Target, Bcr-Abl Kinase
Fides G. Nyaisonga
Submitted in Partial Fulfillment of the Prerequisite for Honors
in
Chemistry
© 2016 Fides Nyaisonga
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
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",
2
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.
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.
Gly 8
Asp 8
Phe 8
Thr 5
N- Lobe
C- Lobe
3
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.
4
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.
5
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.
Gly 8
Asp 8
Phe 8
Ile 5
N- Lobe
C- Lobe
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
7
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
8
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.
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
A B
9
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.
10
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
11
knowledge no other published studies have analyzed the robustness
of electrostatic charge
optimization and component analysis to conformational dynamics
using molecular dynamics.
12
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): G l = GSASA + G l + Gv W l + ΔGSASA takes into account
the changes in the 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.
13
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 generated 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 position vector r.
14
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: − ∇ . [ε r ∇ r ] = ρ r − ε r κ r
r
where κ accounts for the ionic strength of the solution.
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
15
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,
= ∑ ( − )
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.
16
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 = ∑ =
17
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 ( ′ C ) and the always unfavorable
quadratic contribution ( ′
makes the net electrostatic binding 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.
18
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
19
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 = k r − r
E = k θ − θ
Edihedral calculates the deviation of a dihedral angle from its
minimum value (16). The
dihedral energy function is periodic and dependent on the
hybridization of the middle atoms.
E l = A [ + cos n( − ) ]
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.
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 6 with increasing distance
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.
ELJ = ε [ σr − σr 6 ]
20
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;
E l = ∑ ∑ kq qr ≠
At each time step t during the simulation the force F is calculated
from the gradient of the
, , = − , ,
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 − Δ, half
the time step. The procedure is
repeated for a given simulation time.
= − + ( − )
= ( − ) +
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
22
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
23
equation (27) where is a time constant. Corrected atom velocities
v’ are then calculated from
equation (28). dTdt = τ T − T
′ = tτ (TT − )
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
25
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% of 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
26
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.
27
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
bar-1 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).
28
Figure 11. A flowchart showing all the methods and structures used
in the study
29
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
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.
30
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.
31
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.
Imatinib with WT Imatinib with mutant
32
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.
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 with WT Ponatinib with mutant
33
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
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.
34
Imatinib
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
RMSD = 0.37 RMSD = 0.38
Charges
35
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.
36
Ponatinib
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
B. WT C. Mutant A. Original
Charges
37
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
I, IV & VII Gain in I,
IV & VII
VII
VII
Optimal II, III, IV, V, VII II, III, IV, V &
VII
IV, V & VI IV, V & VI
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
38
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
39
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
RMSD = 0.32 RMSD = 0.35
40
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.
41
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.
42
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.
8.87
8.42
1.0
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.
44
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
RMSD = 0.32 RMSD = 0.20
45
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.
46
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.
47
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.
48
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
49
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.
50
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.
51
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.
52
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
53
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
54
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.
55
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