Department of Molecular Physiology and Biological Physics,
University of Virginia Health Sciences Center, Charlottesville,
Virginia 22906-0011 USA
We present an approach for calculating conformational
changes in membrane proteins using limited distance information. The method, named restraint-driven Cartesian transformations, involves 1)
the use of relative distance changes; 2) the systematic sampling of
rigid body movements in Cartesian space; 3) a penalty evaluation; and
4) model refinement using energy minimization. As a test case, we have
analyzed the structural basis of activation gating in the
Streptomyces lividans potassium channel
(KcsA). A total of 10 pairs of distance restraints
derived from site-directed spin labeling and electron paramagnetic
resonance (SDSL-EPR) spectra were used to calculate the open
conformation of the second transmembrane domains of KcsA
(TM2). The SDSL-EPR based structure reveals a gating mechanism
consistent with a scissoring-type motion of the TM2 segments that
includes a pivot point near middle of the helix. The present approach
considerably reduces the amount of time and effort required to
establish the overall nature of conformational changes in membrane
proteins. It is expected that this approach can be implemented into
restrained molecular dynamics protocol to calculate the structure and
conformational changes in a variety of membrane protein systems.
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INTRODUCTION |
Site-directed spin labeling, in combination with
electron paramagnetic resonance spectroscopy (SDSL-EPR) has become a
powerful tool in obtaining structural and dynamical information of both soluble and membrane proteins of arbitrary size (Hubbell and Altenbach, 1994
; Hubbell et al., 1998, 2000). In particular, SDSL-EPR has been
quite successful in identifying secondary structure elements and
tertiary folds in membrane protein systems (Perozo et al., 1998;
Poirier et al., 1998; Koteiche and McHaourab, 1999; Cortes et al.,
2001).
In SDSL, a nitroxide spin probe is covalently attached into a given
site in a protein by changing that particular residue to cysteine via
standard mutagenesis methods, followed by covalent attachment of a
nitroxide moiety using sulfhydryl chemistry. Typically, a
methanethiosulfonate-based spin label (MTSSL) is used due to its high
reactivity and specificity toward free sulfhydryl groups (Fig.
1 A). Once the spin label is
incorporated into the target cysteine, detection of the local EPR
signal allows for a detailed structural characterization of the
environment surrounding a particular position.
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FIGURE 1
(A) Methanethiosulfonate spin label
sidechain; (B) KcsA x-ray structure;
(C) KcsA TM2 segments. B
and C were generated using the program Molscript
(Kraulis, 1991).
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Using SDSL-EPR, the dynamics and structural information of a protein
can be obtained through the analysis of three different experimental
parameters: probe mobility, solvent accessibility, and inter-spin
distances (Hubbell et al., 1998). The first two parameters are sequence
dependent and can be used to draw local secondary structure and help
infer tertiary or quaternary contact points in proteins. Distance
information can be extracted from the extent of spectral broadening due
to through-space electron-electron dipolar interactions (Likhtenshtein,
1976; Eaton and Eaton, 1989; Rabenstein and Shin, 1995; Hustedt et al.,
1997; Steinhoff et al., 1997). Inter-spin distances can be estimated in
the range of 8 to 25 Å using a number of approaches, including Fourier
deconvolution methods (Rabenstein and Shin, 1995; Steinhoff and
Hubbell, 1996) and the global analysis of mutifrequency spectra
(Hustedt et al., 1997).
By combining multiple SDSL-EPR data, it is possible to develop a
strategy to determine protein folds at the backbone level (Mchaourab
and Perozo, 2000). However, given the significant investment in labor
and costs necessary to engineer the large numbers of labeling sites
required to fully explore the conformational space of a protein of
unknown structure, traditional approaches used to compute solution
structures are not compatible with the limited number of SDSL-EPR data.
Therefore, an alternative approach needs to be developed to efficiently
use EPR data in the determination of protein folds and conformational
rearrangements in proteins.
Molecular modeling of integral membrane proteins is regarded as
considerably less challenging than that of soluble proteins due to the
large energetic restrictions imposed by the lipid bilayer (Bowie,
1997a,b; Booth and Curran, 1999; Pappu et al., 1999; White and Wimley,
1999; Capener et al., 2000). Membrane proteins reach the proper
molecular conformations with limited folding solutions. Because of the
influence of hydrophobic protein-lipid interactions, the specific
requirements of transmembrane helix packing are typically used,
providing powerful constraints in structure prediction of membrane
proteins (Donnelly et al., 1993; Son and Sansom, 1999). By combining
this knowledge basis with structural data from experimental techniques,
the generation of membrane protein folds can be significantly simplified, a fact that must be taken into consideration for the analysis of the vast amounts of genomic data coming from massive sequencing projects.
There are a number of examples in which membrane protein modeling has
been pursued using a limited number of experimental structural
restraints. This includes various conformational search algorithms such
as simulated annealing with Monte Carlo, with molecular dynamics
(SA/MD), or with distance geometry protocols (Herzyk and Hubbard, 1995;
Sansom et al., 1995; Pogozheva et al., 1997; Sansom, 1998). In these
approaches, the 
-helix serves as a template transmembrane
conformation for each system.
The evaluation of transmembrane helix packing solutions is mostly based
on penalty calculations or potential energy functions. For instance, an
SA/MD technique incorporating distance restraints derived from
mutagenesis data was used to model the closed conformation of the pore
domain of the nicotinic acetylcholine receptor (Sansom et al., 1995).
The structure of a tetrameric transmembrane H+
channel from the influenza A virus was modeled by adding the potential
term for the helical orientation derived from site-directed infrared
dichroism data into the MD calculations (Kukol et al., 1999). Simulated
annealing with Monte Carlo was used to model the arrangement of the
seven transmembrane helices of bacteriorhodopsin on the basis of
potential calculations (Son and Sansom, 1999). By considering
theoretical and experimental data within a rigid body assembly, a
number of membrane proteins have been modeled (Herzyk and Hubbard,
1995, 1998). It should be noted that the latter technique made use of
restraints based on SDSL-EPR accessibility data. Recently, spin probe
mobility, accessibility parameters, and interspin interaction
parameters of the N- and C-termini of the K+
KcsA channel were incorporated as structural restraints in
SA/MD calculations, resulting in a three-dimensional folding
model of the full-length potassium channel (Cortes et al., 2001).
The bacterial K+ channel from
Streptomyces lividans KcsA is a homo-tetrameric integral
membrane protein in which each subunit contains two transmembrane (TM)
domains cradling a pore region that includes the signature sequence
(GYGD) critical for ion permeation and selectivity (Doyle et al.,
1998). Because of the functional importance of potassium channels, the
availability of the KcsA crystal structure (Fig. 1
B) has prompted a number of theoretical studies, trying to
extend the structural description of the ion permeation and selectivity
mechanisms (Roux and MacKinnon, 1999; Allen et al., 2000; Aqvist and
Luzhkov, 2000; Berneche and Roux, 2000; Guidoni et al., 2000;
Shrivastava and Sansom, 2000). Evidence from ion flux experiments and
electrophysiological and EPR studies suggested that the conformation of
the crystal structure corresponds to a closed state, that the open
state can be stabilized at low pH, and that the activation gating is
associated with a significant structural rearrangement of the two
transmembrane domains (Cuello et al., 1998; Perozo et al., 1998, 1999).
However, the structural details of the open channel conformation are
yet to be described, owing to the current lack of high-quality crystals
of KcsA in acidic pH and to the fact that the size of
KcsA makes it too large to be analyzed by solution nuclear
magnetic resonance (NMR) methods.
This report presents an approach we call restraint-driven
cartesian transformations (ReDCaT) in which a limited number of distance restraints have been used to determine conformational changes
in membrane protein systems. As a test case, we have analyzed the
structural basis of activation gating in the potassium channel KcsA. We have focused our analysis on the structural
rearrangement of the second transmembrane segments (TM2, Fig. 1
C) because of its functional significance and its strategic
location near the predicted fourfold axis of symmetry. We show that the
ReDCaT approach is a useful alternative in the determination of
conformational changes in membrane proteins. The relativity simplicity
of its implementation, its low computational cost, and the overall
robustness of the method (derived from an analysis of the sensitivity
to the number and location of the restrains) makes ReDCaT an ideal choice in combination with reporter-group-based structural constraints.
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MATERIALS AND METHODS |
Experimental methods
Sample preparation
Design, expression, and characterization of KcsA
tandem dimer mutants have been described in detail by Liu et al.
(2001). Briefly, tandem dimers were constructed with different
oligopeptide linkers, having rTEV protease recognition site in a
pQE-32-based KcsA vector (Cortes and Perozo, 1997). This
resulted in pseudo-tetrameric cysteine mutants of
KcsA. Expression of KcsA and tandem dimers was
followed using the protocol described by Cortes et al. (1997). A
cobalt-based metal chelate chromatography was used to purify the
protein sample.
EPR spectroscopy and distance determination
Reconstituted samples were spin labeled with MTSSL
as described in Liu et al. (2001). The spectra were obtained from an
EMX X-band EPR spectrometer (Bruker Instruments, Billerica, MA)
with loop-gap resonator at 50 µW of microwave power and 1-G field
modulation (100 kHz) at 150 K. From the relation of the average
magnetic field splitting, the distance measurement can be estimated
through the dipolar broadening function (B) using Fourier
deconvolution method (Rabenstein and Shin, 1995).
|
(1)
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In practice, B is obtained from the inverse Fourier
transform (denoted by F
1) of the
division of the Fourier transform of the fully (double)-labeled spectra
(F(D)) by that of the under (single)-labeled
spectra (F(S)). The EPR spectra of the fully- and
under-labeling mutants recorded at two different pH conditions were
analyzed to obtain interspin distances between diagonal TM2 subunits.
Computational details
The method can be divided into three main steps: 1) defining
distance restraints; 2) performing ReDCaT; and 3) refinement of the
calculated ReDCaT conformers. Details of these steps are described below.
Restraints
For a residue ith, the upper
(
rupl(i)) and lower
(rlol(i)) bounds for the
experimental distance changes between diagonal subunits are defined
by
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(2)
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(3)
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in which repr(i)
is the distance change of the residue
ith calculated by the subtraction of
the EPR interspin distance in the open state from that of the closed
state. The distance deviation factor, 
, was introduced to define a
range between the upper and lower limits of the restraints. was
parameterized on the basis of the estimated experimental deviation for
the interspin determination from EPR spectra and was varied to estimate
its optimal value. Eqs. 2 and 3 were applied on all 10 distance
datasets (Table 1), giving rise to the
SDSL-EPR restraints.
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TABLE 1
Experimental interspin distance dataset
(ropen and rclosed) and
the distance changes of two diagonal subunits of
(repr)
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ReDCaT protocol
The flowchart of the ReDCaT method is shown in Fig.
2. The x-ray coordinates of the bacterial
potassium channel at the atomic resolution of 3.2 Å was obtained from
the Research Collaboratory for Structural Bioinformatics (www.rcsb.org)
with the PDB code 1bl8 (Fig. 1 B) (Doyle et al.,
1998). Each TM2 segment contains 34 amino acids, where L86 and Q119 cap
the N and C termini, respectively (Fig. 1 C). The known
three-dimensional structure was used both as a structural template and
as the reference C-C distances in the closed state. Fig.
3 illustrates how the structural
coordinates were transformed before implementation into in ReDCaT. The
result from the subtraction of the distances between the reference and the generated configuration was used to calculate the penalty parameter. Description of the two main routines, configuration generation and penalty calculation, follows.
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FIGURE 3
Graphical representation of rigid body TM2 bundles and
definition of degrees of freedom: (A) the rotation and
the translation applied to the four segments symmetrically (the
z axis is also the axis of molecular symmetry);
(B) rotational ( 1 4) and
translational ( ) parameters for each individual segment in the local
axis; (C) a rotation (4) on the segment
itself (projection on the main helical axis).
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Configuration generation
The procedure used to generate the configuration of
the tetrameric system follows assumptions of rigid body rearrangements and symmetric relationships. All x-ray atomic coordinates belonging to
the TM2 segment of the subunits A, B, C, and D of the reference structure were transformed into a new Cartesian coordinate frame. The
transformed coordinates in the new frame were generated in such a way
that the virtual fourfold axis of symmetry is aligned to the
z axis, whereas the ±x and ±y-axes
pass through the defined rotating center of the individual subunit
(Fig. 3 A). Here, the vector of the core axis is essentially
normal to the membrane bilayer, and each segment has its own vector as
the TM2 -helix representation. The position of each TM element is
defined by the transformation of the local x, y,
and z, where the origin of the local axes was placed at the
center of the rotation (Fig. 3 B). This allows for an easy
way to manipulate configurations of the system and helps further
structural analysis. There are two pieces of evidence supporting the
view that conformational changes in KcsA involve rigid body
rearrangements of the TM segments. On one hand, the circular dichroism
and Fourier transform infrared studies suggest that the closing and
opening of the channel is not accompanied by substantial changes in the
secondary structure content of the channel (Tatulian et al., 1998,
Perozo et al. 1999). Additionally, Fourier analysis of EPR data
periodicities showed that angular frequencies derived from sequential
mobility and spin coupling measurements along TM2 do not change
significantly upon channel opening (Perozo et al. 1999). In view of
this evidence, the dihedral angles of each subunit were kept fix during
sampling configurations.
Multiple configurations of this system can be generated by varying a
total of five degrees of freedom that include four rotations (1-4) and one
translation (). Each rigid body element was subjected to rotation
with angles 1, 2, and
3 along the local x-,
y-, z-axes, respectively (Fig. 3 B),
whereas the 4 was applied to rotate TM2
segments about its helical vector (Fig. 3 C). Combined with
a lateral of the translation parallel to the plane of the bilayer,
adequate sampling of the different configurations can be achieved.
Equivalent changes of these five parameters were applied to each
subunit to maintain the channel symmetry.
Next, the range and the step size of these parameters is defined.
The range for 1 and 2
rotations was limited to within 0 and 
, whereas
3 and 4 were allowed
to vary between 0 and 2. For , a range of 0 to 40 Å is
defined. The step size was 10° for all rotations/tilts and 0.4 Å for
the lateral translation. These increments were tested and found to
provide efficient conformational search within a reasonable
three-dimensional boundary and prevent the generation of mirror-image
structures. Under these conditions, a single run generates a total of
approximately forty million configurations, a number that can be easily
handled by a Pentium III personal computer.
Penalty function
The penalty function, P, is defined by a sum of the
distance violations of the restrained residues. The penalty function is given by:
|
(4)
|
|
(5)
|
in which viol and k are the violation and
the constant of the restrained residue
ith, respectively. The parameter
k is an arbitrary value and is used as a weighting factor.
Distance changes calculated from the configuration and the reference
x-ray structure, rcalc, are in a
form of:
|
(6)
|
in which 
ref and
calc are, respectively, the
average C-C distance of the reference and the generated
configuration from both pairs of diagonal subunits (A-C and B-D) in the
system. rupl and
rlol were taken from Eq. 2
described in the previous section.
Refinement
Because the lowest penalty ReDCaT structures are not calculated
taken into account their conformational energy, it is essential to
subsequently refine a given ensemble to prevent steric clashes that
will lead to energetically unfavorable conformations. In the refinement
stage, full atomic models were used by this purpose. Fifty ReDCaT
structures generated from the two best runs R2 and R4 (see Results for
definitions) were subjected to energy minimization. Sidechain
conformations were assigned according to the x-ray internal coordinates. The missing sidechain of R117 was built based on the Amber
amino acid library. Hydrogen atoms were added taking into account
charged residues, which presumably hold a positive charge for R89 and
R117 and a negative charge for E118. All energy calculations were
performed using the program Amber 6 (Case et al., 1999) with the
Cornell force field for proteins (Cornell et al., 1995).
The 50 structures were subjected to energy minimization with a total of
5000 steps of steepest descent and then conjugate gradient methods. The
cutoff distance for nonbonded interactions was 12 Å, and a
distance-dependence dielectric was used throughout the refinement.
After that, an average structure was computed from the family and then
energetically minimized once again. The final refined structure was
obtained after this step. Protein structures were displayed and
analyzed using the program Procheck-NMR (Laskowski et al., 1996),
Rasmol (Sayle, 1994), Molmol (Koradi et al., 1996), and Weblab Viewer
(Accelrys Inc., San Diego, CA).
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RESULTS |
EPR and distance measurements
Being a homotetramer, wild-type KcsA cannot be
used in the determination of intersubunit distances because the
combination of spin-spin dipolar interactions from next neighboring and
diagonally related subunits results in nonreliable distance data. This
interference can be eliminated using a tandem dimer
constructs so that only two identical residues located in diagonal
subunits are available for spin labeling. This allows the
measurement of interspin distances from dipolar couplings
from two unpaired electrons instead of four (Liu et al.,
2001). Absorption EPR spectra were obtained, and the diagonal
inter-subunit distances between two spinlabeled residues were
calculated (Table 1) under conditions that stabilize the closed (pH
7.0) and the open state (pH 4.0). Experimental details and
interpretation of these data have been described elsewhere (Liu et al.,
2001).
Tests of the methodology
We tested the approach by running a ReDCaT series with the
following objectives: 1) seeking an appropriate distance range between
the upper and the lower bounds; 2) examining the reliability of the
method; and 3) testing the sensitivity of the restraints. To accomplish
these goals, a number of independent runs include: 1) varying the
distance deviation parameter ; 2) determining the closed bundle
structure by reversing the value of the constraints and comparing the
result of the calculation with the reference x-ray structure; 3)
changing the helix center of rotation; and 4) assessing the relative
importance of individual SDSL-EPR restraints. For simplicity, each run
is denoted as R# (see context for details). Twenty-five structures
having the lowest penalty values were selected in each of the runs. For
structural comparison, the global root-mean-square deviation
(RMSD) from an ensemble of 25 structures, and the pairwise RMSD
(between the two average structures of different ensembles) for the
backbone atoms were used unless stated otherwise. The symbol 
R#
denotes the average structure from the ensemble.
Starting a reference run
A total of 10 SDSL-EPR restraints (Table 1) were incorporated in
the R1 run. Based on the reported distance deviations determined from
continuous wave-EPR spectra (Rabenstein and Shin, 1995), the
value was initially set to 1 Å, giving rise to a 4-Å spread in
the distance range of SDSL-EPR restraints (Eq. 2 in Materials and
Methods). The force constant, k (Eq. 4), was set to 50 Å2. As shown in Table
2 and Fig.
4 A, the RMSD of the ensemble of the resulting 25 ReDCaT structures from this run was 1.27 ± 0.8 Å. Thus, using a small number of restraints the ReDCaT strategy was able to generate structures with a low RMSD. It should be noted
that for this initial run (R1) the deviation in the global RMSD values
(±0.8 Å) stems from the conformational differences between two
apparent clusters (with ~0.3 and 0.7 probability, respectively)
within the ensemble (Fig. 4 A). The RMSD between the
clusters is approximately over 2 Å. The structures of the two clusters
are well defined around the cytoplasmic end of TM2 domains (residue
104-119), whereas the structural convergence of its N-terminal half
(residue 86-103) is relatively poor. Clearly, this stems from the fact
that most of the restrained residues are located near the cytoplasmic
half of TM2.
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FIGURE 4
Two-dimensional projection of the per-residue
-carbon diagonal subunit distance (left) and a
backbone stereo view of the corresponding 25 ReDCaT conformers
generated using the program MolMol (Koradi et al., 1996)
(right): R1 (A) and R2
(B). The arrows indicate residues from which
experimental EPR data were used as ReDCaT restraints.
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Reducing the restraining constant of residues 117 and 119
As described in the Materials and Methods section, all reference
distances were obtained from the KcsA x-ray structure. This structure was obtained after chymotrypsin treatment of full-length channel, which renders a channel with its C-terminus truncated near
residue 125 (Doyle et al., 1998). Experimental evidence on the
functional consequences of the chymotrypsin cut in KcsA
indicates that the C-terminus can influence pH dependence of activation gating and can affect the dynamics of the cytoplasmic end of TM2 (Cortes et al., 2001). Given that all the EPR-based distance
information used as constraints in ReDCaT was obtained from full-length
channels, we have taken into consideration possible edge effects in the x-ray coordinates due to the chymotrypsin cut by allowing some additional softness in the restraints around this region. This was done
in the second run R2 by decreasing the weighting restraining constant
k for the last two distance restraints at positions 117 and
119 (the k value was decreased ~5 times as compared with
the R1 run).
The global RMSD was 0.91 ± 0.4 Å, a considerable
improvement in terms of the precision of the ensemble of the structures
in relation to R1 (Table 2). In this case all 25 ReDCaT
conformers were well defined and fall into single cluster (Fig. 4
B). This ensemble is similar to the more populated cluster
obtained from R1 as judged by the 0.83-Å pairwise RMSD between the
average structures of the two families (R2 and R1). Here we used the
dataset and the resulting structures of R2 to serve as internal control
for further tests.
Parameterization of
The parameter defines the allowed range in the upper and the
lower limits of the distance constraints. In an attempt to determine
the sensitivity of the ReDCaT approach to the uncertainty in the
EPR-derived distances, we have systematically varied to determine
its effect on the structure convergence.
Search conditions used in R3 to R6 were the same as those of R2, except
for the SDSL-EPR restraints. The distance range of the restraints was
varied within 2, 6, 8, and 10 Å corresponding to of 0.5, 1.5, 2.0, and 2.5, respectively. The results of this test are presented in Fig.
5 A and Table 2. The
global RMSD of these runs increase from 0.94 to 2.42 Å. The ensembles
of R2, R3, and R4 are quite similar to each other, whereas R5 and R6 failed to converge as a consequence of the wider restraints. The C
profiles of R3 and R4 with respect to that of R2 were very similar with
a range of 0.12 to 0.27 Å for the pairwise RMSD among the average
structures of these families (Table 3).
However, the penalty ratio in the run R3 is approximately twice as
large as that of R2, whereas that of R4 was lower (0.24). By
considering the penalty and RMSD, the used in R3 (0.5 Å) appears
to generate too narrowly defined restraints, giving substantially
increasing penalty without improving the structural precision. From the
results of the best converging runs (R2 and R4), the optimal values are in the 1.0 to 1.5 Å range.
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FIGURE 5
(A) The projected distance of the
-carbon diagonal-subunit of the 25 ReDCaT conformers obtained from
the run R3 to R6. (B) Summary of the global RMSD for all
runs (R1-R28) present in this report. The error bars correspond to
standard deviation of RMSD values.
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Testing the location of the helical center of rotation
Three of the five degrees of freedom imposed on the Cartesian
transformation of the individual helices involve axial tilts. Because
of this, we set out to test the influence of the location of center of
rotation in each TM2 helix on the intra-ensemble deviations. In the R1
to R6 runs, the -carbon of the residue 86 was defined as the center
of rotation of each subunit. The following seven runs, R8 to R14,
tested sequential locations for the rotating center according to the
-carbon of the following six residues: 90, 95, 100, 108, 113, 119, and an additional one at the center of mass of the TM2 segment. Again,
these runs were carried out using the same dataset and search
conditions as those used in R2. Remarkably, results of R8 to R14 (Table
4) suggest that the helical center of
rotation has a negligible influence in the ensemble deviations, as the
structures of all compared ensembles are practicably indistinguishable
from each other. The pairwise RMSD values among the average structures
of R2 and R8 to R14 extended from 0.09 to 0.67 Å, suggesting the same
transmembrane helix packing. The results indicate that the efficiency
of the ReDCaT sampling configurations is not influenced by the defined center of the TM rotations. Any rotating centers can be chosen.
Comparison with crystal structure
As a way to directly compare the ensemble deviations of
ReDCaT-generated structures with KcsA crystal structure, we
require an equivalent TM2 bundle structure in the closed state. This
can be obtained by performing a backward run, in which the starting reference structure was in the open state and the ReDCaT protocol was
applied reversing the sign and the distance range of the restrains. The
backward run, R7, was carried out using the same search procedure as in
R2. This is illustrated in Fig. 6, in
which the original closed TM2 bundle (derived from the crystal
structure) is shown in red, the open ReDCaT structure in blue, and the
closed ReDCaT structure in green, overlapped to the x-ray structure.
The intra-family RMSD of 25 conformers in the closed state was
1.02 ± 0.3 Å, and showed an average backbone deviation of 0.65 Å with respect to the x-ray structure. These results illustrate that
the back-calculated ReDCaT conformers are remarkably close to the x-ray
structure and that the structure from the open conformation can be
brought back to the closed conformation using the inversed restraints.
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FIGURE 6
Backward calculation procedure: the x-ray crystal
structure (red), the average open state
(blue), and the back-calculated 25 ReDCaT conformers
(green) superimposed with the x-ray structure.
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Sensitivity of the restraints
How does each restraint affect the calculation of the open model?
To further understand the sensitivity of the SDSL-EPR restraints, 10 ReDCaT runs, R15 to R24, were performed eliminating one distance constraint each time. From this test, the observed RMSDs within the
ensembles R16 to R24 were between 0.67 and 1.04, indicating the
convergence of the selected conformers (Tables
5).
However, the pairwise RMSD (Table 6)
showed that some of these runs failed to provide an accurate model.
Particularly, the precision and accuracy of R15 and R16 appear
compromised. The pairwise RMSD of R15)100
and R16103 with respect to the target
increased to 8.25 and 9.08 Å, respectively. Consequently, distance
restraints from residues 100 and 103 appear to be the critical to
obtain accurate models.
In the case of R18, R19, and R22, RMSD comparison revealed that
excluding the restraint from residues 108, 109, and 116 generated significant differences in TM packing compared with the target structure with pairwise RMSD of R18108,
R19109, and
R22116 being 1.38, 2.99, and 2.30 Å,
respectively. For the R17, R20, R21, R23, and R24 runs, the ensembles
were identical to that of R2, implying that these particular positions
exert little influence on the overall quality of the structures and
suggests that given the right choice of distances, equivalent
structures can be obtained with fewer constraints. From this test, we
conclude that the quality of the model depends not only on the number
of restraints but also the choice of restraints.
Influence of the number of restraints
From the previous section it is clear that using fewer than the 10 available constraints still produced reliable bundle structures using
ReDCaT. To specifically test the minimal number of constraints still
tolerated by the method, a series of runs were generated in which
restraints were taken out in pairs, threes, and up to five (R25-R28).
The ensembles of these runs show the pairwise RMSDs in the range of
0.26 to 1.42 Å, suggesting that these individual runs converged fairly
well, provided that the critical distance restraints (100 and 103) were
included in the calculation (Table 7).
Obviously, the intra-family deviations of these ensembles increase as
the number of the restraints used in the calculation decrease. However,
the effects of the sequential restrain deletion were not linearly
additive, particularly in the runs with deletions of four and five
restraints.
Calculated structures
From the tests described above, runs R2 and R4 appear to generate
the best set of structures. Fifty structures obtained from these two
ensembles were subjected to the refinement, and the results are
summarizes in Table 8. Refinement
resulted in a substantial improvement of the van der Waals and
electrostatic energies (data not shown). In the refined models, ~91%
of nonglycine and nonproline residues fall in the most favored regions
of the Ramachandran diagram and no residue drops in the disallowed
regions. The backbone RMSD of the final refined structure,
refReDCaTmin, compared with the ReDCaT structures,
{ReDCaT}, indicates no significant change after the refinement
(~1.3 Å). The tendency of diagonal distance changes for the refined
structure is consistent to that of ReDCaT (Fig.
7).
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FIGURE 7
Diagonal distance changes from the closed to the open
state for selected residues. Comparison between the changes in
experimental interspin distances (EPR) and the mean C-C distances
of {ReDCaT} and {refReDCaT}. Error bar represents the range of
distance restraints.
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Fig. 7 shows the magnitude and the direction of C diagonal distances
of the calculated structures with respect to the x-ray structure and
compared with the pH-dependent distance change (from pH 7 to pH 4)
observed from the experimental EPR. Most of the distance change data
from the EPR experiments are in agreement with the direction of the
mainchain movement of the calculated TM2 bundle. In this study, 7 of
the 10 C-C distances were shifted with the same trend as the
change of the interspin distances (residues 103, 109, 112, 115, 116, 117, and 119). The direction of interspin distance changes for residues
100, 107, and 108 is in apparent discrepancy with the results
calculated from the ReDCaT, but the violations of the distance change
in these restraints do not exceed 2 Å, considerably about the
intrinsic resolution of the EPR-based distance determinations. With the
exception of the magnitude in distance change for residue 109, the
general tendency of the helical conformational change suggests a much
larger separation at the C-terminal end of the helix. It is possible
that in this particular position additional nitroxide side-chain
rearrangements might be contributing to the observed inter-subunit
distance change.
Conformational changes and structural features of the open channel
model
Comparison of the helical rearrangements of TM2 between the
KcsA crystal structure and the ReDCaT models are summarized
in Table 8 and Figs. 8 and
9 . The backbone RMSD between the x-ray crystal structure and the average refined ReDCaT conformations was 3.4 Å. The position and orientation of the four segments in the open state
derived from SDSL-EPR restraints reflect an approximate change in
tilting and twisting of the inner transmembrane segments in the x-ray
crystal structure (Fig. 8).
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FIGURE 8
Proposed model for the structural rearrangements of the
four inner helices upon activation gating. A and
B illustrate the rotation of TM2 segments from the
closed (red) to the open (blue) states.
z and xy are described in the text.
(C) Spacefill representation showing an orientation of
residue in three different regions, 101-105, 106-110, and 116-119.
For clarification, the sidechain atoms are colored in green and
yellow.
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FIGURE 9
Backbone RMSD per residues between the closed (x-ray)
and the open refReDCaTmin conformations.
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To provide a systematic structure analysis of conformational changes,
we first introduced three fundamental components,
z, xy, and
hx as a measurement of the helical
reorientations in the two states. The sign of these components is
regarded as directions of the TM2 movement with respect to the x-ray
structure. From an extracellular point of view, a counterclockwise
rotation about the axis of symmetry of the channel molecule corresponds to a negative z. On the other hand, the
sign of xy is defined by watching the
domain movement from the lateral view. A positive xy implies movement of TM2 toward the
equatorial plane of bilayer (the x-y plane),
whereas a negative sign suggests tilts toward the core axis.
hx measures the rotation of the helix
itself and the definition for the sign of
hx is the same as that applied to
z.
Upon pH-dependent activation, TM2 moves according to the following
transformations: z of 8 ± 3°,
xy of +8 ± 3°, and
hx of 32 ± 3°. Therefore, the
corresponding mechanical process of the inner helices in channel gating
involves: 1) counterclockwise rotations around the virtual four-fold
axis of symmetry (Fig. 8 A); 2) tilts of TM2 toward the
x-y plane (Fig. 8 B); and 3) a
counterclockwise helical rotation along the helical axis (Fig. 8).
These results are in direct agreement with the types of molecular rearrangements proposed previously based on more qualitative data (Perozo et al., 1999).
An increasing of the helix-crossing angle (the angle between two
diagonal TM2 bundles) ~16° suggests that a scissor-like motion is
associated with channel gating. From the RMSD calculation between closed (crystal structure) and open
(refReDCaTmin) conformations (Fig. 9), the
largest deviation occurs around the residues located near the
cytoplasmic entrance. This includes residue V115-Q119. This clearly
suggests that KcsA gating must be associated with a
significant change in the diameter of the intercellular vestibule of
the channel. By using a full-atom representation of the open TM2
bundle, the relative proximity changes between inter-subunit residues
116 to 119 further support this idea (Fig. 8 C). In the open
state, the inter-subunit residues located around the upper portion
(residues 101-105) pack relatively tighter than those in the closed
state, whereas those near the intracellular side (residues 116-119)
move apart from each other (Fig. 8 C). This generates a wide
cytoplasmic cavity able to accept multiple water molecules and is
likely to interact with larger channel blockers. The diameter at the
narrowest point of the permeating pathway (residues 106-110) slightly
increases (~1.0 Å), which likely favors the ion translocation process.
Testing alternative models
Because the open models before and after the structure
refinement are only slightly different, we have further built
additional models using ReDCaT to examine whether or not the magnitude
and the direction obtained from our model represent the best solution to the open TM2 bundle structure. In this test, we used the restrained dataset with = 1.5 Å and the values of the rotational
parameters (1-4)
were sequentially varied following a combinatorial approach, in such a
way that new configurations were generated with the same magnitude of
the mean values of z,
xy, and hx in
Table 8. Here, only the translational parameter was varied to
generate structures in each examined direction, and a total of five
structures with the lowest penalty value was collected for each
ensemble. A total of 12 ensembles including eight different directions
(I-VIII) from the combination of the parameters plus additional four
directions (IX-XII) were shown in Table
9. Fig.
10 shows the 12 ensembles of which the
generated models (from light blue to blue) were superimposed with the
x-ray structure (red).
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FIGURE 10
C traces of the tested models (shading from
light blue to blue) for 12 different
ensembles. Each ensemble was superimposed onto the x-ray crystal
structure (red).
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With the exception of ensemble XI, the relative penalty of the ensemble
I, the structures most similar to the final refined model, confirms
that the structural rearrangements are most consistent to the SDSL-EPR
restraints. As illustrated by ensemble II (only hx has an opposite sign with respect to the
ensemble I), a clockwise rotation about the segment itself produces a
dramatic increase in restrain violation, again suggesting that
counterclockwise rotation of the helix itself is best supported by the
data. Similarly, ensemble III demonstrates that a helical tilt toward
the axis of symmetry is very unfavorable (also seen in ensemble IV).
The models from a clockwise rotation in ensemble V are of interest because of an increase of ~40% of the relative penalty. However, it
became even worse when the magnitude of clockwise rotation increased
(data not shown). The other three ensembles VI to VIII strongly
disagree to SDSL-EPR restraints. Again, the two most inconsistent
models compose of the positive z (clockwise
rotation) and the negative xy (move toward
the axis) as shown the ensemble VII and VIII. In addition, four
additional ensembles IX to XII were generated for the same purpose. The
failure of the ensembles IX, X, and XII was due to the higher relative
penalties with respect to that of the ensemble I.
From the model test, the relative penalty of ensemble XI is slightly
lower than that of the ensemble I. Both two ensembles are similar
except for no tilting along the z axis. It is difficult to
analyze these differences quantitatively because they are very small. A
fine search for z in the range of +8° to
8° suggested that the minimum of the penalty was obtained between
4° and 6°, implying that more favorable models include the
counterclockwise rotation about the axis. From this test, the direction
and magnitude of the tilt and the twist confirm the results in Table 8
and are taken as the best answers for the conformational changes based on the SDSL-EPR data.
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DISCUSSION |
Despite recent spectacular successes, high-resolution structural
determinations of membrane proteins by means of traditional structural
methods (x-ray crystallography, multidimensional NMR) remains a
challenging problem. A number of alternative, lower resolution
approaches have shown great promise in elucidating the overall
structural properties of these complex systems, particularly in
relation to functionally relevant conformational changes. Reporter group techniques represent a very attractive approach to provide structural information in membrane protein systems because the data are
generally obtained at room temperature, in membrane-embedded conditions, and in physiological solutions. A number of examples document the application of site-directed spin labeling (SDSL-EPR) and
the use of fluorescent probes to attack structural problems in membrane
proteins (Hubbell et al., 2000; Selvin, 2000; Weiss, 2000). One key
disadvantage, however, is that the number of SDSL-EPR restraints (and
other reporter-group techniques) in a given system is limited by the
efficiency of the protein expression, labeling, and purification steps.
Thus, each SDSL-EPR sample produces only one distance information, and
this information in limited to the level of the backbone fold.
A number of efforts for calculating the global fold of protein
structures using a small number of restraints have been reported (Smith-Brown et al., 1993; Aszodi et al., 1995; Skolnick et al., 1997).
These methods can produce adequate tertiary folds of monomeric proteins
from an extended protein chain. However, the atomic resolution of
models generated by the methods is typically low to moderate with
RMSD > 4.0 Å. Conformational rearrangements at this resolution may be hard to detect using these methods. Additionally, it will be
difficult to assess the model quality required for analysis of the
structure-function relationship that is important step toward the
elucidation of function.
In this study we have introduced ReDCaT, an approach for calculating
structural rearrangements in membrane proteins using few numbers of
distance data. The framework of our method was adapted based on the
limited availability of experimental information. Parameterizations
were performed to find out appropriate computational strategies
compromising between the level of the experimental quality, the
structural features of the system studied, and the assumptions used in
the approach. ReDCaT has several advantages when compared with other
computational methods using distance constraints. The use of C (or
C
) distance changes instead of absolute interspin distances by
giving a 6 Å ( = 1.5 Å) distance deviation results in a
much-simplified approach without the complicated treatment for the spin
label sidechain. Additionally, distance data from different mutants can
be used as part of the same SDSL-EPR restraint dataset because the
restraints are, in many cases, independent of the spin probe
conformation. Thus, only a single model representing the backbone
polypeptide is needed by assuming little or no mainchain perturbations
due to the mutagenesis and spin labeling.
In determining a given conformational change, knowledge of a reference
structure is critical because the initial coordinates are used twofold:
1) as a structural transmembrane template and 2) as a source for
penalty calculations. Another useful feature of the approach is that
the use of the rigid body transformation and the symmetric relationship
reduces substantially the searchable space, resulting in a simple and
rapid sampling method.
The approach presented here is generally applicable in the analysis of
conformational changes of membrane protein systems. At present, the
computational procedure is well adapted to members of the
voltage-dependent channel superfamily because of their similarity of
the structural features: the four-fold symmetry relationship, the
homologous repeating subunits, and the rigid body movement. We expect
that this approach can also be applied to other nonsymmetric membrane
proteins such as bacteriorhodopsin and members of the G-protein-coupled
receptor superfamily, because there is clear evidence pointing to
helical rigid-body movements upon ligand activation (Farrens et al.,
1996; Subramaniam and Henderson, 2000).
It should be noted that analysis of probe dynamics and the use of
accessibility parameters from the power saturation EPR spectra have
great potential to be used as additional structural restraints. It has
been shown that these parameters are proportional to the solvent
exposed surface area of proteins (Mchaourab et al., 1996; Mchaourab and
Perozo, 2000; Columbus et al., 2001). Although implementing this approach would require a large number of cysteine-mutants, the
relationship between geometric methods and additional solvent accessibility constraints is worth exploring in the near future. In
this case, the initial reference structure may no longer be needed to
calculate secondary structures and tertiary folds. Furthermore, these
restraints would be also applicable to soluble proteins. Incorporating
these types of restraints would fulfill some deficiencies of our
approach, enabling to calculate more accurate models.
Limitations and caveats of the method
Although it is clear that the ReDCaT approach is able to generate
reliable information regarding the structural basis of conformational changes in membrane proteins, the method has intrinsic limitations that
must be taken into account when applied to different systems. One
important caveat is the requirement for an initial reference structure.
This will certainly limit the generality of the approach, because
obtaining medium-to-high resolution structures of membrane proteins is
still a challenging problem.
A key consideration in the generalized use of reporter group techniques
as a source of structural constraints is not only the possible
perturbations that the probe might generate, but also the intrinsic
difficulty in correlating changes in inter-probe distances with actual
changes in inter-residue distances. One should keep in mind that a
measurable change in interspin distance involves three possible
processes: motion of the backbone, motion of the sidechain, or both.
This remains an unresolved problem in the use of spin labels or
fluorescent probes. However, recent analysis of spin label
conformations by x-ray crystallography strongly suggest that for the
standard methanethiosulfonate spin label (that used in generated the
present data set), the nitroxide side chain adopts a fairly compact
structure and never populate a large range of its conformational space
(Langen et al., 2000). In fact, these results tend to confirm the
empirically determined value of in the 1.0 to 1.5 Å range and
suggest that the spin dipole in the nitroxide sidechain located within
5 Å of the C.
The rigid body approach appears to be appropriate, particularly in
membrane protein systems because transmembrane segments are unlikely to
undergo major changes in secondary structure during conformational
changes. By taking advantage of the predicted four-fold symmetry of ion
channels, it is reasonable to assume that restraints based on multiple
distance changes along a rigid body segment would be able to overcome
the limited accuracy of individual distance data during structure
calculations. As shown in this report, these assumptions, combined with
proper ranges for the distance boundaries, appear to produce consistent results.
An additional factor to consider is the need to further refine the
resulting structures from ReDCaT by evaluating potential energy
functions of the ensemble average, because the method is purely
geometric (Sansom and Kerr, 1993; Sansom et al., 1997). We found that
the steric conflicts between clashing residues of neighboring helices
were eliminated with a simple refinement step. Although the refined
structure still agrees with the experimental restraints, gaining of
nonbonding energy was achieved at the expense of slight increases in
the value of the penalty function (Table 8). A reverse ReDCaT run using
the sterically refined open gate model revealed that the RMSD between
the x-ray crystal structure and the new closed average model increased
slightly to ~0.7 Å. Thus, ReDCaT is robust, and the refinement does
not generate substantial alteration of the structure.
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CONCLUSION |
A novel approach to determine the conformational rearrangement of
the membrane proteins using a small number of SDSL-EPR restraints was
proposed. The method is simple, rapid, and needs only the limited
information from this reporter group techniques to derive reliable
conformational changes of the proteins. Two important aspects are
highlighted. On one hand, the development of a strategy is to use
experimental information from SDSL-EPR experiments to calculate
rigid-body movements of membrane proteins in three dimensions. Second,
use of this approach allowed us to propose a molecular description of
the structural rearrangement of the potassium KcsA channel
upon activation gating. The present study demonstrates that ReDCaT can
be very useful in the analysis of conformational rearrangement of
membrane proteins.
In developing ReDCaT, we considered using the distance ratio
instead of the distance difference in evaluating the use of
experimental distances. The approach is described as follows.
For any two interacting spins, the intensity of the electron-electron
dipolar coupling is related to interspin separation as
TOP
ABSTRACT
INTRODUCTION
) of the EPR signal from the
same spin-spin interactions in the open and the closed states is
estimated as
