summary Thermodynamic relation between ∆G und K D 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)