Synthetic Adenine Receptors:  Direct Calculation of Binding Affinity and Entropy

Abstract

A novel method for calculating binding free energies is applied to a series of water-soluble adenine receptors that have been characterized experimentally. The calculations use a predominant states method, "Mining Minima", to identify and account for the low-energy conformations of the free and bound species. The CHARMM force field is used to estimate potential energies, and an adjusted form of the generalized Born/ surface area model is used to estimate solvation energies as a function of conformation. The computed binding free energies agree with experiment to within 2.9 kJ/mol (0.7 kcal/mol) and reproduce observed trends across the series of receptors. Preorganization of two rotatable bonds enhances the calculated affinity of one receptor/ adenine complex by -2.5 kJ/mol (-0.6 kcal/mol), and the change in translational/rotational entropy (-T∆S°t rans/rot ) is 30 kJ/mol (7 kcal/mol). The concept of the translational/rotational entropy change upon binding in the present model is compared with others previously presented in the literature.

Poisson–Boltzmann model analysis of binding mRNA cap analogues to the translation initiation factor eIF4E

“…Minh and coworkers estimated the entropic cost of acetylcholinesterase binding to fasciculin-2 as 30 cal/mole K [45], what leads to about 9 kcal/mole at room temperature. Luo and Gilson [47] for the binding of adenine to synthetic adenine receptors and Hermans and Wang [46] for the binding of benzene to a lysozyme cavity, obtained −T ∆S t,r of about 7 kcal/mole. Lazaridis and coworkers based on molecular dynamics simulations with implicit solvation of the binding of biotin, biotin analogs and two peptides to avidin and streptavidin [43], estimated −T ∆S t,r as about 6 kcal/mole.…”

Calculations of protein-ligand binding entropy of relative and overall molecular motions

“…They obtained the total entropy of 8.3 kcal/mol using Schlitter's formula, 8.5 kcal/mol using quasiharmonic analysis, 6.0 kcal/mol using uniform distribution of the ligand center of mass and Euler angels, 5.4 kcal/mol using Gaussian distribution of the ligand center of mass and Euler angels. Luo and Gilson [64] took a different approach to compute the translational and rotational entropy. They used the ''Mining Minima'' method to analyze binding of adenine to synthetic adenine receptors and obtained the value of 7 kcal/mol.…”

Novel knowledge-based potentials for ligand docking: variational approach to the old problem

“…However at present binding free energy cannot not be obtained exactly from ab initio calculations and statistical mechanics, and therefore various approximate methods [1,2] have been used to calculate protein-ligand binding free energy change DG. These methods fall into three main categories: force-field-based approaches [3][4][5][6][7][8], knowledge-based approaches [9][10][11][12][13][14] and regression-based (empirical) approaches [15][16][17][18]. De novo drug design and virtual database screening [19] demand fast estimates of binding affinity of millions of generated ligands to the protein targets.…”

“…in virtual screening experiments), but at the same time a number of entropic effects, which are not pair-wise functions of atom-to-atom relative positions per se, fall out of the consideration. Force-field-based models [3][4][5][6][7][8]29] utilize a decomposition of the protein-ligand binding free energy in the form of…”

“…Entropy terms DG tr , DG H and DG v are essentially not pair-wise functions and thus cannot be considered with traditionally derived knowledge-based potentials. The estimates of the lost effect only due to the DG tr are as follows: 3.6-4.8 kcal/mol [33], 4.5-6 kcal/mol [7], 7 kcal/mol [6], 15 kcal/mol [30]. The conformational entropy changes do not accounted in the common knowledge-based scheme, also should be included additionally especially for large flexible ligands [14,37].…”