1. Art and Diseño

Article No. jmbi.1999.3039 available online at http://www.idealibrary.com on
J. Mol. Biol. (1999) 291, 1191±1206
An NMR Investigation of Solution Aggregation
Reactions Preceding the Misassembly of Aciddenatured Cold Shock Protein A into Fibrils
Andrei T. Alexandrescu* and Klara Rathgeb-Szabo
Department of Structural
Biology, Biozentrum University
of Basel, Basel
CH-4056, Switzerland
At pH 2.0, acid-denatured CspA undergoes a slow self-assembly process,
which results in the formation of insoluble ®brils. 1H-15N HSQC, 3D
HSQC-NOESY, and 15N T2 NMR experiments have been used to characterize the soluble components of this reaction. The kinetics of self-assembly show a lag phase followed by an exponential increase in
polymerization. A single set of 1H-15N HSQC cross-peaks, corresponding
to acid-denatured monomers, is observed during the entire course of the
reaction. Under lag phase conditions, 15N resonances of residues that constitute the b-strands of native CspA are selectively broadened with
increasing protein concentration. The dependence of 15N T2 values on
spin echo period duration demonstrates that line broadening is due to
fast NMR exchange between acid-denatured monomers and soluble
aggregates. Exchange contributions to T2 relaxation correlate with the
squares of the chemical shift differences between native and aciddenatured CspA, and point to a stabilization of native-like structure
upon aggregation. Time-dependent changes in 15N T2 relaxation accompanying the exponential phase of polymerization suggest that the ®rst
three b-strands may be predominantly responsible for association interfaces that promote aggregate growth. CspA serves as a useful model system for exploring the conformational determinants of denatured protein
misassembly.
# 1999 Academic Press
*Corresponding author
Keywords: protein folding; protein aggregation; amyloid ®brils; OB-fold;
residual structure
Introduction
Protein self-association is relevant to normal biological function (Kyte, 1995), pathology (Hofrichter
et al., 1974; Kelly, 1996; Booth et al., 1997; Luh et al.,
1997; Pruisiner, 1997), and biotechnology (Arvinte
et al., 1993). In spite of its importance to protein
chemistry, the biophysical and structural determinants of protein association remain very poorly
understood. Aggregation of denatured proteins
Abbreviations used: CspA, cold shock protein A; OB,
oligonucleotide/oligosaccharide binding; HSQC,
heteronuclear single quantum coherence; NOESY,
nuclear Overhauser enhancement spectroscopy;
T2, transverse relaxation time; R2 transverse relaxation
time (ˆ1/T2; FID, free induction decay; CPMG,
Carr-Purcell-Meiboom-Gill; r2, coef®cient of
determination; t1, indirect evolution time.
E-mail address of the corresponding author:
[email protected]
0022-2836/99/351191±16 $30.00/0
has often been attributed to non-speci®c hydrophobic interactions (Jaenicke & Seckler, 1997).
Recent evidence, however, indicates a role for
speci®city in at least some types of association
reactions. Inclusion bodies, apparently amorphous
aggregates, trap a homogeneous population of
polypeptides, implying speci®city at the level of
self-recognition (Betts et al., 1997). Protein amyloid
®brils formed from homogeneous protein preparations in vitro share distinct morphologies by
electron microscopy and X-ray ®ber diffraction,
regardless of the protein from which they originate
(Sunde & Blake, 1997; Guijarro et al., 1998). This
begs the question of how highly organized polymeric structures such as ®brils can assemble from
denatured proteins (Arvinte et al., 1993; Lai et al.,
1996; Guijarro et al., 1998).
Electron microscopy and X-ray ®ber diffraction
have made possible signi®cant progress towards
the structural characterization of the end products of protein ®brilogenesis (Sunde & Blake,
# 1999 Academic Press
1192
1997; Seilheimer et al., 1997; Goldsbury et al.,
1999). Nevertheless, relatively little is known
about the initial stages of this process in
solution. NMR is an established technique for
the structural characterization of small monomeric proteins (Cavanagh et al., 1996). Solution
NMR may additionally prove an extremely
powerful complement to the array of methods
used to study protein association. A unique
advantage of NMR is the ability to monitor conformational properties in solution at atomic resolution. A well-known constraint on solution
NMR is the dependence of signal line width on
T2, the time constant for spin-spin relaxation
(Cavanagh et al., 1996). T2 increases with
increasing ¯exibility, and decreases with increasing macroscopic rotational correlation time. In
principle, the T2 dependence of the NMR signal
can offer advantages in the study of molecular
association. The increase in NMR sensitivity with
fast internal motion can serve as a ®lter for sites
whose magnetic environments are least affected
by association (Bushuev & Gudkov, 1988). Conversely, for a distribution of aggregation states,
T2 relaxation can serve as a ®lter for species
with
molecular
masses
below
40 kDa
(Gronenborn & Clore, 1996). In the condition of
fast exchange on the NMR time-scale, transfer of
magnetization from associated to dissociated
species can in favorable cases provide structural
information on complexes whose molecular size
precludes direct NMR detection (Feeney &
Birdsall, 1993; Blommers et al., 1999; Carlomango
et al., 1999). Finally, there is increasing evidence
that mispairing of residual structure in
denatured proteins may play a key role in both
protein association (Uversky et al., 1999) and
protein ®bril formation (Kelly, 1996; Booth et al.,
1997; Lai et al., 1996; Wetzel, 1997). NMR spectroscopy is unique in its ability to characterize
the conformational properties of denatured proteins at atomic resolution (Alexandrescu et al.,
1994; Zhang et al., 1997; Eliezer et al., 1998; Fong
et al. 1998; Schwalbe et al., 1997), and has the
potential to provide information on the structural
underpinnings of protein misfolding.
The subject of the present study, cold shock protein A (CspA), is synthesized by Escherichia coli in
response to an abrupt shift in growth temperature
from 37 C to 10 C (Chatterjee et al., 1993). The 70
amino acid protein (7.4 kDa) is believed to function
as an RNA chaperone, facilitating translation at
low temperatures by preventing the formation of
mRNA secondary structure (Jiang et al., 1997).
CspA cooperatively binds single-stranded RNA
with little sequence speci®city. The cooperativity of
binding is dependent on CspA concentration but
not on the molar ratio of CspA to RNA, requiring
a minimal concentration of 30 mM protein (Jiang
et al., 1997). The native structure of CspA consists
of a ®ve-stranded b-barrel (Schindelin et al., 1994;
Feng et al., 1998). In the SCOP classi®cation
(Murzin et al., 1995), the topology of CspA is
Aggregation of Acid-denatured CspA
assigned to the OB-fold superfamily (Murzin,
1993). The OB-fold superfamily includes at least 15
non-homologous proteins (Gerstein & Levitt, 1997)
that typically share oligonucleotide or oligosaccharide binding functions (Murzin, 1993). Our
group has been interested in identifying conserved
themes in the folding and misfolding of the three
non-homologous OB-fold proteins: CspA, staphylococcal nuclease (SN), and the anticodon binding
domain of the LysS lysyl-tRNA synthetase (LysN)
(Alexandrescu et al., 1999).
As monitored by circular dichroism and ¯uorimetry, CspA homologs from E. coli, B. subtilis,
B. caldolyticus, and T. maritima exhibit fast, apparently two-state folding transitions when refolded
from concentrated solutions of urea or guanidinium hydrochloride (Schindler et al., 1995; Perl
et al., 1998; Reid et al., 1998). Indeed, we took
advantage of the fact that structure and association
are suppressed in 6 M urea, to obtain NMR assignments for the acid-denatured form of the protein
(Alexandrescu & Rathgeb-Szabo, 1998). Acid denaturation is believed to result from the electrostatic
repulsion of the net excess of positive charges on a
protein at acidic pH (Goto et al., 1990). As the
hydrophobic effect is operational, acid denaturation has often been observed to lead to more structured denatured proteins than those obtained in
concentrated solutions of urea or guanidinium
hydrochloride. These species often have a high
propensity to aggregate (Fink, 1995).
Results
Morphology of fibrils and polymerization
kinetics
At pH 2.0, concentrated solutions of aciddenatured CspA undergo a slow polymerization
reaction; eventually forming clear, translucent, viscous gels. Electron microscopy of the gels revealed
the presence of ribbon-like polymers (Figure 1),
with morphology similar to that of protein amyloid
®brils (Seilheimer et al., 1997; Guijaro et al., 1998).
The polymers are long, unbranched, with an average diameter of about 12 nm; and show a twisting
repeat of about 130 nm, similar to that reported for
mature ®brils of b-amyloid peptides (Seilheimer
et al., 1997). Suspensions of the ®brils induce a red
lmax,bound ˆ 513 nm,
shift
(lmax,free ˆ 497 nm,
AU,max ˆ 532 nm) in the Congo Red dye solution
binding assay (Klunk et al., 1989), another characteristic shared with amyloid ®brils (Guijaro et al.,
1998).
The time course for CspA self-assembly was
examined using a turbidimetric assay (Andreu &
Timasheff, 1986; Arvinte et al., 1993; Lai et al.,
1996), and by NMR. Kinetic pro®les obtained by
both methods are characterized by an initial lag
phase (td), followed by an exponential increase in
polymerization, which reaches a plateau (Aplateau)
as the free monomer concentration decreases to
solubility (Figure 2). Similar kinetics have been
Aggregation of Acid-denatured CspA
1193
Figure 1. Electron micrographs of negatively stained
CspA ®brils at (a) low and (b) high magni®cation. The
scale bar in both Figures represents 200 nm.
Figure 2. Kinetics of ®bril formation. (a) Changes in
the A340 of a 0.72 mM CspA sample as a function of
incubation time at pH 2.0. The upper inset shows the
dependence of the logarithm of td on the logarithm of
protein concentration (y ˆ 2.0 ÿ 2.1x; r2 ˆ 0.94). The
lower inset shows the protein concentration dependence
of the absorbance plateau (y ˆ ÿ 0.3 ‡ 2.3x; r2 ˆ 0.997).
(b) 1H-15N HSQC cross-peak intensities as a function of
time for a 0.75 mM sample of acid-denatured CspA. The
inset is an expansion of the early part of the progress
curve. Intensities are normalized to a value of unity for
the earliest time point, to compensate for differences in
initial line widths as a function of residue position in
the protein sequence. (*), Gly17; (), Ala36; (‡), Gly61.
observed for the self-assembly of a number of proteins and are usually interpreted in terms of a
nucleation growth (Hofrichter et al., 1974; Andreu
& Timasheff, 1986), or a double nucleation mechanism (Ferrone et al., 1985; Arvinte et al., 1993;
Kanaori & Nosaka, 1996). Only the latter accounts
for the lag phase prior to the onset of polymerization (Ferrone et al., 1985). For CspA, the lag time
td decreases with the power, 2.1(0.4), of the protein concentration. The critical concentration Cr,
de®ned as the minimal protein concentration
required for polymerization, can be calculated
from a linear extrapolation of turbidimetric Aplateau
values as a function of protein concentration to
Aplateau ˆ 0 (Andreu & Timasheff, 1986). The Cr
value thus obtained for acid-denatured CspA is
130(20) mM.
Figure 2(b) shows the time course for the selfassembly of a 0.75 mM solution of acid-denatured
CspA as followed by decreases in the intensities of
the protein's 1H-15N HSQC correlations. Alternatively, volume integrals gave very similar results.
The NMR progress curves show an initial lag
phase of about the same duration as that observed
in the turbidimetric assay, followed by an approximately tenfold decrease in 1H-15N HSQC peak
intensities over a period of six days. The tenfold
drop in signal intensities from an initial 0.75 mM
sample indicates that 75 mM CspA remains in
solution at the plateau of polymer growth. This
concentration is roughly consistent with the critical
concentration of 130 mM obtained from turbidimetric measurements. To a ®rst approximation,
residues from different positions in the protein
show the same kinetic pro®le (Figure 2(b)). On closer inspection resonances from the N-terminal half
of the molecule (roughly residues 8 to 39) appear
to be more severely broadened after six days than
1194
those from the C-terminal half of the protein
(Figure 3). Over the course of six days there are
small changes in chemical shifts; the largest of
which are of the order of 0.03 ppm and 0.4 ppm
for 1H and 15N resonances, respectively. With the
possible exception of 1H-15N HSQC spectra
acquired close to the limit where signal decays into
baseline noise, no new resonances are detected
during the entire course of polymerization. In principle, a single set of NMR resonances could arise
from magnetically equivalent monomers related by
a symmetry axis in a closed oligomer (Dames et al.,
1998). Such an oligomer, however, should exhibit a
larger chemical shift dispersion. Moreover, hydrogen protection factors measured for 2.8 mM and
0.4 mM samples of acid-denatured CspA are uniformly close to unity (not shown). The observation
of a single set of resonances during the course of
polymerization, with chemical shifts similar to
those of CspA in 6 M urea, indicates that the NMR
experiment is exclusively monitoring signals of
unfolded monomers from a solution component of
the sample. Changes in chemical shifts and line
widths during the course of polymerization, however, suggest that NMR signals are subject to fast
averaging between monomers and soluble aggregates.
Protein concentration dependence of T2
To further characterize the self-assembly of
acid-denatured CspA, we tried to distinguish
empirically between the properties of the protein
during the lag phase and those during the exponential phase of polymerization (Kanaori &
Nosaka, 1996). A series of 1H-15N HSQC spectra
collected as a function of protein concentration is
Aggregation of Acid-denatured CspA
shown in Figure 4. The spectra were recorded in
times shorter or comparable to the corresponding
td values, and thus re¯ect association of the protein during the lag phase of polymerization. At
the lowest protein concentrations (0.14 mM), line
widths at half height (n*1/2) are relatively uniform as a function of residue position in the
protein sequence (Figure 5(a)). In the range of
protein concentrations between 0.72 mM and
3.6 mM, line widths increased roughly with the
square of the protein concentration, suggesting a
dimerization reaction with a dissociation constant
in the millimolar range. The concentration
dependence of line widths is non-uniform as a
function of residue position in the sequence
(Figure 4). For the 3.6 mM sample where line
broadening effects are most pronounced, there is
a clear correlation between line widths and the
secondary structure of the native protein
(Figure 5(b)). Residues located in strands b1
through b4 of the native CspA structure show
the broadest resonances; residues from the intervening loops, the sharpest. Notable exceptions
are residue Lys16 in loop L12, and residues
Gly48 preceding strand b4. The two residues
show large line broadening effects (also see
Figures 5(c) and 6(e)), and have unusually large
15
N chemical shift differences of 4.5 ppm
between the acid-denatured and native protein.
For comparison the remainder of residues outside the native b-sheet, have 15N chemical shift
differences of 1.8(1.4) ppm (mean s.d.). The
second notable exception is strand b5, which
shows small line broadening contributions. The
15
N chemical shift differences between native
and acid-denatured CspA are 1.8(0.8) for
strand b5, and 4.4(2.8) for strands b1-b4.
Figure 3. 1H-15N HSQC spectra of 0.75 mM CspA after 100 minutes (left panel) and six days (right panel) at pH 2.0.
The spectra correspond to the ®rst and penultimate time points in Figure 2(b). Acquisition and processing parameters
for the two spectra are identical; the spectrum obtained after six days is plotted at a tenfold lower contour level to
account for the tenfold decrease in peak intensities. NMR resonance assignments (Alexandrescu & Rathgeb-Szabo,
1998) are indicated in the left panel.
Aggregation of Acid-denatured CspA
1195
Figure 4. 1H-15N HSQC spectra of lag-phase acid-denatured CspA as a function of protein concentration. The
glycine region of the spectra is omitted for clarity. Contour levels for the plots were normalized for protein concentration and the number of transients averaged (see Methods). The differential line broadening as a function of native
secondary structure is illustrated with 1H-15N HSQC correlations representative of each of the loops and b-strands in
native CspA. The complete set of assignments is given in Figure 3. The ®ve strands of b-sheet in the X-ray structure
of the native protein (Schindelin et al., 1994) consist of residues: 5-13, b1; 18-23, b2; 30-33, b3; 50-56,b4; 63-69, b5.
To obtain information on the factors that contribute to line broadening, 15N T2 relaxation data were
acquired on a 0.74 mM sample of acid-denatured
CspA using a 2D variant of the CPMG method
(Farrow et al., 1994). Two separate T2 data sets
were collected, with values of 500 and 125 ms
for the spin echo period (tse) between successive
180 15N pulses in the CPMG sequence
(Bloom et al., 1965). Quantitative comparisons
between line width and T2 data are not possible.
The n*1/2 values contain contributions from both
natural line width and ®eld inhomogeneity,
whereas the latter effects are suppressed in T2 data
measured with the CPMG pulse sequence (Farrar
& Becker, 1971). Nevertheless, the R2 (R2 ˆ 1/T2)
values obtained with tse ˆ 500 ms show the same
trend as a function of secondary structure as the
n*1/2 data. Strands b1-b4 manifest higher R2
values than the loops (Figure 5(c)); b5 again represents an exception. With the shorter spin echo
period (tse ˆ 125 ms), R2 values are markedly
reduced and tend towards uniform values as a
function of residue position in the sequence
(Figure 5(d)). The attenuation of R2 values
obtained with the shorter spin echo period demonstrates a contribution to transverse relaxation from
motion on the 0.1 ms time-scale of tse (Bloom
et al., 1965; Orekhov et al., 1994; Alexandrescu et al.,
1996). This time-scale is at least three orders of
magnitude slower than that for dipolar contributions to transverse relaxation (Cavanagh et al.,
1996), so it can be safely concluded that the trans-
verse relaxation rates contain contributions from
exchange between monomers and aggregates.
In the limit of moderately fast exchange
(kex > 2pd) the exchange contribution to transverse relaxation (Figure 5(e)) is expected to be proportional to the square of the difference in
resonance frequencies between the interconverting
species (SandstroÈm, 1982; Orekhov et al., 1994). The
squares of the chemical shift differences, (d)2,
between native and acid-denatured CspA are summarized in Figure 5(f). The 40 data points considered in Figure 5(e) and (f) are linearly correlated
with an r2-factor of 0.64. The probability that this
correlation occurs by chance is statistically
excluded (P < 10ÿ4). An r2 of 0.64 indicates that
64 % of the variance in R2 is explained by the
variation in (d)2. It is worth considering some of
the factors that might affect this correlation. First,
the uncertainties in R2 values are 15 % of the
actual values, leading to scatter in the data.
Second, the chemical shifts of aggregated CspA are
modeled as those of the native monomeric protein.
Additional chemical shift differences should occur
for residues located in association interfaces; however, we have no way to model these. Finally,
the native state assignments of Feng et al. (1998)
were obtained at pH 6.0. Even if the structure
stabilized on aggregation were very similar to that
of the native protein, differences in chemical shifts
should result from changes in the ionization states
of acidic groups at pH 2.0 (for example, the very
large (d)2 for the C terminus (Figure5(f)). Indeed,
1196
Aggregation of Acid-denatured CspA
Figure 5. Dependence of line widths on association state. (a) 15N line widths at half height (n*1/2) obtained from
the 1H-15N HSQC spectrum (Figure 4) recorded on the 0.14 mM sample of acid-denatured CspA. (b) Differences in
15
N n*1/2 values between 0.14 mM and 3.6 mM samples. On the basis of the negative values, we estimate the uncertainties in n*1/2 to be of the order of 0.7 Hz. (c) 15N R2 values obtained for a 0.74 mM sample of acid-denatured
CspA with a tse of 500 ms. (d) 15N R2 values as above, except with tse ˆ 125 ms. (e) Differences between 15N R2 values
collected with the two spin echo periods (R2, tse ˆ 500 ÿ R2, tse ˆ 125). (f) The square of 15N chemical shift differences between acid-denatured (pH 2.0, 20 C) and native CspA (pH 6.0, 30 C). Chemical shifts were taken from published assignments (Alexandrescu & Rathgeb-Szabo, 1998; Feng et al., 1998), and are only shown for residues for
which R2 values could be determined. Horizontal bars at the top of the plots indicate the sequence positions of the
®ve b-strands in the X-ray structure of the native protein.
if residues that titrate between pH 6.0 and 2.0 are
excluded (Asp, Glu, His, C-term), the r2-factor for
the correlation between (d)2 and R2 increases to
0.72.
T2 changes accompanying polymerization
To examine how the relaxation properties of
acid-denatured CspA change during the course of
polymerization, a series of eight 15N T2 relaxation
data sets were collected on a 2.0 mM protein
sample as a function of incubation time at pH 2.0.
Each of the T2 data sets took ®ve hours to record;
consequently, the lag time for polymerization (20
minutes) is within the dead time of the experiment.
2D 1H-15N HSQC spectra were collected before
and after each T2 relaxation data set. The decreases
in 1H-15N HSQC cross-peak intensities accompanying polymerization are illustrated with the three
residues Met5, Gly48, and Val67 (Figure 6(a)).
Within experimental uncertainty the rate constant
for the decrease in HSQC peak intensities is the
same for all three residues, ÿ2.2 10ÿ3 minÿ1. The
more subtle and heterogeneous changes in T2
values as a function of time are illustrated with the
same three residues (Figure 6(b)-(d)). Of 42 residues that could be analyzed, the T2 values of 22
(class I) decayed exponentially with time, as illustrated by Met5 (Figure 6(b)). A second set of nine
residues (class II) showed exponential increases in
T2 values, as illustrated by Gly48 (Figure 6(c)). In
class III, as illustrated by Val67 (Figure 6(d)), the
time course of 11 residues showed an initial exponential decrease, followed by an exponential
increase in T2 values. All residues in class I, are
from the N-terminal half of the molecule (residues
3 to 41). Except for Phe18 and Asp25, all residues
in class II and III are from the C-terminal half of
the molecule (residues 42 to 70).
R2 values (R2 ˆ 1/T2) from the ®rst experiment,
completed 400 minutes after adjusting the sample
pH to 2.0, are shown in Figure 6(e). The pattern of
R2 values is much the same as that for the lag
phase data obtained for the 0.74 mM sample
Aggregation of Acid-denatured CspA
(Figure 5(c)), except that the maxima and minima
as a function of residue position in the sequence
are more pronounced. The uncertainties in the R2
values decrease from 9 % for the 0.74 mM sample
(Figure 5(c)) to 2 % for the 2.0 mM sample
(Figure 6(e)). The higher precision re¯ects the
improved signal-to-noise at the higher protein concentration. Figure 6(f) shows the difference in R2
values between the third (1000 minute) and ®rst
(400 minute) time points. The 1000 minute data
shows a selective increase in the R2 values of residues from the N-terminal half of the molecule.
Note that the protein sequence pattern in
Figure 6(f) is very different from that in Figure 6(e).
The ®rst three strands of b-sheet as well as the
intervening loops show increases in R2 values, so
that the b-strands are no longer clearly demarcated. Increases in R2 values extend beyond strand
b3 to about residue 41, in the middle of loop L34.
The R2 values for the C-terminal half of the molecule, including strand b4, are apparently invariant. These observations indicate that the changes
in R2 values accompanying polymerization are not
simply an ampli®cation of the exchange broadening effects observed during the lag phase.
Figure 6(g) and (h) summarizes the rate constants for T2 changes as a function of residue position in the protein sequence. Negative and
positive rate constants are associated with
decreases and increases in T2 values, respectively.
Residues from the N-terminal half of the molecule
show a continuous decrease in T2 values, with the
exception of Phe18 and Asp25. Residues from the
C-terminal half show either a continuous increase,
or an increase following an initial decrease in T2
values.
NOESY spectroscopy
3D 1H-15N NOESY-HSQC experiments present a
formidable challenge for acid-denatured CspA. The
chemical shift dispersion is typical of denatured
proteins, and resonance overlap is severe. Further
complexity is engendered by the dependence of
the NOESY spectra on protein concentration, and
on the time of incubation at pH 2.0. In total, four
3D 1H-15N NOESY-HSQC spectra were used to
characterize acid-denatured CspA. An additional
200 ms mixing time control spectrum was recorded
on a 2 mM CspA sample in the presence of 6 M
urea, conditions under which aggregation is suppressed (Alexandrescu & Rathgeb-Szabo, 1998).
The optimal results for the acid-denatured protein
were obtained for a 200 ms mixing time experiment recorded on a 1 mM sample of CspA. The
total acquisition time was 40 hours. An experiment
recorded on a 0.5 mM sample under the same conditions resulted in lower sensitivity, as demonstrated by the absence of some of the intraresidue
NOEs observed for the 1 mM sample. In a spectrum recorded on a 2.0 mM sample, all but the
strongest daN(i, i ‡ 1) NOEs were bleached into
1197
the baseline noise due to the faster rate of polymerization at the higher protein concentration.
Figure 7(a) shows strips from the 3D 1H-15N
NOESY-HSQC spectrum recorded on the 1 mM
CspA sample. The spectrum manifests strong
intraresidue daN(i, i), and interresidue daN(i, i ‡ 1)
NOEs typical of denatured proteins (Alexandrescu
et al., 1994; Schwalbe et al., 1997; Zhang et al.,
1997). The ratio of the daN(i, i ‡ 1)/daN(i, i) NOEs
varies systematically as a function of the protein
sequence (Figure 7(b)). A similar, albeit weaker,
trend is also observed for the protein in the presence of 6 M urea (Figure 7(c)).
The conclusion that monomeric and aggregated
forms of CspA are in fast exchange on the chemical
shift time-scale, led us to explore the possibility
that NOEs might be transferred from aggregates to
monomers. To this end we examined the NOESY
spectrum for correlations that could correspond to
contacts observed in the native structure. Four
cross-peaks (Figure 8(a)), all involving Gly19, connect protons of residues that are far apart in the
Ê in
protein sequence, but separated by less than 5 A
the X-ray structure of native CspA. The HN proton
of Val32 (Figure 8(a)) shows an additional correlation to 4.37 ppm. There are three phenylalanine
residues (F31, F20, F18) with Ha protons within
Ê of the amide proton of Val32. None, however,
5A
resonates at 4.37 ppm. The most likely assignment
for this correlation is to daN(F12, V32), which corÊ in the structure of
responds to a distance of 6.4 A
CspA. An additional cross-peak consistent with the
native structure, daa(V9, I21), is reproducibly
observed in a series of 2D 1H-NOESY spectra
recorded in 2H2O as a function of incubation time
at pH 2 (not shown). All of the cross-peaks correspond to contacts within strands b1 through b3.
Considering the remainder of the subset of daN,
dNN, and daa NOEs predicted by the native
b-sheet hydrogen bonding network of CspA, about
12 potential NOEs were not observed, and the
identi®cation of a further 22 was precluded by resonance overlap.
A second set of six weak cross-peaks in the 3D
1
H-15N NOESY-HSQC spectrum are not consistent
with the native structure, and suggest a non-native
intermolecular parallel pairing of strands b1 and
b3 (Figure 8(b)). In the native structure (Figure 9(a))
the pairing of strands b1 and b3 is precluded by
an anti-parallel interaction between strand b4 and
the N-terminal half of strand b1, and by a short
parallel interaction between strands b3 and b5.
The cross-peaks attributed to long-range contacts
in Figure 8 are extremely weak. In an attempt to
improve sensitivity, we recorded a 300 ms 3D
1
H-15N NOESY-HSQC data set on a 0.8 mM
sample of acid-denatured CspA. The number of
scans per transient was doubled, for a total acquisition time of four days. The quality of the spectrum was comparable, although poorer than that
of the spectrum shown in Figures 7 and 8. Many of
the trivial intraresidue and sequential NOEs were
much more intense, due to the longer (300 ms)
1198
Aggregation of Acid-denatured CspA
Figure 6 (legend shown opposite)
1199
Aggregation of Acid-denatured CspA
mixing time. Line widths were larger, probably as
a consequence of the greater extent of polymerization during the four-day acquisition period,
resulting in greater resonance overlap. Of the 11
cross-peaks attributed to long-range contacts in
Figure 8, four were not observed in the 300 ms
mixing time spectrum. The two cross-peaks
daN(F12, V32) and daN(I8, A36) could not be
resolved due to the stronger overlap in the 300 ms
NOESY spectrum. The native daN(G19, N13), and
the four non-native daN(T6, H33), daN(K4, V32),
daN(F31, K4), dgN(V32, M5) correlations were
detected in both the 200 ms and 300 ms mixing
time NOESY spectra. None of the correlations
attributed to long-range NOEs was observed in a
3D 1H-15N NOESY-HSQC recorded on a 2 mM
CspA sample in 6 M urea, although the sensitivity
of this experiment was considerably, better, due to
the higher protein concentration and the longer T2
values in the absence of aggregation.
Discussion
Conformational preferences in denatured CspA
NOESY spectra of acid-denatured CspA show
increased daN(i, i ‡ 1)/daN(i, i) NOE ratios for
residues that are located in the b-strands of the
native protein (Figure 7(b)). The magnitude of the
NOE depends on both the internuclear distance
and the effective correlation time (Cavanagh et al.,
1996; Freund et al., 1996). Whereas the NOE is
directly proportional to the effective correlation
time, its dependence on the inverse of the sixth
power of internuclear distance implies a much
higher sensitivity to spatial proximity. Differences
in backbone ¯exibility (Figure 5(d)) are thus an
unlikely source for the variability in NOE ratios.
The increased daN(i, i ‡ 1)/daN(i, i) NOE ratios
are most consistent with conformational preferences for the ``b`` region of f, c space (Saulitis &
Liepins, 1990). Within the limits of the native
b-strand, some residues show small NOE ratios.
These exceptions correspond to glycine, or residues
following glycine: Gly7-Lys8 in b1, Gly17-Phe18Gly19-Phe20 in b2, Gly65-Asn66 in b5. For strand
b3, the stretch of residues with large NOE ratios
continues beyond His33, the end-point in the native
structure. Interestingly, the secondary structure
prediction programs GOR IV (Garnier et al., 1996),
and PhDsec (Rost & Sander, 1993) have strand b3
extending to Ala36 and Ile37, respectively.
A similar pattern of NOE ratios is observed for
CspA in 6 M urea (Figure 7(c)). This suggests that
the differences in NOE ratios are not associated
with aggregation, and that the conformational preferences for the b region of f, c space persist
under strongly denaturing conditions. That
increased daN(i, i ‡ 1)/daN(i, i) NOE ratios are
observed over stretches of residues, suggests that
on a time average these segments of the molecule
may have an increased propensity to exist in
extended b-strand conformations. This could contribute to the extremely fast refolding of CspA
under native conditions (Reid et al., 1998), and
could provide a template for the intermolecular
mispairing of acid-denatured CspA.
Association during the lag phase
The kinetics of CspA self-assembly (Figure 2)
conform to the double nucleation mechanism
(Ferrone et al., 1985). The double nucleation mechanism postulates two types of aggregation reactions. Polymerization is initiated by aggregation in
bulk solution in a process called homogeneous
nucleation. In the presence of pre-formed polymers, additional nuclei may form on polymer surfaces by the second mechanism, heterogeneous
nucleation. Aggregates formed by both mechanisms are in constant equilibrium with monomers
(Ferrone et al., 1985). Addition of monomers is
initially entropically opposed, until the formation
of a critical nucleus, beyond which further association becomes more favorable than dissociation.
With an increasing concentration of polymers, the
number of sites for heterogeneous association
increases, so that the rate of nucleation increases
with the extent of polymerization. The initially
small number of sites for heterogeneous nucleation
is responsible for the apparent delay time td, before
the exponential increase in polymerization
becomes detectable. As incorporation of protein
into insoluble polymers is essentially irreversible
(Ferrone et al., 1985), NMR signal averaging can
only be in¯uenced by soluble aggregates that have
not yet reached the size required for the formation
of a critical homogeneous or heterogeneous
nucleus (Kanaori & Nosaka, 1995).
During the lag phase for polymerization, resonances are broadened with increasing protein
concentration (Figures 4, 5(b)). The sensitivity of
15
N R2 values to the duration of the CPMG spin
echo period (Figure 5(c)-(e)), indicates that line
Figure 6. Time-dependent changes in NMR spectra accompanying the growth phase of self-assembly.
(a) Time course followed by decreases in 1H-15N HSQC peak intensities for residues Met5, Gly48, and Val67. Symbols: squares, Met5; ®lled circles, Gly48; diamonds, Val67. The three residues show the same rate constant for the
decrease in peak intensity: ÿ2.2(0.2) 10ÿ3 minÿ1. Time dependence of T2 for the same three residues: (b) Met5,
exponential decrease; (c) Gly48, exponential increase; (d) Val67, exponential decrease followed by an exponential
increase. (e) R2 values for a 2.0 mM sample of CspA after 400 minutes at pH 2.0. (f) Differences between R2 values
recorded 1000 and 400 minutes after initiation of unfolding. (g) Rate constants associated with decreases in T2 values
as a function of time. (h) Rate constants for increases in T2 values as a function of time.
1200
Aggregation of Acid-denatured CspA
Figure 7. NOE ratios (daN(i, i ‡ 1)/daN(i, i)) in acid and urea-denatured CspA. (a) Strips from the 1HN-1H planes
of the 200 ms 3D 1H-15N NOESY-HSQC spectrum recorded on a 1 mM sample of acid-denatured CspA, illustrating
daN(i, i) and daN(i, i ‡ 1) NOEs for residues Glu56 through Ile37. Intraresidue connectivities are labeled with Greek
letters, stars indicate overlapping cross-peaks. The sequence dependence of daN(i, i ‡ 1)/daN(i, i) NOE ratios is
summarized in (b) for acid-denatured CspA and (c) for urea-denatured CspA (2 mM protein, pH 2.7, 6 M urea). The
horizontal lines in (b) and (c) indicate the means.
broadening is not a consequence of an increase in
rotational correlation time but a manifestation of
fast chemical exchange between monomers and
aggregates. That concentration-dependent line
broadening is most pronounced for residues in the
b-strands of the native protein, and that exchange
contributions to R2 correlate with chemical shift
differences between the native and acid-denatured
protein, point to a stabilization of native-like structure on association of acid-denatured CspA. On the
basis of the present data, it is not possible to determine the types of association interfaces responsible
for lag phase aggregation. In particular, structure
formation is coupled to association, and it is not
possible to separate the contributions of the two
processes to line broadening.
It has been suggested that partially folded intermediates, may play a general role in both aggregation (Jaenike & Seckler, 1997; Uversky et al., 1999)
and ®bril formation (Kelly, 1996; Wetzel, 1997;
Booth et al. 1997; Guijarro et al., 1998). The precursors of some amyloid ®brils, including calcitonin
(Arvinte et al., 1993) and amyloid b-peptides
(Zagorski & Barrow, 1992), however, appear to
have no detectable structure in their monomeric
forms. With the exception of the variability in
daN(i, i ‡ 1)/daN(i, i) NOE ratios, acid-denatured
CspA monomers also appear to be largely unstructured. It is important to note, however, that the
stability of structure in protein aggregates is concentration dependent (Kammerer et al., 1995). By
Le Chatelier's principle (Dickerson et al., 1979), a
small subset of the denatured state conformational
ensemble could be selectively ampli®ed upon
aggregation. Similarly, the promotion of rare conformations within the folded state ensemble on
aggregation might account for the macroscopic
conformational changes observed in some ®bril
assembly processes (Kelly, 1996; Pruisiner, 1997).
Association during the growth phase
The ®ve-stranded b-barrel of native CspA is
formed from two orthogonal b-sheets: a b-meander
consisting of strands b1 through b3, and a b-hairpin consisting of strands b4 and b5 (Figure 9(a)).
Residue Lys10 forms a b-bulge in strand b1, a conserved feature of OB-fold proteins (Murzin, 1993).
The resulting bend allows the N terminus of strand
Aggregation of Acid-denatured CspA
1201
Figure 8. 3D 1H-15N NOESY-HSQC strips illustrating sequential (gray lines) and long-range connectivities (labeled
arrows). Stars indicate overlapping cross-peaks. The strips were taken from the same 3D matrix as in Figure 7. Strips
in (a) illustrate long-range connectivities consistent with the native structure of CspA. The strips in (b) illustrate longrange connectivities consistent with a non-native pairing of strands b1 and b3.
b1 to pair with strand b4 from the second b-sheet,
forming a closed b-barrel.
The growth phase of polymerization is
accompanied by changes in the 15N R2 values of
the acid-denatured protein. One source for
increases in R2 values is the increase in sample viscosity accompanying polymerization. By itself,
however, an increase in sample viscosity cannot
explain the differences between the R2 values of
the N and C-terminal halves of the molecule
(Figure 6(f)). Furthermore, an increase in sample
viscosity is inconsistent with the time-dependent
decreases in R2 values (increases in T2 values) for
residues 42 through 70 from the C-terminal half of
the molecule (Figure 6(h)). The differences in R2
values between the lag and the exponential growth
phase of polymerization presuppose a change in
the population of aggregates interconverting with
unfolded CspA monomers. In particular, as the
number of sites for heterogeneous aggregation
increases during the exponential phase of polymerization, fast exchange between monomers and
aggregates could increasingly re¯ect heterogeneous
aggregation.
The mean difference in 15N chemical shifts
between native and acid-denatured CspA is 3
ppm. If we assume a similar difference between
the chemical shifts of unfolded CspA monomers
and folded CspA aggregates, kex must be in excess
of about 1000 sÿ1 in order to satisfy the condition
of fast exchange on the chemical shift time-scale
(kex > 2pd). An interconversion rate suf®ciently
high for fast exchange on the chemical shift timescale is almost certain to satisfy the condition of
fast exchange on the R2 time-scale (kex > R2). The
resulting averaged R2 values could re¯ect the
dynamic properties of aggregates, including contributions from anisotropic rotational diffusion.
The larger 15N R2 values for the N-terminal compared to the C-terminal half of CspA could be consistent with exchange between monomers and a
population of elongated rod-like aggregates in
which the native CspA monomer fold is preserved
(Figure 9(a)); and in which strands b1-b3 stack
along the long axis of the aggregates. The molecular tumbling of a rod-shaped aggregate can be
approximated by the axially symmetric rotational
diffusion tensor Dzz 6ˆ Dxx ˆ Dyy. In an axially
symmetric molecule, 1H-15N bond vectors that
align with angles y of 0 or 180 with respect
to the unique axis of the diffusion tensor will correspond to maxima in R2 values as a function of position in the protein sequence (Tjandra et al., 1997).
If the native pairing of strands b1 through b3 is
1202
Aggregation of Acid-denatured CspA
Figure 9. (a) Molscript (Kraulis, 1991) diagram of the native CspA fold (Schindelin et al., 1994). (b) Model for an
intermolecular, parallel mispairing of strands b1 and b3, based on non-native NOE connectivities between strands b1
and b3 (Figure 8(b)), and changes in T2 values during the polymerization phase of CspA self-assembly (Figure 6(h)).
Disruption of the native antiparallel b1-b4 interaction, uncouples the b1-b3 meander (light gray) from the b4-b5 hairpin (dark gray). This frees the N-terminal half of strand b1 for a parallel interaction with strand b3 from another
molecule.
preserved, and additional intermolecular mispairing aligns the b1-b3 meanders perpendicular to the
long axis of the aggregates, the 1H-15N bond
vectors in b1-b3 will alternate between parallel
(y 0 ) and antiparallel (y 180 ) orientations
with respect to the long axis of the aggregate.
These orientations will correspond to maxima in
15
N R2 values as a function of y. Conversely,
strands b4-b5, which are orthogonal to b1-b3 in the
native structure (Figure 9(a)), will have 1H-15N
bond vectors aligned at angles of 90 and 270 with respect to the unique axis of the diffusion tensor, corresponding to minima in R2 values. Some
of the HN bond vectors in the loops should align
differently than HN bond vectors in the b-strands,
or should have no alignment preferences if the
loops are ¯exible. The time-dependent changes in
R2 values, however, show little distinction
between the loops and b-stands. Furthermore, the
observation
that
all
residues
from
the
C-terminal half of the molecule show a phase
during which R2 values decrease as a function of
time (Figure 6(h)) is dif®cult to explain in terms of
changes in rotational anisotropy.
A mechanism that could account for the
decreases in R2 values for the C-terminal portion
of the molecule is an increase in the ¯exibility of
this region. NOESY spectra of acid-denatured
CspA (Figure 8(b)) suggest the presence of a population of molecules with a non-native parallel pairing of strands b1 and b3. An intermolecular
association interface based on this type of interaction is illustrated in Figure 9(b). The non-native
parallel pairing of strands b1 and b3 precludes the
native pairing between strands b1 and b4, and
between b3 and b5. The uncoupling of strands
b4-b5 from the rest of the protein, and the resultant
increase in ¯exibility, could account for the time
dependent decreases in R2 values observed for the
C-terminal half of the molecule. Note that the pro-
posed non-native pairing, implies a C-terminal
extension of strand b3 from His33 to Ala36
(Figure 8(b)). Residues showing continuous
increases in R2 values as a function of time extend
beyond b3 to residue 41 (Figure 6(f), (h)); an observation that might re¯ect a restriction in the ¯exibility of this region on intermolecular pairing of
strands b1 and b3.
Although there is apparent agreement between
the time dependent changes in R2 values and the
NOESY data, it should be emphasized that the
NOESY data are highly tentative. The putative
intermolecular interaction between b1 and b3 is
supported by only six NOE cross-peaks, all of
which are extremely weak. Furthermore, the 40
hour acquisition time for the 3D 1H-15N NOESYHSQC experiments spans both the lag and polymerization phases of self-assembly. Consequently, it
is not possible to establish if the appearance of the
NOE correlations attributed to the non-native pairing of strands b1 and b3, coincide with the timedependent changes in R2 values. The safest
conclusion that can be drawn on the basis of the
time-dependent changes in R2 values is that the
types of aggregates that predominate during the
growth phase of polymerization differ from those
initially formed during the lag phase. That only
residues from the N-terminal half of the CspA
show a continuous increase in R2 during polymerization suggests that the association interfaces
that predominate in aggregate growth reside
within this portion of the molecule.
CspA is believed to bind nucleic acids predominantly through hydrophobic interactions. On the
basis of chemical shift perturbation data, the nucleic
acid-binding epitope of CspA is localized within
strands b1, b2, b3 and loops L12, L34, and L45
(Feng et al., 1998). The b1-b3 meander has an
unusually high proportion of surface-exposed
hydrophobic residues (Schindelin et al., 1994),
1203
Aggregation of Acid-denatured CspA
which appear to be involved in the hydrophobic
binding mode of the protein (Feng et al., 1998). The
misassembly of acid-denatured CspA into ®brils
could be a consequence of the high sequence hydrophobicity required for the protein's normal nucleic
acid binding function, coupled with a relatively
high stability of residual structure at acidic pH.
Methods
Sample preparation
The E.coli CspA gene was expressed using the pET11CspA vector (Chatterjee et al., 1993), transformed into
E. coli strain BL21(DE3). 15N-labeled protein samples
were prepared by growing the bacteria in Mops media
(Serpersu et al., 1986), containing 15NH4Cl (1 g/l).
Protein puri®cation was performed according to a published procedure (Chatterjee et al., 1993) which included
Q-Sepharose anion exchange, and SP-Sepharose cation
exchange chromatography. Fractions containing pure
CspA (as judged by SDS-PAGE) were pooled, dialyzed
three times against Milli-Q water, lyophilized, and stored
at ÿ20 C prior to use. Lyophilized CspA samples were
dissolved in H2O, or 90 % H2O/10 % 2H2O for NMR
work, and contained no added buffers or salts. Protein
concentrations were determined at neutral pH using an
extinction coef®cient, e280, of 8600 Mÿ1 cmÿ1 (Feng et al.,
1998). Fibril formation was initiated by adjusting
samples from pH 6 to 7, to a ®nal pH value of 2.0(0.1),
using 1 M HCl stock solutions. The time of initial
exposure to pH 2.0 was de®ned as the start of the
polymerization reaction (t ˆ 0). Each experiment on aciddenatured CspA was performed on a fresh protein
sample.
Electron microscopy
A suspension of ®brils formed from a 1 mM solution
of acid-denatured CspA was applied to a carbon-coated
400-mesh/inch copper grid, washed, negatively stained
with 0.75 % (w/v) uranyl formate (pH 4.25), and airdried (Bremer et al., 1998). Samples were examined in
a Hitachi H-8000 transmission electron microscope
operated at 100 kV. Electron micrographs were recorded
on Kodak SO-163 electron image ®lm at a nominal
magni®cation of 20,000 or 50,000.
Kinetics of polymerization
Turbidimetric assays were performed at 23 C, monitoring the increase in A340 nm as a function of time
(Andreu & Timasheff, 1986; Arvinte et al., 1993). All
NMR data were recorded at a temperature of 20 C on
Varian Unity‡ or Bruker Avance spectrometers operating at 600 MHz. To characterize the time course of
polymerization by NMR, a total of 24 1H-15N HSQC
spectra (1024 100 complex points; spectral widths
5500 1400 Hz) were collected on a 0.72 mM sample of
CspA, following adjustment of the pH to 2.0. All HSQC
spectra were acquired with eight transients per FID. The
sample was kept in the NMR probe thermostated at
20 C for the ®rst 3.5 days of measurements. For the last
three time points (time >5000 minutes) the sample was
removed from the NMR probe and kept at room
temperature prior to data acquisition. 1H-15N HSQC
spectra were processed with 70 shifted sine bell ®ltering, and zero ®lling in both dimensions.
Concentration dependence of NMR signals
1
H-15N HSQC spectra were recorded on separate 0.14,
0.72, 1.8, and 3.6 mM samples of CspA, immediately
after adjusting the pH of the samples from 6.4 to 2.0.
Data acquisition times for the three lowest protein concentrations were much shorter than the corresponding
lag times for polymerization. The 1H-15N HSQC spectrum for the 3.6 mM sample was completed in 17 minutes, a time slightly longer than the seven minute td
predicted (Figure 2(a)) for this protein concentration.
Spectra were processed with 90o shifted sine bell ®ltering, and zero ®lling in both dimensions. To correct for
differences in protein concentration, raw cross-peak
intensities in the more dilute sample were multiplied by
a factor (concc/concd), where concc is the higher protein
concentration. Similarly, to correct for differences in the
number of transients averaged, raw intensities in spectra
with the lower number of transients were multiplied by
a factor (N2/N1), where N2 is the larger number of transients. After correcting for differences in protein concentration and in the number of transients averaged,
residues whose line widths were invariant as a function
of protein concentration, gave cross-peak intensities that
were constant within 10 % in all four spectra. This
demonstrates that the extent of polymerization during
data acquisition was negligible for all the protein concentrations studied, and that spectra predominantly re¯ect
the properties of CspA during the lag phase for polymerization. Line widths at half height (n*1/2) were calculated from simulated annealing ®ts of a Gaussian line
shape to 15N traces of 1H-15N HSQC crosspeaks, using
the ``optimize peak'' routine of Felix 95.0.
T2 as a function of spin echo period
To characterize 15N T2 relaxation times as a function
of the spin-echo period, tse, 2D data sets (1024 100
complex points; spectral widths 5500 1400 Hz) were
collected on a 0.74 mM sample of acid-denatured CspA
using a variant of the CPMG method (Farrow et al.,
1994; Alexandrescu et al., 1996). The T2 relaxation data
were collected as an interleaved array (Alexandrescu
et al., 1996) of 24 FIDs for each complex 15N t1 increment,
consisting of six T2 relaxation periods (10, 50, 100, 150,
200, 300 ms), and two CPMG tse values (125 and 500 ms).
The acquisition time for each complex 15N t1 increment
was about ®ve minutes. The entire experiment was completed within 9.5 hours of adjusting the sample to pH 2.0,
a time about twice as long as the td for this protein concentration. The data in Figure 2(b) obtained for a comparable protein concentration predict an upper limit for
decreases in peak intensities during 9.5 hours of 20 %.
An exponential decrease in peak intensity during the
course of a 2D experiment can give rise to a non-T2 line
broadening contribution for the indirectly acquired (15N)
frequency (Balbach et al., 1996). With the present acquisition scheme, however, relaxation parameters are
sampled within each 15N t1 increment cycle, so that a
decrease in peak intensities would have to occur on a
time-scale of ®ve minutes in order to affect the measured
15
N T2 values. T2 changes during the course of the
experiment could present another complication. As a
test, T2 values were determined from the data set truncated to include only the ®rst 1/4 of t1 increments. This
corresponds to an two hour acquisition time that is
well within the lag time for polymerization. The mean
uncertainty in R2(tse,500 ms ÿ tse,125 ms) values rises from
15 % to 36 % when only the ®rst 1/4 of the data are
1204
used, re¯ecting the lower signal-to-noise when less
transients are averaged. Within experimental uncertainty, however, the R2(tse,500 ms ÿ tse,125 ms) values are
invariant between the truncated and full data. T2 data
sets were processed with Lorentzian-to-Gaussian ®ltering functions (exponential line widths of 7 Hz in t2,
2 Hz in t1), and zero ®lling.
T2 as a function of time
A series of eight 15N T2 relaxation data sets were collected on a 2.0 mM sample of acid-denatured CspA as a
function of time. For each data set seven relaxation
periods (16, 32, 64, 96, 128, 256, 400 ms) were used to
determine 15N T2 values. The relaxation periods were
interleaved between 15N t1 increments, as described
above. All data were collected with a tse value of 500 ms.
The acquisition time for each T2 data set was ®ve hours.
1
H-15N HSQC spectra were acquired before and after
each relaxation experiment, to allow comparison of the
time course of polymerization monitored by decreases in
1
H-15N HSQC intensities with that described by changes
in T2 relaxation times. 1H-15N HSQC intensities showed
an exponential decay towards an asymptotic baseline
during polymerization (y ˆ A exp(kobs x) ‡ C). By
contrast, time-dependent changes in T2 relaxation were
heterogeneous. Of 54 residues that could be resolved,
experimental uncertainties for ten were too large to
permit an analysis of the time dependence of T2. For
another two residues (Trp11, Thr22) the T2 values
decayed too fast to allow the determination of a rate
constant. For the remaining 42 residues, least squares ®ts
of the T2 data as a function of time were obtained for
each of the three functions: y ˆ A exp(kobs x); y ˆ
A exp(kobs x) ‡ C; y ˆ A exp(kobs,1 x) ‡ B exp(kobs,2 x),
where A and B are amplitude, C is a base line constant,
and where the sign of kobs can be either negative or
positive. The three functions have two, three and four
adjustable parameters, respectively. The F-test on the
limiting ratio of the reduced sum of squared errors was
used to determine if models with increased degrees of
freedom gave signi®cantly better ®ts to the experimental
data (Shoemaker et al., 1981). Owing to the decrease in
signal intensities accompanying polymerization the
mean experimental uncertainties in T2 values increased
from 2 % for the ®rst time point, to 15 % for the last time
point. Consequently, T2 values were weighted according
to experimental uncertainties in least squares ®ts of T2
data versus time.
NOESY spectroscopy
The 200 ms mixing time 3D 1H-15N NOESY-HSQC
experiment shown in Figures 7 and 8, was recorded on a
1 mM sample of acid-denatured CspA. The spectrum
was acquired with 1024 100 32 complex points for
the direct 1H, indirect 1H, and 15N dimensions, respectively. The corresponding spectral widths were 5500,
5500, and 1400 Hz. The total acquisition time was 40
hours. All dimensions were processed with Lorentzianto-Gaussian ®ltering functions (exponential line width
7 Hz), and zero ®lling. A baseline correction was applied
to the indirectly detected 1H dimension using the FLATT
algorithm (GuÈntert & WuÈthrich, 1992).
Aggregation of Acid-denatured CspA
Acknowledgements
This work was supported by grants 31-43091.95 and
21-46992.96 from the Swiss National Science Foundation
to A.T.A. We thank Harald Schwalbe (University of
Frankfurt) for his suggestion that line broadening effects
in acid-denatured CspA might be due to chemical
exchange, and Wolfgang Jahnke (Physics, Novartis AG)
for sharing pulse sequences. We thank Ueli Aebi and the
late Markus HaÈner for the electron microscopy work.
Markus was a terri®c colleague. His friendship and
expertise will be sorely missed.
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Edited by P. E. Wright
(Received 24 March 1999; received in revised form 15 July 1999; accepted 16 July 1999)