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

Abstract

Several strategies for evaluation of the protein-ligand binding free energies are examined. Particular emphasis is placed on the Linear Response Approximation (LRA) (Lee et. al., Prot Eng 1992;5:215-228) and the Linear Interaction Energy (LIE) method (Aqvist 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 examination 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 introduction of a thermodynamic cycle that decomposes the total binding free energy to electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Prot Eng 1992;5:215-228). The electrostatic contribution is evaluated within the LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potentials of both the polar and non-polar (where all residual charges are set to zero) 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 the LRA and LIE methods. The difference is, however, that the LIE method neglects 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 present case that the contribution from the non-polar states to the protein-ligand binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganized environment to stabilize the residual charges of the ligand. This contribution can be particularly important in cases of charged ligands. The analysis of the non-electrostatic term is much more complex. It is concluded that within the LRA method one has to complete the relevant thermodynamic cycle by evaluating the binding free energy of the "non-polar" ligand, l;, where 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 the cycle. In order to elucidate the nature of this non-electrostatic term and the origin of the scaling constant beta, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, DeltaG(bind,l;). Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate DeltaG(bind,l;) by the PDLD approach, augmented by microscopic calculations of the change in configurational entropy upon binding. This evaluation takes into account the van der Waals, hydrophobic, water penetration and entr...

How valence bond theory can help you understand your (bio)chemical reaction

“…But, since valence bond theory allows one to express the wave-function as a superposition of various structures, one can add other electronic description of the chemical system. The reagent can thus be described by a superposition of structures 1, 25 3, 4 and 6: in 3, the bond between carbon and its chloride is considered as fully ionic with positively charged carbon; in 6, the same bond is again fully ionic but with positively charged chlorine and finally in structure 4, the two electrons of the chloride anion are split between the two chlorine giving rise to a 30 long bond between them. In the product, structures 1 and 6 are replaced by their symmetrical counterparts structures 2 and 5.…”

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“…In addition, case studies where VB theory gives more insights than MO theory will also be discussed. The current tutorial review will start by providing a 30 solid theoretical foundation with which to understand modern applications of VB theory. We will follow this by listing and discussing interesting applications of valence bond theory, in order to demonstrate that valence bond theory is (and always has been) an essential tool to analyze the fate of electrons during 35 chemical reactions.…”

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