0
Copyright
1994
by
the
American Chemical
Society
New
Concepts
in
Biochemistry
w
Volume
33,
Number
27
July
12,
1994
Protein Hydrogen Exchange
in
Denaturant:
Quantitative Analysis
by
a
Two-Process
Model?
Hong
Qian,*J
Stephen
L.
Mayo,$
and
Andrew
Morton11
Division
of
Chemistry, California Institute
of
Technology,
MS
139-
74,
Pasadena, California
91
125, Division
of
Biology,
California Institute
of
Technology,
MS
147-75,
Pasadena, California
91
125,
and
Institute
of
Molecular
Biology,
University
of
Oregon, Eugene, Oregon
97403
Received
April
5,
1994;
Revised Manuscript Received
May
18,
I994
Recent measurements
have
shown
that
hydrogen exchange
(HX)
rates
of
the
amides
of
ribonuclease
A
(RNase
A)
are
a function
of denaturant
concentration,
even
at concentrations
well below
the
denaturation transition
(Mayo
&
Baldwin,
1993). This
behavior was
interpreted
as
being
due to
a
combination
of
two mechanisms,
termed
limited
structural
fluctuation and
local unfolding.
The
authors
also concluded
that
the
local unfolding reactions
entailed a
novel
structural
transition, termed
global unlocking.
Two issues
must
be addressed in considering
the
HX
behavior
of proteins in
denaturant:
the
mechanism
of exchange
from
the
native protein
and
the
significance
of exchange
from
the
unfolded
state.
This
paper addresses
the latter
of
these
issues, using
a quantitative
formalism derived from existing
HX
models
(Englander
&
Kallenbach, 1983;
Wagner
&
Wuthrich,
1979; Woodward
&
Rosenberg, 197 1; Woodward
&
Hilton, 1980). In particular,
the
two
routes
of
HX
via
native-like
and
globally unfolded
states
are
integrated
to allow
a quantitative
analysis
of the
transition between
the
two routes.
Exchange from
native
and
native-like
states
typically domi-
nates
the
observed
rates
in
the
absence
of
denaturant,
but
becomes less significant relative
to the
unfolded
state
in more
strongly
denaturing
conditions, including conditions
below
the
global unfolding
transition.
It
is
concluded
that the
available
data are
insufficient
to
discriminate
between
the
various models for
HX
from
native-like
states.
THE
MODEL
Proton exchange
from
protein
amides
is generally described
using
a kinetic mechanism developed in Linderstrom-Lang’s
laboratory
(Hvidt
&
Nielsen,
1966).
Under
typical experi-
mental
conditions
(“EX2
regime”)
this
kinetic mechanism
attributes
the
slow
HX
rates
of
native
proteins
to
a fast
equilibration
between exchange-incompetent
and
exchange-
competent
conformations, prior
to
a relatively
slow
chemical
exchange
step
(eq
1):
KOP
kx
HX
incompetent
+
HX
competent
-
exchanged
(1)
The
observed
exchange
rate
constant for
the EX2
regime
is
given
by
(Hvidt
&
Nielsen,
1966)
where
kopand
k,l
are
the
rateconstants
for
the
pre-equilibration
between
competent
(“open”)
and
incompetent (“closed”)
forms;
the
equilibrium constant for
the
pre-equilibration
step
is given
by
Kop
=
kop/kcl. Values
of
k,,
the
intrinsic
rate
constant
of exchange
for
the
competent amide,
depend
on
pH
and
local
seauence and
have been
directlv determined
usinn
-
short,
unstrictured
peptides
(Bai
et
al.,
i993).
Experimentally determined
rate
constants
are
often nor-
malized relative
to
the
intrinsic
exchange
rate
Constant
k,
to
H.Q. isa
fellow of the
Program in
Mathematics
and
Molecular Biology
at
U.C.
Berkeley, which is supported
by
the
NSF
Grant
DMS
8720208.
S.L.M.
acknowledges
suDmrt
from the Rita
Allen
Foundation
and
the
David
and
LucilePackaid
Foundation.
A.M.
is
a Howard
Hughes
Predoctoral Fellow.
obtain a
phenomenological protection
factor.
The
Carlsberg
formulation
allows one
to
assign
a structural
interpretation
to
the
protection
factor.
It makes no assumptions,
however,
about
the
structural nature
of
the
global events leading
to
exchange competence. Clearly, global unfolding
of the
protein
*
To
whom correspondence should be addressed.
*
Division
of
Chemistry, California Institute
of
Technology.
f
Division
of
Biology, California Institute
of
Technology.
11
University of Oregon.
0006-2960/94/0433-8167%04.50/0
0
1994
American Chemical
Society
8168
Biochemistry,
Vol.
33,
No.
27,
1994
can lead
to
exchange competence
of
the
protein
chain
(Robertson
&
Baldwin,
1991).
Conformational fluctuations
in
the
native
state
of
the
protein
can
also
allow
local
regions
of
the
chain
to
become
competent.
The
two-process model
described
by
Woodward
and
Hilton
(1980)
formalizes
the
observation
that
both global unfolding
of
proteins
and
some
type
of
local
fluctuation
from
the
native
state
can lead
to
exchange. We
now
present
a further
development wherein
we
explicitly
include
the
denaturant
dependences
of
the
two
processes in
a quantitative
fashion.
To
interpret
measurements
of
HX
rates
in
terms
of
equilibria
between
conformations
having
different
exchange competence,
we
construct
an
equilibrium
model which
includes competent conformations
arising
from both global unfolding
and
local fluctuations.
The
denaturant
dependence
of
these
equilibria
are
then
used
to
predict
the
total amounts
of exchange competent species
(and
their
observed
exchange behavior) under
different conditions.
The
global unfolding process
has
been
relatively
well
characterized
in
many
proteins,
including
RNase.
In par-
ticular,
the
denaturant
dependence
of
global unfolding may
be
modeled relatively
simply, using
either
the
linear free
energy
or stoichiometric binding models
(Pace,
1975).
We
will
use
the
former
in
our analysis
below.
The structural nature
of
local
fluctuations
which
can
lead
to exchange competence
is not
well
characterized.
The
degree
to which
local
fluctuations
involve
local
unfolding
of the
chain
is expected
to
be
related to
the denaturant
dependence
of
the
free
energy difference
between
the
native
and
locally
fluctuated
conformations (Schellman,
1978;
Mayo
&
Baldwin,
1993).
In
order
to
assess
whether
the denaturant
dependence
of
the
observed
HX
measurements can
be
explained
solely via
the
effects
of
global unfolding,
we
make
the
assumption
that
the
local
fluctuations have
no
denaturant
dependence
and
hence
are
as
folded
as the
native
state. With
these assumptions,
we
can
show
that
all
theobserved
denaturant
dependenceof
Mayo
and
Baldwin’s
measurements
can
be
accounted
for
by
the
denaturant
dependence
of the
global unfolding reaction
alone.
We
make no
further
assumptions concerning
the
extent
or
nature
of
the
fluctuations
which
lead
to
local
exchange
competence,
nor
whether
the
individual fluctuations
are
correlated with one
another.
Note
that
conformations
arising
by
local
fluctuations from
the
native
state
are
defined only
locally,
with reference
to
an
individual amide. These
different locally
defined
species
are
not
mutually
disjoint
and thus
cannot
be
included
in
a single
equilibrium. Instead,
we
define
a separate
equilibrium
for
each
amidei,
consisting
of threespecies:
a nativeconformation,
Ni,
with
the ith
amide
in
a nonexchanging environment;
a
locally
fluctuated
conformation,
It,
with
the ith
amide
in
an
exchange-competent environment;
and
an
unfolded confor-
mation,
U,
with
the ith amide (and,
in
fact,
every
amide)
in
an
exchange-competent environment.
Since
we
assume
that
state
It is indistinguishable from
Ni
in any global unfolding measurement,
all
the
individual
three-
state
equilibria
are
related
via
the
global unfolding
reaction.
Thus
all
the
conformations explored
by
the
protein
in solution
may
be
classified
as either
folded
or
unfolded
on
the
basis
of
global
properties
such
as CD
or viscosity.
Those conformations
which
are
folded may then
be
further
divided
on
the
basis
of
local
properties
into
those
which
arecompetent
or incompetent
for
exchange
at a particular
amide. Only
this
second
division
depends
on
which
amide
is under consideration.
Note that
this
implies
that the
sum
[Nil
+
[Ii]
is independent
of
i.
These
points
are
illustrated
in
Figure
1.
New Concepts
in
Biochemistry
amide
i
amide
j
FIGURE
1:
Conformational
phase
space
of a protein
may
be
divided
into
three
regions
corresponding to unfolded, native,
and
intermediate
species.
The
distinction
between
regions
U
and
N
+
I
is made
according
to global unfolding
criteria
such
as
CD
and
is independent
of the particular
amide
under
consideration.
The
distinction
between
N
and
I
regions
is
made
based
on
local
properties
of
the
polypeptide
chain.
Some
conformations
may
belong
to both
intermediate
It
and
I/:
thevarious intermediate
forms
are
not
necessarily
mutually disjoint.
With reference
to a
particular
amide,
we
define
the
following
equilibrium:
KIJ
KU
I,
+
N,
*
U
with
intrinsic
equilibrium constants
(3)
(4)
The
equilibria
between
Ni and
1,
and
between
Ni
and
U
correspond
to the
two
parallel
processes
by
which
the ith
amide
can become competent
for
exchange. Unfortunately,
the
individual
equilibria
are
not
directly
measurable.
One
can
measure,
however,
the
equilibrium
between
all
globally folded
and
globally
denatured
forms.
We
define
this
equilibrium
as
K,.
It is independent
of
the
choice
of
any
particular
amide.
One
can
also
measure
the
equilibrium
between
all
exchange-
competent
and
exchange-incompetent forms,
which
we
define
as
Kh.
Unlike
K,,
this
requires reference
to a
specific
amide.
The
corresponding
free
energies
for
global unfolding
and
acquisition
of exchange competence can
be
expressed
in terms
of
the
intrinsic
equilibrium constants:
K2,i
1
+
K1,i
=
-RT
In
-
[VI
[Nil
+
[Iil
AG,
=
-RT
In K,
=
-RT
In
[I,]
+
[VI
-
-
AGh
=
-RT
In
Kh
=
-RT
In
[Nil
-RTln
W1.i
+
K*,J
=
-RTln
[K,,,
+
(1
+
K1,i)Kgl
(6)
Equation
6
indicates
that
the
observed
HX
behavior depends
on
both
the
global
and
local
conformational
equilibria.
Thus,
if the
global unfolding
free
energy
is known,
then
the
observed
HX
behavior,
AGhx,
can
be
determined from eq
6
with
K1,i
as a parameter.
RESULTS
Denaturant Dependence
of
AG,
and
A&.
We first
show
that the
denaturant
dependence
of
the
Ni
*
U
transition
(K2,i)
is
the
same
as
the denaturant
dependence
of
the
global
unfolding
transition
(K,).
The standard
treatment
of
the
denaturant
dependence
of
the
global unfolding
transition
is
the
linear free
energy
model
(Pace,
1975):
AG,
=
A$
-
m,[D]
=
-RT
In
(gemIWIRT)
(7)
In
this
model,
mg
is related
to
the
differential
interaction
of
the
denaturant
with
the
folded
and
unfolded
forms
of
the
protein.
The
superscript
0
indicates values
in the
absence
of
denaturant.
New
Concepts
in
Biochemistry
-10
Biochemistry,
Vol.
33,
No.
27,
1994
8169
-
/'
~
I.
I.
I.
I,
1-
4
h
3
E
0
1
.o
10
-2
....
I.,..I....II.,
,
$1.
0.0
0.5
1
.o
1.5
2.0
FIGURE
2:
Model
predictions
for
single
proton
HX
rates
as functions
of
denaturant
concentration
as
in
eq
9. The
plot
was
made
using
Aq
=
6 kcal/mol;
m,
=
3 kcal/(mol-M).
Values
of
Klc
are
indicated
by
each curve.
The
symbols
are data
from
Mayo and
Baldwin's
Figure
1 after
subtracting
3.6
kcal/mol
as suggested
by
the
original authors
(C58, H12, E49,
and
N44
from
top
to bottom).
Note
that
there
are
two
types
of behavior: for
large
and small
Kl,i,
the
data are
basically
linear
(C58,
N44);
for
intermediate
range
Kl,,,
the
curves
are
nonlinear
(H12,
E49). The
transition
point,
where
KZJ
=
K~J,
is at
[D]
=
--,
-0.30,
0.48,
0.71, 1.01, 1.52, 1.86, and
1.98
for
each
of the
respective curves.
For
KIJ
ranging
between
0
and
0.1,
all
curves
converge
at the
global
unfolding
midpoint:
[D]
=
2 M.
[D]:
denaturant concentration
(M)
Combining eqs
5
and
7,
and
assuming
that
the
transition
represented
by
K1,i
is insensitive
to
denaturant,
we
have
Thus
the
global unfolding dependence
on
[D]
is the
same as
the
dependence
of K2,ion
[D].
Both
are
invariant
with respect
to
the
intermediate
state
Ii,
as
expected.
The
denaturant
dependence
of
AG,
is more
complex.
When
eqs
6-8
are
combined,
the
observed
AGhx
as
a function
of
denaturant
concentration
[D]
is given
as
AGh,
=
-RTh
(Kl,i
+
@,l&D1/RT)
=
-
RTln
[Klc
+
(1
+
K,,i)gemg[D1/RT]
(9)
This
is not
a
linear function
of
[D].
This
arises because
AGhx
is derived
from
the
population
ratio
of
Ni
relative
to
both
U
and
Ii.
Under
conditions where
K1.i
>>
K~J,
then
[It]
>>
[VI,
and
HX
will
be
dominated
by
local fluctations.
Where
K2,i
>>
Kl,i,
then
[VI
>>
[Ill,
and
HX
will
be
dominated
by
global
unfolding.
The
limiting
slopes
of
the
plot
of
AGhx
vs
[D]
will
be
0
and
mg
in
the
two respective cases.
Values
of
AG,(D)
and
mg
are
obtainable
using
optical
probes
of
global
structure
such
as
peptide
CD
(Mayo
&
Baldwin,
1993).
Given
these
values,
the
model
predicts a family
of
curves which
depend
only on
K1,i
(eq
9).
In
Figure
2
we
show
the
results
of
fitting
eq
9
to
the
data
of
Mayo
and
Baldwin.
The
only
adjustable
parameter
for
each curve
is Kl,i.
The
curves
are
extended
to
higher
denaturant
concentrations
to
clearly
illustrate their
biphasic
nature.
The
current
two-
process model
fits
the
observed
HX
data
well,
without
invoking
specific
structural
models
for
denaturant
dependence
of
exchange from
the
native
state.
Relation
between
AGx
and
mhx.
Mayo
and
Baldwin
demonstrated
a correlation
between
AG:,
and
mhx.
The
0.0
0.2
0.4
0.6
0.8
1
.o
mohrlmg
FIGURE
3:
Relation
between
A@,
and
mk.
Note
that
our
model
allows
no
AGk
greater
than
AGE
and
that
mk
cannot
be greater
than
m,
nor less
than
zero.
Ot
1
This
relation
is illustrated
by
the
curve
in Figure
3.
For those
amides
with
low
values
of
m!,,
there
is a very
little constraint
on possible
values
of
AG:,,
and
there
is no
expectation
that
AG,
should
reach
a particular
value
when
mk
is zero.
Mayo
and
Baldwin
interpreted
the
apparent
linear correlation
between
AG,
and
m:
as
supporting
their
model
of
a
common
exchange
mechanism
for
their
previously
identified class
1
and
2a
amides,
involving
denaturant
dependent
local unfolding
of
the
protein.
The
value
of
the
apparent
intercept
led
them
to
postulate
a
"global unlocking"
step
in
all
local unfolding
reactions.
Figure
3
demonstrates
that
thiscorrelation
is related
to the
transition
between two
exchange
mechanisms,
one
of
which is
exchange
via
global unfolding. Because
the
cor-
8170
Biochemistry,
Vol.
33,
No.
27,
1994
relation is not expected
to be linear,
there
is no need
to postulate
a global unlocking
step.
Correlation
between
AGh,
at
[D]
=
0
and
[D]*,
We
can
also
apply
the
quantitative
analysis
to the
data
of
Kim
and
Woodward
(1993)
on
BPTI.
They
have measured values
of
koh
in
the
presence
and absence
of
8 M urea.
BPTI
is
predominantly folded
under both
of
these conditions.
Again,
from
eq
6 we
have
New Concepts in Biochemistry
correlation
in
the
plot
of
AG,
vs
mh,.
This
is
a testable
prediction.
The
rates
of
exchange
from
these
faster amides
can be measured
by
modifying
the
experimental
protocol
(work
in progress).
The
stated
purpose
of
the
Mayo and
Baldwin experiment
was
to determine
the denaturant
dependence
of exchange
due
to
local
fluctuations
of
the
native
state,
on
the
assumption
that
this
dependence
would
reveal something
of
the
structural
nature
of these
fluctuations. This remains
an
important
issue.
Any
analysis,
however,
must
take
into
account
the
contribution
of the
unfolded
state
to the
apparent denaturant
dependence,
and this
requires
that
exchange be measured
under
conditions
where global unfolding does not
dominate
the
observed
exchange.
We
have presented
a quantitative
formalism for
doing this.
The
EX2
kinetic scheme, described above, allows one
to
determine
equilibria simply
by
measuring
the rate
constant
for
an
irreversible labeling process
(eq
2).
The
ability
to
distinguish
the
two species is
determined
not
by
their
relative
concentrations but
by
their
relative
concentrations
scaled
by
their
intrinsic
rate
constants,
which
can differ
by
many
orders
of magnitude. This ability is not restricted
to HX
experiments;
an
excellent discussion
of
another
use is
given
by
Vas
and
Boross (1974).
Results from such
analyses should be
considered with
caution,
however:
Kop may not
be
measured
under
the
same
conditions
as
Kg,
and
the
value
of
k,
determined
from
model systems may not
be
the
same
as
the
actual
rate
constant
for
the
exchanging
form
under experimental condi-
tions.
Mayo
and
Baldwin
noted
a discrepancy
of
3.6
kcal/mol
between
the
values
of
AG;
and
AGL
of
Cys 58. Because
Cys
58 exchanges
primarily through
global unfolding,
even
in the
absence
of
denaturant,
these
two values might be expected
to
be
equal. Such
discrepancies
are
seen in systems
other
than
RNase
A.
A discrepancy
of
1.4
kcal/mol
exists between
the
global unfolding
free
energies
of
BPTI determined
by
calorimetry and
HX
(Kim
&
Woodward, 1993; Kim
et
al.,
1993).
Bai
et al.
(1994)
have also observed
an
offset
of
2
kcal/mol for
cytochrome
c.
Mayo
and
Baldwin
attributed the
RNase
A
discrepancy
to
a difference
in
the
intrinsic
rate
constant
for exchange
from
the
unfolded
states. A
possible
explanation
for such
a difference could
be
the
presence
of
residual
structurein the
unfolded protein
at low
concentrations
of denaturant,
although residual
structure
in heat-denatured
RNase
A does not cause such
an
effect (Robertson
&
Baldwin,
1991). More direct
explanations include differences
in
the
solution conditions (e.g.,
D2O
vs
H2O).
The
present
model
offers no independent explanation
of
the
discrepancy.
We
have
followed
Mayo and
Baldwin
and
implicitly assumed
a
uniform
protection
factor
of
-400 in
our
treatment
of
the
observed
data.
The
contribution
to
observed
HX
rates
from
the
globally
unfolded
state
is unlikely
to
be
as
simple
as
suggested.
Nonetheless, this simple
model
does explain
the
available
data.
It
demonstrates
the
role
of
the
globally unfolded
state
in
determining
HX
behavior,
even
at concentrations
of denaturant
well
below
the
global unfolding
transition.
It also indicates
the
conditions
that
must
be
met
to
assess
the
effects
of
perturbants
on
HX
from conformations
other
than
the
globally
unfolded
form.
ACKNOWLEDGMENT
We
thank
many
colleagues,
particularly
Buzz
Baldwin,
Doug
Barrick,
Jay
Luo, and
Alyce
Su,
for helpful discus-
sions,Walter Englander for sending
us a copy
of his manuscript
prior to publication,
and
Rick
Dahlquist,
Brian
Matthews,
where
the
asterisk
stands
for
conditions
at
any
urea
concentration:
AG;
=
Aq
-
m
[D]*.
Equation
11
is
compared
to the
normalized
data
of
Kim
and
Woodward
on
HX
in
BPTI (Figure 4).
DISCUSSION
It is believed
that
protein
HX
rates
which
are
slow
relative
to rates
in short, unstructured
oligopeptides reflect
a dynamic
structural
process.
A
clear example
of such
a process
leading
to exchange competence is
the
global unfolding
of
a protein.
Globally unfolded proteins have
HX
rates
comparable
to those
of
unstructured
peptides
(Robertson
&
Baldwin,
1991).
A
variety
of
local
fluctuations
can
also lead
to
exchange
competence.
Either
global or local processes
can
dominate
exchange, depending on
their
respective values
of
Kop
(Hvidt
&
Nielsen, 1966).
This
realization
has
been
expressed
by
Woodward
and
co-
workers
as the
two-process model
(Woodward
&
Hilton, 1980).
Excellent descriptions
of
the
model
are
given
by
Kim
and
Woodward
(1993)
and
by
Englander and
Kallenbach
(1983).
We
have specifically addressed
the
denaturant
dependences
of
the
two
processes
and
show
that the
observed exchange
in
RNase
A and BPTI can
be described
quantitatively
using
only
a simple
model
for
the
denaturant
dependence
of
global
unfolding.
Whatever their
structural nature,
a denaturant
dependence
of
local fluctuations need not be
invoked
to explain
the
observed
data.
For
each amide,
the
crossover
between
the
two regimes is
determined
by
the
relative
values
of
K1.i
and
K~J,
corresponding
to the
relative
stability
of
U and
Ii
(regardless
of
the
stability
of
each
relative
to
Ni).
The
physical meaning
of
the
experimentally
measurable
quantities
AGhx
and
mhx
becomes
apparent
in
light
of
the
present model.
The
former reports
the
equilibrium between
all exchange competent and incompetent species, while
the
latter
reports
the
equilibrium between
the
two exchange-
competent states, Ii and U:
Thus
the
existence and
stability
of
equilibrium
intermediates
under native conditions
can
be
quantitatively
assessed.
They
differ significantly from
the
unfolded
state
in their dependences
on
denaturant.
A
global unlocking
step
was
postulated
by
Mayo and
Baldwin
to
explain
why
amides
which
have
little
or no
dependence
on
denaturant
(i.e.,
mh,
=
0)
do
not
have
koh
=
k,.
The
present model obviates
the
need for such
a step:
at
very
low
mk,
the
dependence
of
AGb
on
mhx
becomes
infinitely
steep
(Figure
3).
The
reason
Mayo and
Baldwin did not
observe
amides
with
low
values
of
AGh,
(i.e, where
kobs
approaches
k,)
is
that
they were experimentally
unable
to
measure
rate
constants
for
faster
amides. Could these
faster
rates
be
measured,
the
present
model
predicts
a nonlinear
New Concepts
in
Biochemistry
John
Schellman,
and
Ingrid Vetter for critical
reading
of
the
manuscript.
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