Physico-Chemical and Computational Approaches to Drug Discovery

By F. Javier Luque, Xavier Barril

The Royal Society of Chemistry

Copyright © 2012 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-1-84973-353-3

Contents

Chapter 1 Recognition of Ligands by Macromolecular Targets Salomé Llabrés, Jordi Juárez, Flavio Forti, Ramón Pouplana and F. Javier Luque, 1,
Chapter 2 Thermodynamics of Ligand Binding György G. Ferenczy and György M. Keserü, 23,
Chapter 3 Continuum Solvation in Biomolecular Systems Traian Sulea and Enrico O. Purisima, 80,
Chapter 4 Bioavailability Prediction at Early Drug Discovery Stages: In Vitro Assays and Simple Physico-Chemical Rules Jordi Munoz-Muriedas, 104,
Chapter 5 Molecular Descriptors for Database Mining. Translating Empirical Chemistry into Mathematics: Tools for QSAR and In Silico Screening Based on the Hydrophobicity of Small Molecules Francesca Spyrakis, Pietro Cozzini and Glen E. Kellogg, 128,
Chapter 6 Pharmacophore Models in Drug Design Valerie J. Gillet, 151,
Chapter 7 Docking and Virtual Screening Garrett M. Morris, 171,
Chapter 8 Binding Free Energy Calculation and Scoring in Small-Molecule Docking Claudio N. Cavasotto, 195,
Chapter 9 Accounting for Target Flexibility During Ligand–Receptor Docking Simon Leis and Martin Zacharias, 223,
Chapter 10 COMparative BINding Energy (COMBINE) Analysis as a Structure-Based 3D-QSAR Method Antonio Morreale and Federico Gago, 244,
Chapter 11 Enhanced Sampling Methods in Drug Design Walter Rocchia, Matteo Masetti and Andrea Cavalli, 273,
Chapter 12 Expanding the Target Space: Druggability Assessments Peter Schmidtke, Daniel Alvarez-Garcia, Jesus Seco and Xavier Barril, 302,
Chapter 13 Computational Strategies and Challenges for Targeting Protein–Protein Interactions with Small Molecules Daniela Grimme, Domingo González-Ruiz and Holger Gohlke, 319,
Chapter 14 Using Molecular Simulations and Metadynamics to Predict Binding Free Energies and Kinetics: the Case of Cox and Cdk2 Giorgio Saladino and Francesco L. Gervasio, 360,
Chapter 15 Computer-Assisted Design of Drug-Like Synthetic Libraries P. Seneci, V. Frecera and S. Miertus, 372,
Subject Index, 399,

CHAPTER 1

Recognition of Ligands by Macromolecular Targets

SALOMÉ LLABRÉ S, JORDI JUÁREZ, FLAVIO FORTI, RAMÓN POUPLANA AND F. JAVIER LUQUE

Departament de Fisicoquímica and Institut de Biomedicina (IBUB), Facultat de Farmàcia, Universitat de Barcelona, Av. Diagonal 643, E-08028 Barcelona, Spain

1.1 Physical Basis of Ligand–Protein Binding

Molecular recognition and binding is essential in mediating a variety of processes and functions in the cell. Enzyme catalysis, receptor signalling, storage of small molecules, transport through membranes and immunological response are examples that illustrate the relevance of recognition and binding between biomolecules. The rules of physics provide the basic principles to understand molecular association, and the affinity between interacting partners can be related to macroscopic observables through the laws of thermodynamics.

Under thermodynamic equilibrium conditions, the noncovalent, reversible binding of a small molecule (ligand; L) to a given protein (target; R) is determined by the standard Gibbs free energy (ΔG° Eq. 1.1), which is composed of an enthalpic (ΔH°) and an entropic (–TΔS°) term.

Raq + Laq [??] R’L’aq

ΔG° = ΔH° – TΔS° (1.1)

The binding affinity can be expressed either in terms of the standard free energy difference between bound and unbound states, or alternatively in terms of the equilibrium constant (K) for the formation of the complex between the interacting partners (Eq. 1.2).

ΔG° = -RTlnK (1.2)

where R is the gas constant and T is the temperature.

The binding affinity between a ligand and its macromolecular target reflects a subtle balance between enthalpic and entropic contributions, which are generally interpreted by decomposing the protein–ligand binding into a number of separate contributions. The structural (shape and size) and chemical (nature and spatial distribution of functional groups) complementarity between the ligand and the residues that are present in the binding pocket modulates the binding affinity through a variety of intermolecular interactions (Figure 1.1). They include electrostatic interactions between the permanent charge distribution of the molecules, the induction of changes in the charge distribution due to the interaction between partners, the stabilizing contribution arising from dispersion forces, and the repulsion between electron clouds at close distances. These energy contributions contribute to typical interactions such as salt bridges, standard hydrogen bonds (where a hydrogen bond bound to an electronegative atom X forms an attractive interaction with another electronegative atom Y: X–H···Y) and van der Waals forces. However, there has been an enrichment in the number and nature of intermolecular interactions, including interactions such as cation– π or anion–π complexes, non-standard hydrogen bonds (C–H···X, C–H···π, blue-shifting hydrogen bonds) and halogen bonding.

The net stabilizing energy due to ligand–protein interactions compensates for unfavorable contributions to the binding. Thus, molecular association implies dehydration of the complementary surfaces of both ligand and target and reorganization of water molecules around the ligand–protein complex. Therefore, the energy gain due to the seemingly favorable interactions formed in the complex must counterbalance the cost due to breaking interactions of the separate partners with hydrating waters. For simple neutral organic compounds the hydration free energies generally lie in a relatively narrow range (for instance, the experimental values for the transfer of ethane and acetamide from the gas phase to water amount to +1.8 and -9.7 kcal mol-1, respectively).15 However, the hydration free energy of charged compounds is much larger, which reflects the strengthening of the interactions with water molecules (as an example, hydration free energies of –73 and –77 kcal mol-1 have been determined for the ethylammonium cation and acetate anion).16 Accordingly, there must be a sizable compensation between the energy cost of dehydrating both ligand and binding site residues and the energy gain due to the protein–ligand interactions upon burial of the ligand in the binding pocket.

Protein–ligand binding is often accompanied by conformational changes in the interacting partners. Beyond the rigid “lock-and-key” model, binding events include a broader range of potential scenarios, such as the popular “induced fit” mechanism, the alternative “conformational selection” process, or even more complex models that combine the selection of specific conformations with the induction of structural readjustments by the binding partner. However, even predicting the energy cost associated with conformational changes in the ligand has proved to be very challenging, as noted by the uncertainties associated with the choice of the level of theory used to determine the cost of selecting the bioactive conformation. As an example, we simply quote that Tirado-Rives and Jorgensen concluded that the uncertainty in determining the conformer-focusing penalty can be anticipated conservatively to be in the 5–10 kcal mol-1 range.

Finally, one must take into account the entropy changes, which include the loss of translational and rotational degrees of freedom upon molecular association, the reduction in the number of accessible states associated with internal rotations of both ligand and protein, and the reorganization of water molecules upon formation of the complex. As an example, we quote here a recent study by Gilson and co-workers where they examined the entropy loss for the binding of amprenavir to HIV protease. They estimated that amprenavir loses 26.4 kcal mol-1 of configurational entropy upon binding, including both the conformational and vibrational contributions and accounting for changes in mobility along translational, rotational and internal coordinates. Finally, they also noticed that the loss of entropy results primarily from the narrowness of the energy wells of bound amprenavir relative to free ligand, as the change in vibrational entropy was estimated to be 24.6 kcal mol-1.

Ligand–protein binding affinities generally fall into a narrow range varying between 10-2 and 10-12 M. Remarkably, at 298 K an uncertainty in the binding free energy of 1.36 kcal mol-1 alters the binding constant by one order of magnitude, which highlights the need to estimate accurately the binding affinity. Nevertheless, the difficulty in predicting the binding affinity stems from the fact that the relatively narrow range of binding free energies is the result of compensation between generally large enthalpic and entropic terms, so that small changes in the binding free energy can mask sizable and mutually compensating changes in both enthalpy and entropy. Since the enthalpic and entropic components comprise useful information on the details of protein–ligand interaction, monitoring binding thermodynamics and discriminating between enthalpy-driven and entropy-driven optimizations can be relevant for the success of drug discovery programs (see also Chapter 2 for a detailed review). Therefore, not only the binding free energy but also the thermodynamic signature encoded by its enthalpic and entropic components are valuable for guiding lead discovery and optimization.

Predicting accurately the binding free energy is a formidable challenge to current computational methods, due to the large magnitude of the separate contributions to the binding free energy and the compensation between enthalpic and entropic terms. However, this is a fundamental ingredient for the success of drug discovery, especially when one realizes that the maximal free energy contribution per non-hydrogen atom in a drug-like ligand amounts to ca. -1.5 kcal mol-1. Therefore, maximizing the structural and chemical complementarity between a ligand and its target, and enhancing the synergistic cooperativity between ligand–protein interactions, should be effective guidelines for the success of drug discovery.

1.2 Prediction of Binding Affinities: Free Energy Calculations

A qualitative understanding of the physico-chemical features that contribute to drug binding is valuable for the analysis of structure–activity relationships encoded in pharmacophoric models, as the pharmacophore represents the ensemble of steric and electronic features necessary to ensure the optimal supramolecular interaction with a specific biological target. However, a quantitatively accurate estimate of the binding affinity is required in other instances, such as lead optimization. The use of classical simulations in conjunction with free energy calculations have proved to be very valuable for predicting relative binding affinities arising from small chemical differences between structurally related compounds. The most popular methods are free energy perturbation and thermodynamic integration.

In a general context, the free energy difference between systems A and B, which might represent the two ligands that bind to a common target or a mutation of a specific residue in the binding site of the target, can be expressed as indicated in eqn (1.3):

[MATHEMATICAL EXPRESSION OMITTED] (1.3)

where ΔH = HB – HA and <>A stands for the ensemble average over a system described by Hamiltonian HA.

When systems A and B differ in a significant way, the practical solution of eqn (1.3) requires the decomposition of the alchemical transformation A->B into a number of successive steps, which is accomplished by defining a coupling parameter (λ) that controls the smooth change between initial and final states. Thus, at each intermediate step, one can define the Hamiltonian H(λ) as indicated in eqn (1.4):

H(λ)=λHB + (1 – λ)HA (1.4)

In free energy perturbation calculations, the free energy change for the transformation of ligand L1 into L2, either free in solution or in the protein– ligand complex, can be determined by the addition of the free energy changes for each of the distinct windows leading from the initial (λ = 0) to the final (λ = 1) states, as noted in eqn (1.5):

[MATHEMATICAL EXPRESSION OMITTED] (1.5)

where ΔHλ = Hλ+Δλ – Hλ.

Thermodynamic integration provides an alternative solution, where the change in free energy between the initial and final states can be determined as indicated in eqn (1.6), where one has to evaluate the ensemble average of the derivative of the Hamiltonian with respect to the coupling parameter λ:

[MATHEMATICAL EXPRESSION OMITTED] (1.6)

These techniques rely on a rigorous formalism that permits estimation of the absolute and relative binding affinities. Computation of the absolute binding affinity can be achieved by using the double decoupling methodology, where the interaction of the ligand with the molecular environment (i.e., water molecules in the free state, and the hydrated complex in the bound state) is turned on/off in different stages. To this end, the ligand is converted from a fully interacting state in the bound complex to an ideally constrained state, where interactions with the environment are turned off but the ligand is constrained to stay in the vicinity of the protein. This is convenient in order to avoid the ligand having to explore the entire simulation box, which would be extremely demanding to achieve convergence in the computed free energy change. When the ligand is fully decoupled, it is a molecule of ideal gas still constrained to occupy a given region, and release of the restraining potential (affording the ligand to occupy the whole volume and to rotate freely) provides a correction term to the free energy. Finally, the binding free energy is determined upon addition of the free energy required for removing the ligand from the bulk solvent to the gas phase.

Prediction of relative binding free energies have larger practical interest, as the relative binding affinity between two ligands can be related to specific chemical modifications introduced in a drug candidate during lead optimization. As shown in Figure 1.2, this can be determined by alchemical mutations that convert the two ligands (L1 and L2) in the unbound and bound states, allowing for an extensive sampling of the protein–ligand complex (and the free ligand in solution) in a realistic environment.

If evaluated accurately, the free energy change should be independent of path and simulation protocol. Nevertheless, a number of practical considerations must be taken into account. First, the use of the thermodynamic cycle shown in Figure 1.2 is convenient because (i) it permits the simulation of non-chemical processes in order to calculate the relative binding affinity between ligands L1 and L2, avoiding the difficulty to carry out in a reversible way the direct association between each ligand with the target, and (ii) the comparison of the free energy changes for the alchemical transformation between ligands in solution and in the complex might benefit from the cancellation of errors in the simulations in unbound and bound states. However, the accuracy of the free energy changes is limited by different factors, such as the assumption of the simulated systems to be in equilibrium, or the need to include all relevant configurations in the ensemble. Even in the absence of large conformational changes that mediate ligand binding, which would require enhanced sampling techniques (see Chapter 11 for a review), the accuracy of the results is mainly limited by the quality of the force fields, which generally rely on a pairwise description of intermolecular interactions.

1.3 Quantum Mechanical-Guided Refinements in Interaction Energy Potentials

Classical force fields only represent approximately the intermolecular interactions that mediate the recognition between ligands and proteins. Although the use of simplified expressions is understandable in terms of providing an efficient sampling, as well as of facilitating the parametrization of the large number of functional groups that can be incorporated in drug-like molecules, there is concern regarding the suitability of current biomolecular force fields to provide accurate estimates of free energy differences. As noted by Michel and Essex, it seems reasonable to expect that free energy calculations cannot predict binding free energies more accurately than they can predict solvation free energies, where the uncertainties obtained for small organic compounds can be estimated to be around 1 kcal mol-1. Larger deviations can be expected for more complex, flexible polyfunctional drug-like molecules.

(Continues…)Excerpted from Physico-Chemical and Computational Approaches to Drug Discovery by F. Javier Luque, Xavier Barril. Copyright © 2012 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.