University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2007

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1 ecture 21 8/15/07 University o Washington Department o Chemistry Chemistry 452/456 Summer Quarter Cooperative Binding Cooperativity reers to the inluence that inding at one site has on inding to another site. I inding at one site enhances inding at another site, the eect is called positive cooperativity. I inding at one site diminishes the ainity or other sites, the eect is called negative cooperativity. In iochemistry the general phenomenon o long-range eects o ligand inding is called allostery. Homoallostery: inluence on ligand-inding o ligands o the same ind Heteroallostery: inluence on ligand-inding o ligands o a dierent ind Hill Plots and llosteric Eects I a straight line is oserved over the entire range o ligand concentration [], the inding is non-cooperative and the sites are identical I the curve has a slope >1 in some range o [], the inding must e positively cooperative. I the curve has a slope <1 in some range o [], the iopolymer P either has more than one class o inding site or the inding is negatively cooperative. Example: Fully cooperative inding (all or nothing) N N [ ] ν ν = log log N N = + log[ ] where = θ = 1 [ ] 1 + N In reality ull cooperativity is not realized and the value o N derived rom a Hill plot may not relect the numer o inding sites and may not even e an integer. For example, hemogloin has our inding sites or oxygen gas, ut in the Hill plot or oxygen inding to hemogloin it is ound that N=2.8. his value or N indicates that some cooperativity exits etween the inding sites, ut inding to hemogloin is not all or nothing. lso, the Hill plot may deviate rom linearity, with regions o partial linearity or with slopes >1 or <1. B. Models or Cooperative Binding: a. here is no unique interpretation or a Hill plot with slope>1 or <1. Models must e advanced to explain the data and more than one model may account or the data.. Monod-Wyman-Changeaux (MWC) heory: In the asence o ligand, the iopolymer exists in two orms and that are in dynamic equilirium ; = In the state, all inding sites ind ligand wealy

2 o In the state, all inding sites ind ligand tightly o In the asence o ligand, the orm is avored, i.e. []>>[] o s ligand is added, the orm is avored B + B B + B 2 2 etc. etc. he equiliria etween the various orms o ound and unound is characterized y the equilirium constant. he equiliria etween the various orms o ound and unound is characterized y the equilirium constant. he ratio C =. ssume two inding sites on and ν = Sustitute [ ] [ ] imiting ehavior: 2 2 = and C = as as ν = = 2 ν 0 C F HG F HG ln ln ln[ ] as log-log limiting ehavior ln ln + ln[ ] as his ehavior produces a Hill plot with the ollowing appearance I J I J

3 Figure 21.1: Hill Plot or a Cooperative Binding C. Derivation o the Dierential Heat o dsorption rom Isotherm Equations Consider the equilirium ( g) ( ). he equilirium 1 constant =, where P 0 is the equilirium pressure o the gas. P0 hen the simple angmuir isotherm equation is ν P P θ = = θ = =, or P = P0. N P P0 P θ From the equations aove the general orm or an isotherm is P = ( θ ). t equilirium the chemical potential o the ree gas is equal to the chemical potential o the gas i.e. µ ree 0 From the relationship µ ree ree + ln P, the equilirium condition µ ree, and the general isotherm equation P = ( θ ), we otain 0 µ ree + ln ( ( θ) ) We can now otain the molar enthalpy o adsorption using the Gis- Helmholtz equation ( µ ) ln / 0 ( ( θ )) = H = H ree gas + ( 1/ ) ( 1/ )

4 he dierential heat o adsorption is then 0 ln ( ( θ )) Hdi = H ree gas H = ( 1/ ) D. Isthermal itration Calorimetry Enthalpies o inding etween two molecules in solution or the enthalpy o inding etween a molecule in solution and a surace may e measured y isothermal titration calorimetry (IC). IC intrumentation is schematized in Figure ) Figure21.2 Schematic o an isothermal titration calorimeter wo vessels are thermally isolated rom the surroundings. he control or reerence vessel contains a uered solution. he reaction vessel contains a uered solution o a macromolecule or some other inding target. Initially the temperatures o the control and reaction vessels are indentical ( =0). he injection system delivers into the reaction vessel at a measured rate a ligand solution. Depending on whether the inding is exothermic or endothermic the temperature o the reaction vessel will increase ( >0) or decrease ( <0). he heat o inding q can e otained given a nowledge o the solution heat capacity: q = C (21.1) he enthalpy o inding is related to the heat o inding y q = Vc H (21.2) where V is the volume o the solution in the reaction vessel and c is the concentration o ound ligand. o calculate the enthalpy o inding rom Equation (21.2) we require the concentration o ound ligand. he total ligand delivered into the reaction vessel

5 will partition into ree ligand with concentration c and ound ligand with concentration c : c = c + c = ν cp + c (21.3) Equation (21.3) can e solved or c i we assume an expression or ν. he simplest approach is to assume a model o independent ligand inding and use Equation (12.30) cn to sustitute ν = : ( c ) cn c = ν cp + c = cp + c (21.4) ( c ) where N is the numer o ligand inding sites and is the inding equilirium constant. Equation (21.4) can e rearranged into standard quadratic orm: 2 c + ( Nc P c + 1) c c= 0 (21.5) and solved using the quadratic ormula 1/2 2 ( Nc P c + 1) ± ( Nc P c 1) 4c + + c = (21.6) 2 Comining Equation (21.6) with Equation (21.3) we otain a inal expression or the ound ligand concentration: 1/2 2 ( Nc P c 1) ( Nc P c 1) 4c c = c c = c (21.7) 2 Near the saturation point where virtually all N sites on the target protein are illed, the ound ligand concentration approaches Nc P in which case Equation (23.2) can e approximated y q VNcP H (21.8) and the inding enthalpy is q H (21.9) VNc P Pierce, aman, and Nall have used IC to study the inding o two monoclonal antiodies 2B5 and 5F8 to horse heart cytochrome c. Because the volume o the solution in the reaction vessel changes upon addition o the titrant, calorimetric heat has to e corrected or the heat o dilution. Figure shows an experimental calorimetric titration o a solution o M 5F8 with cytochrome c corrected or the heat o dilution. he quantities N, H, and are otained y itting o the calorimetric data in Figure 21.3 using Equations (21.2) and (21.7).

6 Figure 21.3 Isothermal titration calorimetry applied to the study o inding etween M 58 and horse heart cytochrome c. ) Calorimetric heat otained y adding a cytochrome c to a solution o M 5F8 (=298, ph=7). B) plot o q versus time, otained y integration o each pea in part. C) Binding enthalpy measured y IC as a unction o temperature. Source: C.S. aman, M.J. llen, and B.. Nall (1995) Biochemistry 34, Sample Prolem 21.1 IC study o inding etween horse heart cytochrome c and M 5F8 yield =1.4x10 10 and H = J mol -1. From these data calculate the Gis energy o inding G and the entropy o inding S. ssume =298. Solution: he Gis energy is otained rom the relation G = ln = ( 8.31Jmol )( 298) ln ( ) = 57.8Jmol t constant temperature the entropy is otained rom -1-1 H 90.7Jmol ( 57.8Jmol ) G -1 S = = = 110J 298 he change in heat capacity as a result o inding C p can also e otained rom IC i the inding enthalpy is measured as a unction o temperature. n example is shown in Figure 12.25C where H or M 5F8 inding to cytochrome c is plotted as a unction o temperature. In Figure 12.25C a straight line is itted to the our experimental points to otain

7 H H C p = = 172cal mol = 719Jmol P

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2014

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2014 Lecture 10 1/31/14 University o Washington Department o Chemistry Chemistry 453 Winter Quarter 014 A on-cooperative & Fully Cooperative inding: Scatchard & Hill Plots Assume binding siteswe have derived