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274 D. Antunes et al.
computational burden associated with exhaustive FEP simulations. This combination of AL and FEP allows for imp roved sampling efficiency by focusing computational resources on the most promising candidates. In the following sections, we
provide an overview of various intriguing applications of FEP in a range of scenarios
that pose challenges to the methodology.
2.1 Validating Binding Poses
The FEP approach is commonly employed for binding mode validation, delivering
mechanistic insights into binding events and confirming the binding poses of ligands
at the receptor site. However, to accurately predict the binding free energies of a
congeneric ligand series, it is crucial to know at least one ligand’s binding pose
within the series. Failure to precisely adhere to the experimentally confirmed binding
mode may result in diminished accuracy in binding free energy predictions through
FEP calculations. Therefore, the correct prediction of the observed binding free
energies validates the binding mode [50].
Additionally, this methodology can be used to elucidate different binding mode
hypotheses for a given ligand at the receptor site. By comparing the free energies
associated with different binding poses, FEP calculations can be used to identify the
correct binding pose of the ligand [51].
2.2 Dealing with Solvent
Free energy methods play a crucial role in drug discovery by identifying affinitybinding molecules for specific proteins. To comprehend protein–ligand interactions
in aqueous environments, it is imperative to analyze the contributions of proteins,
ligands, and solvent particles, particularly emphasizing the influential role of binding
site water molecules. One way to address this issue is to perform MDmix simulations, which have been applied to various biological systems, including protein–
ligand interactions, protein–protein interactions, and protein folding. They have
been shown to be particularly useful in identifying binding hotspots, allosteric
sites, and cryptic pockets on protein surfaces, which can be exploited in drug design
and development.
Structure-based drug discovery increasingly uses cosolvent or mixed-solvent MD
(MDmix) simulations as a useful, effective, and widely used computational tool in
SBDD for its accuracy in identifying ligand-binding sites and understanding molecular interactions [52]. Because polar interactions are sensitive to local surroundings
and water molecules, features such as protein flexibility and solvation effects limit
predictions, even though accurate representation of binding sites is essential for
directing drug discovery efforts. To overcome these problems, MDmix is presented
as a techni que that provides more accurate interaction maps than conventional
10 Free Energy Perturbation and Free-Energy Calculations Applied to Drug Design 275
potentials, such as GRID [53], and among its facilities, it allo ws water
displaceability predictions that are superior to techniques depend only on pure
water solvation theories [54]. However, problems arise from presumptions regarding
the transferability of free energy values and the precision of computed binding free
energy maps (ΔG
), particularly for cosolvent molecules that are significantly
bind
affected by solvent environments and are only transferable to larger drug-like
molecules. Decomposing the molecular binding free energy into precise atomic
contributions and accounting for the impact of the remaining molecules improves
the suitability of the free energy grids for directing rational ligand design by
exposing both known and hidden binding hotspots with potential for drug development [55]. Remarkably, MDmix simulations calculate atomic contributions to the
binding free energy, enabling precise and transportable maps for drug design.
Another topic that deserves attention is the perturbations in the structure and
energetics of the binding site water network resulting from minor chemical modi fications of small-molecule ligands, which are highly relevant, especially during the
hit-to-lead and lead optimization phases of structure-based drug discovery. This
entails sampling various configurations of the protein–ligand complex in an aqueous
environment, following the Boltzmann distribution. However, certain drug design
projects encounter challenges when the crystal structure of the binding pocket
reveals a cavity that lacks a water-exchange channel. Conformational fluctuations
that sporadically open the cavity pose significant timescale discrepanci es with
current simulation methods, posing difficulties in accurately calculating the binding
free energy when pocket hydration undergoes changes between the initial and final
states.
Conventional molecular dynamics (MD, see Chap. 8) simulations are unable to
accurately capture the changes in hydration that occur within buried cavities. This
shortcoming leads to a static number of water molecules that fail to adjust to ligand
modifications, resulting in one of the challenges faced during calculations, which
involves equilibrating water molecules between the bulk solvent and the buried
cavities.
An insufficient sampling of water movements within the binding site during
perturbations between these states results in pronounced hysteresis, introducing
structural inaccuracies and potential errors in the computed free energies, particularly when running perturbations in both the forward and backward directions. For
example, in alchemical calculations of absolute binding free energy (ABFE),
decoupling of the ligand from the binding site results in an unoccupied binding
pocket that typically becomes solvated. Cheng and Roux aimed to overcome this
issue by calculating the absolute binding free energy on a system formed by a
camphor molecule and cytochrome P450 and employing the GCMC/MD (grand
canonical Monte Carlo/molecular dynamics) [56]. The Grand Canonical Monte
Carlo (GCMC) is a computational method used to sample the solvent environment
around a solute molecule and is mostly used to study the thermodynamics and
kinetics of solvation processes [57]. In GCMC simulations, the number of solvent
molecules is not fixed but rather fluctuates according to the chemical potential of the
solvent, allowing solvent exchange between the bulk and solute environments.
276 D. Antunes et al.
Using GCMC solvent sampling and the double decoupling method, before the
alchemical ligand transformation, the authors reduced the hysteresis and improved
the accuracy of the FEP calculations for alchemical ligand transformations with
water displacement. The Grand Canonical Monte Carlo (GCMC) method is
implemented in FEP+ [28].
Conversely, Relative Binding Free Energy (RBFE) calculations provided reliable
predictions of ΔΔG values when applied to ligands with chemical similarity.
However, this approach encounters sampling limitations when computing the
reversible path of transforming one ligand into another within the binding site,
particularly in cases where the ligands vary in size or polarity, because the perturbation may allow additional water molecules to occupy the region of the binding site.
In a study conducted in 2009, Michel et al. [58] highlighted that the growth of
functional groups displacing buried water molecules leads to their entrapment in
energetically unfavorable states. One way to address this issue is to decouple the
water molecule before the alchemical transformation, incorporating the associated
free energy of the displaced water molecule as a correction to the relative binding
free energy. This approach requires prior knowledge of the confined water, which
contrasts with the sampling done in the Grand-Canonical ensemble.
In another study, a computational RBFE experiment was conducted to examine
the effect of adding a functional group to a molecule, which leads to the displacement of buried water molecules at the binding site [11]. FEP calculations applied to
six sets of congeneric ligands demonstrated a strong dependence of the predicted
ΔΔG value on the initial solvation state of the binding site, specifically concerning
the displacement of the water molecules. They also showed that current FEP protocols with even long timescales do not solve the problem of trapped water molecules and lack re-solvation. So, a proposed alternative approach would be to
incorporate a Grand Canonical Monte Carlo (GCMC) solvent sampling stage before
the λ-hopping step to enhance the solvent’s equilibration. In this line, Ben-Shalom
et al. [59] incorporated Monte Carlo (MC) steps that allow water molecule exchange
into and out of the binding pocket without following a physically realizable path to
overcome the inadequate sampling of water moves. They developed a hybrid Monte
Carlo/MD (MC/MD) method for the equilibration of water between the bulk solvent
and buried cavities while sampling from the intended distrib ution of states. A hybrid
Grand Canonical/Molecular Dynamics (GC/MD) approach during ligand perturbations in FEP calculations reduces hysteresis and improves accuracy compared to
pure MD simulations and experimental data in several test cases. However, this also
introduces complexities associated with the chemical potential of water and fluctuations in the number of water molecules in the simulated system. The AMBER
simulation package offers this method, alternating between blocks of standard MD
steps and blocks of translational MC water movement attempts within a rectangular
region overlapping the protein interior and the bulk solvent. These translational
moves enable water molecules to exchange between the bulk and buried cavities
while maintaining a Boltzmann distribution of states. Specifically, water molecules
can enter or exit the buried binding site as a ligand undergoes growth or contraction
during the alchemical process of RBFE calculation. This approach is particularly
10 Free Energy Perturbation and Free-Energy Calculations Applied to Drug Design 277
valuable in drug discovery applications, especially in scenarios in which prior
knowledge of the number of buried waters is unavailable, and it aims to address
the problem of occluded binding sites.
Alternatively, the Grand Canonical Alchemical Perturbation (GCAP) method is a
simulation technique that combines the grand canonical ensemble (μVT) with
conventional alchemical free energy methods to calculate the relative binding
affinities between ligands at a chosen level of hydration. This allows for the dynamic
adaptation of water networks during ligand binding simulations, enabling the isolation of the contribution of water network displacement to relative affinity [60]. This
method can be performed in one or two dimensions using a two-dimensional
approach, allowing the transformation of the ligand along two coupling parameters.
Although initially developed for ligand binding simulations, the GCAP method
shows potential for application in other simulations where water molecules, such
as protein–protein or protein–nucleic acid interactions, significantly affect the free
energy of the system [60]. The effectiveness of its application in these contexts
should be evaluated on a case-by-case basis, which requires further research.
2.3 FEP and Allostery
The FEP methodology has also proven its value in cases where the ligand binds to
allosteric sites instead of to orthosteric sites. Allosteric inhibitors are molecules that
bind to a receptor at a site different from the active site and alter the shape and
activity of the receptor. They can slow or stop enzymatic reactions by prevent ing the
substrate from fitting into the active site. Allosteric inhibitors offer several benefits
over orthosteric inhibitors, including enhanced specificity and fewer side
effects [61].
In 2021, Liang et al. [62] applied FEP to evaluate ten SHP2 allosteric inhibitors
that differ in their chemical structures. SHP2 is a protein that regulates various
cellular processes, and its dysfunction is associated with cancer, diabetes, and
autoimmune diseases [63]. However, designing and optimizing SHP2 allosteric
inhibitors is challenging because slight structural variations can lead to significant
changes in their biological activities [64]. FEP is particularly suitable for calculating
the binding free energy because it can capture the structural sensitivity of the SHP2
allosteric inhibitors. In this work, the authors tested three working schemes using a
different number of aaaaaa-windows and different times per window. Particularly,
they test ed the methodology’s performance using 16, 32, and 64 intermediate
aaaaaa-states, considering for each scheme simulation times of 16 ps, 32 ps, and
64 ps per window. Ultimately, they achieved an error of 0.5 kcal mol
predicted and experimental values. They also compared FEP and MMPBSA calculations and confirmed that FEP provides more precise predictions of the absolute free
-1
between the
278 D. Antunes et al.
energy of the SHP2 allosteric inhibitors. It is important to recognize that accurately
sampling large-scale movements to induce allosterism is a difficult task, especially
when working within a limited timeframe. Despite this, the calculated RMSE was
remarkably low, which suggests that the allosteric site in this instance can be
considered relatively rigid.
FEP can also be used to discriminate the binding poses of orthosteric ligands in
the presence or absence of an allosteric antagonist. Xiaoli et al. [65] showed that
absolute free-energy calculations using FEP were essential for determining the
correct pose of the ligand in a tertiary system composed of the protein C5aR1, the
ligand PMX53, and the allosteric antagonist NDT9513727. The authors applied
Accelerated Gaussian Molecular Dynamics to investigate the binding mechanism of
PMX53 and identified two different binding modes for PMX53 (poses 1 and 2) in
both the binary and ternary complexes. FEP simulations were run using NAMD3
with two simulation systems: the crystal structure for pose 1, and the GaMD
simulation final structure for pose 2. Before conducting FEP simulations, a relaxation stage of 100 ns was applied. The resulting structures from the MD simulations
were used as inputs for FEP simulations. The preparation of the input files and posttreatment FEP simulations were performed using BFEE2 protocols [66]. To enhance
the precision of the free-energy estimation, FEP simulations involving the reversible
coupling of PMX53 to its environment, such as the binding site of C5aR1 or
solvation, were conducted bidirectionally.
FEP simulations confirmed that pose 2 was the most stable binding mode in the
ternary complex. Simultaneously, in the binary system, the ligand alternated
between the two poses, with pose 1 being preferred to pose 2. In pose 1, the side
chain of Arg6 of PMX53 extends to TM6-TM7 in the GPCR crystal structure. In
contrast, at position 2, the side chain of Arg6 of PMX53 formed a salt bridge with
Glu199 on TM5, making this interaction extremely stable, as the allosteric antagonist stabilized TM5 by facilitating a tight hydrophobic stack between TM4 and TM5
on the extracellular side.
2.4 FEP and Covalent Ligands
Over the past five decades, there has been a notable increase in the development of
covalent inhibitors (Fig. 10.2a and b)[67, 68]. Although the biggest challenge in the
development of covalent inhibitors is their lack of specificity or selectivity, modulation of electrophilic warhead reactivity and optimization of noncovalent interactions may improve target receptor recognition and covalent inhibitor selectivity
[69]. As covalent drug development benefits from warhead reactivity and binding
site mechanism prediction [70], there is a substantial demand for computational
techniques that can optimize covalent inhibitor design.
However, there is modest utilization of FEP in the context of covalent drug
optimization, especially because the interconnectedness of several processes that
make up the binding process of covalent inhibitors makes the computational
10 Free Energy Perturbation and Free-Energy Calculations Applied to Drug Design 279
AB
Irreversible
covalent
binding
reactive group
Reversible
covalent
binding
reactive group
C
∆
G
n1
∆
G
s
∆
G
n2
Fig. 10.2 Representation of irreversible (a) and reversible (b) covalent binding by reactive ligands.
(c) Thermodynamic cycle of covalent inhibitor binding using alchemical FEP simulations. The free
energy to mutate from ligand 1 to ligand 2 is calculated in the bulk solution (ΔG
binding pocket (ΔG
), and in the covalently bonded protein-ligand complexes (ΔGc)
n
∆
G
∆
G
c1
∆
n
∆
G
c2
G
c
), in the protein
s
prediction of their binding affinity extremely difficult [69]. Two separate free
energies are important for the covalent ligand binding [44]. The first is the binding
free energy required to produce the noncovalently bound protein-ligand complex
before the chemical reaction takes place. This refers to the difference in free energy
between the protein – ligand complex, before the chemical reaction, and the independently solvated ligand and protein (ΔG
in Fig. 10.2c). The second is the free
n1
energy associated with the formation of the covalent bond. It is defined as the
difference in free energy between the covalent bonded protein–ligand and the
protein–ligand complex before the reaction (ΔG
in Fig. 10.2c). The total binding
c1
free energy can be calculated by summing the two aforementioned free energies. By
gradually transforming the Hamiltonian from the first to the second state using FEP,
we can calculate the free energy to mutate ligand A to ligand B in bulk solution (ΔG
in Fig. 10.2c), in the protein binding pocket (ΔGnin Fig. 10.2c), and in the
covalently bonded protein–ligand complexes (ΔG
in Fig. 10.2c). Analogous to
c
the conventional FEP calculations employed for noncovalent binding (i.e., the
relative binding free energy difference between the first two vertical legs of
Fig. 10.2c ), it is also possible to derive the relative overall binding free energy
difference between the two covalent ligands (i.e., the difference of ΔG
and ΔGc, the
s
first and third vertical legs of Fig. 10.2c)[69, 71].
s
280 D. Antunes et al.
With this thermodynamic cycle in min d, in 2017, Kuhn et al. [44] developed a
protocol that uses FEP to select reversible covalent inhibitors based on their covalent
binding state. This approach effectively computed the relative binding free energy of
covalent ligands that had the same warhead and when the substitutions are far from
the covalent interaction site. In this protocol, these conditions to the ligand series
were imposed due to the use of a harmonic potential to model the covalent interaction between the ligand’s warhead and the protein residue. Therefore, estimation of
the free energy difference between the ligands caused by the varying reactivity of
different warheads is not possible in this approach.
Subsequent studies have employed this thermodynamic cycle to analyze both
covalent and noncovalent binding states using relative binding free-energy calculations [44, 69, 72, 73]. Chatterjee et al. [69] found the relation between the overall
association constant 1/K
(ΔΔG
) and the noncovalent state (ΔΔGn) for two ligands with the same warhead
c
and the relative binding free energy of the covalent state
d
with the equation:
ΔΔG
1
= Ae
K
d
c
-
RT
þ Be
ΔΔG
n
-
RT
where A and B are constants. The authors also suggested that if the covalent binding
is much stronger (at least 5.5 kcal/mol) than the noncovalent binding, the
noncovalent state becomes negligible in predicting the overall binding selectivity
of covalent inhibitors. If this criterion is not met, a single quantum mechanical
calculation of the warhead core structure to assess the energy of the covalent linkage
can help estimate the differences in affinity between covalent and noncovalent
states [69].
Following Chatterjee et al. [69], Lameira et al. [73] compared the relative binding
free energy from FEP of halogenated reversible covalent inhibitors of human
cathepsin L (hCatL) with experimental binding kinetics results. They observed that
the overall reversible covalent binding of the inhibitors could be predicted by
employing the covalent and noncovalent states. Furthermore, the relative binding
free energies of dipeptidyl nitrile inhibitors were accurately predicted using FEP and
that an extra point charge improves the description of the halogen bond between the
inhibitors and the protein.
It should be noted that most studies have employed the FEP methodology to
predict and understand the binding process and selectivity of reversible covalent
inhibitors. Therefore, using FEP for lead optimization of reversible covalent inhibitors can offer rigorous and comprehensive information about the relative contributions of covalent and noncovalent binding states to the overall binding affinity
[72]. This opens new possibilities for tailoring noncovalent interactions and improving reversible covalent drugs.
10 Free Energy Perturbation and Free-Energy Calculations Applied to Drug Design 281
2.5 Applications of FEP in Scaffold Hopping
Scaffold hopping is the process of replacing the central core scaffold of a bioactive
molecule while maintaining similar pharmacophore features [74]. This technique is
valuable in drug design as it allows for the exploration of new regions of chemical
space and the identification of alternative lead compounds with improved properties.
Accurate scaffold hopping requires methods that can predict changes in the binding
affinity between different ligand scaffolds. FEP approaches are powerful tools for
modeling challenging scaffold hopping transformations [75].
In a recent study, Wu et al. [76] demonstrated the first applicati on of an
FEP-guided scaffold hopping stra tegy to discover novel phosphodiesterase-5
(PDE5) inhibitors. Compound L1, which contains a new scaffold relative to the
known inhibitors tadalafil and LW1607, was identified using a protocol that integrates molecular docking and FEP absolute binding free energy (ABFE) calcul ations
[76]. The predicted FEP energies (ΔG
matched experimental binding data (ΔG
1.13 kcal/mol. The lead compound L12 was identified with an improved IC
8.3 nM through two rounds of FEP-guided optimization. The compound contains a
completely distinct scaffold [76].
Recent enhancements in FEP methodologies have expanded their capabilities for
modeling scaffold hopping. The FEP+ approach integrates enhanced sampling
techniques to accurately reconstruct conformational changes during large ligand
topology modifications [28]. This method enables rigorous computation of binding
affinity changes between chemically diverse inhibitors [28]. Software tools such as
QligFEP have also applied FEP to retrospectively validate experimentally observed
scaffold hopping hits between distinct compounds [77 ].
) between ligands and PDE5 closely
FEP
) with a mean absolute deviation of
EXP
of
50
2.6 Positional Analogue Scanning
Positional analogue scanning (PAS) is a method that analyzes the effects of minor
chemical substitutions at different sites in a molecule. This allows for the elucidation
of structure–activity relationships. During lead optimization campaigns, a routine
technique is employed to improve potency and drug-like properties by modulating
steric, electronic, and hydrophobic interactions with the target protein. However, due
to financial and time constraints, exhaustive synthesis and experimental testing of all
positional analogues are often impractical. Computational scanning methods based
on FEP calculations can accurately predict changes in binding affinity upon substitution. This enabled the prioritization of the most promising analogues for
synthesis [78].
For example, perturbative fluorine scanning uses automated FEP protocols to
rank the impact of adding fluorine at multiple positions efficiently. This was
demonstrated by Wade et al. [79] for over 100 analogue pairs. FEP enables reliable
282 D. Antunes et al.
identification of “activity cliffs,” which are subtle chemical modifications that
significantly affect potency. Assisting with lead optimization efforts, Pérez-Benito
et al. [80] showed that FEP-based positional scanning may locate activity cliffs
within 1.39 kcal/mol of experimental values. Recently, Hu and Muegge [81] utilized
Amber GPU-TI to perform RBFE calculations to evaluate the impact of PAS on
potency changes for 14 protein targets and 20 analogue sets. They predicted shifts in
binding affinity with a mean unsigned error of only 0.74 kcal/mol and a root-meansquare deviation of 0.91 kcal/mol over 120 calculations. This finding suggests that
RBFE calculations are suitable for prioritizing position al analogues for synthesis and
testing during lead optimization campaigns [43, 81 ].
2.7 Combinations and Alternative Approaches
Drug design techniques that leverage the parallel nature of computations are becoming increasingly common to enhance sampling in calculations. The Replica
Exchange class of methodologies (REMD) is a popular choice among several
strategies available for coupling to computationally intensive methods, such as
FEP, to improve the statistical convergence in calculations of binding free energy.
REMD techniques use many parallel copies of a system under various simulation
conditions [30]. Subsequently, based on the Metropolis Monte Carlo approval
criterion, switching between two copies are attempted regularly. Thus, to enhance
the sampling of traditional FEP simulations, several REMD approaches have been
successfully combined with FEP [82], including conventional REMD [83], Hamiltonian replica exchange (H-REMD) [84], and replica exchange with solute tempering (REST) [85]. However, there are situations in which high- energy barriers
produce conformational states of a solute that remain weakly sampled during an
alchemical transformation, making these approaches inadequate. Furthermore, in the
case of two-dimensional exchange spaces, such as those of FEP/H-REMD, the
significant number of replicas needed for the method likely offsets its actual
advantages.
Although FEP and its combinations provide accurate estimates of binding affinities, screening of large libraries of compounds with substantial modifications
between them can impact the overall complex lead optimization phase of a drug
discovery project. Thus, over the years, numerous research groups have investigated
alternative simulation methods to conventional free-energy methods to achieve
comparable accuracy while requiring less sampling. Recently, there has been a
resurgence of interest in methods such as nonequilibrium free-energy calculations
and expanded ensemble methods such as lambda dynamics (λ-dynamics) [17, 86,
87].
In nonequilibrium methods, a great er amount of sample time is allocated to the
physical end states. These end states encompass the fully interacting ligand bound to
the protein, as well as the decoupled ligand that lacks interactions with the protein
environment. In addition, only very short simulations are usually performed for
10 Free Energy Perturbation and Free-Energy Calculations Applied to Drug Design 283
A B
O
-dynamics
pertubation graph
Fig. 10.3 Alchemical perturbation connection graphs. (a) In the λ-dynamics methodology, a
connected graph of ligand end states is sampled because in this method, all physical and intermediate λ states are sampled within a single simulation (represented by solid lines). (b) In FEP
methodology a “star map” connected graph is sampled via pairwise perturbations when run without
redundant calculations for cycle closure, thus, many intermediate simulations are required
(represented as dashed lines). (Adapted from the study by Robo et al. [98])
pertubation graph
FEP
nonphysical intermediate states that connect the end states, thereby imp roving the
efficiency of the approach [88]. The exploration of the alchemical path occurs
through rapid switching transitions in a single simulation, in which the ligand is
switched between interacting and noninteracting states [89, 90]. Many
nonequilibrium approaches operate in a pairwise manner; however, by employing
numerous independent runs, these methods appear to have a higher likelihood of
exploring many potential pathways [88]. They also exhibit a high degree of
parallelizability, rendering them favorable options for high-performance computing
(HPC) or cloud compu ting environments [91, 92].
In contrast to FEP, the concept behind λ-dynamics is to calculate the free energy
differences between multiple thermodynamic states in a single calculation to
increase efficiency by facilit ating better scalability (Fig. 10.3). In λ-dynamics, the
coupling parameter λ is treated as a dynamic variable with a fictitious mass and is
propagated along the atomic coordinates throughout the course of the simulation
[93]. Thus, it is feasible to obtain estimates of the free energy for an entire “leg” of
the thermodynamic cycle within a single simulation [94]. Multiple ligands can be
evaluated simultaneously in a given simulation where the potential energy term
correlated with each ligand is scaled according to its λ value [95, 96]. Thus, in the
context of structure-based drug design, λ-dynamics simulations can act similarly to
competitive binding experiments, in which all ligands compete for a shared receptor
based on their respective free energies [94, 95, 97]. However, to collectively sample
multiple ligands within a single λ-dynamics simulation, the free energy barriers