The Chemical Shift Baseline for High-Pressure NMR Spectra of Proteins

Article abstract of DOI:10.1002/anie.201602054

High-pressure (HP) NMR spectroscopy is an important method for detecting rare functional states of proteins by analyzing the pressure response of chemical shifts. However, for the analysis of the shifts it is mandatory to understand the origin of the observed pressure dependence. Here we present experimental HP NMR data on the¹⁵N-enriched peptide bond model, N-methylacetamide (NMA), in water, combined with quantum-chemical computations of the magnetic parameters using a pressure-sensitive solvation model. Theoretical analysis of NMA and the experimentally used internal reference standard 4,4-dimethyl-4-silapentane-1-sulfonic (DSS) reveal that a substantial part of observed shifts can be attributed to purely solvent-induced electronic polarization of the backbone. DSS is only marginally responsive to pressure changes and is therefore a reliable sensor for variations in the local magnetic field caused by pressure-induced changes of the magnetic susceptibility of the solvent.

Full text of DOI:10.1002/anie.201602054

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International Edition: DOI: 10.1002/anie.201602054
German Edition: DOI: 10.1002/ange.201602054
High-Pressure NMR Spectroscopy
The Chemical Shift Baseline for High-Pressure NMR Spectra of
Proteins
Roland Frach, Patrick Kibies, Saraphina Bçttcher, Tim Pongratz, Steven Strohfeldt,
Simon Kurrmann, Joerg Koehler, Martin Hofmann, Werner Kremer, Hans Robert Kalbitzer,
Oliver Reiser, Dominik Horinek, and Stefan M. Kast*
Abstract: High-pressure (HP) NMR spectroscopy is an
important method for detecting rare functional states of
proteins by analyzing the pressure response of chemical
shifts. However, for the analysis of the shifts it is mandatory
to understand the origin of the observed pressure dependence.
Here we present experimental HP NMR data on the 15N-
enriched peptide bond model, N-methylacetamide (NMA), in
water, combined with quantum-chemical computations of the
magnetic parameters using a pressure-sensitive solvation
model. Theoretical analysis of NMA and the experimentally
used internal reference standard 4,4-dimethyl-4-silapentane-1-
sulfonic (DSS) reveal that a substantial part of observed shifts
can be attributed to purely solvent-induced electronic polar-
ization of the backbone. DSS is only marginally responsive to
pressure changes and is therefore a reliable sensor for
variations in the local magnetic field caused by pressure-
induced changes of the magnetic susceptibility of the solvent.
shift changes are rather small, calling for the use of an internal
standard. For measurements conducted at ambient pressure
and in polar solvents 4,4-dimethyl-4-silapentane-1-sulfonic
acid (DSS) has been recommended by the IUPAC.[3] The
presence of a polar solvent at HP may, however, lead to
perturbations of the electronic structure of solutes that in turn
can influence chemical shifts and, possibly, also coupling
constants due to a change of dielectric properties and/or
coordination patterns compared to ambient conditions. Con-
sequently, an understanding of the pure solvent contribution
to NMR parameters as a function of pressure is necessary in
order to define a baseline that distinguishes inherent solvent-
induced from conformational contributions in observed
spectra.
Here we report the pressure sensitivity of chemical shifts
of the most elementary fragment of a protein backbone, N-
methylacetamide (NMA) as a prototypical compound from
both an experimental and a computational point of view.
NMA is structurally simple such that electronic effects can be
distinguished effectively from conformational issues. We
determined pressure-dependent NMR spectra to elucidate
the intrinsic chemical shift dependence of the amide group
nuclei, that is, 1H, 13C, and 15N, where the latter isotope needed
to be introduced synthetically. Since experimental spectra in
protic solvents are commonly referenced to the methylsilyl
group of the anion of DSS, the intrinsic pressure dependence
of its shielding constant has to be known. Ideally this
parameter is pressure-transparent, that is, it would mainly
sense the variation of the local magnetic field arising from the
pressure-dependent change in the magnetic susceptibility of
the bulk solvent and not from changes related to its molecular
structure. Therefore, it is necessary to determine the inherent
pressure response of (isotropic) magnetic shielding constants
s of relevant DSS nuclei. This is even more pertinent since
empirical scaling factors have been defined and recom-
mended in the literature[3] that make it possible to indirectly
reference nuclei other than hydrogen with respect to the
proton resonance of the DSS methyl groups. Such parameters
have been determined for ambient conditions, and in order to
establish DSS as a good HP NMR standard in protic solvents
the transferability of these parameters to extreme conditions
must be examined. This is particularly important for accurate
calculations in order to match the experimental and the
computational chemical shift scale or, in other words, to
understand what is really measured under extreme conditions.
Theory can supplement experiment with difficult to
obtain data on shielding constants if two challenges are
met: 1) A quantum-chemical (QC) methodology is required
H
igh-pressure (HP) NMR spectroscopy has become
a major method for studying rare conformational states of
proteins, which are crucial for the understanding of protein
function[1] and are relevant for the development of a new type
of inhibitory compounds called intrinsic allosteric inhibitors.[2]
In this context, mainly the pressure (p) dependence of the 1H,
13C, and 15N chemical shifts d(p) of peptide backbone nuclei is
analyzed in order to detect different conformational states of
the protein in thermal equilibrium. The observed chemical
[*] Dr. R. Frach, P. Kibies, S. Bçttcher, T. Pongratz, S. Strohfeldt,
Prof. Dr. S. M. Kast
Physikalische Chemie III
Fakultꢀt fꢁr Chemie und Chemische Biologie, TU Dortmund
Otto-Hahn-Strasse 4a, 44227 Dortmund (Germany)
E-mail: stefan.kast@tu-dortmund.de
S. Kurrmann, Dr. J. Koehler, Prof. Dr. W. Kremer,
Prof. Dr. H. R. Kalbitzer
Institut fꢁr Biophysik und physikalische Biochemie
Fakultꢀt fꢁr Biologie und Vorklin. Medizin
Universitꢀt Regensburg (Germany)
M. Hofmann, Prof. Dr. O. Reiser
Institut fꢁr Organische Chemie
Fakultꢀt fꢁr Chemie und Pharmazie
Universitꢀt Regensburg (Germany)
Prof. Dr. D. Horinek
Institut fꢁr Physikalische und Theoretische Chemie
Fakultꢀt fꢁr Chemie und Pharmazie
Universitꢀt Regensburg (Germany)
Supporting information for this article can be found under:
http://dx.doi.org/10.1002/anie.201602054.
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that properly accounts for HP solvent conditions in the
electronic Schrçdinger equation and yields reasonable results
for NMR parameters in solution, and 2) the scaling factor
approach must be circumvented for indirect referencing (vide
infra). Issue (1) is addressed by employing the formalism of
the “embedded cluster reference interaction site model” (EC-
RISM).[4] This represents an integral equation-based
approach to couple QC and liquid state theory that we have
developed and applied over the past years and which has
significant predictive advantages[5–7] over simpler continuum
electrostatics approximations such as the polarizable contin-
uum model (PCM).[8] In short, EC-RISM yields mutually self-
consistent electronic and solvent structures around a solute by
mapping the solvent charge distribution onto discrete back-
ground point charges that polarize the electronic Hamilto-
nian. Solving the Schrçdinger equation yields a solvent-
polarized electrostatic potential between solute and solvent
sites used as input for a calculation of solvent site distribution
functions around the solute from three-dimensional (3D)
RISM integral equation theory.[9] An estimate of conforma-
tional populations in solution is directly possible since EC-
RISM provides the free energy of each conformer as the sum
of the electronic energy and the analytically available excess
chemical potential. The 3D RISM part requires a property of
the pure solvent as input, the so-called site–site “solvent
susceptibility” c. This function reflects the density response of
the solvent upon insertion of a solute and contains intra- and
(pressure-dependent) intermolecular solvent site distribu-
tions, representing essentially the quantity that allows for
introducing pressure as a variable in QC calculations. c can be
derived either from 1D RISM calculations within a certain
approximation (frequently the so-called “hypernetted chain”
or HNC model) or taken directly from molecular dynamics
(MD) simulations.[10] In this study both approaches were
followed.
RISM-based NMR calculations),[7] only five unique relevant
conformations remain for further analysis (Figure 1), justified
from the corresponding populations derived from free
energies (Tables S2 and S3 in the Supporting Information)
Figure 1. Pressure-dependent abundance of the predominant opti-
mized DSS conformations (shown on top), left: principal form, right:
other conformers, in aqueous and methanol solution from normalized
Boltzmann factors considering the sum of electronic energy and
excess chemical potential at 298.15 K, neglecting vibrational and
rotational entropy contributions. B3LYP/6-31+G(d,p) calculations
have been combined with different solvation models, PCM (corre-
sponding to 1 bar only) and EC-RISM with susceptibilities c from
various sources (MD “SIM”ulation and HNC), numbers in parenthe-
ses reflect the conformer index. Filled circles represent PCM, filled and
open squares EC-RISM data.
as shown in Figure 1 for both water and methanol. PCM data
reflect ambient (1 bar) conditions, which compare well with
EC-RISM results at this pressure for both HNC- and MD-
generated susceptibilities. The fully stretched conformation is
most abundant in both solvents. We note in passing that water
and methanol apparently accommodate DSS differently.
While geometries and their energetic ordering are similar,
the pressure effect on populations is inverted. The major
difference between HNC and simulated (SIM) c data is the
larger population slope at lower pressures for the latter.
Furthermore, SIM results in water show a remarkable
discontinuity at around 4 kbar, which has also been identified
for the TMAO dipole moment.[10] All further NMR-related
observables were computed by Boltzmann averaging over the
five dominant forms using EC-RISM free energies computed
with the respective solvent models.
Results for pressure-dependent isotropic shielding con-
stants of the DSS methyl group from “gauge-invariant atomic
orbital” (GIAO) EC-RISM/QC calculations in water and
methanol are presented in Figure 2 and in Tables S4 and S5.
Most importantly, the absolute pressure dependence of both
1H and 13C are small throughout, even close to being
negligible for protons (< 0.01 ppm over 10 kbar in both
water and methanol), rendering the experimental determi-
nation of such small magnetic-susceptibility-corrected shifts
EC-RISM has been successfully applied separately in
both realms, the computation of shifts of NMA in water under
ambient conditions[7] and the characterization of pressure-
induced intramolecular polarization on trimethylamine-N-
oxide (TMAO).[10] The latter results were used to derive an
effective pressure-dependent force field for TMAO/water
mixtures that, employed within classical MD simulations, is
able to reproduce hydration patterns from reference ab initio
MD and experimental densities between 1 bar and 10 kbar.
Here, shielding and shift predictions for NMA relative to DSS
are combined with HP solvent conditions and compared with
measured data to test the combination of EC-RISM-pre-
dicted NMR parameters with HP-induced polarization. An
agreement between experimental and computational trends
of pressure-dependent shifts would allow for conclusions
about features of DSS as a universal HP NMR standard and
the pure solvent-induced baseline shift of protein NMR.
We began our study by investigating properties of DSS in
two representative solvents, water and methanol, covering
a wide range of pressures. After exhaustively generating
conformations and geometry optimization using PCM
(default settings for water and methanol in Gaussian 09[11]
)
with the 6-31 + G(d,p) basis set and the B3LYP functional
(representing a reasonably efficient combination for EC-
2
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(typically denoted by the symbol X)[3] of NMR frequencies of
1
non-protons and H are determined. Here, this problem is
resolved by reproducing computationally the experiments by
which X factors were determined.[3] For 13C, NMA shieldings
are referenced at all pressures to DSS methyl-C at 1 bar, that
is, to sref(1 bar);[12] for 15N a two-step procedure is followed by
first computing the shift relative to aqueous ammonia and
then adding the experimentally known shift at 1 bar between
dissolved and pure liquid ammonia of À19.4 ppm.[12,13] Due to
the lack of nitrogen in DSS, there is no way to refer to
a pressure-dependent standard, that is, sref(p). Such an
approach essentially implies that the pressure dependence
of the standard is a priori excluded. In the case of 13C the
validity of this assumption can be tested directly since this
approach can be compared with the (direct) pressure-
dependent reference to calculate 13C DSS shielding constants.
Similarly, NMA proton shieldings referenced to DSS at the
respective pressure (as applied in experiments) can also be
compared with referencing to 1 bar shieldings only. This
comparison (middle column of Figure 3) clearly demonstrates
Figure 2. Pressure-dependent shielding constants of the DSS anion
from GIAO/EC-RISM/B3LYP/6-31+G(d,p) calculations in water (top)
and methanol (bottom) for 13C (left) and 1H (right) of the DSS methyl
groups with c taken from MD (orange) and HNC (blue). Data reflect
arithmetic averages over equivalent nuclei.
very difficult. This is a first indication that DSS could indeed
represent a good standard, if the major contribution to the
solvent shift originates from the target species, in our case
NMA. This can be examined by referencing NMA to DSS and
studying the computational results (Table S6) in comparison
with HP NMR experiments (Table S7), as depicted for
aqueous NMA solutions in Figure 3.
The indirect referencing issue (2) mentioned above is
related to the fact that QC calculations of chemical shifts
benefit substantially from linear error compensation in
computing the difference between shielding constants of
target and reference compounds, the quantities directly
accessible from QC. This advantage is lost when ratios
1
that the inherent pressure-dependence of DSS H shielding
constants is negligible since the two approaches yield practi-
cally identical results (open vs. filled symbols). In this sense,
DSS truly is a good standard, suitable for HP NMR setups as
it is almost transparent to pressure changes. 13C behaves only
slightly worse which is not unexpected from Figure 2.
Table 1 (full data in Table S8) shows regression parame-
ters for all experimental and computational shift data. The
obtained prediction of the chemical shifts at ambient pressure
is rather good in comparison to the quality of purely empirical
shift prediction methods.[14] Theory mostly overestimates
slopes (except for 15N with cHNC), coming mainly from the
low-pressure range in the
case of cSIM, where simu-
lated water distribution
functions needed as input
apparently vary more dras-
tically with pressure than
experimentally expected.
HNC here performs quan-
titatively better, likely due
to error compensation
between an “underpolariz-
ing” environment as seen
earlier for TMAO in
water[10] and an overpolar-
ized electronic wave func-
tion within the chosen
level of theory. Obviously,
there is a need to develop
Figure 3. Pressure-dependent chemical shifts of the NMA amide nuclei 13C (left), 1H (middle), and 15N (right)
in water from theory (top) and experiment (middle) along with corresponding regression-corrected deviations
from values at 1 bar (bottom). Calculation results using GIAO/EC-RISM/B3LYP/6-31+G(d,p) are shown in
blue for c taken from MD and in orange for HNC. Experimental data shown in gray are directly referenced to
sref(p;1H) for 1H and indirectly to sref(1 bar,1H) for 13C and 15N; the open symbol for 13C at 1 bar is the
regression estimate for experimental data missing due to technical issues with the high-pressure system.
Dashed lines correspond to fits of raw data by second-order polynomials with coefficients shown in Table 1
and Table S8. Filled and open symbols in the top and bottom rows reflect the reference shielding constants
used for defining shifts, 1 bar for all pressures and the corresponding pressure pairs, respectively, which is
possible for all nuclei except 15N.
better approximations for
the pressure-dependent
solvation contribution
along with appropriate
QC models. Overall, how-
ever, the computed slopes
are positive throughout, in
agreement with experi-
ment, indicating that the
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Table 1: Linear (B1) and quadratic (B2) coefficients obtained from fitting exper-
Acknowledgements
imental and theoretical NMA shift data to second-order polynomials of the form
d(p)=d(0)+B1 p+B2 p2 corresponding to data shown in Figure 3. Full data
including statistical uncertainties are reported in Table S8.
This interdisciplinary work was supported by the
Deutsche Forschungsgemeinschaft (DFG) within
the Research Unit “Exploring the Dynamical Land-
scape of Biomolecular Systems by Pressure Pertur-
bation” (FOR 1979). Calculations were performed
using in-house resources, the LiDOng cluster
(ITMC TU Dortmund), and the Regensburg Com-
puter Centre (hardware supported by the DFG,
INST 89/347-1 FUGG).
Nucleus
B1(13C)[a] B2(13C)[b] B1(1H)[a] B2(1H)[b] B1(15N)[a] B2(15N)[b]
exptl
0.048
À0.007
0.011
0.000
0.53(1)
À0.05(8)
À0.0(7)
–
cSIM(sref(1 bar)) 0.35(0)
cSIM(sref(p)) 0.37(0)
cHNC(sref(1 bar)) 0.07(4)
cHNC(sref(p)) 0.09(9)
À0.02(3) 0.1(0)
À0.02(3) 0.0(9)
À0.00(7) 1.(0)
À0.00(6)
À0.001
À0.001
–
À0.003
À0.004
0.021
0.023
0.13(7)
–
À0.006
–
[a] In ppmkbarÀ1. [b] In ppmkbarÀ2
.
Keywords: computational chemistry · high-pressure chemistry ·
theoretical approach presented here captures the essential
physics of pressure-induced modulation of magnetic shielding
properties. Moreover, predicted quadratic parameters, also
summarized in Table 1, which reflect in proteins mainly large
conformational fluctuations but are still a puzzle in random
coil peptides, are in even better agreement with experiment,
being negative throughout or negligible for 1H.
isotopes · NMR spectroscopy · proteins
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tationally supported pressure dependence of NMA shifts with
respect to DSS reveals an intrinsic, purely solvation-induced
baseline shift contribution to observed shifts of protein
backbone nuclei, independent of the reference originating
from electronic polarization. DSS is by all measures a suitable
NMR standard for HP conditions due to its pressure-trans-
parent magnetic properties. Remarkably, the experimental
1H, 13C, and 15N NMA slopes (0.011, 0.048, and
0.53 ppmkbarÀ1) are in the same range as the values found
earlier for random coil peptides. The average values (in
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1
ppmkbarÀ1) are 0.038[15] and 0.052[16] for H, 0.062[17] for 13C,
and 0.29[16] for 15N, but show a large spread dependent on the
type of amino acid studied. In proteins individual amino acids
can show very different B1 and B2 values since they are also
influenced by global conformational transitions.[18] The data
here reveal that, significantly, also the solvent-induced
electronic polarization contribute to pressure-dependent
shielding constants. For a conformational interpretation of
HP NMR on proteins it will therefore be necessary to study
the coupled polarization effects induced by the solvent and by
the protein background. These problems along with the
development of quantitatively accurate QC/solvation models
to allow for spectral assignments represent a substantial
challenge to future combined experimental and theoretical
efforts.
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Experimental Section
NMR experiments were performed with synthetically obtained 15n-
enriched NMA in aqueous solution at 298 K (see the Supporting
Information for details). Pure solvent c functions for water were
taken from earlier work;[10] a similar procedure was adopted for
extracting data for
a
MeOH force field model.[19] EC-RISM
calculations on DSS and NMAwere performed following the strategy
outlined for ambient conditions.[7] Full details are provided in the
Supporting Information.
Received: February 28, 2016
Published online: && &&, &&&&
4
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Communications
High-Pressure NMR Spectroscopy
Solvent-induced electronic polarization in
high-pressure NMR spectra of proteins: A
pressurized polar solvent environment
influences the electronic structure of both
the reference standard and the target
protein. Combined experimental and
computational effort elucidates the pres-
sure transparency of the common stan-
dard 4,4-dimethyl-4-silapentane-1-sulfon-
ic acid (DSS, see picture) and the intrin-
sic, polarization-related chemical shift of
N-methylacetamide, a prototype of the
protein backbone.
R. Frach, P. Kibies, S. Bçttcher,
T. Pongratz, S. Strohfeldt, S. Kurrmann,
J. Koehler, M. Hofmann, W. Kremer,
H. R. Kalbitzer, O. Reiser, D. Horinek,
S. M. Kast*
&&&& — &&&&
The Chemical Shift Baseline for High-
Pressure NMR Spectra of Proteins
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