Computational methods for calculating binding free energies of ligands in COX-1

YASMIN SHAMSUDIN KHAN

Licentiate thesis 2014 Department of Cell and Molecular Biology

Uppsala University

Abstract Khan, Y.S. 2014. Computational Methods for calculating binding free ener-gies in COX-1. Department of Cell and Molecular Biology. 38 pp. Uppsala. Accurate calculations of binding free energies can be useful in the process of drug discovery, especially in the hit generation and hit to lead optimiza-tion. Over the past few decades, computer simulations have become estab-lished methods for furthering the understanding of biochemical processes and properties. In this thesis, several computational methods were used to calculate binding affinities for a challenging test set consisting of 45 struc-turally diverse and well-known non-steroidal anti-inflammatory drugs (NSAIDs). The data set represents a wide range in the binding affinities to the drug target cyclooxygenase-1 (COX-1), which is a target known to be difficult for computational docking studies, one of the most common com-putational methods used in drug discovery. We optimized a protocol combining molecular docking, molecular dynam-ics simulations and the linear interaction energy (LIE) method, achieving excellent agreement between the experimentally observed and the calculated affinities. This demonstrates that the LIE method is a useful method for pre-dicting binding affinities, even for a challenging set of diverse molecules, provided that the initial docking poses is accurate enough. The results were further improved when the average of several experimental assays was considered, rather than using the experimental data from one assay. As such, we suggest that this computational model is useful for un-derstanding protein-ligand interactions and binding affinities, thus making it a great model for use in designing and testing new pain-relieving pharma-ceuticals. Keywords: molecular dynamics simulations, binding free energy, linear in-teraction energy, molecular docking, cyclooxygenase-1 Yasmin Shamsudin Khan, Department of Cell and Molecular Biology, Com-putational and Systems Biology, Box 596, Uppsala university, SE-75124 Uppsala, Sweden. © Yasmin Shamsudin Khan 2014

To my Family.

Publication

This thesis is based on the paper below, which is referred to in the text as Paper I.

I Shamsudin Khan, Y., Gutiérrez-de-Terán, H., Boukharta, L., Åqvist, J. (2014) Towards an Optimal Docking and Free Energy Calculation Scheme in Ligand Design with Application to COX-1 Inhibitors. J. Chem. Inf. Mod-el. 2014, 54, 1488-1499.

Contents

Introduction ....................................................................................................................... 13  

Computational Methods .................................................................................................... 15  Homology Modelling .................................................................................................... 15  Molecular Mechanics and Force Fields ........................................................................ 16  Automated Molecular Docking and Scoring ................................................................ 17  

Scoring Functions .................................................................................................... 18  Molecular Dynamics ..................................................................................................... 20  

Spherical Boundary Conditions ............................................................................... 20  

The Linear Interaction Energy Method ............................................................................. 22  The non-polar term ....................................................................................................... 23  The offset parameter γ .................................................................................................. 23  The polar term ............................................................................................................... 23  The Electrostatic Correction term ................................................................................. 24  

Experimental Binding Affinities ....................................................................................... 26  

Prostaglandin H2 Synthase ................................................................................................ 27  Non-steroidal anti-inflammatory drugs (NSAIDs) ....................................................... 28  Cyclooxygenase-1 ......................................................................................................... 29  

Computational Schemes for calculating Binding Affinities in COX-1 ............................. 30  

Conclusions and Future Work ........................................................................................... 33  

Acknowledgements ........................................................................................................... 34  

References ......................................................................................................................... 35  

Abbreviations

COX Cyclooxygenase (Prostaglandin h2 synthase) hCOX-1 Human cyclooxygenase-1 oCOX-1 Ovine cyclooxygenase-1 HTS High-throughput screening GA Genetic search algorithm GLIDE Grid-based ligand docking with energetics GOLD Genetic optimization for ligand docking LIE Linear interaction energy MD Molecular dynamics MMFF Molecular mechanics force field NMR Nuclear magnetic resonance NSAID Non-steroidal anti-inflammatory drug OPLS-AA Optimized potentials for liquid simulations all-atom PBC Periodic boundary conditions SCAAS Surface constrained all-atom solvent SBC Spherical boundary conditions

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13

Introduction

Figure 1. A systematic overview of the pipeline for drug research In the drug industry it is estimated that it takes 12-15 years from the time a drug target is identified until a drug hits the market. Figure 1 shows the process, which starts with tar-get identification (red), followed by the drug discovery phase (purple), preclinical studies (blue) and clinical trials (orange) before getting the sought after approval of the final drug (green) by the authorities. One should know, however, that on average only 1 out of 5000 compounds makes it through the pipeline all the way to reach the market1. Out of these original 5000 compounds, around 95% of the compounds are filtered out during the drug discovery phase. However, by using various screening methods, many molecules that are obviously not suitable drug candidates can be filtered out at an earlier stage of the pro-cess. This initial filtering is important, because it reduces the overall cost of the research. As a result, currently only around 2% of the leads that are tested in the preclinical studies passes through into clinical trials. However, once arrived to that stage, around 20% of all drugs will make it through to the approval phase. This means that a lot of money is spent on compounds that are not suitable as drugs. Consequently, this is reflected in the cost of the drugs and the time it takes for a drug to enter the market. As the cost for drug devel-opment is on the rise2, is it possible to break the trend so that a higher percentage of the leads will go through the preclinical phase?

Today large databases of various compounds are freely or commercially available and every year new crystal structures of proteins and enzymes are solved. Currently, pharma-ceutical companies employ some method to screen available databases in the drug dis-covery phase. One popular method is high-throughput screening (HTS), in which large numbers of experimental assays are performed in an automated way with the help of ro-bots. Although HTS methods are fast, they accrue considerable associated costs.

There are other, computer-based methods for screening databases, including virtual

screening methods such as molecular docking. Here, compounds found in available data-bases of structure libraries can quickly be evaluated and filtered in ordinary or high-end computers in order to produce likely drug candidates that can be tested in experimental assays. Although such methods are less expensive as compared to HTS methods, studies have shown that they are not very good methods for identifying drug leads3. However, as computers are getting faster every year, if computers could be used to screen large data-bases of compounds against known drug targets while accurately reproducing their prop-erties, time and money could be saved in pharmaceutical research and industry. In Paper I a comprehensive analysis of four computational protocols are performed in which binding affinities are calculated for a large and diverse challenging data set of non-steroidal anti-inflammatory drugs (NSAIDs), as binders of the enzyme cyclooxygenase-1 (COX-1). The enzyme is a well-characterized drug target known to be one of the en-zymes participating in the arachidonic pathway, which regulates blood clotting and pain sensitization among other biological processes. It is also known to be a difficult system for automated molecular docking. However, in each of the schemes described in the pa-per, molecular docking is performed as an initial step followed by molecular dynamics

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(MD) simulations. The average ligand-surrounding energies from the simulations were collected and coupled to the linear interaction energy (LIE) method. The results from these combined methods show a great improvement in estimating binding affinities as compared to the use of docking programs alone. Through the best scheme binding affini-ties could be estimated with average unsigned errors below 1 kcal/mol for the whole data set, demonstrating the usefulness of this model for understanding the chemical properties of the protein and ligands.

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Computational Methods

The theoretical and computational methods used in Paper I is summarized in this chapter and the computational methods are briefly illustrated in Figure 2.

Figure 2. Computational methods used in this thesis: homology modelling, molecular docking and molecular dynamics simulations.

Homology Modelling Experimental screening assays are done on proteins or nucleic acids extracted from bio-logical organisms. Today, there are means to model such biological systems using com-putational methods. Although there are many structures made available by crystallo-graphic methods and nuclear magnetic resonance (NMR), many drug targets are still not readily available. However, if the protein sequence is known, homology models can be created. This is done by aligning the sequence to a previously solved similar structure through the use of a homology modelling program such as Modeller4. In Paper I, a homology model of a human COX-1 (hCOX-1) was created based on the highest resolution crystal structure available. It should be noted that ever since the first crystal structure of (sheep) COX-1 was published in 19945, all of the subsequent COX-1 crystal structures co-crystallized with a variety of ligands have been very similar, indicat-ing that the structure is highly conserved. Thus, although the template structure came from sheep COX-1 (oCOX-1), the high se-quence similarity (91% sequence identity) and the small differences found among the oCOX-1 crystal structures suggested that the homology model should greatly resemble the template crystal structure. The visual comparison of the structures confirmed the simi-larity between the template and the generated model and it was noted that the main struc-

16

tural differences between the two models were confined to the protein surface. The gen-erated Ramachandran plot showed good stereochemical quality, with 94% of non-proline non-glycine residues in the most favored regions and the remaining 6% in additional al-lowed regions (as compared to 90% and 10% respectively for the template crystal struc-ture). As such, it was determined that the generated model was of high enough quality to be used for both molecular docking and MD simulations.

Molecular Mechanics and Force Fields Molecular mechanics (MM) is an important method for modelling and simulation of bio-molecules. In MM atoms follow the dynamics of classical mechanics and each atom is treated as a spherical particle with a mass, partial charge and van der Waals radius. Mole-cules are built by connecting atoms together using harmonic or Morse potentials. Thus, all interactions between atoms can be divided into bonded and non-bonded terms. The potential energy of a system can be calculated and evaluated using a set of potentials, typically described as in equations 1 and 2, where the parameters can be calibrated using experimental data or results from quantum chemical calculations. Bonded terms:

Upot=12𝑘! b-b0 2+

bonds

12𝑘θ(θ-θ0)

2

angles

+12𝑘ξ(ξ-ξ0)

2

impropers

(1)

+ 12kφ[1+cos(nφ-δ)]

dihedrals

Non-bonded terms:

(2)

Upot=qiqj4πε0rij!"#$  !"#$%  !,!

+Aijrij12 -Bijrij6

Here, the bonded terms describe the bond stretching, angle bending, improper dihedral bending and dihedral rotation angles respectively while the non-bonded terms describe the electrostatic and the van der Waals interactions, illustrated in Figure 3.

Figure 3. Illustration of the bonded and non-bonded interactions described by equations 1 and 2: Bond stretching, angle bending, dihedral angle rotation, improper dihedral bending, Lennard-Jones and electrostatic interactions.

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Complete sets of the parameters in equations 1 and 2 can be found in what are collective-ly called force fields, or molecular mechanics force fields. The potential energies de-scribed by the force fields correspond to the interactions between all atoms in any given system, which make them attractive for use in scoring functions of docking programs as well as for energetic evaluation of MD simulations. Different force fields are generally optimized for different types of systems. In Paper I the force field OPLS-AA6 was consistently used for minimization of modelled ligands, in molecular docking and for evaluating MD simulations.

Automated Molecular Docking and Scoring In the field of drug discovery scientists want to find as many drug candidates as possible in the shortest of times. This can be achieved by using HTS or virtual screening methods. One very popular virtual screening method is called molecular docking. This is a comput-er-based method in which the binding modes of ligands are estimated by a molecular docking algorithm, often with little or no manual intervention after the initial setup of the system. Each binding mode is evaluated and given an associated score. Thus, the docking programs have two important tasks to fulfill: conformational search of the ligand in the binding pocket and ranking the docking pose by estimating the corresponding interaction energies, using a scoring function. In Paper I two different docking programs were employed to dock the ligands to the COX-1 binding site: GOLD (genetic optimization for ligand docking)7 and GLIDE (grid-based ligand docking with energetics)8. The two programs employ different methods in placing and evaluating the molecules into the binding site. GOLD7 is a docking program provided by the Cambridge Crystallographic Data Centre (CCDC). It uses a genetic search algorithm (GA) based on Mendelian genetics for finding possible binding modes.7,9 In the implementation of genetic algorithms to the docking problem, the process of evolution is mimicked by applying genetic operators to a pool of docking poses generated for the ligand, which are described by sets of 3D variables (“genes”). The first generation of conformations are generated and allowed to “evolve” by crossbreeding and mutation of the 3D variables (defining position, orientations, state of each rotatable bond, etc.). There is also the possibility of migrating an individual from one pool of conformations to another pool in order to introduce larger diversity. The fit-ness of the resulting docking poses is evaluated at each evolutionary operation with a scoring function (see below). The new conformation will replace an earlier generation conformation in the pool of breeding conformations if the fitness improves. This cycle is then repeated until there is no more or only marginal improvement in fitness in the final generation of conformations. GLIDE8 is a docking program provided with the Schrödinger Suite. It tries to mimic a full systematic search of the conformational, orientational and positional space of the docked ligand by using a series of hierarchical filters for determining the location of the ligand in the binding pocket. This is then followed by ligand torsion-angle minimization and a minimization of the ligand inside the binding pocket using the OPLS-AA force field. The lowest energy poses are then selected for a Monte Carlo procedure that examines nearby torsional minima and the poses are finally scored using a combination of a scoring func-tion and the MM interaction energy while taking into account the ligand strain energy.8

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Scoring Functions To quickly estimate the binding free energies of a given docking pose, mathematical functions, commonly known as scoring functions, are used. These can be categorized into three main groups: knowledge-based, empirical and molecular mechanics force field scoring functions.10 In order to save computational time scoring functions only consider the direct contact interactions between the ligand and the protein, thus disregarding any long-range interactions. Furthermore, only a few scoring functions consider solvation effects and entropy effects, adding to their limitations for estimating accurate binding affinities.

Internal ranking As a molecule is docked to a site, several different poses are generated. Each of the poses is evaluated and scored using the selected scoring function. Thus, an internal ranking between all poses of the molecule in the site is created. The top ranked pose is the pose that the docking program suggests is the lowest energy (“the best”) pose of the molecule in that specific site. In theory, this would be the same pose the molecule would display in a crystal structure of the complex. However, in Paper I it is shown that the top ranked pose is not always the lowest energy pose. Although the success-rate of finding low-energy poses differed between different scoring functions, none of the tested scoring functions would consistently rank the lowest energy pose as the top ranked pose for all tested ligands. However, for most scoring functions, low energy conformations could be found among the top ten ranked poses for almost all ligands.

External ranking Just as the different poses of one molecule in the same site are evaluated with scoring functions, the highest scores obtained for each molecule can then be compared to create an external ranking, thus determining which molecule is the better binder. It has been shown in previous papers that cyclooxygenase-1 (COX-1) is a difficult drug target for screening with automated docking.11,12 In Paper I the Pearson correlation coef-ficient between experimental and calculated affinities for the scoring functions considered ranged between 0.1 and 0.4, further demonstrating that none of the scoring functions used in the study could be relied upon to create an accurate ranking of the 45 non-steroidal inflammatory drugs (NSAIDs) tested.

Force field scoring functions Force field scoring functions are based on or completely composed of molecular mechan-ics force fields such as AMBER13, CHARMM14, GROMOS15 and OPLS-AA6. Although many force field scoring functions are well parameterized, they are more computationally demanding as compared to the knowledge-based and empirical scoring functions. Thus, they are less likely to be used in docking programs used in virtual screening. However, there are docking programs that have implemented “MM-like” scoring functions. One such example is GoldScore9, implemented in GOLD. In GOLD up to version 5.0 the default scoring function is GoldScore, which uses only four terms to calculate the fitness score: ligand intramolecular (int) and protein-ligand (ext) hydrogen-bond (hb) and van der Waals (vdw) score (S) according to the equation

GOLD Fitness=Shb_ext+  Svdw_ext+  Shb_int+Svdw_int   (3)

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Knowledge-based Scoring Functions

Knowledge-based scoring functions are based on so called knowledge-based force fields and sometimes referred to as statistical potentials or potentials of mean force (PMF)16 and consist of several weighted molecular features related to ligand-receptor binding modes. Based on a large number of x-ray crystals of protein-ligand complexes (“the knowledge base”), new protein-ligand complexes are assessed on the basis of similarities to the complexes found in the knowledge base. These kinds of functions therefor need to be constantly updated as the experimental database is expanded.

The Astex Statistical Potential (ASP) fitness function17 found in the GOLD docking program is a knowledge-based scoring function based on atom-atom distance potentials derived from a database of protein-ligand complexes found in protein data banks. ASP is the only one of its category used in this thesis, and also the scoring function with the weakest performance overall in ranking the docked poses and ligands to hCOX-1 among all the scoring functions used in Paper I.

Empirical Scoring Functions Empirical scoring functions use the sum of various empirical energy terms to approxi-mate the binding energy. In Paper I the majority of scoring functions are empirical scor-ing functions, represented by ChemPLP18 and ChemScore19 in the GOLD docking pro-gram and GlideScore SP8 and GlideScore XP20 in the GLIDE docking program.

ChemScore Chemscore19 is one of the oldest scoring functions still in use today. It is parameterized against known binding affinities. Chemscore includes terms for hydrogen bonding (Shbond), acceptor-metal (Smetal) and lipophilic (Slipo) interactions in the function while tak-ing into account the loss of conformational entropy of the ligand upon binding to the pro-tein (Hrot).

                           ∆Gbinding= ∆G0+ ∆GhbondShbond+ ∆GmetalSmetal+ ∆GlipoSlipo+ ∆GrotHrot (4) The ChemScore function implemented in GOLD adds extra terms in the form of a clash term, an intramolecular strain term and a term for loss of covalent bonding: ΔGbinding

' = ∆Gbinding+Eclash+Eint+Ecov (5)

ChemPLP ChemPLP18 utilizes the ChemScore hydrogen bonding term, but uses several linear po-tentials (PLP, Piecewise Linear Potential) to model van der Waals and repulsive terms. It is a faster scoring function than GoldScore and is the current default scoring function in GOLD.

GlideScore SP and GlideScore XP GLIDE has two scoring functions- GlideScore Standard Precision (SP)8 and GlideScore Extra Precision (XP)20. Both of these scoring functions are based on ChemScore, but with added weighted components to the hydrogen-bonding term, a modification to the metal-ligand interaction term and added solvation terms to account for solvation effects.8 The major difference between GlideScore SP and GlideScore XP is that GlideScore XP is a “harder” function in that it gives large penalties to poses that violate established physi-cal chemistry principles, such as the lack of solvent exposure of charged or strongly polar groups. For GlideScore SP, the coefficients for these penalties are smaller, thus allowing

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ligands with a reasonable probability to bind in the active site to be docked, even if the structure is not optimally placed in the binding site.

Molecular Dynamics Although molecular docking is a fast and efficient way to quickly estimate the binding mode of a ligand into a binding pocket, it is not the most accurate method for determining interaction energies.3,7 Molecular docking programs calculate their scores from a single ligand pose fitted into a snapshot of the protein or enzyme. Although this method saves computational time, it can also be a source of inaccuracy. In molecular dynamics (MD) simulations the system is simulated under thermal fluctua-tions, such as it is in real biological systems. All atoms are treated as spheres with attrib-utes such as mass, partial charges and van der Waals radii according to the rules of mo-lecular mechanics described in a previous chapter, allowing to calculate the potential energy at each configuration. However, as it is not enough to calculate the potential ener-gy at one specific time step, an ensemble of thermally accessible configurations sampled according to the Boltzmann distribution must be sampled in order to relate the potential energy of a simulated system to experimentally measurable thermodynamic properties. In MD atoms are moved according to Newton’s laws of motion and the force of each atom i at the time t is calculated from the gradient (∇) of the force field potential energy func-tion. The acceleration of each atom is calculated using Newton’s second law (equation 6) and the velocity and time can be approximated from it using a truncated Taylor expan-sion. ai t =

𝐅!!!= − !

!!∇iUpot (6)

In Paper I, the MD program Q21 is used for all MD simulations. Q uses the Verlet leap-frog MD algorithm, with positions and velocities obtained from equations 7 and 8 re-spectively. ri(t+ ∆𝑡) = ri(t)+ vi t+

∆!!∆t (7)

vi t+∆!!

= vi t−∆!!+ ai(t)∆t (8)

Here, 𝐫! and 𝐯! are the position and velocity of the atom i and ∆t is the time step. In Paper I the time step was consistently set to 1fs, but it is possible to also use a larger time step, as long as it is small enough to capture the fastest movements of the system.

Spherical Boundary Conditions It is important to consider what the most suitable system would be for studying the phe-nomena of interest when performing MD simulations. The most common approach is to use so-called periodic boundary conditions (PBC). Here, the entire biological system of interest is placed in a box, which is periodically replicated in all directions of the space. Hence, as a molecule leaves the box through one of the walls of the box a new equivalent molecule will enter from the opposite wall to keep the number of molecules in the system constant. It is important that the box size is large enough to not only contain the biomole-cule of interest, but also to avoid artificial periodicity effects. This kind of setup is partic-ularly useful i.e. to study the effect of large-scale conformational changes. However, an-other setup is possible where one concentrates on a particular region of the biomolecule, such as the binding site to study the phenomena of ligand binding: the spherical boundary conditions (SBC). In the SBC model, the, the boundary regions are constrained by using positional restraints while the water molecules used for solvating the system use polariza-tion restraints similar to the SCAAS model in the boundary regions.22 The structure is solvated only in the regions of the protein where unrestrained MD simu-lations are applied. The focus of the simulation sphere is on the binding site (Figure 4)

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where the system is unconstrained (red/green), thus allowing free movement of solutes and solvent. At the edge of the sphere (cyan) a half-harmonic potential is applied to keep the solvent molecules from leaving the sphere, thereby controlling the density of the sol-vent molecules inside the sphere in order to reproduce the density of bulk water. In this thesis all MD simulations were carried out using the MD program Q, which is very well suited for simulations using spherical boundary conditions (SBC).

Figure 4. Illustration of the two regions (red/green and blue) of the SCAAS model as applied to COX-1. The grey region illustrates the part of the protein not included in MD simulations. There are advantages of using a spherical system as an alternative to the frequently used PBC models: i) a focused MD simulations using a reduced SBC model are not as time-consuming as simulations in larger boxes using PBC, where the whole protein needs to be considered, as the speed is exponentially dependent on the number of particles that need to be considered; ii) a faster convergence is achieved due to the lack of possible confor-mational fluctuations distal to the binding site,23 iii) the electrostatic interactions are in principle considered explicitly. Though this is certainly the case for all ligand atoms, approximations such as the local reaction field24 to calculate the long-range interactions for other parts of the system contribute to further speed up the process. For all the above, the SBC model was employed to study the ligand binding process in the COX-1 system. In addition, one should keep in mind that the COX enzymes function as homodimers, with each monomer having its own COX and peroxidase active site. Fur-thermore, it is known that COX exhibit half-of site activity25,26, such that during catalysis only one of the monomers is active. Consequently, by including only one monomer in the simulation, the monomer in focus could be evaluated without the possibility of large scale conformational fluctuations caused by the other monomer. The use of SBC is thus an appropriate model since there is no need to simulate the whole protein, thus achieving faster convergence and fewer energy evaluations, while disregarding conformational changes caused by activity in the non-catalytic monomer. In Paper I simulation spheres centered on the binding site and extending 20Å were used for the MD simulations, as illustrated in Figure 4. Although the duration of some simula-tions was 5ns, for most of the ligands convergence of the simulations was achieved with-in 2ns.

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The Linear Interaction Energy Method

The linear interaction energy (LIE) method27,28 is a semi-empirical method used for calcu-lating ligand binding free energies (∆Gbind

calc ) after making only two MD simulations. Fol-lowing the thermodynamic cycle in Figure 5, an expression for the binding free energies can be obtained by the equation

   ∆Gbind  = ∆Gbound  polar −  ∆Gfree

polar  + ∆∆Gbindnon-polar (9)

Here, ∆Gbound  

polar and  ∆Gfreepolar are the free energies of turning on the ligand-surrounding elec-

trostatic interaction energy when the ligand is bound to the target and in the free state, respectively. The ∆∆Gbind

non-polar is the free energy difference of the ligand bound in the target and in the free state as the ligand-surrounding interactions are turned off.

Figure 5. The thermodynamic cycle used for calculating LIE binding free energies. The double-headed red and gray arrows represent ligand-surrounding and ligand-ligand electrostatic interac-tions, respectively. The LIE method attempts to estimate the terms from equation 9 through the lower corners of the thermodynamic cycle in Figure 5. Thus, one simulation is made of the ligand in a sphere of solvent (i.e. water), while the second simulation has the ligand embedded in the solvated target structure. The sampled ligand-surrounding (l-s) energies of both states are then collected and the averages of the polar Ul-s

el and non-polar Ul-svdw interactions are

used for calculating ∆Gbindcalc through the use of the LIE equation: ∆Gbind

calc = α∆ Ul-svdw +β∆ Ul-s

el +γ (10)

The LIE method has previously been successfully applied for calculating binding affini-ties of ligands to such various systems as the HIV-RT29, malarial plasmepsins30, the po-tassium ion channels hERG31, KcsA32 and Kv1.533, β –secretase34, GH78 rhamnosidase35, lectins36, etc.37

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The non-polar term The scaling factor for non-polar interaction energies, α, can be deduced through the ob-servation that the solvation free energy of non-polar molecules is roughly proportional to their size, much in the same way van der Waals interaction energies between solutes and their surroundings are roughly proportional to the size of the solute, suggesting an ap-proximate linear relation between the ∆∆Gbind

non-polar in Figure 5 and ∆ Ul-svdw . Although

the empirically deduced value of α = 0.18 has been used in a wide variety of ligands and receptors with great success, in theory, the value of α should vary between different lig-and-receptor systems. To test the robustness of the parameterization α was freely parame-terized on the data set used in Paper I. The resulting value was 0.2, demonstrated further the applicability of using the standard empirical value of 0.18 for the investigated system.

The offset parameter γ Apart from the scaling factors α and β, a third constant, γ, is present in equation 10. γ can be used as an offset parameter to fix the absolute scale between the experimental and calculated binding free energies. γ seems to be specific to both the data set investigated and the conditions in the binding site and has been determined to values between 18 and −1129,36. A negative γ suggests that the binding site is hydrophobic, which is also the case in Paper I as the value of γ was calculated to −6.4 for the whole dataset of 45 NSAIDs.

The polar term The scaling factor β scales the electrostatic polar interactions based on the linear response approximation (LRA), 30,31 previously used for binding free energy calculations.24,27,38 ∆Goff→on =

!!Ul-sel

off + Ul-sel

on (11) The LRA (equation 11) is based on Zwanzigs formula39, which can be used for calculat-ing free energies between two different states. In LIE, the two states are represented by the systems in which the electrostatic interactions are turned “off” and “on” respectively. In water it is possible to approximate the “off” term to 0 as the dipoles of the water mole-cules will orient themselves in a random manner around the ligand when the electrostatic interactions are turned off. In protein-ligand complexes the approximation has also been shown to be valid. However, it has also been demonstrated that in cases where there is preorganization in the active site, this approximation is not completely accurate. 40,41 In the first parameterization of the LIE method, β was set to 0.5, the theoretical exact value given from linear response theory (equation 11) for the binding of charged mole-cules. However, subsequent studies have shown that β will deviate from that value for uncharged molecules and that the value of β for such molecules will be dependent on the properties of the ligand28,38,42. For uncharged ligands Hansson and co-workers proposed a classification based on the number of hydroxyl groups on the ligand as shown in Table 1.

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Table 1. Classes of β proposed by Hansson and co-workers used in Paper I. Class of compounds Number of OH-groups β

charged Not applicable 0.50

0 0.43

neutral 1 0.37 ≥ 2 0.33

There is also a model proposed by Almlöf and co-workers where more functional groups are included in the parameterization of β, as shown in Table 2. Table 2. Classes of β proposed by Almlöf and co-workers. For the data set used in Paper I both of the parameterizations of β by Hansson and Almlöf was tested and compared. There was a small improvement in the average unsigned error of 0.1kcal/mol when using the Almlöf parameterization. However, the small improve-ment could not be tied to any overall improvements of any specific sub-class of ligands. However, due to the complexity of calculating β using the Almlöf parameterization, it did not seem optimal for such a diverse data set. Thus, in Paper I β was set to 0.5 for all lig-ands bearing a charge, following linear response theory, while β for the uncharged lig-ands was determined according to the Hansson parameterization (Table 1). By using dif-ferent values of β for the uncharged ligands according to the classification in Table 1, the statistical results improved, as compared to using only one standard value for the whole dataset of uncharged ligands. Considering the large structural variance in the dataset used in the study, these results further demonstrates the robustness of this classification for β.

The Electrostatic Correction term For MD simulations using SBC the simulation sphere consist of a core where all residues are unconstrained and the charge of the titratable residues manually set to either their charged state “on” or the neutral state “off”. Outside of this sphere all charged residues are set in the “off” states. To compensate for all neutral residues, an electrostatic correc-tion term (∆Gcorr

el ) needs to be added to the LIE binding free energy to account for all long-range electrostatic interactions between charged ligands and the residues which have been switched “off” in the simulation setup.43 The correction term is calculated using equation 12:

∆Gcorrel =332

qp qlεrpll !

(12)

The correction term corresponds to Coulomb’s law with an effective dielectric constant of water. It is dependent on the formal charges of the neutralized ionic group (qp), the partial charge of the ligand atom (ql) and the distance between the ligand atom and the central atom in the ionic group (rpl).

Class of compounds Functional group β

𝛽! Standard 0.43 ∆𝛽! Alcohols -0.06 ∆𝛽! 1, 2-amines -0.04 ∆𝛽! 1-amides -0.02 ∆𝛽! COOH -0.03 ∆𝛽! anions 0.02 ∆𝛽! cations 0.09

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In Paper I the dielectric constant ε was set to 80.22,44 The resulting correction term was thus calculated to −1.1 for all carboxylated (negatively charged) ligands. The addition of the correction term to the calculated binding free energies improved the statistical results of the dataset by decreasing the average unsigned error by 0.1-0.4 kcal/mol.

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Experimental Binding Affinities

To assess the reliability of a computational protocol for estimating binding affinities the calculated binding affinities is compared to experimental data, if such data exists. To calculate experimental binding free energies (∆𝐺!"#$

!"# ) from IC50–values the Cheng-Prusoff equation45 can be used:

∆Gbindexp = -RT lnKa=RT lnKd=RT ln IC50+c (13)

Here, the variable c is dependent on the fixed substrate concentration (S) and the concen-tration of substrate at the point where the enzyme activity is at half of the maximum (KM) and is defined as: c = -RT ln 1+ S

KM (14)  

Figure 6. Experimental values plotted against the Warner experimental assay In Paper I several experimental assays were compared to the calculated binding affinities. To compare the different experimental assays they were plotted against each other (Fig-ure 6). It was found that the constant c was comparable between the different assays, thus making it possible to use the averages of the different assays for assessing the predictabil-ity of the calculated binding affinities.

27

Prostaglandin H2 Synthase

Prostaglandin H2 (PGH2) synthase is a heme protein also known as cyclooxygenase and generally abbreviated as COX. The enzyme is a homodimer and has two catalytic sites in each monomer. In the cyclooxygenase site (Figure 6) the arachidonic acid (AA) reacts with two molecules of O2 mediated by Tyr385 to form prostaglandin G2 (PGG2). This reaction is followed by the reduction of PGG2 to PGH2 at the peroxidase site. PGH2 can further react and be transformed into various prostaglandins (PGs) and thromboxanes.46

Figure 6. Overview of the binding site of hCOX-1. The natural substrate AA (magenta)47 and the inhibitor BFL (yellow)48 are occupying the binding site in the salt-bridge conformation interacting with Arg120. The selective COX-2 inhibitor celecoxib (cyan)49 is occupying the side pocket (high-lighted blue sphere) and parts of the binding site. Some PGs act as messenger molecules and regulate the contraction and relaxation of smooth muscle tissue while others are known to be involved in regulating blood clot for-mation. Thromboxanes are known to facilitate platelet aggregation. However, to many people the most interesting product of the AA cascade is the formation of PGE2, which is a PG responsible for pain sensitization, thus being responsible for the feeling of pain. It is possible to relieve the pain by inhibiting the first step of the cascade, which is the for-mation of PGG2 from AA at the cyclooxygenase site by introducing an inhibitor. Many such inhibitors exist and they are often referred to as non-steroidal anti-inflammatory drugs (NSAIDs). Some of the most commonly used examples of drugs belonging to this class of pain-relievers are acetylsalicylic acid (Aspirin), ibuprofen and diclofenac.

There are at least three known isoforms of COX. COX-15 is present in most tissues

and blood cells while COX-250 is induced during inflammation. COX-3 (or COX-1b)51 has only been isolated from brains. It is generally believed that COX-2 is the isoform responsible for pain inhibition by traditional NSAIDs while inhibition of COX-1 causes the side effects common to these drugs, such as formation of gastric ulcers. Furthermore, it has been hypothesized that the well-known pain-relieving drug paracetamol (or aceta-minophen) does not inhibit either COX-1 or COX-2, but only COX-351. Recent efforts have been focused on finding more efficient pain-relieving drugs by creating COX-2 selective inhibitors, referred to as coxibs. Unfortunately, coxibs were found to increase the occurrence of cardiac failure due to blood clotting in the heart (myocardial infarc-tion).52-54

28

Although it seems that COX-2 is the main target for pain-relief, the inhibition of COX-1 and its subsequent prevention of thromboxane formation might have a heart protection effect that is missing for selective inhibitors of COX-2. Therefor, in designing new anti-analgesic compounds considerations need to be made as to the binding of both COX-1 and COX-2. However, with a balanced binding profile to both enzymes better analgesics can be designed which do not cause gastric ulcers, such as traditional NSAIDs, nor cause myocardial infarction like the newer generation of NSAIDs, the coxibs.

Non-steroidal anti-inflammatory drugs (NSAIDs) Non-steroidal anti-inflammatory drugs (NSAIDs) are one of the most commonly used classes of pharmaceuticals. Although they are often used to counter fevers and pain, it is well recognized that there is low awareness of their side-effects,55 which for traditional NSAIDs include kidney problems56,57, gastric intestinal bleeding and formation of peptic ulcers58. The structural diversity among the NSAIDs is large and the modes of binding in the binding site differ according to the structure of the inhibitor. Apart from acetylsalicylic acid (aspirin), all NSAIDs are reversible inhibitors of COX-1. In COX-2 celecoxib and many of its analogues are also irreversible inhibitors. Reversible inhibitors compete with the natural substrate arachidonic acid (AA) by binding to the key anchoring residue Arg120 and blocking the binding site in either one or both of the COX binding pockets.59 Since the COX enzymes display half-of site activity it is enough for AA to bind to one of the binding pockets. Interestingly, the binding of one ligand into one of the pockets results in a negatively allosteric modulation on the binding capacity of the other binding pocket.25,26 Traditional NSAIDs are known to be non-selective, thus inhibiting both COX-1 and COX-2 approximately equally well. Such inhibitors generally consist of one, two or three benzene rings, fused or apart, with a carboxylate head, mimicking the natural substrate.

Figure 6. Sample structures of traditional NSAIDs. From the left: acetylsalicylic acid (Aspirin), ibuprofen, indomethacine and diclofenac. It was demonstrated in Paper I that the lowest energy conformation for these ligands are achieved when the carboxylates are oriented towards the Arg120, shown in Figure 7. Overall, polar interactions were found to be important for this class of NSAIDs, including water interactions with the carboxylate group and interaction between polar groups of the ligand to the nearby Ser530. The newer generation of NSAIDs is COX-2 selective and generally known as coxibs. In COX-2 the side pocket is larger as compared to COX-1. It has been suggested that the selectivity between the isoforms stem from the non-polar interactions of the bulkier lig-ands, which make use of the side-pocket. In Paper I some coxibs were analogues of the structures shown in Figure 8.

29

Figure 8. Sample structures of coxibs. From the left: celecoxib, nimesulide and piroxicam. In Paper I it was concluded that the occupancy of the sidepocket in COX-1 is important for many coxibs, most particularly to celecoxib analogues and nimesulide analogues. However, due to the small size of the pocket, docking programs had great difficulty in placing the ligands in such a way as to occupy it.

Cyclooxygenase-1 Although both COX-1 and COX-2 are of interest for biological and pharmacological reasons, COX-1 is an especially interesting enzyme to study. One of the reasons is that, besides being well-characterized at the structural level, it seems to be a very difficult system for docking studies.11,12 This is particularly confounding as many of the docking programs which have difficulties docking and scoring ligands to COX-1 do very well in docking ligands to COX-2, even though COX-1 and COX-2 are very similar.11,12,60 In the binding site and the adjacent side-pocket there is only a difference of two amino acids, the Ile523 to Val (shown in Figure 7) and a His to Arg. The observed discrepancy in docking results could be caused by the difference in size between the binding pockets of COX-1 and COX-2. It has been estimated that COX-2 has about 25% more space61 due to the change of Ile to Val. The occurrence of Ile in COX-1 decreases the size of the side-pocket as compared to COX-2 and also works as steric hin-drance for ligands to access the pocket. This is reflected in the results of the different scoring functions as they rank the different poses of celecoxib analogues and carboxylat-ed ligands. None of the scoring functions included celecoxib analogues occupying the side-pocket among their top-ranked poses, even though this is the pose solved in crystal structures. Among the carboxylated ligands many top-ranked ligands lacked the key salt-bridge interaction obtained as the carboxylate is oriented to the Arg120. Here, the biggest differences could be seen in the results of the scoring functions Glidescore SP and Glidescore XP, which are both included in the molecular docking program GLIDE. Glidescore SP placed 88% of the carboxylated ligands in the salt-bridge conformation, while Glidescore XP only placed 65% of the carboxylated ligands in the same orientation. Since Glidescore XP is known to penalize non-physical conformations harder than Glidescore SP the difficulty in docking could be attributed to the narrower binding site in COX-1. In Paper I key interactions between ligands and some of the residues in the binding site of COX-1 were identified. The binding pocket is shown in Figure 7. It consists of a narrow channel gated by the residues Arg120 and Tyr355. The Arg120 is responsible for the strongest protein-ligand interaction as it forms a salt-bridge with the carboxylate head of the natural substrate AA as well as traditional carboxylated NSAIDs. Ser530 positioned in the middle of the binding site makes an important contribution to the binding affinities of some inhibitors as it has the ability to chelate polar groups on the inhibitors. It was also observed that water interactions are important for achieving good binding free energies.

30

Computational Schemes for calculating Binding Affinities in COX-1

In Paper I four computational schemes are presented for calculating binding affinities of a diverse set of ligands to COX-1. Each scheme starts with molecular docking to the ho-mology model hCOX-1 and the selection of initial ligand poses for the MD simulations. The interaction energies from these simulations are then evaluated using the LIE method and the resulting binding free energies are then plotted against the experimental binding affinities. The various schemes differ only in the selection of the best ligands pose, since this was identified as the limiting step for obtaining good estimations of binding affini-ties. In order to design the optimal protocol several schemes were tested and evaluated.

Figure 9. An overview of the computational schemes tested in Paper I. The first scheme is a fully automated procedure in which docking programs are used for docking and the built-in scoring functions decide which docked pose will be used as the initial ligand structure in MD simulations.

31

In the second scheme some manual intervention is used as the initial ligand structure for MD simulations are manually selected from the pool of docked ligands instead of relying on the ligand pose ranking of the scoring function. The third scheme is the scheme with most manual intervention as ligands used for MD simulations were manually docked, guided by pharmacophore knowledge gained from previous studies and the results of schemes 1 and 2. Here, the known salt-bridge interac-tions between carboxylated ligands and the Arg12059 were prioritized among the possible ligand orientations. Furthermore, polar interactions with the Ser530 residue were also considered important. For celecoxib and nimesulide analogues the side-pocket occupancy was identified as the most important feature. Thus, all such ligands were placed in such a manner as to occupy the side pocket. The fourth (and most successful) scheme makes use of all LIE binding affinities calculat-ed from schemes 1-3. For each ligand in each of the schemes the simulation that yields the lowest binding free energy is selected and plotted against the experimental affinity. Table 2. A summary of the statistical results of the computational schemes 1-4.

Scheme Scoring Function Salt-bridgea ± 2kcal/mol,b <ǀerrǀ>c

Scheme 1

ASP 42% 11% 9.50

ChemScore 65% 26% 7.01

GoldScore 77% 32% 5.93

ChemPLP 73% 29% 5.83

GlideScore SP 88% 21% 5.49

GlideScore XP 65% 24% 8.55

Scheme 2

ASP 77% 18% 6.62

ChemScore 100% 29% 3.99

GoldScore 100% 37% 4.39

ChemPLP 96% 37% 3.70

Scheme 3 100% 63% (69%) 2.06 (1.75)

Scheme 4 100% 92% (100%) 1.36 (1.01) a The percentage of carboxylated ligands docked in the salt-bridge orientation. b The percentage of ligands with calculated LIE binding affinities within 2kcal/mol of the experi-mental binding affinity. c The average unsigned error between the LIE binding affinities and the experimental binding affinities. Numbers in parenthesis calculated after removal of the outliers discussed in Paper I. From the results shown in Table 2, a correlation can be observed between initial ligand orientation and average unsigned error between the calculated and experimental affinities. As the percentage of ligands in the salt-bridge orientation is increased between Scheme 1 and Scheme 2, the corresponding average unsigned error decreases. Furthermore, increas-ing the manual intervention with regards to initial ligand pose for MD simulations im-proves the overall results. For instance, Scheme 3, which was the approach that needed

32

the most user intervention, performed significantly better than Scheme 1, which was fully automated in this regard. However, although it was also noted that docking scores were fairly insensitive to the changes in orientation, binding affinities calculated with the LIE method was particularly sensitive to the salt-bridge interactions facilitated by a ligand orientation in which the carboxylate head is oriented towards the residue Arg120. Overall the study confirmed that the docking programs used for the study had problems both in docking the compounds to the binding site and in ranking them internally and externally. With regards to the relative performance of each single scoring function con-sidered, it is obvious from Table 2 that the least successful was the knowledge-based scoring function ASP. However, none of the scoring functions could be relied upon to consistently dock all ligands in low-energy docking poses in COX-1. One other point that was highlighted in Paper I was the large variance in experimental affinities for some compounds.59,62 This could be a large source of error when trying to predict experimental binding affinities. However, it was shown that, for compounds of large experimental variation, statistical measurements improved when using an average of the experimental values, as opposed to using only one assay.

33

Conclusions and Future Work

Previously, the LIE method had been used to calculate binding affinities of series of simi-lar ligands to various targets. In Paper I a three-step process, which includes MD simula-tions and the LIE method as a complement to molecular docking, has been tested and evaluated. It was found that the largest obstacle for the method to become an integrated part of the drug discovery phase was the docking step. However, as docking poses im-proved, so did the calculated binding affinities. In Paper I the importance of getting a consistent ligand orientation for a subset of the ligands as the initial docking pose used in MD simulations was emphasized. It was neces-sary for the initial orientation of the charged carboxylated ligands to be docked in a salt-bridge conformation in order for the carboxylates to form a salt-bridge with the Arg120. It was found that for this subset of ligands the salt-bridge interaction was the key to get good correlation with experimental data. Failure of the docking program to achieve this initial ligand orientation would consequently lead to high calculated binding affinities, which in real drug design projects would be classified as false negatives. However, by making use of several initial starting orientations and poses for MD simulations (Scheme 4) the lowest average energies of almost all ligands in the dataset could be found to corre-late to their respective experimental values. Thus, the method described in Paper I can be used not only to reproduce binding affinities, but also for internal scoring and ranking of ligand conformations. We also emphasized that when predicting binding affinities, and in particular at the stage of testing and/or parameterizing a computational protocol, one should carefully analyze the experimental binding affinities available as this can also have associated errors. Here, the average of experimental binding data was considered for comparison with calculated binding affinities and it was demonstrated that using the average instead of relying on one specific data set would improve the statistical results. In future work it would be interesting to use the same data set to investigate their binding affinities and protein-ligand interactions to hCOX-2 using MD simulations and the LIE method. Considering that there seems to be a connection between the side effects of a NSAID and the selectivity profile of the drug, good models in which new NSAIDs can be tested in both COX-1 and COX-2 would be useful when designing new pain-relieving pharmaceuticals.

34

Acknowledgements

I would like to thank:

My supervisor Johan Åqvist for giving me the opportunity to learn. My assistant supervisor Hugo Gutiérrez de Terán for being patient. Present and previous members of the Åqvist group for being great teachers and friends. My family for all the support throughout everything.

35

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