Calculation of the Absolute Free Energy of Binding and Related Entropies with the HSMD-TI Method: The FKBP12-L8 Complex

Structure and chemistry of enzymatic active sites that play a role in the switch and conformation mechanism

Enzymes, which are biological molecules, are constructed from polypeptide chains, and these molecules are activated through reaction mechanisms. It is the role of enzymes to speed up chemical reactions that are used to build or break down cell structures. Activation energy is reduced by the enzymes' selective binding of substrates in a protected environment. In enzyme tertiary structures, the active sites are commonly situated in a "cleft," which necessitates the diffusion of substrates and products. The amino acid residues of the active site may be far apart in the primary structure owing to the folding required for tertiary structure. Due to their critical role in substrate binding and attraction, changes in amino acid structure at or near the enzyme's active site usually alter enzyme activity. At the enzyme's active site, or where the chemical reactions occur, the substrate is bound. Enzyme substrates are the primary targets of the enzyme's active site, which is designed to assist in the chemical reaction. This chapter elucidates the summary of structure and chemistry of enzymes, their active site features, charges and role of water in the structures to clarify the biochemistry of the enzymes in the depth of atomic features.

Absolute Free Energy of Binding and Entropy of the FKBP12-FK506 Complex: Effects of the Force Field

The hypothetical scanning molecular dynamics (HSMD) method combined with thermodynamic integration (HSMD-TI) has been extended recently for calculating ΔA(0)-the absolute free energy of binding of a ligand to a protein. With HSMD-TI, ΔA(0) is obtained in a new way as a sum of several components, among them is ΔSligand-the change in the conformational entropy as the ligand is transferred from the bulk solvent to the active site-this entropy is obtained by a specific reconstruction procedure. This unique aspect of HSMD (which is useful in rational drug design) is in particular important for treating large ligands, where ΔSligand might be significant. Technically, one should verify that the results for ΔSligand converge-a property that might become more difficult for large ligands; therefore, studying ligands of increasing size would define the range of applicability of HSMD-TI for binding. In this paper, we check the performance of HSMD-TI by applying it to the relatively large ligand FK506 (126 atoms) complexed with the protein FKBP12, where ΔA(0) = -12.8 kcal/mol is known experimentally as well as the crystal structure of the complex. This structure was initially equilibrated by carrying out a 100 ns molecular dynamics trajectory, where the system is modeled by the AMBER force field, TIP3P water, and Particle Mesh Ewald. HSMD-TI calculations were carried out in three conformational regions defined by the intervals [0.2,2], [2,5], and [5,100] ns along the trajectory, where local equilibration of the total energy has been observed; we obtained ΔA(0) = -13.6 ± 1.1, -16.6 ± 1.4, and -16.7 ± 1.4 kcal/mol, respectively indicating the following: (1) The second and third regions belong to the same conformational subspace of the complex, which is different from the [0.2,2] ns subspace. (2) The unsatisfactory result for ΔA(0) obtained in the well equilibrated (hence theoretically preferred) latter regions reflects the nonperfect modeling used, which however (3) has led to the experimental ΔA(0) in the [0.2,2] ns region close to the crystal structure. Keeping the complex near its crystal structure has been a successful approach in the literature. To check this avenue further, we applied harmonic restraints on backbone atoms and obtained unsatisfactory results for ΔA(0), suggesting that implementation of this approach is not straightforward. Converging results for ΔSligand were obtained in all regions, where the result ΔSligand([0.2,2]) = 7.1 ± 1.2 kcal/mol is less region dependent than ΔA(0) and is relatively large probably due to the large ligand.

Prediction of the binding affinity of compounds with diverse scaffolds by MP-CAFEE

Accurate methods to predict the binding affinities of compounds for target molecules are powerful tools in structure-based drug design (SBDD). A recently developed method called massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) successfully predicted the binding affinities of compounds with relatively similar scaffolds. We investigate the applicability of MP-CAFEE for predicting the affinity of compounds having more diverse scaffolds for the target p38α, a mitogen-activated protein kinase. The calculated and experimental binding affinities correlate well, showing that MP-CAFEE can accurately rank the compounds with diverse scaffolds. We propose a method to determine the optimal number of sampling runs with respect to a predefined level of accuracy, which is established according to the stage in the SBDD process being considered. The optimal number of sampling runs for two key stages-lead identification and lead optimization-is estimated to be five and eight or more, respectively, in our model system using Cochrans sample size formula.

Standard binding free energies from computer simulations: What is the best strategy?

Accurate prediction of standard binding free energies describing protein:ligand association remains a daunting computational endeavor. This challenge is rooted to a large extent in the considerable changes in conformational, translational and rotational entropies underlying the binding process that atomistic simulations cannot easily capture. In spite of significant methodological advances, reflected in a continuously improving agreement with experiment, a characterization of alternate strategies aimed at measuring binding affinities, notably their respective advantages and drawbacks, is somewhat lacking. Here, two distinct avenues to determine the standard binding free energy are compared in the case of a short, proline-rich peptide associating to the Src homology domain 3 of tyrosine kinase Abl. These avenues - one relying upon alchemical transformations and the other on potentials of mean force (PMFs) - invoke a series of geometrical restraints acting on collective variables designed to alleviate sampling limitations inherent to classical molecular dynamics simulations. The experimental binding free energy of ΔG_bind = -7.99 kcal/mol is well reproduced by the two strategies developed herein, with ΔG_bind = -7.7 for the alchemical route and ΔG_bind = -7.8 kcal/mol for the alternate PMF-based route. In detailing the underpinnings of these numerical strategies devised for the accurate determination of standard binding free energies, many practical elements of the proposed rigorous, conceptual framework are clarified, thereby paving way to tackle virtually any recognition and association phenomenon.

Absolute free energy of binding of avidin/biotin, revisited

The binding of biotin to avidin is one of the strongest in nature with absolute free energy of binding, ΔA(0) = -20.4 kcal/mol. Therefore, this complex became a target for a large number of computational studies, which all, however, are based on approximate techniques or simplified models and have led to a wide range of results Therefore, ΔA(0) is calculated here by rigorous statistical mechanical methods and models that consider long-range electrostatics. (1) We apply our method, "hypothetical scanning molecular dynamics with thermodynamic integration" (HSMD-TI) to avidin-biotin modeled by periodic boundary conditions with particle mesh ewald (PME). (2) We apply the double decoupling method (DDM) to this system modeled by the spherical solvent boundary potential (SSBP) and the generalized solvent boundary potential (GSBP). The corresponding results for neutral biotin, ΔA(0) = -29.1 ± 0.8 and -25.2 ± 0.5 kcal/mol are significantly lower than the experimental value; we also provide the result for a charged biotin, ΔA(0) = -33.3 ± 0.8 kcal/mol. It is plausible to suggest that this disagreement with the experiment may stem from ignoring the (positive) contribution of a mobile loop that changes its structure upon ligand binding.