A Computational Analysis of Electrostatic Interactions Between Chronic Myeloid Leukemia Drugs and the Target, Bcr-Abl Kinase

Fides G. Nyaisonga

Advisor: Mala L. Radhakrishnan

Submitted in Partial Fulfillment of the Prerequisite for Honors in Chemistry

April 2016

Acknowledgements I owe my gratitude to all those people who have made this research possible. First and foremost, my deepest gratitude is to my advisor, Professor Mala Radhakrishnan for guiding me throughout the research and writing process. Her patience and support has helped me overcome many challenges during the course of this research.

I would also like to thank Professor Don Elmore for his help and insightful comments at different stages of my research. He was extremely helpful when I was learning how to do molecular dynamic simulations. Special thanks to Professor Rachel Stanley for all the personal conversations we have had concerning the thesis process and for her constructive comments during the committee meetings. I am also grateful for Professor Megan Kerr for agreeing to be on my thesis committee.

Special thanks to my lab mates, Nusrat, Laura and Diane for encouraging me to finish the project and for making lab a fun environment. Also, most results described in this work were accomplished with the help and support of previous lab members, including Lucy Liu and Lucica

Hiller.

Thanks to all my WASA friends, especially Khalayi and Mebatsion, for providing support and friendship that I needed and for constantly checking on me.

I especially thank my parents, Secilia and George, my sister, Laura and my brothers

Gervas and Andrew for their unwavering love and patience throughout the four years at

Wellesley. Their unconditional love and trust has enabled me to explore and pursue my passions, however many they were. I also thank my host family, Deborah and George Tall, for their love and care and for giving me a home away from home.

Finally, I appreciate the support of Wellesley College for providing me with great research opportunities for the past four years. I would specially like to thank the President’s

Office for the financial support for a wonderful summer research experience.

Table of Contents Introduction ...... 1

Type chapter level (level 1) ...... 4 Type chapter level (level 2) ...... 5 Type chapter title (level 3)...... 6

1. Introduction

Chronic myeloid leukemia (CML) is a malignant blood disorder representing about 20% of adult leukemia and is characterized by the presence of the Philadephia (Ph) chromosome1. Ph refers to a shortened chromosome created by the fusion of the breakpoint cluster region (BCR) gene on chromosome 22 to the Abelson proto-oncogene (ABL) on chromosome 91-2. The ABL gene encodes a tyrosine kinase that binds to ATP and catalyzes selective phosphorylation of tyrosine hydroxyl groups to control and amplify intercellular signals3-5. The activity of a normal kinase is tightly regulated under normal conditions6. In contrast, the Bcr-Abl oncoprotein translated from the BCR-ABL fusion gene is a constantly active cytoplasmic kinase.

The solved crystal structure of the Abl kinase shows a catalytic domain that consists of two lobes; the N-terminal lobe and C-terminal lobe4, 7-9. The N-lobe consists of five -sheets and one -helix while the C-lobe consists mainly of -helices (Figure 1). The ATP binding∝ site is located at the cleft between the two lobes. The activation of the kinase is controlled by the activation loop arising from the C-lobe. This loop is characterized by the Asp 381-Phe 382-Gly

383 (DFG) motif. In the kinase’s active form, the activation loop adopts a "DFG-in" conformation with Asp 381 oriented towards the binding site. This orientation allows the Asp

381 residue to coordinate the Mg2+ ions for catalysis.

The inactive form of the kinase, "DFG-out", is associated with Asp 381 being rotated away from the active site and thus unable to coordinate and stabilize the catalytic ion. In addition, in this “DFG-out” conformation, the binding of ATP is also blocked by Phe 382 being positioned towards the binding cleft (Figure 1)5, 7, 10. Residue Thr 315, termed the "gatekeeper",

is located at the back of the ATP binding pocket, and its interaction with small molecules inhibitors determines their binding and specificity at the binding pocket11.

The discovery of the Bcr-Abl oncoprotein followed by structure-based drug design have led to the development of specific inhibitory molecules that fit into and replace ATP from the binding site to inhibit the kinase's activity. In 2002, imatinib mesylate (Imatinib, Gleevec®, or STI571,

Novartis Pharma AG) became the first rationally designed tyrosine kinase inhibitor (TKI) clinically approved for CML treatment8.

N- Lobe ATP Binding Site

Thr 5

Phe 8 Gly 8

Asp 8

C- Lobe

Figure 1. The DFG-motif near the ATP binding site. The “DFG-out” conformation of Abl is characterized by a near 1800 rotation of the motif, with residue Phe 382 oriented towards the binding site, preventing ATP from binding. The "gatekeeper" residue points directly towards the ATP binding site.

Studies on the crystal structure of imatinib bound to the Abl kinase showed that imatinib binds specifically and stabilizes the “DFG-out” conformation shown in Figure 1, resulting in the apoptotic death of Ph-positive cells3-4, 8, 12. Imatinib binds to the ATP binding site through hydrogen bond interactions with residues Thr 315, Met 318, Glu 286, and Asp 381 as shown in

Figure 2. In addition, there is a strong indication that the nitrogen atom of the piperazine group on imatinib is protonated and forms hydrogen bonds with the carbonyl oxygen atoms of Ile 360 and His 36113-16. This interaction is supported by experimental results that yielded a large equilibrium constant of the protonation of the corresponding nitrogen17. A large protonation constant makes this nitrogen the most basic site of imatinib, facilitating its role as a hydrogen bond donor17.

Figure 2. (A) Imatinib bound to Abl kinase. Hydrogen bonds are formed between the N5 of imatinib and the backbone of Met 318, N13 and the side chain hydroxyl of Thr 315, N20 and the side chain of Glu 286, the carbonyl O30 and the backbone of Asp 381, and the protonated methyl piperazine with the backbone of Ile 360 and His 361. (B) Structure of imatinib.

Imatinib quickly became the first-line treatment of CML with 98% of early stage patients showing a complete hematologic response and an overall 5 year survival rate of 84%18.

However, about 35% of patients in advanced phase CML were shown to eventually develop resistance or intolerance towards imatinib1, 19-20.

Acquired resistance to imatinib is predominantly caused by a single amino acid substitution on the Abl binding site weakening or preventing the interaction of the drug to the protein1. A broad spectrum of kinase domain mutations that cause resistance have been reported21-23. Most notably is the clinically active “gatekeeper” mutation, T315I, which accounts for 15-20% of all mutation incidences24-25. The hydroxyl of the “gatekeeper” residue, Thr 315, in the wild type (WT) Abl forms a hydrogen bond to the amine linker between the pyridine and the phenyl rings of imatinib (Figure 2). The substitution of the polar Thr with a nonpolar Ile disrupts this hydrogen bond. In addition, the bulky ethyl group of Ile causes a steric clash with the phenyl ring of imatinib preventing the drug from binding to the mutant Abl while still allowing access to

ATP5, 10, 26-27.

N- Lobe ATP Binding Site

Ile 5

Phe 8 Gly 8

Asp 8

C- Lobe

Figure 3. T315I mutant. Ile 315 blocks the entrance of TKIs into the binding site.

In response to imatinib resistance, second generation TKIs including dasatinib (BMS-

3582, Bristol-Myers Squibb and Otsuka Pharmaceutical Co., Ltd) and nilotinib (AMN107,

Novartis Pharma AG) were developed to improve the inhibitor's affinity and potency towards the mutated form of Abl. Dasatinib binds to the activated form of Abl (DFG-in conformation) and is able to inhibit most clinical mutations that affect the DFG-out state28. Nilotinib on the other hand, although structurally related to imatinib, is 30 times more potent29. However, similarly to imatinib, both dasatinib and nilotinib form a hydrogen bond with Thr 315 and are critically affected by the T315I mutation.

Ponatinib (AP2454, Ariad Pharmaceuticals), a third generation inhibitor, became the first

TKI to have activity against the T315I mutation. X-ray crystallographic analysis of ponatinib bound to T315 Abl shows that ponatinib, like imatinib, binds to the “DFG-out” conformation, maintaining hydrogen bonding interactions with multiple residues including Phe 382 of the DFG motif 24-25, 27, 30.

Figure 4. (A) The binding of ponatinib to the wild type Abl kinase. A total of six hydrogen bonds are formed between ponatinib and Abl; N1 of ponatinib with the backbone of Met 318, carbonyl O28 with the backbone of Asp 381, N29 with the side chain of Glu 286, protonated N39 with the backbones of Ile 360 and His 361. (B) Structure of ponatinib

Unlike all previous TKIs, ponatinib utilizes a linear triple bond linkage between purine and methyl phenyl groups (Figure 4) to avoid steric clash with the Ile 315 residue. This, together with multiple contacts it forms with the binding site of Abl, makes ponatinib less susceptible to

single amino acid mutations. As a result, ponatinib showed remarkable efficacy in phase I studies whereby 98% of patients achieved and maintained complete hematologic response25.

Figure 5. T315 mutation affects the topology of ATP binding region. A bulky side chain of Ile 315 interrupts hydrogen bond formation between imatinib and Abl and causes a steric clash with the phenyl ring of imatinib. The crystal structure of imatinib bound to T315I Abl is not available, and this complex was therefore computationally-generated in this study

Unfortunately, treatment with ponatinib is associated with increased reports of vascular toxicity including stroke, myocardial infarct and arterial thrombosis, at a higher rate than reported in clinical trials31-32. Ponatinib's toxicity is linked to its increased off -target inhibition of survival pathways shared by both cancer and cardiac cells33. Consequently, ponatinib is now only prescribed under strict regulations to patients with T315I mutation and those for whom all other therapies have failed32.

The urgent need for CML inhibitors with improved selective therapies and reduced side effects led to the structure-based design of PF-114 (Fusion Pharmaceuticals). PF-114 has the

same potency as ponatinib but with reduced inhibition of off-target kinases and a better selective profile34. The molecular design of PF-114 involved modification of the structure of ponatinib by replacing the C22 atom of the imidazole ring with a partially negatively charged nitrogen atom to increase repulsion with the carbonyl oxygen present in many off-target kinases (Figure 6). In addition, in order to disrupt hydrogen bond formation between water molecules present in the active site of some off-target kinases, N19 on ponatinib was replaced by a C atom35. Early preclinical cellular and in vivo studies showed that PF-114 inhibited 90% activity of 11 kinases including the T315I mutant compared to 47 kinases suppressed by ponatinib34.

A B

Figure 6. Structure-based design of PF-114. A) PF-114 has a partially negatively charged nitrogen instead of C22 on ponatinib(B), and N19 on ponatinib is replaced by a carbon atom on PF-114.

As the PF-114 example shows, understanding the effect and influence of protein-ligand interactions is a very crucial step in the design of better inhibitors. Structure-based and computer-aided designs have played a key role in the discovery, design, and optimization of

cancer therapies, as has been evident in the treatment of CML. Advances in molecular medicine and computational capacity have enhanced our understanding of the inner workings of CML at a molecular level. New and improved CML inhibitors can be developed based on molecular modification and optimization of previous inhibitors.

Several computational studies, including those using continuum electrostatics calculations, charge optimization, and molecular dynamics (MD) simulations have provided insight into the binding and function of TKIs, serving as predictive tools for the design of high affinity, low toxicity drugs. Determining the electrostatic component of the binding free energy can be a reasonable approach for predicting binding and estimating differences in binding affinities of similar ligands to a common receptor. Examination of the charge distribution allows for determination of the physical properties of a good ligand.

Previous studies have calculated and compared the electrostatic binding free energies of

CML inhibitors to explain their binding conformation36. The comparative analysis of the electrostatic binding energies between imatinib bound to the wild type Abl and that bound to the mutant showed that hydrogen bond formation plays a key role in binding, and loss of this bond

(together with other interactions) is the major cause of imatinib resistance37.

Electrostatic calculations using MD simulations may also provide insight into the effects of structural fluctuations that may be crucial when studying protein ligand interactions. MD simulations on the complex of imatinib with both wild type and mutant T315I kinases have been performed to identify and explain resistance of imatinib to different Abl mutations14, 37-38. A dynamical study on ponatinib complexed with several Abl mutants revealed that the interactions between ponatinib and individual residues in Bcr-Abl kinase are affected by other remote residue mutations39.

MD simulations have also been carried out to calculate the absolute free energy of binding between imatinib and Abl13. In particular, MD free energy simulations conducted by

Aleksandrov and Simonson investigated the protonation state of imatinib as it binds to Abl. The study showed that imatinib is indeed positively charged on the methylated nitrogen of its piperazine ring while occupying the binding pocket of Abl14-15.

We have previously used charge optimization techniques within the continuum electrostatic framework to analyze the electrostatic binding free energy of five TKIs including imatinib, dasatinib, nilotinib and ponatinib to both wild type and mutant Abl. Charge optimization determines the hypothetical optimal charge distribution on the drug that will bind most tightly to the receptor. The optimal charge distribution obtained may be used as a template in the design of better drugs. Additionally, we have applied component analysis methods to identify chemical moieties of unprotonated imatinib and ponatinib that contribute favorably or unfavorably to the electrostatic free energy of binding40. Our previous studies have also looked at differences in the electrostatic binding free energy and optimal charge distribution between unprotonated and protonated imatinib41.

In this study, charge optimization is again carried out to comparatively study the binding of protonated ponatinib and imatinib to both mutant and wild type Abl. However, we have now also carried out MD simulations on the ponatinib-WT complex and charge optimization on MD snapshots using a continuum electrostatics framework to analyze the robustness of the binding free energy calculations to the conformational dynamics of the complex. Optimizing the drug in different conformations of the complex allows for a detailed examination of any significant changes in the average optimal charge distribution due to structural fluctuations. To our

knowledge no other published studies have analyzed the robustness of electrostatic charge optimization and component analysis to conformational dynamics using molecular dynamics.

2. Theory and Models

During the binding process, a drug (ligand) and a protein come together to form a complex driven by their binding affinity. The binding affinity can be quantified by computing the change in Gibbs free energy of the following process: protein + drug protein::drug complex

Several⇌ factors contribute to the total change in Gibbs free energy (ΔGtotal):

l SASA l v Wl ΔGSASA∆G takes = into ∆G account+ ∆G the changes in+ the∆G system's solvent+ ⋯ accessible surface area upon formation of a complex and is a coarse model for the hydrophobic effect. ΔGvan der Waals measures changes in van der Waals interactions during the formation of a complex. ΔGelectrostatic determines the interaction between charges on a drug and those on protein in the presence of solvent. Studies have shown that electrostatic interactions play an important role in binding because they affect the protein-ligand specificity and affinity42-44. Our study focuses on the electrostatic component of the binding energy.

In order to accurately study electrostatic interactions, our models need to take into account the effect of a polar solvent surrounding the system. The solvent can be modeled either explicitly or implicitly. Explicit modeling considers each water molecule and simulates its motion over time through molecular dynamics (MD) simulations, while implicit approaches often utilize the continuum electrostatic framework, considering only the average effects of the solvent.

2.1 Continuum Electrostatic Framework In the continuum electrostatic framework, electrostatic interactions are modeled implicitly by considering the solvent as a high-dielectric continuous medium and other molecules as lower dielectric cavities with embedded partial charges (Figure 7). The polarizability of a medium by an electric field is represented by a dimensionless factor known as the dielectric constant ε. The higher the value of ε is, the more polarizable the medium. Water is much more easily polarizable than other molecules and thus, it is usually assigned a high dielectric constant between 60 and

80, while proteins and other small molecules are given dielectric constant values between 2 and

4045. In our work we use a dielectric constant of 80 for water and 4 for protein and ligand molecules.

Figure 7. The continuum electrostatic framework representation of charged ligand (L) and receptor (R) in a solvent of high dielectric medium. The electrostatic potential in a spatially varying dielectric can be determined by solving the Poisson equation :

� −∇ ∙ �∇� = where is the electrostatic potential generatedϵ by a charge distribution in a polarizable continuum with� a dielectric constant ε, and is the permittivity of free space� constant. The

variables , ε and are all functions of the positionϵ vector r.

� �

Assuming a system of fixed charge distribution, , the Poisson equation can be extended to implicitly model salt ions through Debye-Huckel theory, � resulting in the Linearized Poisson-

Boltzmann equation (LPBE)46:

where accounts for −ϵthe ionic∇ . [ε strengthr∇ϕr ]of= the ρ solution.r − ϵ εrκ rϕr κ

The PBE can be solved numerically using finite difference methods in which a molecule is mapped onto a three dimensional grid and a set of linear equations derived from the LPBE is used to solve for the electrostatic potential at each grid point46-49.

Figure 8. Numerical solution of the PBE using the finite difference method. A two-dimensional representation of a Cartesian grid used in the finite difference approximation. The interior of the molecule is assigned a lower dielectric constant than the exterior of the molecule (i.e., solvent.)

The electrostatic energy of the system is then the product of the potential at a point i and charge distribution at that point (equation 4). In order to avoid double counting of energy of interaction between a pair of charges, the factor of is added into the free energy equation. The factor also accounts for the entropic penalty incurred by the charges in dielectric continuum model, which assumes a linear response of the solvent to the field generated by the ligand and

the receptor's charge distribution43, 50. This entropic penalty leads to the electrostatic energy being calculated actually being a free energy:

� = ∑ � In this work we assume that the ligand and the receptor are completely isolated in their unbound states and that the ligand binds rigidly to the receptor to form the complex. The electrostatic binding free energy, , is the energy difference between the two states, bound and unbound, and is given in�� the equation below51;

�� = ∑ (� − �)

Figure 9. Schematic representation of the unbound and bound states of the ligand and receptor. In our work we assume that the ligand and receptor are completely isolated from each other in the unbound state even though the schematic shows them a finite distance apart.

2.2 Charge Optimization Charge optimization is a computational technique developed by Tidor et al. that allows for the calculation of the hypothetical, optimal charge distribution on the drug that minimizes the electrostatic binding energy and maximizes the binding affinity for the protein42, 52-53.

In their unbound states, both receptor and ligand are surrounded by and favorably interact with water. To allow formation of the complex, they have to get rid of water at their binding interfaces. The energy cost associated with this process is given in terms of desolavation penalties. The electrostatic binding energy can thus be written as the sum of three terms: the ligand desolvation penalty, receptor desolavtion penalty and interaction terms. These terms can be expressed in matrix-vector notation as follows:

′ ′ ′ � � � �� = �� + �� + �� Vectors qL and qR contain the ligand and the receptor partial atomic charges, respectively, while matrices L and R contain electrostatic unit potential differences between the bound and unbound states in equation 5, derived from the LPBE, for the ligand and the receptor, respectively. The matrix C is the electrostatic unit potential that accounts for the electrostatic interaction between the ligand and the receptor. The elements of these matrices are defined as follows:

� � � = �,( ) − �,( )

� � C� = ∑ � =

Where is the electrostatic potential on atom j of the ligand (bound to the � , receptor) located � at (when) a charge of +1 is put at atom i and m is the number of receptor � atoms54.

As the ligand charge distribution is varied, the receptor desolvation penalty remains constant and the interaction term varies linearly with respect to ligand charges. The ligand desolvation penalty varies quadratically due to the linear response that exists between the ligand charges and the solvent reaction field generated by them. The combination of the (hopefully) favorable linear contribution ( ) and the always unfavorable quadratic contribution ( ′ ′ makes the net electrostatic binding�C� free energy quadratic in nature (equation 6), with�� all� nonnegative second derivatives (i.e., L is a positive semi-definite matrix). Consequently, its minimum value can be determined by setting the gradient of equation 6 to zero with respect to ligand charges, and solving for the optimal charges as shown below;

�

�∆� = �,� + �� = ��

is a set of ligand charges that minimizes producing the best

�, possible electrostatic contribution to the total binding energy.�� These optimal charges can be compared with actual charges to determine what parts of the drug can be improved to increase binding affinity.

The minimum is then calculated as follows:

�� − = −.� �� ′ ′ ′ Constraints�� on optimal = charge �, magnitudes��, + are�� usually� + imposed�,� in� the calculations above to yield physically reasonable charge distributions.

2.3 Molecular Dynamics Simulations

MD simulations provide a description of molecular motion as a function of time to increase our understanding of the dynamical properties of molecules and their interactions at the atomic level.

Previous simulation studies have allowed for predictions of macromolecular properties that have been successfully validated with experimental data55. MD simulations involve step-by-step numerical integration of σewton’s classical equation of motion over short time steps to produce trajectories for the system. There are several software packages available for MD simulations including GROMACS56, CHARMM57, AMBER58, and CP2K59. In classical MD, each atom has a well-defined position and momentum at all times throughout the simulation. The initial positions of atoms are often obtained from X-ray crystallography or NMR spectroscopy studies done on the molecule. The initial velocities of the atoms are sampled from the Maxwell velocity distribution at a given temperature and assigned randomly to each atom in the system.

Forces in the system are generated by the atom-atom interactions given in terms of a molecular mechanics energy function, which sums all interactions between chemically bonded and non-bonded atoms, as expressed in equation (13).

E = Ebond + Eangle + Edihedral + Evan der Waals + Eelectrostatic (13)

Bonded Non-bonded

The “bonded” contributions involve atoms connected up to three bonds away and are divided into three components: interactions due to bonds, angles, and dihedrals. Ebond is the energy of deviation of each covalent bond length (r) from its equilibrium value (r0), calculated using equation (14) for every bond in a molecule and then summed for the system. Eangle takes into account the deviation of each bond angle from the equilibrium and is calculated using

equation (15) for every bond angle and summed for the system. Both energy terms use the simple harmonic oscillator approximation. Parameters k, ro and θo are obtained from quantum mechanics on model molecules for each type of bond or angle.

E = kr − r Edihedral calculates the E deviation= ofk aθ dihedral− θ angle from its minimum value (16). The dihedral energy function is periodic and dependent on the hybridization of the middle atoms.

El = A [ + cos n(ϕ − ϕ)] A is the amplitude of a given dihedral which depends on bulkiness, n affects the periodic frequency for the hybridization of the group and is an offset or phase. All are parameters obtained from quantum calculations or experiment. ϕ

Evan der Waals is the sum of London dispersion forces and “steric” repulsions. The attractive

London dispersion forces (LDF) are caused by induced dipole interactions due to instantaneous variation of electron charge density. The LDF are weak and fall off as with increasing distance 6 r. Steric repulsions, on the other hand, are quantum mechanical phenomena that occur as a result of electron exchange repulsions when two atoms are brought close together. To mimic this behavior of electrons in molecular mechanics models, a repulsive term is introduced to Evan der Waals to give a Lennard Jones (L-J) potential expressed in equation (17). The parameter is a finite distance at which the intermolecular potential between two atoms is set to zero and ε is related to the depth of the potential well.

6 σ σ ELJ = ε [ − ] r r

Eelectrostatic in molecular mechanics involves the calculation of electrostatic interactions between two charges using a point charge model. In this model, each atom has a partial atomic charge that accounts for its nuclear charge and electron density. The partial atomic charges are often determined from quantum mechanics by a commonly used electrostatic potential (ESP) method60. In this method, a set of point charges that best recreate the true potential is found by calculating apparent potential of what the molecule will appear to another molecule. With such parameterized charges, the columbic interaction between two charges i and j separated by a distance r is then determined using coulomb’s law;

l kq q E = ∑ ∑ ≠ r At each time step t during the simulation the force F is calculated from the gradient of the energy as shown in equation (19) for all coordinates (x, y and z).

,, �� Once the forces are � known, = the − acceleration a of each atom can be determined using �, , σewton’s second law of motion as shown below, where m is the mass of the atom.

,, ,, Acceleration is defined� as the= rate �� of change of velocity. From the acceleration a determined above, the velocity of each atom is calculated.

��,, �,, = �� The atom’s position for each coordinate is determined from the velocity v as shown in equation (22).

��,, �,, = �� Assuming constant acceleration and taking short time steps (Δt) to ensure that there is no significant change in the forces, new positions and velocities on all atoms are calculated using equations (23) and (24) respectively to update system’s configuration.

,, ,, ,, � = � + � ∆�

In GROMACS, the MD software package used in this work, the integration of position and velocity formulae above over a period of time is done through a second order leap-frog algorithm61.The algorithm uses equations (25) and (26) to update the configuration of each atom by taking its position r at time t and its velocity v at , half the time step. The procedure is repeated for a given simulation time. � − Δ�

�� = �� − ∆� + � (� − ∆�) ∆� �� = � (� − ∆�) + ��∆� Explicit modeling of the solvent in MD simulations is achieved by surrounding a system with a large number of solvent molecules and simulating their motions over time. The SPC water model is used to predict the physical properties of the solvent62. In the SPC model, water is treated as a rigid molecule, i.e., constant bond lengths and angles with positive charges on the hydrogen atoms and a negative charge on the oxygen. The columbic interactions are calculated

between all pairs of charges and the LJ potentials are computed between two water molecules at a single interaction point centered on the oxygen atom.

As discussed above, the coulombic potential decays slowly with distance 1/r; thus, long- range electrostatic interactions must be considered. In order to avoid having an infinite system size or truncating these interactions, GROMACS utilizes periodic boundary conditions. In periodic boundary conditions, thermodynamic limits are established by surrounding the system with translated copies of itself. The energy is determined by taking into account partial charges of the system together with all periodic images.

Figure 10. Periodic boundary conditions. When a particle leaves the primary image (highlighted in red), the periodic image enters on the opposite side.

The sum of electrostatic forces is approximated using a smooth particle mesh Ewald

(PME) method63. In the PME method, the charges of atoms are mapped onto a grid and the columbic interactions are calculated as the sum of short and long range interactions. The long- range interactions are handled by means of Fourier transform methods at each grid point.

As with experimental conditions, the temperature of the MD simulations must be controlled to avoid system overheating. The temperature in the GROMACS algorithm is kept constant by a

Berendsen thermostat64. The thermostat works by coupling the system to an external heat bath at temperature T0. Any deviation of the system temperature T from T0 is corrected according to

equation (27) where is a time constant. Corrected atom velocities v’ are then calculated from equation (28).

dT = T − T dt τ

′ ∆t T � = ( − ) τ T

3. Methods

Structure Preparation

Structures used in this study were prepared as part of previous studies40 in a manner briefly described here: Three initial X-ray structures were obtained: WT Abl complexed with imatinib

(PDB ID 2HYY)9, with ponatinib (PDB ID 3OXZ)30, and the T315I Abl mutant complexed with ponatinib (PDB ID 3IK3)24. Imatinib bound to the mutant Abl was modeled using CHARMM from the WT Abl-imatinib crystal structure by introducing the T315I mutation followed by energy minimization. Note that in this study, like other computational studies, Abl kinase was used as structural model for the relevant portion of the clinically- relevant Bcr-Abl kinase.

All crystallographic water molecules were removed except those with at least three potential hydrogen bond contacts within 3.3Å. The amide groups of asparagine and glutamine were flipped as necessary based on visual inspection of potential hydrogen-bonding interactions.

The tautomerization states of histidines were determined and assigned also based on potential hydrogen bonds with nearby residues accordingly. Missing hydrogen atoms on structures were added by the HBUILD65 tool in CHARMM using the CHARMm22 force field66. Solvent exposed lysine and arginine amino acids were protonated while glutamic and aspartic acid residues were deprotonated according to the physiological pH 7.

Partial atomic charges of each drug molecule were obtained by performing quantum mechanical geometry optimizations using Gaussian 0367 followed by calculation of molecular electrostatic potentials using the Merz-Kollman (MK) population analysis method, as described in Liu’s thesis40.

The MK method computes molecular electrostatic potentials from the wave function at different points along the surface of the molecule. The charge distribution is made to replicate

this electrostatic potential. The magnitude of the derived partial atomic charges are restrained by using two stage restrained electrostatic charge fitting (RESP)68 procedure to obtain the final charge distribution.

Charge Optimization

A finite difference solver69 was used to solve the LPBE in order to obtain electrostatic desolvation and interaction potentials shown in equation 5. These potentials were solved on a

201 x 201 x 201 grid using a three-tiered focusing procedure with system occupancy of 23%, 92% and 184% ofÅ the grid; this resulted in a resolution of 6.14 grids per angstrom at the highest focusing. In some cases (specified in the results) PARSE radii and charges were used for all atoms except fluorines, whose radii were obtained from Parm99 AMBER van der Waals radii40, in other cases GROMACS radii and charges were used for all atoms. The solvent dielectric constant was set to 80 and the dielectric constant of the protein-drug complex was set to 4.

Constrained charge optimizations were conducted using the General Algebraic Modeling

System (GAMS)70-71 in which charge magnitudes were constrained to lie between 1e and –1e.

Sensitivity Analysis

In order to assess the improvement in binding affinity after charge optimization, sensitivity analysis was carried out. In this method, the sensitivity of the electrostatic binding free energy to an atom’s charge, i.e, the impact the atom’s charge has on binding, approximately corresponds to the atom’s corresponding diagonal element of the L matrix. Qualitatively speaking, the larger the value of an atom’s corresponding diagonal element, the more important the atom is for determining the optimal electrostatic binding free energy43, 54. The information obtained can then

be used to select target areas of the drug where optimization yields the greatest improvement in binding affinity.

Component Analysis

In order to quantify the contributions of drug moieties to the overall electrostatic binding energy, each drug was divided into seven moieties and atomic charges on each moiety were systematically set to zero to calculate a new . The contribution of a given moiety is

given by whereby; ∆�

∆∆�

∆∆� = ∆� − ∆�

A value greater than +1 signifies that a particular moiety has a favorable electrostatic∆∆� contribution to binding while a value less than -1 indicates unfavorable contribution.

values close to zero indicate that the moiety does not contribute substantially toward binding.∆∆�

MD simulations

All MD simulations were performed using the GROMACS software package (version 5.0.5) with the gromos96 43a1 united atom forcefield72. Missing residues on the protein loop were built in using the MODELLER program73-74 . The comparative models were produced after aligning the protein sequence with a template obtained by performing a BLAST search. The final protein structures included residues W274 - K279, E385 - D392 and D394 - D397.

To set up the complex for simulation, a tutorial prepared by Lemkul was followed75.

GROMACS drug topologies were generated using the PRODRG tool76, and all ionizable protein residues were considered in their standard ionization state at a neutral pH; Lys and Arg residues were protonated while Asp and Glu were not. The structure was placed in a cubic box of size

8.77 x 8.77 x 8.77 nm3. 5 Na+ and 6 Cl- ions of 0.1 M concentration were added to achieve neutral charge for the system. The system was then subjected to 10000 steps of steepest descent energy minimization before a 150 ns MD simulation was carried out.

Throughout the simulation the temperature was maintained at 310K using the Berendsen thermostat with a coupling constant of T = 0.1 ps, the pressure was maintained at 1 bar by coupling the system to an isotropic pressure� bath with an isothermal compressibility of 4.6 x 10-5

-1 bar and a coupling constant of P = 1 ps. The length of all bonds was constrained using the

LINear Constraint Solver (LINCS)� aligorithm77. The time step for integrating the equations of motion was 2 fs.

The Root Mean Square Deviation (RMSD) and Root Mean Square Fluctuation (RMSF) during the simulation was analyzed using the analysis tools within GROMACS and were visualized using MATLAB. MD trajectories were visualized using VMD78.

Figures were generated using VMD and Swiss-PdbViewer79. Certain mathematical calculations and plotting functions were performed in MATLAB (release 2012b, The

Mathworks, Inc., Natick, MA).

Figure 11. A flowchart showing all the methods and structures used in the study

4. Results

Using component analysis, charge optimization, and sensitivity analysis within the continuum electrostatic framework,we examined the electrostatic component of the binding free energetics of imatinib and ponatinib bound to WT and T315I mutant Abl. We also carried out MD simulations to assess the robustness of the optimal charge distribution and component contributions to the conformational changes of the complex.

Imatinib and ponatinib bind in their protonated form

Previous computational results predict protonation of N29 of imatinib (Figure 2) when bound to

Abl. To test this prediction we determined the preferred protonation state of imatinib bound to

WT and mutant Abl by comparing their relative electrostatic binding free energies with protonated and unprotonated N29. We then extended the analysis to protonated and unprotonated

N39 of ponatinib (Figure 4). Results are shown in Tables 1 and 2 below.

Protonated Unprotonated Imatinib Imatinib

∆� ∆� − ∆� WT 10.25 12.96 -2.71 (kcal/mol)

Mutant 12.20 15.13 -2.93 (kcal/mol)

1.95 2.17

Table∆� 1. Electrostatic− ∆�� binding free energies of protonated and unprotonated imatinib with Abl kinase. Protonated imatinib shows a more favorable electrostatic interaction with WT and mutant Abl compared to unprotonated imatinib.

Protonated Unprotonated Ponatinib Ponatinib

WT ∆� 7.89 11.69 -3.80∆� − ∆� (kcal/mol)

Mutant 6.99 11.53 -4.54 (kcal/mol)

-0.9 -0.16

Table∆� 2. Electrostatic− ∆� �� binding free energies of protonated and unprotonated ponatinib with Abl kinase. Protonated ponatinib shows a favorable electrostatic interaction with WT and mutant Abl compared to unprotonated ponatinib. Ponatinib shows a more favorable electrostatic energy when bound to mutant than to WT Abl.

Protonation improves the electrostatic binding free energy in all cases. The electrostatic binding free energy of protonated drugs was consistently less than that of unprotonated drugs by about ~3 kcal/mol for imatinib and ~4 kcal/mol for ponatinib. Interestingly, ponatinib bound to mutant Abl showed the greatest relative increase in electrostatic binding affinity upon protonation. The results agree well with MD free energy simulations that showed a strong preference for a drug to bind to Abl in its protonated state with a net positive charge, as it favorably interacts with negatively charged residues in the binding site13-15. Also, the pKa of the

N atom in a freely solvated piperazinyl group is 9.85, and thus, at a physiological pH of 7.4, the equilibrium already favors protonation15.

Therefore, in all subsequent analyses, we will consider only the protonated forms of the drugs and will not explicitly refer to them as “protonated”.

Component analysis quantifies the contribution of drug moieties to binding The contribution of drug moieties to the overall electrostatic binding free energy was determined by the change in electrostatic binding free energy when charges on moieties were set to zero

. The results are shown in Figures 12 and 13.

∆∆�

Imatinib with WT Imatinib with mutant

Figure 12: Component analysis of imatinib for favorable contribution. The Structure of imatinib colored by atom type with Abl residues that form hydrogen bonds shown in yellow. The energetic contributions of moieties that form hydrogen bonds with the WT and mutant Abl residues are shown. The contribution of a moiety is given by a value. Blue boxes represent favorable moieties with a value greater than 1. None of the moieties shown contributed unfavorably to binding ( . ∆∆� ∆∆� ∆∆� < − Component analysis shows that many moieties that form hydrogen bonds with Abl residues contributed favorably to binding with a value greater than 1 kcal/mol.

Interestingly, moiety III, which forms hydrogen bonds with∆∆� Asp 381 and Glu 286, had the most favorable contribution to binding when bound to WT ( = 1.91 kcal/mol). However, its contribution decreased by 0.86 kcal/mol when bound to T315I∆∆� mutant. Moiety VII, which forms hydrogen bond with Met 318, also showed a favorable contribution for imatinib bonded to WT

( = 1.67 kcal/mol) but became less favorable with the T315I mutant ( = 0.67 kcal/mol).

The∆∆� decrease in binding affinity by about 1 kcal/mol in both cases suggests∆∆� that T315I mutation may be responsible for the loss of binding at these moieties.

On the other hand, moiety I contributed more favorably to binding for imatinib bound to the mutant = 1.1 kcal/mol) than it did to imatinib with WT = 0.74 kcal/mol).

Notably,∆∆� moiety V, which forms a hydrogen bond with ∆residue∆� Thr 315 on WT, did not contribute significantly favorably or unfavorably to binding in either WT or mutant Abl.

Ponatinib with WT Ponatinib with mutant

Figure 13: Component analysis of ponatinib for favorable contribution. The Structure of ponatinib colored by atom type. Abl residues that form hydrogen bonds are shown in yellow. The energetic contributions of moieties that form hydrogen bonds with the WT and mutant Abl residues are shown. The contribution of a moiety is given by a value. Blue boxes represent favorable moieties with a value greater than 1. None of the moieties shown contributed unfavorably to binding ( . ∆∆� ∆∆� ∆∆� < − Component analysis shows that many moieties of ponatinib that form hydrogen bonds with Abl residues contributed favorably to binding. Similarly to imatinib, the moiety that interacts with Glu 286 and Asp 381 (moiety IV), contributed most favorably to binding in WT

( = 3.51 kcal/mol). Unlike imatinib, the binding affinity of the moiety improved by 0.21 kcal/mol∆∆� for ponatinib bound to mutant Abl ( = 3.72 kcal/mol).

∆∆�

Ponatinib showed a slight loss of binding at moiety VII, which forms hydrogen bond with

Met 318 when bound to mutant Abl, with a decrease in binding contribution of 0.32 kcal/mol while the contribution of moiety I increased by 0.68 kcal/mol in mutant compared to that of ponatinib with WT. As was the case with imatinib, the T315I mutation may also be responsible in affecting binding at these moieties.

All other moieties including moiety VI near residue 315 did not contribute either favorably or unfavorably to binding.

The hypothetical, optimal charge distribution for maximum binding affinity We carried out charge optimization to determine the charge distribution that minimizes the electrostatic binding free energy and therefore maximizes the binding affinity of the drug for

Abl. Additionally, sensitivity analysis was carried out to determine the impact of atoms' charge values on the electrostatic binding free energy. The effect of charge optimization on the overall electrostatic binding free energy is shown in Table 3, and optimal charge distributions are shown on Figures 14 and 15 for imatinib and ponatinib respectively.

Imatinib Ponatinib

∆� WT Mutant WT Mutant

Original (kcal/mol) 10.25 12.20 7.89 6.99

Optimal (kcal/mol) 1.87 3.53 1.09 0.55

- 8.38 - 8.67 - 6.80 - 6.44

Table∆� 3. Charge− ∆� optimization and electrostatic binding free energy. Charge optimization minimizes the electrostatic binding energy producing the best possible electrostatic contribution to the binding energy. The electrostatic binding energy improved by ~8-9 kcal/mol for imatinib and ~6-7 kcal/mol for ponatinib.

Imatinib A. Original B. WT C. Mutant Charges

RMSD = 0.37 RMSD = 0.38

Figure 14. Charge optimization and sensitivity analysis of imatinib with WT and mutant Abl. A) Charge distribution before optimization. Charges were constrained to range from 1.0 e (blue) to -1.0 e (red). B) Charge differences between optimal and original charge distribution of imatinib bound to WT. C) Charge differences of imatinib bound to mutant. Red indicates atoms that are too positive in the original drug and need to be more negative to be optimal. Blue indicates atoms that are too negative as they are and need to be more positive to be optimal while white is for optimal atoms. Radii of atoms in B and C indicate the sensitivity of the binding free energy to the atoms’ charges with larger atoms yielding greater sensitivity. The root mean square deviation of optimal charge from original is also shown, in units of elementary charge.

Charge optimization improved the electrostatic binding free energy by approximately 8-9 kcal/mol in imatinib bound to WT and mutant Abl and by about 6-7 kcal/mol in ponatinib with

WT and mutant.

Charge optimization of imatinib resulted in a highly charged methylpiperazine (moiety I) with some H atoms of the methyl group shown to be too positive to be optimal and C atoms shown to be too negative to be optimal for binding. In particular, the binding energy is shown to

be highly sensitive to changes in the partial charge of the H atom on the protonated N29. This H is shown to be slightly too positive for optimal binding while N29 is optimal for binding. The binding energy is also somewhat sensitive to the H atom's charges of moiety V near residue 315.

This H is shown is also slightly too positive for optimal binding. The N atom of the same moiety is too negative for optimal binding and its sensitivity value suggests that its charge does not greatly affect the binding energy.

Atoms of moiety III of imatinib that form hydrogen bonds with Glu 286 and Asp 381 are optimal for imatinib bound to WT while O30 and N20 are too negative for imatinib bound to the mutant Abl. Other atoms that are shown to be far from their optimal values for WT and mutant including C and N atoms of moiety VI. The C atom is too positive while the two N atoms are too negative for optimal binding.

The results also show that the atoms in moieties II, IV and VII are relatively close to their optimal charge in both WT and mutant Abl.

Ponatinib

A. Original B. WT C. Mutant Charges

RMSD = 0.36 RMSD = 0.28

Figure 15. Charge optimization and sensitivity analysis of ponatinib with WT and mutant Abl. A) Original charge distribution before optimization. Charges were constrained to lie between -1.0 e (red) to 1.0 e (blue). B) Charge differences between optimal and original charge distribution of ponatinib bound to WT. C) Charge differences of ponatinib bound to mutant. Red indicates atoms that are too positive in the original drug and need to be negative to be optimal; blue indicates atoms that are too negative as they are and need to be positive to be optimal, while white is for optimal atoms. Radii of atoms in B and C indicate the sensitivity of the binding free energy to the atoms’ charges with larger atoms yielding greater sensitivity. The root mean square deviation of optimal charge from original is also shown, in units of elementary charge.

Charge optimization of the methylpiperazine moiety (moiety I) yielded a somewhat similar optimal charge distribution for WT and mutant complexes, except for one H atom of the methyl group which is too positive for ponatinib bound to WT and shown to be optimal for mutant. σevertheless, the atom’s small radius suggests that the change of its charges would not necessarily affect the overall binding energy.

In both WT and mutant, the differences in optimal and original charge distributions reveal that the carbon atom of moiety III is far from its optimal charge, and it needs to be more

negative to be optimal while the F atoms of the same moiety are slightly too negative for optimal binding. The C atom of moiety IV that interacts with Glu 286 and Asp 381 is slightly too negative to be optimal in ponatinib bound to WT, but optimal in mutant with similar sensitivity.

Interestingly, the electrostatic binding free energy is highly sensitive to the charges of atoms in moiety V, which is also found in imatinib, as well as to the charges of atoms in moiety

VII which, like moiety VII of imatinib, interacts with residue Met 318.

The triple bond of moiety VI is also shown to be optimal and binding energy is only slightly sensitive to charges of its atoms.

Imatinib Ponatinib

WT Mutant WT Mutant

Favorable I, III & VII I & III I, IV & VII Gain in I, moieties Loss of binding at IV & VII VII

Sensitive atoms H on I, IV, V and H on I, IV, V and III, V & VII III, V & VII VII VII

Optimal II, III, IV, V, VII II, III, IV, V & IV, V & VI IV, V & VI VII

Not Optimal I , VI I, VI I, II & VII I, II & VII Table 4. Summary of component analysis, charge optimization and sensitivity analysis results for imatinib and ponatinib bound to WT and mutant Abl. Favorable moieties have a > 1 contribution to the overall binding energy. Electrostatic binding free energy is sensitive to the changes of atoms within moieties listed in “Sensitive atoms” in the Table. ∆∆�

The GROMACS structure is a reasonable starting structure for MD simulations To assess the robustness of a subset of our results above to the conformational dynamics, we carried out a 150 ns MD simulation using ponatinib bound to WT Abl. The MD simulation was

carried out on a structure prepared in GROMACS using united atoms radii and GROMACS charges (herein referred to as “GROMACS structure”) whereas the results shown above were using the PARSE radii and charges, which have been parameterized especially for continuum electrostatic calculations40 (and will be referred to as “PARSED structure”). In order to generate a proper “static” control to which we can compare our dynamical analyses, we repeated charge optimization within the continuum electrostatic framework using the GROMACS structure.

Table 5 and Figure 16 show a comparison of electrostatic binding free energy and charge optimization respectively between the PARSE and GROMACS starting structures.

Electrostatic Binding Free Energy

GROMACS PARSED

∆� (kcal/mol) 8.90 7.89

∆� (kcal/mol) 2.11 0.87

∆� - 6.79 - 7.02

Table∆� 5. Charge− ∆� optimization results comparing GROMACS and PARSED structures in salt concentration of 0.145M. The results show that both structures have similar electrostatic binding free energies and charge optimization improves binding energy in both cases.

Although the GROMACS structure uses “united atoms”, the original electrostatic free energy was similar to the PARSED “all atoms” structure while PARSED had a smaller optimal electrostatic binding free energy

GROMACS PARSED

RMSD = 0.32 RMSD = 0.35 Figure 16. Charge optimization results comparing the difference between optimal charge distribution and original charge distribution of GROMACS and PARSED structures. Optimal charges were not constrained in this case, as they were previously, in order to make sure that the observed robustness is not an artifact of these constraints. Red indicates atoms that are too positive in the original drug and need to be negative to be optimal; blue indicates atoms that are too negative as they are and need to be positive to be optimal, while white is for optimal atoms. Unconstrained charge optimization of PARSED structure yielded some charges that were greater than 1 and –1 for moiety I. For ease visualization, we colored these atoms 1 (blue) and -1 (red). These atoms were also excluded in RMSD calculation.

Both structures show a similar optimal charge distribution of the drug especially for moieties II, IV, V VI and VII. For example, partial atomic charges on the triple bond and moiety

III are shown to be optimal in both structures while some atoms of moiety IV and VII are similarly shown to be far from their optimal value in GROMACS and PARSED.

As is the case with the PARSED structure, some atoms of moiety I in GROMACS are shown to be far from their optimal charges, specifically the C38 (refer to Figure 18A), which is too positive for optimal binding in GROMACS. This charge may correlate with a very red H atom on PARSED, which suggests that it is too positive for optimal binding. It is interesting to

note that the deviations from optimality in moiety I for atoms in the six-membered ring are actually “inverted” when comparing GROMACS and PARSED structures – atoms that are too positive in GROMACS are too negative in PARSE within this moiety. This could partially be consequence of GROMACS using a united atom model for the methyl group and PARSE not doing so – the loss of flexibility in creating additional dipoles and polar groups in the

GROMACS optimal charge distribution could have a “ripple” effect, leading to this inverted pattern.

Though there are some differences, there are still several overall similarities between the

PARSED and GROMACS results, and the GROMACS structure is a reasonable starting structure for MD simulation.

Stability of the system during MD simulation

After carrying out the MD simulation, we determined the stability of the dynamic system by using the GROMACS analysis tools to calculate the Root Mean Square Deviation (RMSD) of the drug and the protein from the reference crystal structure. We also determined the Root Mean

Square Fluctuation (RMSF) of atoms on the drug relative to the reference minimized ponatinib structure. The results are shown in Figures below.

Figure 17. System Stability. The RMSD plot shows that ponatinib (red) equilibrates quickly after 5 ns while Abl (blue) does not become stable until approximately 100 ns. The RMSD stability of the drug through the simulation indicates that there is little mobility of the molecule within the Abl binding pocket.

The RMSD analysis indicated that the drug was equilibrated after 5 ns while the protein became equilibrated only after 100 ns. The average RMSD for the drug was approximately 0.15 nm and that of the protein was 0.25 nm from the aligned minimized reference crystal structure.

The results suggested that the system needs at least 100 ns of simulation to stabilize.

A B

Figure 18. RMSF of ponatinib’s atoms averaged over 50 ns. Radii of atoms in B represent the RMSF value of each atom (scaled by a factor of 50 for ease of visualization). B shows that F34- 36 of moiety III fluctuated the most during the simulation. Slightly higher fluctuations were also seen in all four hydrogen atoms of moiety VII and the methyl group of moeity I i.e., C38.

Figure 14 shows that moiety III was the most mobile area of the drug during the simulation with an average RMSF value of 0.12 nm. Notably, all hydrogen atoms of moiety VII and the methyl group of moiety I were also shown to fluctuate during the simulation. We will later investigate the effect of these fluctuations on the robustness of the optimal charge distribution.

The optimal charge distribution is somewhat affected by the conformational dynamics of the complex. Charge optimization was carried out on 20 trajectory snapshots taken between 100 ns and 150 ns, sampled every 2.5 ns. The mean optimal charge distribution of the samples (herein referred to as

“dynamic structure”) was determined and compared to the charge distribution of the static model. Figure 16 below shows the comparison between optimal charge distributions of the static model and dynamic structure.

Dynamic

Static Mean Standard

Deviatio n ∆� − ∆� ∆� (kcal/mol) 8.87 8.42 1.0 - 0.45 ∆� (kcal/mol) 2.07 4.41 0.9 2.34 ∆� - 6.80 - 4.01 1.0

Table∆� 19. Charge− ∆� optimization and electrostatic free energy. The mean of the dynamic structure was very similar to that of the static structure. Charge optimization showed a greater improvement of binding energy in the static structure than it did in the mean dynamic∆� structure; mean of dynamic structure was greater than optimal of the static structure.

∆� ∆�

A B. Static C. Average MD

RMSD = 0.32 RMSD = 0.20

Figure 20. Charge optimization and sensitivity analysis in static and dynamic structure B) Charge differences between optimal and original charges of the static structure. C) Charge differences between mean optimal and original charge distribution for the dynamic structure. Red indicates atoms that are too positive in the original drug and need to be negative to be optimal. Blue indicates atoms that are too negative as they are and need to be positive to be optimal, while white is for optimal atoms. Radii of atoms in B and C indicate the sensitivity of the binding free energy to the atoms’ charges, with large atoms yielding greater sensitivity.

Charge optimization on the dynamic structure yielded a more hydrophobic drug compared to the static optimization. However, charge optimization of moiety VII yielded similar optimal charge distributions in the mean dynamic and static structures; N19 is shown to be too negative for optimal binding while σ20 is too positive. The change of these atoms’ charges has a slight effect on the overall electrostatic binding free energy in both cases.

Additionally, the optimal charge distribution of the triple bond (moiety VI) is robust to conformational changes and the electrostatic binding free energy is only slightly sensitive to the

change of its atom charges. Similarly, O28 (moiety IV) and H39 (moiety I) are shown to be optimal and robust to dynamics, however, change of their charges affect the overall binding energy. Interestingly, the binding energy is also very sensitive toward the change of charges of

H6, H7 and H28 (moiety V) and moiety VII in both cases and these atoms are close to their optimal charges and remain so during the simulation.

Notably, N29 is optimized to be negatively charged in static model, in disagreement with the dynamic model, which shows that the atom is on average optimal during the simulation.

Additionally, H29 (moiety IV) is shown to be slightly too negative for optimal binding in static model while slightly too positive in the dynamic structure, and the overall electrostatic binding energy in both cases is affected by the change of its charge. Additionally, charge optimization of the static model suggested that C38 (moiety I) is too positive in disagreement with the results from the dynamic structure, which shows that the atom is on average optimal during conformational changes.

Interestingly, F34, F35 and F36 (moiety III) are not only optimal and robust to conformational change, but also slightly affect the overall electrostatic binding free energy. C33 on the other hand, is optimized to be more negative in the mean dynamic structure.

There is no correlation between the standard deviation of an atom’s optimal charge in the dynamic model and its flexibility in the binding pocket As a first step toward understanding the relationship between conformation and design predictions, we plotted the standard deviation of optimal charges for each atom vs. its RMSF in the MD simulation to test the hypothesis that atoms that fluctuated more would have a greater variation in optimal charge.

Figure 21. There is no clear relationship between standard deviation of the atom’s optimal charge and its RMSF value during the simulation. Atom radius in A indicates the standard deviation in the optimal charge of the atom while atom radius in B represents the RMSF for each atom.

Figure 21 shows that most atoms did not fluctuate much from their reference structure and did not show much variation in their optimal charges. Highly flexible atoms (F35- F36) are shown to have small standard deviation while N39 that has the largest variation in its optimal charge has a median RSMF value. Thus our results showed that there is no clear correlation between the standard deviation of the atom and its flexibility in the binding pocket.

5. Discussion

In the first part of this study, we analyzed the electrostatic component of the binding free energy between two leukemia drugs, imatinib and ponatinib, and their biological target, the Abl kinase, using component analysis, charge optimization and sensitivity analysis within the continuum electrostatic framework. Component analysis enabled us to determine the contribution of drug moieties to the binding affinity, while by carrying out charge optimization, we determined the hypothetical, optimal charge distribution of the drug that will have the maximum possible binding affinity.

Our electrostatic energy results showed that imatinib bound the T315I mutant with a higher electrostatic binding energy, by nearly 2 kcal/mol when compared to WT. These results are in good agreement with previous computational studies suggesting that the worsening of electrostatic interactions is partly responsible for the loss of imatinib affinity towards T315I mutant27.

More specifically, the resistance of T315I mutants to imatinib was once hypothesized to be caused mainly by the loss of a hydrogen bond between the “gatekeeper”, Thr 315 and imatinib (at moiety V) due to substitution of Thr by a nonpolar Ile. Interestingly, our component analysis and charge optimization show similar results for imatinib bound to WT and imatinib bound to T315I mutant at this moiety. Component analysis of both complexes shows that this moiety contributes neither favorably nor unfavorably to binding, and charge optimization yielded an optimal H atom on the moiety whose change in charge would have a great effect on the overall binding energy. Also, in both cases the N atom of the moiety is not optimal, but rather, it is too negative for optimal binding. Therefore, the direct interaction of imatinib with residue 315

did not seem to fully explain the energetic differences between WT and mutant Abl and thus does not explain why resistance occurs. This is explored further below.

Some of the imatinib moieties were shown to lose their binding affinities when bound to the T315I mutant. A good example is the loss of binding affinity for the pyridine moiety (moiety

VII, Figure 10) that forms a hydrogen bond with Met 318. Other moieties with noticeable loss of binding affinities in mutant Abl included those that interact with residues Glu 286 and Asp 381.

This loss of binding suggests that the T315I mutation may in fact alter interactions of the drug with other moieties. Our results agree well with several recent computational studies that have shown that induced conformational change of the binding site to accommodate the bulky Ile 315 side chain causes a loss of binding affinity of other remote residues which in turn leads to drug resistance27, 37. For example, in a MD simulation study, Zhou et al., predicted loss of binding due to a slight outward displacement of the imatinib moiety from the binding pocket to accommodate

Ile 31524.

Ponatinib, on the other hand, was designed to have a linear triple bond moiety at this position (moiety VI) in order to surpass the interaction with the residue altogether. Thus, the

T315I mutation should not significantly affect its binding affinity. Our analysis of the electrostatic binding energy shows that indeed, ponatinib binds to both WT and mutant Abl with similar binding affinities. Additionally, component analysis shows that this moiety contributes neither favorably nor unfavorably to the overall binding. Charge optimization shows that the moiety is optimal and the binding energy is insensitive to the changes of its charges. Notably, our

MD analysis of ponatinib bound to WT showed that the optimal charge distribution of the moiety is robust to conformational dynamics of the complex.

Consequently, our analysis shows that the design for better CML inhibitors should consider conserving this triple bond as one way to maintain the drug’s activity towards the T315I mutant. Interestingly, this group is preserved in PF-114 (Figure 6), a recent drug intended to improve upon the selectivity profile of ponatinib.

Interestingly, the methylpiperazine ring that forms hydrogen bonds with Ile 360 and His

361 is shown to contribute more favorably to binding in imatinib bound to the T315I mutant than it does to the WT. Ponatinib also shows a gain in binding affinity at this moiety and the moiety that interacts with Glu 286 and Asp 381 (moiety IV in Figure 9). This gain in binding suggests that T315I mutation may also be cause favorable conformational changes in the binding pocket.

However, different moieties are affected for different drug-protein complexes.

Structure-guided design of new CML drugs aims to optimize several moieties of earlier drugs to improve their potency toward the T315I mutant. For example, the pyridine ring (moiety

VII) of imatinib that forms hydrogen bond with Met 318 was changed to the imidazole pyridazine in ponatinib to improve the binding affinity towards the T315I mutant27. As mentioned earlier, the binding affinity at this moiety is lost when imatinib binds to the T315I mutant.

On the other hand, our results show that the moiety in ponatinib contributes favorably to binding and changing its charges would have great effect on the overall electrostatic binding energy. Charge optimization resulted in more positively charged N19 and C21 atoms and a more negatively charged N20 atom for optimal binding. MD analysis revealed that the optimal charges of N19 and N20 atoms are robust to conformational dynamics, while C21 remains optimal in the dynamic model.

Studies have also associated this moiety to the drug’s selectivity in binding27. For example, the design of PF-114 involved replacement of N19 with a C atom to disrupt hydrogen bond formation in active sites of some off-target kinases thus improving its selectivity profile.

Therefore, our study suggests that further optimization of the group to make better interactions with residue Met 318 might further increase the potency of the future CML drugs within the constraints of maintaining selectivity.

In addition to making hydrogen bonds with Ile 360 and His 361, MD simulations showed that methylpiperazine (moiety I) increases the drug's potency and molecular recognition 27, 80.

Expectedly, the hydrogen atom of the protonated N (N29 on imatinib and N39 on ponatinib) is shown to have great effect in electrostatic binding energy because as we have seen in our study, and other previous studies13-15, protonation at this position improves electrostatic binding interactions. The hydrogen atom is not optimal for imatinib bound to WT or mutant and its optimal charge varies during conformational dynamics in the case of ponatinib bound to WT.

Future studies should carry out MD simulations on ponatinib bound to the mutant to see if comparisons between WT and mutant interactions observed with the static structures are robust to conformational dynamics.

Furthermore, our study showed that the moieties that interact with Glu 286 and Asp 381 in either imatinib or ponatinib have the greatest contribution to the electrostatic binding energy.

Our results are in good agreement with the previous Molecular Mechanics/Poisson Boltzmann surface area study of binding energy that suggested that Glu 286 interactions with the NH group of the moiety is one of the strongest contact points81. In addition, charge optimization results showed that charges of the atoms of this moiety affect the binding energy.

N20, O30, C and the hydrogen atom in imatinib bound to WT are optimal while only the oxygen atom within the moiety is optimal in imatinib bound to mutant. O28 and the hydrogen atom of this moiety are also optimal in ponatinib except C27 of WT and N29 of the mutant.

However, MD analysis of ponatinib bound to the WT shows that on average, all atoms of this moiety are in fact optimal during conformational changes.

Our results show that qualitatively, the binding energy is also sensitive towards the change of charges of the trifluoromethyl group (moiety III on ponatinib). The moiety is also shown to have a negligible contribution towards binding. Charge optimization of the group reveals that the three F atoms are not optimal and need to be more positive for optimal binding while the C atom is optimized to have a negative charge. The function of the trifluoromethyl group is to increases the solubility and lipophilicity of the drug for easier membrane permeability82. Thus, the design for better drugs may consider altering it for better electrostatics only if it is possible to maintain these other qualities.

Our study compared the electrostatic binding energetics of the crystal structure conformation and those at different conformations obtained from ponatinb-WT MD simulations, assuming rigid binding in both cases. Although simulations results strongly rely on the quality of the starting model, our results show that the optimal charge distributions of many atoms did not change much during the simulation and are thus robust to conformational dynamics of the complex. Such atoms include the hydrogen atom of the protonated methypiperazine moiety, the highly flexible F atoms of the trifluoromethyl moiety, the O atom of moiety IV, and he triple bond and hydrogen atoms of moieties V and VII. In addition, the variations in optimal charge values did not relate to the degree of spatial fluctuations of drug atoms. For instance, the fluorine atoms, which were shown to have the most flexibility, had small standard deviations in their

optimal charges, while N39, which showed the most variation in its optimal charge, did not show large fluctuations.

Interestingly, the average optimal charge distribution of the conformational ensemble yielded a more hydrophobic drug. A study on binding specificity suggested that hydrophobic ligands tend to bind more generally to multiple partners with equal affinity than charged ligands i.e. they are more promiscuous83. In deed ponatinib has been shown to bind to multiple targets including all of the clinically active mutants39. Unfortunately, the lack of selectivity is also associated to the toxicity level of the drug33. PF-114 on the other hand, was designed to have a better selectivity profile35. It would be interesting to see if the optimal charge distribution of PF-

114 is more charged as compared to ponatinib. Future work should carry out similar MD analyses on PF-114 to determine its average optimal charge distribution and perform a comparison study with ponatinib.

It is important to note that although we looked only at the electrostatic component of binding to predict and analyze the binding of CML drugs, other components of binding energy, such as van der Waals interactions, contribute to the relative binding energy of these drugs37, 39. Furthermore, our study assumed rigid binding even for the dynamic model. As discussed earlier, conformational changes of the protein and drug heavily influence their binding affinities.

Additionally, there is no available crystal structure of imatinib bound to the T315I mutant

Abl. Thus, the relatively crude model of the complex modeled using CHARMM from the WT- imatinib crystal structure limited our analysis of the complex. By carrying out MD simulations using our crude model as a starting point, we plan to overcome this current limitation. Also, as discussed earlier, MD simulation analysis was also limited by the starting structure and the

parameter set used – understanding the robustness of these model inputs can also be potential future work.

Despite these limitations, our study offers a tool to qualitatively and quantitatively understand the determinants of binding in this system, and it provides insights and predictions that can be tested and corroborated by experiments and other computational studies. We hope that our study will provide more insights into understanding and optimizing the electrostatic component of the binding energy and will aid in the design of improved future CML drugs.

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