High-pressure EPR reveals conformational equilibria
and volumetric properties of spin-labeled proteins
John McCoy and Wayne L. Hubbell1
Jules Stein Eye Institute and Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095
Contributed by Wayne L. Hubbell, December 6, 2010 (sent for review October 5, 2010)
Identifying equilibrium conformational exchange and characteriz-
ing conformational substates is essential for elucidating mecha-
nisms of function in proteins. Site-directed spin labeling has pre-
by some event, but verifying conformational exchange at equili-
brium is more challenging. Conformational exchange (microse-
cond–millisecond) is slow on the EPR time scale, and this proves
to be an advantage in directly revealing the presence of multiple
substates as distinguishable components in the EPR spectrum,
allowing the direct determination of equilibrium constants and
free energy differences. However, rotameric exchange of the spin
label sidechain can alsogive rise to multiple components in the EPR
spectrum. Using spin-labeled mutants of T4 lysozyme, it is shown
that high-pressure EPR can be used to: (i) demonstrate equilibrium
between spectrally resolved states, (ii) aid in distinguishing confor-
mational from rotameric exchange as the origin of the resolved
states, and (iii) determine the relative partial molar volume (Δ¯Vo)
and isothermal compressibility (Δ¯βT) of conformational substates
in two-component equilibria from the pressure dependence of the
equilibrium constant. These volumetric properties provide insight
into the structure of the substates. Finally, the pressure depen-
dence of internal side-chain motion is interpreted in terms of
volume fluctuations on the nanosecond time scale, the magnitude
of which may reflect local backbone flexibility.
tuations on the picosecond–nanosecond time scale and slower
conformational fluctuations on the microsecond and longer time
scale (1–3). Molecular flexibility on these time scales plays a
central role in protein function (4). For example, in recognition-
binding sequences, dynamic disorder on the nanosecond–micro-
second time scale may increase the rate of protein–protein
interactions via a “fly casting” mechanism (5). An emerging
disorder-to-order paradigm for interaction (6) can also give rise
to promiscuity in binding that increases the size of the “inter-
Regulation of protein function is often linked to a conforma-
tional switch triggered by an interaction with a chemical or phy-
sical signal. One mechanistic interpretation of this event is
provided by a “preequilibrium” model, which posits that all pos-
sible conformations of a protein exist at equilibrium with popula-
tions proportional to their relative energies (7). The exchange
(“hopping”) event between different conformers is characterized
by lifetimes in the microsecond–millisecond range (1, 2, 8). In this
model, a conformational switch is viewed as a shift in the relative
populations of existing conformational states rather than the
creation of a new state.
To evaluate the above models and elucidate molecular me-
chanisms of protein function, it is essential to have experimental
means for identifying dynamically disordered sequences and for
characterizing conformational equilibria on a broad range of time
scales. Solution NMR spectroscopy is well-established for this
purpose (9, 10), but it is challenged for many systems of current
interest, including intrinsic membrane proteins in their native
lipid environment, and nonequilibrium systems that evolve in
roteins undergo structural fluctuations that span a wide range
of time scales. Among these motions are fast backbone fluc-
time. For such cases, site-directed spin labeling (SDSL) offers
a promising experimental strategy (11–14).
In the usual implementation, SDSL employs the nitroxide side
chain designated R1 (Fig. 1A). The EPR spectra of R1 in a pro-
tein directly reflect nitroxide motion on the picosecond–nanose-
cond time scale, which overlaps the time domain of fast backbone
fluctuations. Hence, R1 is a direct observer of such motions
and has been used to map sequence-specific backbone motion
in soluble (15) and membrane-bound proteins (14, 16).
An important consequence of the EPR time scale is that
although fast backbone motions are directly reflected in the EPR
spectra, conformational exchange on the microsecond–millise-
cond and longer time scales is too slow to produce relaxation
effects that are reflected in the lineshape; at X-band, exchange
between species with lifetimes >100 ns is in the slow exchange
limit. Instead, the presence of two conformations in equilibrium
will, for particular locations of R1, give rise to two components in
the EPR spectrum, each corresponding to one of the conforma-
tions (17, 18) and of intensity proportional to the population,
permitting the direct determination of the equilibrium constant.
However, two-component EPR spectra can also arise from
equilibrium between two rotameric states of R1 that place the
nitroxide in distinct environments (19, 20). In this report, high-
pressure SDSL-EPR is introduced as a means for distinguishing
conformational and rotameric exchange as the origin of two-com-
ponent EPR spectra and for providing quantitative volumetric
information on conformational substates in equilibrium.
For equilibrium between two states of a system, the pressure-
dependent equilibrium constant KðPÞ relative to that at atmo-
spheric pressure (1 bar) is given to second order in pressure by
where P is the gauge pressure; KðPÞ and Kð0Þ are the equilibrium
constantsatpressuresPandP ¼ 0,respectively;andΔ¯VoandΔ¯βT
are the differences in partial molar volume and partial molar
isothermal compressibility of the two states, respectively, at the
reference pressure and temperature (P ¼ 1 bar and T ¼ 294 K).
According to Eq. 1, application of pressure will produce a rever-
sible shift in the relative populations of states, and this provides
an important test for true equilibrium between states detected in
an EPR spectrum.
Author contributions: J.M. and W.L.H. designed research; J.M. performed research; J.M.
and W.L.H. contributed new reagents/analytic tools; J.M. and W.L.H. analyzed data;
and J.M. and W.L.H. wrote the paper.
The authors declare no conflict of interest.
1To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
This article contains supporting information online at www.pnas.org/lookup/suppl/
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In pioneering NMR studies of high-pressure effects on pro-
teins, Akasaka has demonstrated that the application of pressure
can indeed shift the relative populations of conformational
substates in equilibrium. His findings were summarized in an
empirical “volume theorem,” which states that “volume parallels
conformational order” (21). This is of practical interest, because
low-lying excited states, which are spectroscopically “invisible”
because of their low populations, have reduced conformational
order compared to the ground state (22). According to the the-
orem, excited states have lower molar volumes, and Eq. 1 predicts
that the application of pressure will populate such states, which
may be intimately involved in function. Thus, pressure provides a
simple and elegant means to populate excited states for study by
The above considerations provide a motivation for use of high
pressure in SDSL. In this initial study, the effect of pressure, as
viewed by an R1 spin label, is investigated using T4 lysozyme
(T4L) and destabilized mutants thereof as simple model systems.
The results reveal three classes of behavior reported by R1 due to
a pressure change: (i) site-dependent changes in the internal
dynamics of R1 that can be described by an activation volume,
(ii) shifts in rotameric equilibria of R1 for which lnKðPÞ is linear
in pressure, and (iii) shifts in protein conformational equilibria
where lnKðPÞ is nonlinear in pressure. For the latter two, the be-
havior is described by Eq. 1. Hence,Δ¯Voand Δ¯βTcan be deter-
mined from experimental values of KðPÞ. The linear pressure
dependence of rotameric equilibria indicates that Δ¯βT≈ 0, sug-
gesting a simple means for distinguishing rotameric equilibria of
R1 from conformational exchange, where in general Δ¯βT≠ 0.
The sections below illustrate the three classes of pressure-depen-
dent behavior identified. In all cases, the effect of pressure is
completely and quantitatively reversible. Dynamic parameters
for the nitroxide as a function of pressure (namely, the order
parameter S and effective correlation time τ for anisotropic
motion) are obtained from fits of the spectra to a microscopic
order macroscopic disorder (MOMD) model (Methods). In the
case of two-component EPR spectra, corresponding to two states
of the spin label, the populations and apparent equilibrium con-
stant KðPÞ are also determined from the MOMD fits. In each
case, the fits are provided in SI Text.
Pressure Modulates the Motion of R1 at Solvent-Exposed Sites. The
internal motion and EPR spectra of R1 in proteins are reasonably
well understood through complementary studies from crystallo-
graphy (19, 20, 23, 24), mutagenesis (19, 20, 23), and spectral
analysis (25, 26). One outcome of these studies has been a model
for the structure and internal motion of the R1 side chain at sites
where the nitroxide does not interact with neighboring residues.
In this “χ4∕χ5” model, the motion is constrained and anisotropic
because of backbone interactions (Fig. 1A), giving rise to an
EPR spectrum that can be characterized by an order parameter
S and effective correlation time τ, the latter of which is typically
1–3 ns (26).
To investigate the effect of pressure on the internal motion of
R1, sites in T4L were selected where R1 has a known crystal
structure and an EPR spectrum consistent with the simple model
of Fig. 1A; 82R1 serves as an example (Fig. 1). The crystal struc-
ture reveals the typical sulfur/backbone interaction with no evi-
dence of nitroxide interactions with neighboring residues, and the
crystallographic B factors of the backbone are low (23). The EPR
spectrum at atmospheric pressure (Fig. 1B, black trace) can be
fit with a model of anisotropic motion with S ¼ 0.36, τ ¼ 1.5 ns,
similar to the extensively characterized internal motion of 72R1
(26). We tentatively assume that the motion of 82R1 represents
predominantly internal R1 motion.
The pressure-dependent EPR spectra of 82R1 (Fig. 1B) are
well fit by a model with fixed S and τ increasing with pressure.
Apparently, the increase in τ with pressure does not simply reflect
viscosity increases of the bulk solvent; at 20 °C, the relative visc-
osity of water actually decreases slightly with pressure at low pres-
sure (P ≤ 1 kbar) and increases by approximately 15% at 4 kbar
(27). In addition, replacing water by D2O (viscosity 25% greater
than water) (SI Text) or increasing the viscosity by a factor of 3
with sucrose has no effect on R1 internal motion (18).
According to activated state theories, the pressure dependence
of τ is given by
where τ and τoare the rotational correlation times at gauge pres-
sures P and P ¼ 0, respectively, and ΔV‡is a volume of activation
that corresponds to an increase in volume of a solvent cage
necessary to permit the rotation of the nitroxide (28, 29). A plot
of ln½τ∕τo? versus pressure is linear (Fig. 1C), and the slope gives a
value of 1.2 ? 0.5 mL∕mol for ΔV‡at 294 K.
Another site of known crystal structure where the EPR spec-
trum reflects simple anisotropic motion is 80R1 (Fig. 2A) (24).
Simulation of the EPR spectrum for 80R1 gives S ¼ 0.17,
τ ¼ 1.0 ns at atmospheric pressure. The pressure-dependent
EPR spectra (Fig. 2B) can be fit with a constant S and variable
structure [Protein Data Bank (PDB) ID code 1ZYT]. The bond numbering is
indicated, and the dotted line identifies a noncovalent interaction (Sδ·HCα)
common to solvent-exposed R1 residues. This interaction constrains the inter-
nal motion of the side chain largely to torsional oscillations about the two
terminal dihedral angles χ4and χ5(the χ4∕χ5model) (24, 26). (B) Pressure
dependence of the EPR spectra normalized to the same number of spins.
(C) The nitroxide τ determined from fits to the spectra is plotted as indicated
vs. pressure (dots); the solid line is a fit to Eq. 3.
T4L 82R1. (A) Model of the R1 side chain in 82R1 based on the crystal
structure (24). (B) Pressure dependence of the EPR spectra normalized to the
same number of spins. (C) The nitroxide τ determined from fits to the spectra
is plotted as indicated vs. pressure.
T4L 80R1. (A) Model of the R1 side chain in 80R1 based on the crystal
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www.pnas.org/cgi/doi/10.1073/pnas.1017877108McCoy and Hubbell
linear, and the slope corresponds to ΔV‡¼ 2.3 ? 0.4 mL∕mol at
294 K (Fig. 2C). Interpretation of the activation volumes for
these sites will be considered in Discussion.
lnKðPÞ Is Linear in Pressure for the Equilibrium Between R1 Rotamers
in 44R1. The EPR spectra of R1 residues on the solvent-exposed
surface of a rigid protein often have two components reflecting a
relatively mobile (m) and immobile state (i) due to coexistence
of two rotamers of R1; one such site is 44R1 in the B helix of
T4L. The crystal structure and modeling suggest that equilibrium
between two rotamers about χ4gives rise to the two spectral
components, where the i state arises from an interaction of the
nitroxide ring with glutamate residue E45 in the helix (Fig. 3A)
(19). This conclusion was supported by a dramatic reduction in
the amplitude of the i component in the spectrum of the 44R1/
E45A mutant, which consist largely of the m component (19).
The dependence of the EPR spectra of 44R1 on pressure is
striking (Fig. 3B). Fits of the spectra to a two-state model of R1
show that the changes can be accounted for by a shift in the re-
lative populations of two states. From the populations obtained
from the fits, the apparent equilibrium constant, KðPÞ ¼ ½i?∕½m?
was determined. The mutant 44R1/E45A was also studied to
obtain a set of spectra corresponding to the pressure dependence
of a nearly pure m state, which could then be subtracted from
the spectra of 44R1 at the same pressure to provide the relative
populations and KðPÞ without invoking spectral simulations. The
results of this strategy are in reasonable agreement with KðPÞ
determined by simulations (SI Text).
A plot of the experimental values of ln½KðPÞ∕Kð0Þ? versus P is
shown in Fig. 3C along with a fit to Eq. 1 that gives Δ¯Vo¼
−9.4 ? 2.2 mL∕mol and Δ¯βT¼ 0. Apparently, pressure favors
the interaction with the neighboring glutamate residue because
of a smaller molar volume of the complex.
The correlation times of the individual m and i states also
depend on pressure, as expected from the results of 80R1 and
82R1 presented above. The plot of ln½τ∕τo? versus pressure for
the exposed m state is linear (SI Text) and gives ΔV‡¼ 1.7?
0.4 mL∕mol. Similar analysis for the immobilized state is not
given because the motion of this state has significant contribu-
tions from protein rotary diffusion.
lnKðPÞ Is Nonlinear in Pressure for Conformational Equilibria in Desta-
bilized Mutants of T4L. T4L is exploited as a model system in
development of SDSL technology because of the extensive data
base of WTand mutant crystal structures, including many bearing
the R1 side chain (19, 20, 23, 24), as well as solution NMR
(30–32) and hydrogen exchange data (33–35). The enzyme con-
sists of two independently folding subdomains (N and C). Based
on hydrogen exchange, crystallographic B factors and NMR data,
the individual domains in the WT protein each have only a single
conformation with significant population, although a hinge-
bending motion relates the relative position of the two subdo-
In destabilized mutants of T4L, the subdomains can adopt
additional conformations, and such mutants have provided valu-
able models for exploring conformational equilibria (31, 32). This
approach was adopted here to explore the pressure response of
conformational equilibria as detected by SDSL. For this purpose,
T4L was specifically destabilized by introducing R1 at a partially
buried site (118R1) in combination with urea and at a completely
buried (46R1) site in a short helix.
118R1. The crystal structure of 118R1 shows the R1 side chain to
be partially buried in the hydrophobic interior of the four-helix
bundle that constitutes the core of the C domain (20). The helix
bundle has a near-native fold, but a short helix F (1.5 turn) that
connects two helices of the bundle is unfolded (Fig. 4A). As an-
ticipated from the partially buried location of R1, the EPR spec-
trum of the mutant reflects immobilization of the nitroxide
(Fig. 4B, black trace). Application of pressure to 4 kbar produces
small spectral changes (Fig. 4B) attributable in part to an increase
in viscosity under pressure that slows protein rotary diffusion
(SI Text). It should be noted that changes in protein rotary
diffusion will contribute to the effective nitroxide correlation
time for strongly immobilized states of R1 like 118R1, but not
for more mobile states like 80R1 and 82R1 or the mobile com-
ponent of 44R1 considered above (18).
The equilibrium urea denaturation curve for 118R1 deter-
mined with CD follows a two-state model NðnativeÞ ⇌
UðunfoldedÞ with a midpoint at 3.6 M urea; denaturation is
complete at [urea] >5 M (SI Text). The mutant is destabilized
structure (PDB ID code 2Q9E). The presence of the two rotamers is inferred
from mutagenesis data (see text). (B) Pressure dependence of the EPR spectra
normalized to the same number of spins. (C) The equilibrium constant deter-
mined from fits to the spectra is plotted as indicated vs. pressure (dots); the
solid line is a fit to Eq. 1.
T4L 44R1. (A) Model of the R1 side chain in 44R1 based on the crystal
crystal structure (PDB ID code 2NTH); an unfolded short helix F is indicated
in cyan. (B) The pressure dependence of the EPR spectra in buffer (20 mM
MES, pH 6.8). (C) Pressure-dependent EPR spectra in 8 M urea in buffer.
(D Right) Pressure dependence of EPR spectra in 2 M urea in buffer. (D Left)
The equilibrium constant determined from fits to the spectra is plotted as
indicated vs. pressure. In all cases, the EPR spectra are normalized to the same
number of spins.
T4L 118R1. (A) Model of the R1 side chain in 118R1 based on the
McCoy and Hubbell PNAS Early Edition
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by approximately 1.5 kcal∕mol relative to the WT*. The EPR
spectrum of the U state in 8 M urea at atmospheric pressure
is characteristic of a polypeptide disordered on the nanosecond
time scale (Fig. 4C, black trace). Application of pressure in-
creases the nitroxide correlation time and the center line width
(Fig. 4C); a plot of ln½τ∕τo? versus pressure is linear with ΔV‡¼
4.2 ? 0.5 mL∕mol (SI Text), nearly four times larger than that for
simple internal motion of R1 determined for 82R1 (Fig. 1C). In-
creases in viscosity of the urea solution do not contribute
significantly to increases in correlation time with increasing pres-
sure. At most, the urea concentration increases by approximately
14% at 4 kbar because of solvent compression, causing an in-
crease in relative viscosity of only approximately 8% (37), and
this is too small to produce the observed effects.
In 2 M urea at atmospheric pressure, the N ⇌ U equilibrium is
observed in the EPR spectrum, as evidenced by the presence of a
highly mobile component (m) that amounts to approximately
4% of the population (Fig. 4D, black trace). This provides a very
simple example of a conformational equilibrium. The pressure
dependence of the EPR spectra is shown in Fig. 4D Right. A plot
of ln½KðPÞ∕Kð0Þ?, where KðPÞ ¼ ½m?∕½i?, is strongly nonlinear in
pressure (Fig. 4D Left). A fit of the data to Eq. 1 gives Δ¯Vo¼
−51.0 ? 1.7 mL∕mol and Δ¯βT¼ −0.017 ? 0.001 mL∕molbar.
46R1. Residue L46 is located at buried site in the B helix of the
N domain (Fig. 5A), and R1 would be expected to be immobilized
in the native fold, with a spectrum similar to that of 118R1.
However, at atmospheric pressure the EPR spectrum of 46R1
(Fig. 5B, black trace) (19) reveals a sharp mobile component
(m) in addition to the expected strongly immobilized state (i).
It has been previously shown that the m and i states in 46R1 ori-
ginate from two conformations of the protein as opposed to two
rotamers of R1 (17). Given the narrow spectral lines, the m state
undoubtedly arises from a conformer that is, at least, locally un-
folded in equilibrium with a native-like state.
The pressure dependencies of the EPR spectra and KðPÞ ¼
½m?∕½i? for 46R1 are shown in Fig. 5 B and C. As for 118R1,
the plot of ln½KðPÞ∕Kð0Þ? versus pressure is strikingly nonlinear;
a fit of the data to Eq. 1 gives Δ¯Vo¼ −19.2 ? 0.4 mL∕mol and
Δ¯βT¼ −0.0066 ? 0.0002 mL∕molbar. The much smaller Δ¯Vo
compared to that of 118R1 suggests that the equilibrium
observed is not that for the N ⇌ U equilibrium, but rather an
N ⇌ I equilibrium, where I is an intermediate with incomplete
unfolding. It is known that the stability of the N subdomain is
lower than that for the C subdomain (38) and that intermediate
folding states (I) exist for T4L in which the N and C terminal
subdomains are unfolded and folded, respectively (30, 33, 38, 39).
The broad transition region of the CD-detected urea denatura-
tion curve of 46R1 also suggests a partially unfolded intermediate
state (SI Text). A model consistent with the data for the equili-
brium in 46R1 is N ⇌ I, where I has a folded and unfolded C
and N domain, respectively. However, the conclusions of this
communication do not depend on this model.
Variable Pressure SDSL as a Potential Tool for Investigating Local
Backbone and Side Chain Dynamics. For noninteracting states of
R1 on the protein surface, the pressure dependence of the nitr-
oxide τ provides a volume of activation for rotational diffusion
defined by RT∂lnτ
in terms of the transition state theory as the increase in volume
of the surrounding solvent cage in the transition state necessary
for a rotational diffusive step; this is appropriate for completely
solvent-exposed, noninteracting nitroxides. The volume of activa-
tion scales with the size of the kinetic unit (28, 29), and ΔV‡es-
timated from EPR data on R1 should provide at least qualitative
information on the size of the kinetic unit moving on the nano-
second time scale. For example, the larger ΔV‡for 80R1 relative
to 82R1 could be due to contributions of backbone motions in the
former, which resides in a loop. The largest ΔV‡(4.2 mL∕mol)
was observed for 118R1 in the urea denatured state of T4L.
This is consistent with a larger volume of the kinetic unit, which
includes a segment of the polypeptide chain. Note that if two in-
dependent modes (i.e., R1 motions and backbone fluctuations)
with substantially different values of ΔV‡contribute to the
motion, the ln½τ∕τo? plot may show curvature.
Distinguishing Rotameric and Conformational Equilibria as the Origin
of Two-Component EPR Spectra. EPR spectra of R1 in proteins
are more often than not two-component at the level of resolution
of X-band EPR. One important use of high pressure is to demon-
strate equilibrium between the states represented by the compo-
nents via reversible shifts in the populations. For states in
equilibrium, the origin of the spectral components can be traced
to slow exchange between two rotamers of R1 or between two
conformational substates of the protein (17, 18). In either case,
the apparent equilibrium constant KðPÞ is pressure dependent
and adheres in general to Eq. 1. Site 44R1 provides an example
where two spectral components apparently arise from equili-
brium between two rotamers, one in which the nitroxide is immo-
bilized by an interaction with a neighboring residue in the helix
(Fig. 3B); in the absence of this interaction, the two rotamers
would not be distinguished in the EPR spectrum. One would
expect that the compressibility would differ little between the
two states, and this is indeed the case, as shown by the linear de-
pendence of ln½KðPÞ∕Kð0Þ? on pressure (Fig. 3C). The Δ¯Voof
−9.4 mL∕mol is on the same order as that for formation of an
internal complex in flexible flavinyltryptophan peptides (40),
and pressure-driven interaction of surface side chains has been
previously observed in NMR (41).
Site 44R1 provides the simplest example of this behavior as the
interaction driven by pressure is between the spin label and a re-
sidue on the same helix. A more complex behavior could result if
the spin label interacts through tertiary contact between different
secondary elements where one of them can rearrange under pres-
sure (i.e., has a high compressibility). Such cases will be examined
in future work. Nevertheless, linearity of ln½KðPÞ∕Kð0Þ? versus
pressure provides one criterion to distinguish rotameric from
conformational equilibria and complements other strategies re-
cently developed for this purpose (17, 18).
∂P≡ ΔV‡. For convenience, ΔV‡is interpreted
Manipulating Populations of Protein Conformational Substates and
Measuring Compressibility Differences. In general, conformational
the location of residue L46. (B) The pressure dependence of the EPR spectra
normalized to the same number of spins. (C) The equilibrium constant deter-
mined from fits to the spectra is plotted as indicated vs. pressure (dots); the
solid line is a fit to Eq. 1.
T4L46R1. (A) Ribbon diagram of T4L (PDB ID code 3LZM) showing
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www.pnas.org/cgi/doi/10.1073/pnas.1017877108McCoy and Hubbell
equilibria are characterized by nonzero values of Δ¯Voand Δ¯βT,
and the populations can be manipulated by pressure. The data of
Figs. 4 and 5 clearly reveal this to be the case for the simple ex-
amples of N ⇌ U (118R1 in 2 M urea) and N ⇌ I equilibria
(46R1). At low pressures, the equilibria are reversibly shifted
to the more disordered state, in accordance with the volume
theorem (21). The Δ¯Vo¼ −51.0 mL∕mol for 118R1 falls within
the range of negative values found for N → U transitions for pro-
teins of similar size (42); the smaller value of −19.2 mL∕mol
for the N ⇌ I equilibrium is consistent with the smaller size of
the unfolding unit (the small N terminal domain vs. the entire
At higher pressures, the striking convex curvature of the
ln½KðPÞ∕Kð0Þ? plots (Figs. 4D and 5C) reveals a negative Δ¯βT
in each case; the extrema occur at P ¼ Δ¯Vo∕Δ¯βT, approximately
2.9 kbar for 46R1 and approximately 3 kbar for 118R1. The mag-
nitude and sign of Δ¯βTfor partial and complete unfolding of
proteins is still a matter of debate, even for proteins of similar
size, and likely depends on individual cases (42). Nevertheless,
the negative signs of Δ¯βTfound for the N ⇌ U and N ⇌ I equi-
libria are in agreement with those predicted for Δ¯βS(adiabatic
compressibility) (43), which is similar to Δ¯βTnear room tempera-
Analysis of pressure-dependent fluorescence data on protein
equilibria generally assumes that Δ¯βT≈ 0 (42); hence, reported
values are sparse. However, it has been found that detecting
nonzero values of Δ¯βTmay be problematic with fluorescence
data, and analysis under the assumption of Δ¯βT≈ 0 may substan-
tially influence determined values of Δ¯Vo(45). With SDSL data,
determination of even small values of Δ¯βT, such as those mea-
sured here, are straightforward.
Summary and Future Applications. For R1 at solvent-exposed sites,
the activation volume may reflect contributions from backbone
motion on the nanosecond time scale. If future studies support
this proposal, variable pressure SDSL-EPR will complement
lineshape analysis to identify local backbone flexibility (14, 15).
Because motion about different bonds in the side chain may have
different activation volumes, pressure may also provide a strategy
to investigate details of R1 internal motion.
The time scale of the EPR experiment allows direct determi-
nation of pressure-dependent equilibrium constants KðPÞ for
both R1 rotamer and protein conformational equilibria. The
pressure dependence of KðPÞ can distinguish rotamer from con-
formational exchange in favorable cases; ambiguities that arise
may be resolved with osmotic perturbation (18) and saturation
recovery (17) methods recently introduced for SDSL. Together,
these methods offer an experimental strategy to map sites of
conformational exchange in proteins with SDSL.
Analysis of KðPÞ data for two-state equilibria provides
experimental values of Δ¯βTthat correspond to local changes
in conformation. This is of particular interest for exchange
between globular states where Δ¯βTis proportional to the differ-
Thus, variable pressure SDSL-EPR can provide sequence-speci-
fic data on local volume fluctuations in conformational substates.
The ability of pressure to shift populations of conformational
substates according to the volume theorem leads to two interest-
ing applications. First, pressure can be used to increase the
population of “excited” (22) or “invisible” (31) substates to levels
amenable to study using traditional SDSL methods. Second,
a pressure-jump experiment monitored by EPR can measure
exchange events with characteristic times longer than about
100 μs, limited by the field modulation frequency used in com-
mercial EPR spectrometers. Currently, exchange measurements
δV2i ¼ Δ¯βTkBT, where kBis the Boltzmann constant (46).
with EPR lie in the range of nanoseconds to about 70 μs (17), so
pressure jump would extend the accessible time domain from
nanoseconds to milliseconds and beyond.
Cloning, Expression, Purification and Spin Labeling of T4L mutants. Single cy-
steine mutations were engineered into a pseudo wild-type T4L background
(WT*) in which the two native Cys residues are replaced (C54T/C97A) (47, 48).
Mutations were engineered into chosen sites, expressed, and purified as
previously described (26, 49). Spin labeling of single cysteine mutants was
performed in spin-labeling buffer (50 mM MOPS, 25 mM NaCl at pH 6.8)
as previously described (49). After spin labeling, samples were transferred
to 20 mM MES buffer (pH 6.8), chosen because it has little pH dependence
in the pressure range employed here (50). Desired sample concentrations
were obtained using Microcon filter concentrators (Millipore) with a 10 kDa
cutoff. Final protein concentrations measured by absorption at 280 nm
(ε ¼ 23;327 Lmol−1cm−1) and were typically in the range of 250 to 700 μM.
Hydrostatic Pressure Generation A high-pressure cell was adapted for EPR
from the NMR cell design of Yonker and coworkers (51). Sample cells were
constructed from lengths of polytetrafluoroethylene-coated fused silica
capillary (100-μmi:d: × 360-μmo:d:) obtained commercially (Polymicro Tech-
nology). Details are shown in SI Text.
Pressure was generated with either a hand-operated syringe pump
(High-Pressure Equipment Model 37-5.75-60) rated at 60 kpsi (4.14 kbar)
or with an automated intensifier (Pressure BioSciences Model HUB440) rated
at 55 kpsi (3.79 kbar). Water or 20 mM MES buffer were used as a pressure
transmitting fluid. Pressures were measured using a transducer from Precise
Sensors, Inc., connected in-line with the pump and the sample cell.
EPR Spectroscopy, Spectral Simulations, and Estimation of K. EPR spectroscopy
was carried out at X-band on a BrukerEleXsys 580 fitted with the High
Sensitivity cavity. All spectra were recorded at room temperature (294 K)
with an incident microwave power of 7 mW. Data at atmospheric pressure
was taken before and after the application of pressure to demonstrate
Experimental spectra were fit to an MOMD model using a Labview™
interface (available upon request, email@example.com) of the program NLSL
developed by Freed and coworkers (52, 53). Strategies employed for simula-
tion of spectra for R1 in proteins have been extensively discussed (26, 52, 54)
and are reviewed in SI Text along with parameters and overlays of spectral
simulations obtained for this work.
It has been previously reported that acceptable MOMD fits (χ2< 10−5) are
typically acquired with an uncertainty in the order parameter S and correla-
tion time τ of approximately ?6 and ?15%, respectively (26). These values
were used to estimate the error in the derived equilibrium constant KðPÞ
for MOMD fits of two-component EPR spectra and hence the error in the
reported partial molar volume and isothermal compressibility changes. In or-
der to ensure that motion between the two domains of T4L was not the
source for the observed pressure response, spin-labeled mutants were also
engineered into a cross-linked (21C/142C) derivative of T4L that locks the
domains in the closed configuration (47). Comparison of the spectra of
the spin-labeled mutant 44R1 in both the WT* and cross-linked background
were similar at all pressures (SI Text).
Samples for high pressure contained either sucrose or Ficoll-70 at final
concentrations of 30% wt∕vol or 25% wt∕vol, respectively, to reduce the
effect of protein rotational diffusion on the EPR spectra. These concentra-
tions have been previously determined to give the same microscopic viscosity
with respect to T4L rotational diffusion (18). Under pressure, the viscosity
increase for Ficoll and sucrose solutions due to solvent compression (approxi-
mately 12% volume decrease) is identical and as expected (SI Text). This effect
works as an advantage in further removing overall rotary diffusion effects
from the EPR spectra.
ACKNOWLEDGMENTS. We thank Mark Fleissner for technical assistance and
donation of the T4L 81R1 sample and Joseph Horwitz and Oktay Gasymov
for assistance with the CD spectropolarimetry experiments and resulting data
analysis. In addition, we thank Carlos Lopez, Michael Bridges, and Dmitri R.
Davydov for reading the manuscript and providing insightful comments. This
work was supported by National Institutes of Health Grants R01EY05216
(W.L.H) and 5T32EY007026 (J.M.) and the Jules Stein Professor endowment
(W.L.H.). Figures were generated with the help of the PyMOL Molecular
Graphics System (55).
McCoy and HubbellPNAS Early Edition
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