AutoDock3

AutoDock3¹ from 1998 is a powerful tool used in computational drug design for predicting the binding conformations of flexible ligands to macromolecular targets. The success of AutoDock3 is largely due to its scoring function, which estimates the free energy change upon binding of the ligand to the protein. This section will provide a detailed explanation of the scoring function used in AutoDock3, focusing on its components and their contributions to the overall binding free energy.

Components

The scoring function in AutoDock3 is an empirical free energy function that has been calibrated using a set of 30 protein-ligand complexes with known binding constants. The function is designed to predict the binding free energy change (\(\Delta G_{binding}\)) and is composed of several terms that account for different types of interactions between the ligand and the protein.

The total free energy change upon binding is the sum of all these individual terms:

\[ \Delta G_{binding} = \Delta G_{vdW} + \Delta G_{hbond} + \Delta G_{elec} + \Delta G_{tor} + \Delta G_{sol}\]

This empirical scoring function allows AutoDock3 to predict the binding affinity of a ligand to a protein by evaluating the sum of these contributions, thus providing insights into the strength and nature of the interaction.

Van der Waals

The van der Waals interactions are described using a Lennard-Jones 12-6 potential, which accounts for both attractive (dispersion) and repulsive interactions between non-bonded atoms. The equation for the van der Waals term is:

\[ \Delta G_{vdW} = \sum_{i,j} \left( A_{ij} r_{ij}^{-12} - B_{ij} r_{ij}^{-6} \right)\]

where \(A_{ij}\) and \(B_{ij}\) are the van der Waals parameters for atom pair \(i, j\), and \(r_{ij}\) is the distance between atoms \(i\) and \(j\).

Hydrogen Bonding

Hydrogen bonds are modeled using a directional 12-10 potential, which emphasizes the angle dependency of hydrogen bonds, ensuring that only properly aligned hydrogen bonds contribute significantly to the energy:

\[ \Delta G_{hbond} = \sum_{i,j} \left( C_{ij} r_{ij}^{-12} - D_{ij} r_{ij}^{-10} \right) E(\theta) \]

Here, \(C_{ij}\) and \(D_{ij}\) are parameters specific to the hydrogen bond interaction, and \(E(\theta)\) is an angular term that ensures directionality.

Electrostatic

Electrostatic interactions are calculated using a Coulomb potential with a distance-dependent dielectric function to account for the screening effect in a solvated environment:

\[ \Delta G_{elec} = \sum_{i,j} \frac{q_i q_j}{\epsilon(r_{ij}) r_{ij}} \]

where \(q_i\) and \(q_j\) are the partial charges on atoms \(i\) and \(j\), respectively, and \(\epsilon(r_{ij})\) is the dielectric constant as a function of distance.

Torsional

The torsional free energy term accounts for the loss of rotational freedom of the ligand upon binding and is proportional to the number of rotatable bonds in the ligand:

\[ \Delta G_{tor} = N_{tor} \cdot k_{tor}\]

where \(N_{tor}\) is the number of rotatable bonds, and \(k_{tor}\) is an empirically determined constant.

Desolvation

The desolvation term estimates the free energy change associated with the removal of the ligand from the solvent and its burial in the binding pocket of the protein. It includes contributions from both polar and nonpolar atoms:

\[ \Delta G_{sol} = \sum_{i,j} S_{i,j} V_{j} \exp(-r_{ij}^2 / 2\sigma^2)\]

where \(S_{i,j}\) are solvation parameters, \(V_{j}\) is the volume of the protein atom \(j\), and \(\sigma\) is a parameter related to the solvation shell thickness.

Calibration and Validation

The empirical coefficients for each term in the scoring function were determined through linear regression analysis using a dataset of known protein-ligand complexes.

Protein-ligand complex table

Protein–Ligand Complex	PDB Code	Log Ki
Concanavalin A / α-methyl-D-mannopyranoside	4cna	2
Carboxypeptidase A / glycyl-L-tyrosine	3cpa	3.88
Carboxypeptidase A / phosphonate ZAA(P=O)P(O)2	6cpa	11.52
Cytochrome P-450 / camphor	2cpp	6.07
Dihydrofolate reductase / methotrexate	4dfr	9.7
α-Thrombin / benzamidine	1dwb	2.92
Endothiapepsin / H-256	zer6	7.22
ε-Thrombin / MQPA	1etr	7.4
ε-Thrombin / NAPAP	1ets	8.52
ε-Thrombin / 4-TAPAP	1ett	6.19
FK506-binding protein(FKBP) / immunosuppressant FK506	1fkf	9.7
D-Galactose / D-glucose binding protein / galactose	2gbp	7.6
Hemagglutinin / sialic acid	4hmg	2.55
HIV-1 Protease / A78791	1hvj	10.46
HIV-1 Protease / MVT101	4hvp	6.15
HIV-1 Protease / acylpepstatine	5hvp	5.96
HIV-1 Protease / XK263	1hvr	9.51
Fatty-acid-binding protein / C15COOH	2ifb	5.43
Myoglobin(ferric) / imidazole	1mbi	1.88
McPC603 / phosphocholine	2mcp	5.23
β-Trypsin / benzamidine	3ptb	4.74
Retinol-binding protein / retinol	1rbp	6.72
Thermolysin / Leu-hydroxylamine	4tln	3.72
Thermolysin / phosphoramidon	1tlp	7.55
Thermolysin / n-(1-carboxy-3-phenylpropyl)-Leu-Trp	1tmn	7.3
Thermolysin / Cbz-Phe-p-Leu-Ala(ZFpLA)	4tmn	10.19
Thermolysin / Cbz-Gly-p-Leu-Leu(ZGpLL)	5tmn	8.04
Purine nucleoside phosphorylase(PNP) / guanine	1ulb	5.3
Xylose isomerase / CB3717	2xis	5.82
Triose phosphate isomerase(TIM) / 2-phosphoglycolic acid(PGA)	2ypi	4.82

This calibration process ensures that the scoring function accurately reflects the observed binding affinities. The final model was validated by comparing its predictions with experimental binding constants, demonstrating good correlation and reliability.

Changes from AutoDock2

Similarities

The scoring functions of AutoDock2 and AutoDock3 share several core features. Both versions use a Lennard-Jones 12-6 potential to model van der Waals interactions. This potential captures both the attractive and repulsive forces between non-bonded atoms, and the parameters \(A_{ij}\) and \(B_{ij}\) are derived from well depths (\(\epsilon\)) and equilibrium contact distances (\(r_{eq}\)). Additionally, both versions employ a 12-10 potential to represent hydrogen bonding interactions. The parameters \(C_{ij}\) and \(D_{ij}\) for hydrogen bonds are similarly derived from the well depths and equilibrium distances, ensuring accurate modeling of the directionality and strength of hydrogen bonds.

Electrostatic interactions in both AutoDock2 and AutoDock3 are calculated using Coulomb's law, which describes the force between two charges. Both versions can use a distance-dependent dielectric function to simulate solvent effects, making the electrostatic interaction calculations more realistic by accounting for the varying dielectric environment in the presence of water and other solvents.

Changes

While the core components of the scoring function remain the same, AutoDock3 introduces several significant enhancements and new terms that improve the accuracy and reliability of docking predictions.

One of the key improvements in AutoDock3 is the enhanced electrostatic interaction model. AutoDock3 uses an improved sigmoidal distance-dependent dielectric function to simulate the transition from the low dielectric constant near the protein surface to the high dielectric constant in the bulk solvent. This enhancement provides a more realistic representation of solvent effects, improving the accuracy of electrostatic interaction calculations.

AutoDock3 also introduces a new desolvation term. This term accounts for the energetic cost of removing the ligand from the solvent and placing it into the binding pocket of the protein. The desolvation term is particularly important for accurately predicting binding affinities, especially for hydrophobic interactions where the removal of water molecules plays a crucial role.

Another significant addition in AutoDock3 is the torsional free energy term. This term accounts for the loss of rotational entropy of the ligand upon binding to the protein. The torsional free energy term is proportional to the number of rotatable bonds in the ligand, penalizing flexible ligands that lose more entropy upon binding. This addition improves the prediction of binding affinities for ligands with many rotatable bonds, making the docking results more reliable.

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1. Morris, G. M., Goodsell, D. S., Halliday, R. S., Huey, R., Hart, W. E., Belew, R. K., & Olson, A. J. (1998). Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. Journal of computational chemistry, 19(14), 1639-1662. DOI: 10.1002/(SICI)1096-987X(19981115)19:14<1639::AID-JCC10>3.0.CO;2-B ↩