24 research outputs found
Force and Stress along Simulated Dissociation Pathways of Cucurbituril–Guest Systems
The field of host–guest chemistry provides computationally
tractable yet informative model systems for biomolecular recognition.
We applied molecular dynamics simulations to study the forces and
mechanical stresses associated with forced dissociation of aqueous
cucurbituril–guest complexes with high binding affinities.
First, the unbinding transitions were modeled with constant velocity
pulling (steered dynamics) and a soft spring constant, to model atomic
force microscopy experiments. The computed length–force profiles
yield rupture forces in good agreement with available measurements.
We also used steered dynamics with high spring constants to generate
paths characterized by a tight control over the specified pulling
distance; these paths were then equilibrated via umbrella sampling
simulations and used to compute time-averaged mechanical stresses
along the dissociation pathways. The stress calculations proved to
be informative regarding the key interactions determining the length–force
profiles and rupture forces. In particular, the unbinding transition
of one complex is found to be a stepwise process, which is initially
dominated by electrostatic interactions between the guest’s
ammoniums and the host’s carbonyl groups and subsequently limited
by the extraction of the guest’s bulky bicyclooctane moiety;
the latter step requires some bond stretching at the cucurbituril’s
extraction portal. Conversely, the dissociation of a second complex
with a more slender guest is mainly driven by successive electrostatic
interactions between the different guest’s ammoniums and the
host’s carbonyl groups. The calculations also provide information
on the origins of thermodynamic irreversibilities in these forced
dissociation processes
Evaluating Force Field Performance in Thermodynamic Calculations of Cyclodextrin Host–Guest Binding: Water Models, Partial Charges, and Host Force Field Parameters
Computational
prediction of noncovalent binding free energies with
methods based on molecular mechanical force fields has become increasingly
routine in drug discovery projects, where they promise to speed the
discovery of small molecule ligands to bind targeted proteins with
high affinity. Because the reliability of free energy methods still
has significant room for improvement, new force fields, or modifications
of existing ones, are regularly introduced with the aim of improving
the accuracy of molecular simulations. However, comparatively little
work has been done to systematically assess how well force fields
perform, particularly in relation to the calculation of binding affinities.
Hardware advances have made these calculations feasible, but comprehensive
force field assessments for protein–ligand sized systems still
remain costly. Here, we turn to cyclodextrin host–guest systems,
which feature many hallmarks of protein–ligand binding interactions
but are generally much more tractable due to their small size. We
present absolute binding free energy and enthalpy calculations, using
the attach-pull-release (APR) approach, on a set of 43 cyclodextrin-guest
pairs for which experimental ITC data are available. The test set
comprises both α- and β-cyclodextrin hosts binding a series
of small organic guests, each with one of three functional groups:
ammonium, alcohol, or carboxylate. Four water models are considered
(TIP3P, TIP4Pew, SPC/E, and OPC), along with two partial charge assignment
procedures (RESP and AM1-BCC) and two cyclodextrin host force fields.
The results suggest a complex set of considerations when choosing
a force field for biomolecular simulations. For example, some force
field combinations clearly outperform others at the binding enthalpy
calculations but not for the binding free energy. Additionally, a
force field combination which we expected to be the worst performer
gave the most accurate binding free energies – but the least
accurate binding enthalpies. The results have implications for the
development of improved force fields, and we propose this test set,
and potential future elaborations of it, as a powerful validation
suite to evaluate new force fields and help guide future force field
development
Quantum Mechanical Calculation of Noncovalent Interactions: A Large-Scale Evaluation of PMx, DFT, and SAPT Approaches
Quantum mechanical (QM) calculations
of noncovalent interactions
are uniquely useful as tools to test and improve molecular mechanics
force fields and to model the forces involved in biomolecular binding
and folding. Because the more computationally tractable QM methods
necessarily include approximations, which risk degrading accuracy,
it is essential to evaluate such methods by comparison with high-level
reference calculations. Here, we use the extensive Benchmark Energy
and Geometry Database (BEGDB) of CCSDÂ(T)/CBS reference results to
evaluate the accuracy and speed of widely used QM methods for over
1200 chemically varied gas-phase dimers. In particular, we study the
semiempirical PM6 and PM7 methods; density functional theory (DFT)
approaches B3LYP, B97-D, M062X, and ωB97X-D; and symmetry-adapted
perturbation theory (SAPT) approach. For the PM6 and DFT methods,
we also examine the effects of post hoc corrections for hydrogen bonding
(PM6-DH+, PM6-DH2), halogen atoms (PM6-DH2X), and dispersion (DFT-D3
with zero and Becke–Johnson damping). Several orders of the
SAPT expansion are also compared, ranging from SAPT0 up to SAPT2+3,
where computationally feasible. We find that all DFT methods with
dispersion corrections, as well as SAPT at orders above SAPT2, consistently
provide dimer interaction energies within 1.0 kcal/mol RMSE across
all systems. We also show that a linear scaling of the perturbative
energy terms provided by the fast SAPT0 method yields similar high
accuracy, at particularly low computational cost. The energies of
all the dimer systems from the various QM approaches are included
in the Supporting Information, as are the full SAPT2+(3) energy decomposition
for a subset of over 1000 systems. The latter can be used to guide
the parametrization of molecular mechanics force fields on a term-by-term
basis
Attach-Pull-Release Calculations of Ligand Binding and Conformational Changes on the First BRD4 Bromodomain
Bromodomains,
protein domains involved in epigenetic regulation,
are able to bind small molecules with high affinity. In the present
study, we report free energy calculations for the binding of seven
ligands to the first BRD4 bromodomain, using the attach-pull-release
(APR) method to compute the reversible work of removing the ligands
from the binding site and then allowing the protein to relax conformationally.
We test three different water models, TIP3P, TIP4PEw, and SPC/E, as
well as the GAFF and GAFF2 parameter sets for the ligands. Our simulations
show that the apo crystal structure of BRD4 is only metastable, with
a structural transition happening in the absence of the ligand typically
after 20 ns of simulation. We compute the free energy change for this
transition with a separate APR calculation on the free protein and
include its contribution to the ligand binding free energies, which
generally causes an underestimation of the affinities. By testing
different water models and ligand parameters, we are also able to
assess their influence in our results and determine which one produces
the best agreement with the experimental data. Both free energies
associated with the conformational change and ligand binding are affected
by the choice of water model, with the two sets of ligand parameters
affecting their binding free energies to a lesser degree. Across all
six combinations of water model and ligand potential function, the
Pearson correlation coefficients between calculated and experimental
binding free energies range from 0.55 to 0.83, and the root-mean-square
errors range from 1.4–3.2 kcal/mol. The current protocol also
yields encouraging preliminary results when used to assess the relative
stability of ligand poses generated by docking or other methods, as
illustrated for two different ligands. Our method takes advantage
of the high performance provided by graphics processing units and
can readily be applied to other ligands as well as other protein systems
Mean square fluctuations of the residue-averaged stresses computed from the 1 ms BPTI trajectory.
<p>(Left) Cluster 2; values range from 1.50 to 5.08 Mbar. (Right) Difference between cluster 1 and 2 (cluster 1 minus cluster 2); values range from −90.3 to 63.6 kbar. Purple (negative) and orange (positive) indicate regions where cluster 1 has less or more stress fluctuations than cluster 2, respectively.</p
Formulae for mean principal stress (negative hydrostatic pressure) associated with potential terms in common classical force-fields.
<p>Formulae for mean principal stress (negative hydrostatic pressure) associated with potential terms in common classical force-fields.</p
Stress decomposition of a wave pulse traveling left to right through graphene nanotubes either in the armchair (upper) or zigzag (lower) configurations.
<p>Data are shown for the 450 fs time-point.</p
Computational Calorimetry: High-Precision Calculation of Host–Guest Binding Thermodynamics
We
present a strategy for carrying out high-precision calculations
of binding free energy and binding enthalpy values from molecular
dynamics simulations with explicit solvent. The approach is used to
calculate the thermodynamic profiles for binding of nine small molecule
guests to either the cucurbit[7]Âuril (CB7) or β-cyclodextrin
(βCD) host. For these systems, calculations using commodity
hardware can yield binding free energy and binding enthalpy values
with a precision of ∼0.5 kcal/mol (95% CI) in a matter of days.
Crucially, the self-consistency of the approach is established by
calculating the binding enthalpy directly, via end point potential
energy calculations, and indirectly, via the temperature dependence
of the binding free energy, i.e., by the van’t Hoff equation.
Excellent agreement between the direct and van’t Hoff methods
is demonstrated for both host–guest systems and an ion-pair
model system for which particularly well-converged results are attainable.
Additionally, we find that hydrogen mass repartitioning allows marked
acceleration of the calculations with no discernible cost in precision
or accuracy. Finally, we provide guidance for accurately assessing
numerical uncertainty of the results in settings where complex correlations
in the time series can pose challenges to statistical analysis. The
routine nature and high precision of these binding calculations opens
the possibility of including measured binding thermodynamics as target
data in force field optimization so that simulations may be used to
reliably interpret experimental data and guide molecular design
The delta in residue-averaged hydrostatic pressure between clusters 1 and 2 (solid, blue line) and the associated standard error of the mean (dashed, red line) for all 58 residues of BPTI.
<p>Residues with large (greater in magnitude than 500 bar) are labeled.</p
Residue-averaged differences in stress between clusters 1 and 2 (cluster 1 minus cluster 2).
<p>The left color spectrum applies to the total stress, and the right color spectrum applies to all of the stress components.</p