Chap 11. Forces Between Molecules, and Binding Energies (cont’d)

B. The Binding Energies of Proteins and Ligands The essence of binding between enzymes and substrates: the matching of complementary surfaces sloughing the water of solvation off Required energies for calculation: energies between enzymes and substrates or other ligands Their interaction energies with water and the changes in entropy

1. The Hydrophobic Bond A way of describing the tendency of nonpolar compounds to transfer from an aqueous solution to an organic phase Regaining entropy by water Dispersion energies of hydrocarbons Convenient way of measuring the hydrophobicity of a molecule: measuring the partition between the organic and aqueous phases

a. Simplified macroscopic model for comparing the free energies of transfer of side chains from water to hydrocarbons with transfer to proteins Notional steps 1.Removal of the hydrocarbon to vacuum 2.Creation of a cavity in the hydrocarbon solvent 3.Transfer of the solute to the hydrocarbon solvent and the collapse of the cavity in water cf. w (work of adhesion per unit area) = γ 1 + γ 2 – γ 1/2

Case A: Transfer of hydrocarbon from water to hydrocarbon ΔG trans = -Aγ HC/W Case B: Transfer of hydrocarbon from water to hydrocarbon (protein) with preformed water-filled cabity ΔG trans = -2Aγ HC/W Two principles arise from this analysis 1.The energy of the hydrophobic effect should be proportional to the surface area that is buried 2.The effect should be twice as strong for the binding of hydrocarbons in preformed cavities in proteins

b. Hydrophobicity of small groups: The Hansch equation P 0 : the ratio of the solubility of the parent compound P: the ration of the solubility of the substituted compound The values of π from groups that are not strongly electron- donating or –withdrawing are virtually constant in independent of the group to which they are attached. Their effects are additive. The behavior of groups that can conjugate with the benzene ring, such ad the nitro and amino groups, is variable and depends on the other groups attached to the ring

c. Aqueous solvation energies The incremental free energies of transfer of amino acid side chains from water to near vacuum (low gas pressure): useful in understanding how mutations in proteins affect the energies of the denatured state

2. Hydrogen Bonds, Salt Bridges, and the Hydrogen Bond Inventory E–XH···OH 2 + OH 2 ···B–S E–XH ···B–S + H 2 O ···H 2 O If –XH a good donor and B a good acceptor, two good hydrogen bonds on each side: little change in enthalpy If –XH a poor donor but B a good acceptor, one strong bond and one weak one on each side: little change in enthalpy Hydrogen bonding is relatively isoenthalpic Energetically favorable because of the increase in entropy on the release of bound water molecules

E/OH 2 + OH 2 ···B–S E/B–S + H 2 O ···H 2 O If –XH a weak acceptor and B a good acceptor, one hydrogen bonds on each side: isoenthalpic and an unpaired hydrogen bond acceptor E–NH 3 + ··· OH 2 + OH 2 ··· - O 2 C–S E–NH 3 + ··· - O 2 C–S + H 2 O ···H 2 O If an ammonium ion and a carboxylate, two hydrogen bonds on each side and a favorable electrostatic interaction on the right: In practice, the energies are balanced

C. Experimental Measurements of Incremental Energies A crucial difference between measuring affinity for an enzyme and measuring the partitioning in organic solvents: the solvent can adjust its structure but the enzyme has a predetermined geometry A measure of the relative affinities of two substrates for an enzyme is a measure of the specificity of an interaction and is not a true measure of the binding energy It is safe way to remove groups from a larger substrate than to add to or substitute group 1. Binding versus Specificity

2. Estimation of Increments in Binding Energy from Kinetics Comparing the dissociation constants of R-S and H-S from the enzyme Often underestimating the binding energy of the larger substrate because enzymes frequently use binding energy to lower the activation energies of reactions A better method is to compare k cat /K M

a. Intrinsic binding energies The intrinsic binding energy of a group: the maximum binding energy possible Enzymes often do not utilize all of the intrinsic binding energy of a group: controlling specificity - Phenylalanyl-tRNA synthetase: evolved to bind tyrosine as weakly as possible - Tyrosyl-tRNA synthetase: evolved to bind the –OH of tyrosine as tightly as possible

b. Estimation of the upper limits of binding energies by measurements on the aminoacyl-tRNA synthetases Group Incremental Gibbs energy of transfer from enzyme to water kcal/mol -CH CH 2 CH CH(CH 3 ) S-5.4 -CH 3 : 3.2 kcal/mol for enzymes 0.68 kcal/mol for n-octanol

c. Typical binding energies from measurements on chymotrypsin R-CH(NHAc)CO 2 CH 3, R: an unbranched alkyl chain The decrease in the activation energy is 2.2 times greater than the free energy of trnasfer of the alkyl groups from water to n-octanol 2.2-fold more hydrophobic binding pocket than n-octanol

d. Why are enzymes more hydrophobic than organic solvents? Chymotrypsin 16 water molecules filled in the binding pocket Two unfavorable hydrophobic-water interfaces: one around the substrate and one inside the enzyme The dispersion energy: a further effect on the binding energy (2 kcal/mol)

e. Buried charged groups and high apparent energies E-CO 2 - ···OH 2 + OH 2 ··· + H 3 N-S E-CO 2 - ··· + H 3 N-S + H 2 O···H 2 O E-CO 2 - ···OH 2 + H-S E-CO 2 - ···/H-S + H 2 O···H 2 O Removal of one of the partners to give a buried charge gives large changes in binding energy Huge energy of desolvation of a charged group the structure rearrange so that water can penetrate to protein to solvate the strength the salt bridge

D. Entropy and Binding No detection of the pairing of monomeric complementary bases: A-U Strong binding of a triplet of bases to a complementary anticodon of a tRNA: 2 × 10 3 M -1 Entropy effects: releasing the hydrogen-bonded water molecules cf. the chelate effect

E. Enthalpy-entropy compensation A weak interaction: a bond with a low vibrational frequency – giving an appreciable entropy A particle in a shallow, wide, energy well: more entropy in a deep, narrow well: less entropy Enthalpy-entropy compensation when the bond is broken

F. Summary The dissociation constant of an enzyme and substrate: reflecting the relative stabilities of the substrate – the strength of the hydrogen bonding – the stability of the salt linkages – the dispersion energies – the hydrophobic bonding The absolute energy of interaction between the enzyme and the substrate – the dispersion forces – the absolute energies of the hydrogen bonds and salt linkages