Are Protein Force Fields Getting Better? A Systematic Benchmark on
524 Diverse NMR Measurements
Kyle A. Beauchamp,†
Yu-Shan Lin,‡
Rhiju Das,†,§
and Vijay S. Pande†,‡,
*
†
Biophysics Program, ‡
Chemistry Department, Stanford University, Stanford, California, United States
§
Biochemistry Department, Stanford University, Stanford, California, United States
*S Supporting Information
ABSTRACT: Recent hardware and software advances have enabled simulation studies of protein systems on biophysically
relevant time scales, often revealing the need for improved force fields. Although early force field development was limited by the
lack of direct comparisons between simulation and experiment, recent work from several laboratories has demonstrated direct
calculation of NMR observables from protein simulations. Here, we quantitatively evaluate 11 recent molecular dynamics force
fields in combination with 5 solvent models against a suite of 524 chemical shift and J coupling (3
JHNHα, 3
JHNCβ, 3
JHαC′, 3
JHNC′,
and 3
JHαN) measurements on dipeptides, tripeptides, tetra-alanine, and ubiquitin. Of the force fields examined (ff96, ff99, ff03,
ff03*, ff03w, ff99sb*, ff99sb-ildn, ff99sb-ildn-phi, ff99sb-ildn-NMR, CHARMM27, and OPLS-AA), two force fields (ff99sb-ildnphi,
ff99sb-ildn-NMR) combining recent side chain and backbone torsion modifications achieved high accuracy in our
benchmark. For the two optimal force fields, the calculation error is comparable to the uncertainty in the experimental
comparison. This observation suggests that extracting additional force field improvements from NMR data may require increased
accuracy in J coupling and chemical shift prediction. To further investigate the limitations of current force fields, we also consider
conformational populations of dipeptides, which were recently estimated using vibrational spectroscopy.
1. INTRODUCTION
Molecular dynamics (MD) simulation is a versatile computational
tool that allows investigation of condensed phase systems
including neat alkanes,1
the many phases of water,2
the
solvation and binding of small molecules,3,4
and the folding
dynamics of full protein systems.5,6
Recent gains in computer
performance, parallelized MD codes,7
and optimizations for
graphics processing units8
and other specialized hardware9
have
enabled simulations of aqueous macromolecules over times
exceeding 100 ns in single-day calculations. These accelerations,
however, have begun to reveal inaccuracies in current MD force
fields.
By and large, molecular dynamics force fields are parametrized
to reproduce quantum mechanical calculations on
small model systems,10−13
then adjusted to provide improved
agreement with higher-quality ab initio data,14
crystallographic
structures,15
or experimental data.16−18
Because of the many
design choices inherent in parametrization, force fields yield
considerable differences in predicted biophysical properties. For
example, studies of protein folding have revealed variation in
folding rates between different force fields.19
Similarly,
simulated proteins often have folding midpoint temperatures
that err by 25 K or more.6
Here, we systematically evaluate 11 recent force fields
combined with each of five widely used water models (55
combinations) against a benchmark set of 524 NMR measurements.
The evaluated force fields include recent AMBER,
CHARMM, and OPLS-AA variants; the solvent models include
recent implicit and explicit models. The 524 NMR measurements
include J coupling and chemical shift data of 32 model
systems. Measurements span all 19 nonproline amino acids and
include dipeptide,20,21
tripeptide,22,23
tetrapeptide,22
and full
protein systems;24
importantly, this systematic benchmark
contains model systems not previously considered in the
parametrization of the tested force fields. These comparisons,
which comprise over 25 μs of aggregate simulation, suggest that
explicit solvent simulations with either the ff99sb-ildn-phi or
ff99sb-ildn-NMR force field recover NMR observables with an
accuracy close to the systematic uncertainty inherent in current
models for calculating scalar couplings and chemical shifts. In
addition to quantitative comparisons to NMR experiments, we
also compare conformational populations of the 19 dipeptides
to recent estimates made using vibrational spectroscopy.20,21
2. METHODS
2.1. Benchmark Systems. For our benchmark, we selected
32 protein systems including capped dipeptides (Ace-X-NME,
X ≠ P), tripeptides (XXX, GYG, X ∈ {A,G,V}, Y ∈
{A,V,F,L,S,E,K,M}), alanine tetrapeptide, and ubiquitin. Each
of these systems has NMR data available in the form of
chemical shifts, J couplings, or both. Small peptides provide
minimal model systems for sampling the (ϕ,ψ) torsions that are
a key component of secondary structure formation. On the
other hand, a different balance of forces is at play in larger
systems, which led us to include ubiquitin, a key model system
in protein folding25
and NMR studies.24
2.2. Force Field Benchmark. We aggregated 524 measurements
of chemical shifts and scalar couplings, summarized in
Table S1. Data were taken from the BioMagRes Database26
and
several recent papers.20,22,23
Each of the 32 systems was
simulated using Gromacs 4.5.47
using all combinations of the
Received: November 3, 2011
Published: March 12, 2012
Article
pubs.acs.org/JCTC
© 2012 American Chemical Society 1409 dx.doi.org/10.1021/ct2007814 | J. Chem. Theory Comput. 2012, 8, 1409−1414
GBSA,27
TIP3P, SPC/E, TIP4P-EW,28
and TIP4P/20052
water
models with the ff96,10
ff99,11
ff03,12
ff03w,16
ff03*,17
ff99sb*,17
ff99sb-ildn,14
ff99sb-ildn-phi,18
ff99sb-ildn-NMR,29
CHARMM27,30,31
and OPLS-AA32
force fields. Here, ff99sbildn-phi
refers to a force field combining the ff99sb-ildn side
chain optimizations14
with a recently modified ϕ′ potential.18
Compared to ff99sb-ildn, ff99sb-ildn-phi differs by a
modification of the periodicity two (n = 2) ϕ′ torsional
potential; this term has a strength of 2.00 and 1.80 kcal/mol,
respectively, for the ff99sb-ildn and ff99sb-ildn-phi force fields.
The ff99sb-ildn-NMR force field refers to the combination of
the ff99sb-ildn side chain optimizations with the NMRoptimized
backbone torsions of the ff99sb-NMR force field.29
Each production simulation was 25 ns (20 ns for dipeptides)
in length and held at constant temperature and pressure;
simulations for peptides were started from conformations
generated by PyMol. Ubiquitin simulations were started from
the crystal structure (PDB: 1UBQ).33
For error analysis,
simulations were repeated with independent starting velocities.
For the peptide systems, the independent runs also used
different starting conformations; for ubiquitin, the second set of
runs began from the crystal structure, had independent starting
velocities, and were 50 ns in length. J couplings were estimated
using empirical Karplus relations parametrized by Bax and
Hu;34
chemical shifts were estimated using the Sparta+
program35
(in Figure S1, we consider alternative models for J
couplings and chemical shifts).
All simulations were performed with Gromacs7
4.5.4. Starting
conformations were solvated, neutralized with Na+
or Cl−
,
minimized, and equilibrated before production runs. For
explicit solvent, electrostatics were treated using the particle
mesh Ewald36
method with a real-space cutoff of 1.0 nm. van
der Waals interactions were switched off between 0.7 and 0.9
nm. Temperature control was achieved using the velocity
rescaling thermostat.37
Pressure control (1 atm) was achieved
using either the Berendsen barostat (for equilibration) or the
Parrinello−Rahman38
barostat (for production). For implicit
solvent simulations (GBSA), temperature control was achieved
using a Langevin integrator. The temperatures were chosen to
match experimental conditions; dipeptides were held at 303 K,
GXG tripeptides at 298 K, homotripeptides at 300 K, and
ubiquitin at 303 K. For ubiquitin, the protein was held fixed
during the minimization and equilibration steps.
3. RESULTS
3.1. Optimal Performance from ff99sb-ildn-NMR and
ff99sb-ildn-phi. Converting all 524 measurements into an
uncertainty-weighted objective function (χ2
= ∑i(xi
Expt
− xi)2
/
σi
2
) allows a force field evaluation based on all available data
(Figure 1). We estimate the errors in each comparison as the
uncertainty in the relationship between conformation and
NMR observable; these errors (Tables S2 and S3) were
previously determined during the parametrizations of the
various Karplus relations and the Sparta+ chemical shift model.
On the basis of this analysis, the early (ff96, ff99) force fields
are easily rejected in favor of more recent modifications.
Furthermore, ff99sb-ildn-NMR and ff99sb-ildn-phi most
accurately recapitulate the chosen NMR experiments. Raw
data for TIP4P-EW with several force fields are shown in
Figures S4−S13.
3.2. Accuracy for Dipeptides, Tripeptides, Tetrapeptides,
and Ubiquitin. The model systems in this work consist
of ubiquitin, alanine tetrapeptide, tripeptides, and the 19
capped dipeptides (e.g., Acetyl−Ala−N−methylamide). Because
these systems differ considerably in size, it is important to
ask whether force fields perform well for all classes of model
system. In particular, it is important to avoid overfitting to
experiments probing only small systems, as that could
compromise accuracy on larger systems where less protein is
solvent-exposed. We find that ff99sb-ildn-phi and ff99sb-ildnNMR
provide good performance for all three classes of systems
(Figure 2).
3.3. Performance by Experiment. For five out of 10
experiments, ff99sb-ildn-phi and ff99sb-ildn-NMR achieve
accuracy comparable to the uncertainty of the comparison
(e.g., x2
/n ≈ 1; see Table S4, Figures S14−S23). Moderate
deviations are found for two experiments (3
J(HN
C′), 3
J(Hα
N)),
but large deviations are found for carbonyl chemical shifts
(CS−C), 3
J(Hα
C′), and 3
J(HN
Hα
). First, large errors in carbon
chemical shifts are found for all choices of force field and water
model. This error may indicate systematic error in either the
chemical shifts estimated by Sparta+ or the conformational
propensities of all force fields evaluated here. Because Sparta+
is parametrized empirically using a neural network approach, it
is challenging to further dissect errors in chemical shift
predictions. Second, moderate errors in 3
J(Hα
C′) are observed;
inspection of individual errors (Figure S24) identifies GGG as
Figure 1. Force field evaluation based on all available data. The overall χ2
quantifies the agreement with all 524 experimental measurements.
Journal of Chemical Theory and Computation Article
dx.doi.org/10.1021/ct2007814 | J. Chem. Theory Comput. 2012, 8, 1409−14141410
the largest error contributor. The failure for GGG is consistent
with previous observations18
that improved Karplus parametrizations
may be required for glycine residues. Finally,
moderate errors in 3
J(HN
Hα
) are observed. However, ff99sbildn-phi
and ff99sb-ildn-NMR perform significantly better than
their predecessors ff99sb-ildn and ff99 (Figure 3). The
3
J(HN
Hα
) analysis suggests that correcting backbone tor-
sions16−18,29
has led to real improvements in force field
accuracy.
3.4. Performance By Amino Acid. Another key question
is whether force field performance is consistent among the
different amino acids. Large variations in quality between
different amino acids might indicate a straightforward way to
improve force fields. To formalize the agreement with
experiment, we calculate values of reduced χ2
(Figure 4).
Values of (χ2
/n) under 1 suggest that errors are within the
measurement uncertainty. This analysis leaves 6/19 amino
acids open to further optimization, including ALA, GLY, SER,
VAL, ILE, and ASP. Force field improvements for these
residues could lead to reduced errors in the present benchmark.
For the remaining amino acids, improved accuracy in chemical
shift and J coupling estimation may eventually reveal force field
inadequacies that are within the uncertainty of the present
comparison.
3.5. Populations of 19 Dipeptides. A recent analysis21
used NMR and vibrational spectroscopy to estimate the αR, β,
and PII populations of 19 capped dipeptides. Here, we use
(ϕ,ψ) state definitions39
to estimate conformational populations
from simulation (Figure 5, Figure S25). Because of
uncertainties in state definitions and the fitting procedure used
in the experimental analysis,21
this comparison is less direct
than the NMR comparisons above; despite this limitation,
population analysis provides several insights.
First, with the exception of ff96, the MD force fields
uniformly over-emphasize αR in dipeptide simulations. Second,
the GBSA implicit solvent model aggravates this error, leading
to even further bias toward helical conformations. Third, recent
force fields (ff03*, ff99sb-ildn, ff99sb-ildn-phi, ff03w, ff99sbFigure
2. Accuracy for dipeptides, tripeptides, tetrapeptides, and ubiquitin. For each class of model system, χ2
quantifies the agreement between
simulation and experiment.
Journal of Chemical Theory and Computation Article
dx.doi.org/10.1021/ct2007814 | J. Chem. Theory Comput. 2012, 8, 1409−14141411
ildn-NMR) combined with explicit solvent show close
agreement with the conformational populations estimated
using a PDB-derived coil library.39
This may suggest that
current force fields perform better in the context of a full
protein system or that direct comparison of simulation to IRbased
population estimates is hindered by systematic error.
Although the overestimation of αR in dipeptides suggests that
further decreasing αR may improve current force fields, such
changes are not always feasible. As an example, we point out
that ff99sb is known to under-emphasize17
αR in the helixforming
Ac−(AAQAA)3−NH2.40,41
Thus, it may be challenging
for fixed-charge force fields to simultaneously achieve accurate
helical propensities in both dipeptide and longer protein
systems. To further investigate, we simulated Ac−(AAQAA)3−
NH2 using both ff99sb-ildn-phi and ff99sb-ildn-NMR (Figure
S26). On the basis of this test, ff99sb-ildn-phi is somewhat
underhelical, while ff99sb-ildn-NMR is somewhat overhelical.
This suggests that a future modification of ff99sb-ildn-NMR
with slightly reduced helical content could lead to modest
improvements in force field quality.
4. DISCUSSION
4.1. Optimal Choice of Force Field and Water Model.
The overall χ2
analysis (Figure 1) suggests that the ff99sb-ildnphi
and ff99sb-ildn-NMR force fields (with explicit water) are
best able to recapitulate the 524 NMR measurements in the
present benchmark. These results are robust to different
models for J couplings and chemical shifts (Figure S1), to
sampling uncertainty in the simulations (Figure S2), and to the
relative importance placed on J coupling versus chemical shift
experiments (Figure S3).
Explicit water models (TIP3P, SPC/E, TIP4P-EW, and
TIP4P/2005) outperform GBSA. However, choosing between
TIP3P, SPC/E, TIP4P-EW, and TIP4P/2005 is difficult, as the
results are force field dependent. However, our current analysis
does suggest that variants of ff99sb give reasonable performance
with TIP4P-EW (and, to a lesser extent, TIP4P/2005).
Recent four-point water models have improved thermodynamic
properties;2,28
our results support their broader use in protein
simulations, although further testing may be necessary for
benchmarking the accuracy of long-range forces.
Figure 3. Performance by experiment. The errors in 3
J(HN
Hα
) suggest
that the ff99sb-ildn-phi and ff99sb-ildn-NMR force fields correct a
significant bias in the ϕ potential of the ff99sb-ildn force field. Values
are shown for TIP4P-EW.
Figure 4. Calculated values of reduced χ2
. Reduced χ2
is shown for all
19 amino acids, indicating force field quality as a function of individual
amino acid. Values are shown for TIP4P-EW with five well-performing
force fields. Reduced χ2
values near 1 indicate that force field error is
comparable to the experimental uncertainty, while values much larger
than 1 indicate possible room for force field improvements. Errors for
reduced χ2
are given by (2/n)1/2
, where n is the number of
measurements available for that amino acid. Plotted error bars
underestimate the true error, as error estimates include only the
contribution of the Karplus and chemical shift prediction. This
contribution tends to be the dominant source of error in the present
benchmark.
Figure 5. Estimation of conformational populations from simulation.
The conformational populations for the 19 dipeptides (averaged over
all 19) are shown for various force fields. Individual amino acid
predictions are given in Figure S25. Grid ticks represent population
increments of 0.1; the corners of the triangle represent the
distributions with all β, αR, and PII, respectively. Also shown are
experimental estimates21
and statistics from a PDB-derived coil
library.39
Journal of Chemical Theory and Computation Article
dx.doi.org/10.1021/ct2007814 | J. Chem. Theory Comput. 2012, 8, 1409−14141412
4.2. Future Force Field Development. With the simple
functional forms used, how much can current force fields be
improved? Given the many small but measurable improvements
recently published,14,16−18
it is likely that the current functional
forms may allow further increases in accuracy. The best path for
improvement, however, is complex. The nonbonded terms,
including partial charges, are based on decade-old calculations;
increasing computational resources allows increasingly accurate
QM data to be used for parametrization. More accurate bonded
terms might also be possible. Another possibility is the use of
amino acid specific torsional potentials, rather than identical
potentials for all (nonglycine) residues. Such a procedure
would allow researchers to refine force fields for amino acids
where performance is presently inadequate.
For further developments, a key question is whether to use
ab initio14
or experimental data16−18,29
when fitting parameters.
Fitting to ab initio data is hindered by the difficulty of modeling
solvent effects during parametrization. Furthermore, parameters
such as partial charges may not be transferable between gas and
condensed phase environmentsor even between hydrophobic
and solvent-exposed environments. Fitting to experimental
data is currently hindered by two key limitations. First,
only limited data are available for model systems. Second, the
quantitative connection between simulation and experiment
typically relies on parametrized relationships such as the
Karplus relationship or the chemical shift predictions of Sparta
+. These parametrizations have large uncertainties (typically
larger than the statistical errors in either simulation or
experiment), may contain systematic errors (such as aminoacid
specific biases18
), and rely on protein structural models
that are ensemble averaged (possibly blurring important shorttime-scale
dynamics42
). The current analysis focuses on
agreement with NMR (chemical shift and J coupling)
experiments, which emphasize local bonded interactions.
Other experimental data, such as solvation free energies, may
be critical for evaluating other aspects of force field perform-
ance.
5. CONCLUSIONS
Molecular simulation promises atomic-detail modeling of key
processes in chemistry and biophysics, but only if the
underlying force field has demonstrated accuracy. Here, we
have shown that recent force field enhancements lead to
increased accuracy in recapitulating a benchmark set of 524
NMR measurements. Simulations performed in explicit water
with either the ff99sb-ildn-phi or ff99sb-ildn-NMR force field
achieve RMS errors that are comparable to the uncertainty in
calculating the experimental observables. Future work may
require advances in both force field development and accurate
calculation of NMR observables.
■ ASSOCIATED CONTENT
*S Supporting Information
Additional error analysis is available in the Supporting
Information. The Karplus relations used in this work are
tabulated along with estimates of systematic uncertainty.
Gromacs parameter files and PDBs for the present simulations
are also included. This information is available free of charge via
the Internet at http://pubs.acs.org
■ AUTHOR INFORMATION
Corresponding Author
*E-mail: pande@stanford.edu.
Notes
The authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
We thank NSF CNS-0619926 for computing resources and
NIH R01-GM062868, NSF-DMS-0900700, and NSF-MCB-
0954714 for funding. K.A.B. was supported by a Stanford
Graduate Fellowship. R.D. was supported by a BurroughsWellcome
Foundation Career Award at the Scientific Interface.
We acknowledge the following award for providing computing
resources that have contributed to the research results reported
within this paper. MRI-R2: Acquisition of a Hybrid CPU/GPU
and Visualization Cluster for Multidisciplinary Studies in
Transport Physics with Uncertainty Quantification http://
www.nsf.gov/awardsearch/showAward.do?AwardNumber=
0960306. This award is funded under the American Recovery
and Reinvestment Act of 2009 (Public Law 111-5).
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