Examining methods for calculations of binding free energies: LRA, LIE, PDLD-LRA, and PDLD/S-LRA calculations of ligands binding to an HIV protease

Several strategies for evaluation of the protein-ligand binding free energi es are examined. Particular emphasis is placed on the Linear Response Appro ximation (LRA) (Lee et. al., Prot Eng 1992;5:215-228) and the Linear Intera ction Energy (LIE) method (Angstrom qvist et. al., Prot Eng 1994;7:385-391) . The performance of the Protein Dipoles Langevin Dipoles (PDLD) method and its semi-microscopic version (the PDLD/S method) is also considered. The e xamination is done by using these methods in the evaluating of the binding free energies of neutral C2-symmetric cyclic urea-based molecules to Human Immunodeficiency Virus (HIV) protease. Our starting point is the introducti on of a thermodynamic cycle that decomposes the total binding free energy t o electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Pro t Eng 1992;5:215-228). The electrostatic contribution is evaluated within t he LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potential s of both the polar and non-polar (where all residual charges are set to ze ro) states of the ligand. This average involves a scaling factor of 0.5 for the contributions from each state and this factor is being used in both th e LRA and LIE methods. The difference is, however, that the LIE method negl ects the contribution from trajectories over the potential of the non-polar state. This approximation is entirely valid in studies of ligands in water but not necessarily in active sites of proteins. It is found in the presen t case that the contribution from the non-polar states to the protein-ligan d binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganiz ed environment to stabilize the residual charges of the ligand. This contri bution can be particularly important in cases of charged ligands. The analy sis of the non-electrostatic term is much more complex. It is concluded tha t within the LRA method one has to complete the relevant thermodynamic cycl e by evaluating the binding free energy of the "non-polar" ligand, rho', wh ere all the residual charges are set to zero. It is shown that the LIE term , which involves the scaling of the van der Waals interaction by a constant beta (usually in the order of 0.15 to 0.25), corresponds to this part of t he cycle. In order to elucidate the nature of this non-electrostatic term a nd the origin of the scaling constant beta, it is important to evaluate exp licitly the different contributions to the binding energy of the non-polar ligand, Delta G(bind,rho'). Since this cannot be done at present (for relat ively large ligands) by rigorous free energy perturbation approaches, we ev aluate Delta G(bind,rho') by the PDLD approach, augmented by microscopic ca lculations of the change in configurational entropy upon binding. This eval uation takes into account the van der Waals, hydrophobic, water penetration and entropic contributions, which are the most important free energy contr ibutions that make up the total Delta G(bind,rho'). The sum of these contri butions is scaled by a factor theta and it is argued that obtaining a quant itative balance between these contributions should result in theta = 1. By doing so we should have a reliable estimate of the value of the LIE beta an d a way to understand its origin. The present approach gives theta values b etween 0.5 and 0.73, depending on the approximation used. This is encouragi ng but still not satisfying. Nevertheless, one might be able to use our PDLD approach to estimate the ch ange of the LIE theta between different protein active sites. It is pointed out that the LIE method is quite similar to our original appr oach where the electrostatic term was evaluated by the LRA method and the n on-electrostatic term by the PDLD method (with its vdw, solvation, and hydr ophobic contributions). The practical difference is that the LIE method app roximates the non-electrostatic term by the average of the van der Waals in teraction, while our LRA method evaluates this term by the PDLD method. Thi s point is illustrated by the fact that our LRA approach gives results of s imilar quality to those obtained by the LIE approach. Finally it is found t hat results of similar quality are obtained by the PDLD/S method and the LR A method. This is significant since the PDLD/S method is much faster than t he LRA and LIE methods. However, more studies of the relative accuracy on o ther systems are needed in order to establish their relative merits. (C) 20 00 Wiley-Liss, Inc.