Free Energy Calculations: Approximate Methods for Biological Macromolecules

Abstract

In this chapter we present the most important simplified free energy methods in use today and the main biological problems that have motivated their development. The area in which these methods are perhaps the most valuable is the study of molecular recognition between biological molecules, such as an enzyme and a substrate or inhibitor. Noncovalent association between biomolecules is a key element of the biochemistry and information flow in living systems. Many competing effects can contribute to receptor-ligand binding [1]: changes in rotational, translational, conformational, and vibrational entropy of the partners, entropy changes associated with solvent ordering around hydrophobic or charged groups, solute conformational strain, changes in electrostatic and van der Waals interactions within and between the partners and the solvent, counterion reorganization. Experimental studies often combine structure determination methods with point mutagenesis and thermodynamic measurements to obtain information on the binding [2]. However, there are considerable difficulties in the experimental analysis of longer-range electrostatic contributions, the cooperativity between amino acid residues of a protein, or disordered solvent, for example. Such effects can be determined using rigorous free energy simulations, described in the earlier chapters of this book. They can also be incorporated, at different levels of accuracy, into simplified free energy methods.The basic principle of a receptor-ligand binding analysis by free energy simulations is explained in Fig. 12.1 [3]. Most applications focus on binding free energy differences between a series of ligands or protein mutants. For a review of the relevant statistical thermodynamics see [1]. Like experiments, the rigorous free energy simulation method requires a reversible (or near-reversible [4,5]) path between the initial and final states. The Helmholtz free energy change along the horizontal legs in Fig

Alchemical free energy simulations for biological complexes: powerful but temperamental …

“…The two DG prot results are averaged; see Refs. 29,33 for a more theoretical presentation. Importantly, the method uses explicit solvent simulations of both the protonated and deprotonated states, so that dielectric relaxation of the surroundings in response to the new proton is explicitly included in the model.…”

“…[17][18][19][20][21] Nevertheless, MDFE has not completely regained its initial popularity, partly because it remains fairly complex and expensive to use; partly because of cheaper, more approximate and empirical methods, such as ''Poisson-Boltzmann (PB),'' ''Linear Response, '' and ''Langevin Dipole'' methods. 15,[18][19][20][22][23][24][25][26][27][28][29] 117 medium-throughput studies, because of setup costs (human overhead).In this review, we discuss and illustrate the current status of MDFE for biomolecular recognition studies. We emphasize three main points.…”

“…The simpler models employ a dielectric continuum description of all or part of the system and/or a linear response approximation; they have been abundantly reviewed. 15,[18][19][20]22,23,[25][26][27][28][29] Table 1 compares selected MDFE results for AspRS with PBFE, a variant of ''MM-PBSA, '' 18,25,26,29,41 which treats the protein and ligand as simple dielectric bodies. Agreement with MDFE is generally good using a solute dielectric constant of e P ¼ 4.…”

“…A third example is trypsin:BPTI binding, studied recently by Brandsdal et al 35 An Asp-to-Glu mutation was studied with an approximate free energy method, the Linear Interaction Energy (LIE) method, which is analogous to PB/LRA. 23,[27][28][29] The orientation of a nearby Gln and the protonation states of the Asp sidechain were also examined using LIE, whereas the protonation of the mutated Glu was computed with MDFE. Thus, 24 possible states were compared, using a mixture of MDFE and a simpler method.…”

Nucleotide recognition by the initiation factor aIF5B: Free energy simulations of a neoclassical GTPase

“…A low dielectric value is appropriate for the protein because the conformational changes induced by the proton binding are explicitly modeled (through the use of two MD simulations: one each for the protonated/deprotonated states) 50–52. For a detailed discussion of the dielectric properties of proteins and continuum models in general, see Ref 54–58…”