ARTICLE:
A Re-examination of the Acid Titration
Behavior of Human Mercaptalbumin:
CHANGES IN AMPHOTERIC
PROPERTIES ASSOCIATED WITH THE
N-F TRANSFORMATION
Joseph F. Foster and Patricia Clark
J. Biol. Chem. 1962, 237:3163-3170.
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THE
JOURNAL
OF BIOLOGICAL
Vol. 237, No. 10, October
Printed
CHEMISTRY
1962
in U.S.A.
A Re-examination
of the Acid Titration
Behavior
of Human Mercaptalbumin
CHANGES
IN
AMPHOTERIC
PROPERTIES
ASSOCIATED
JOSEPH F. FOSTER
AND PATRICIA
WITH
THE
N-F
TRANSFORMATION*
CLARKE
From the Department of Chemistry, Purdue University, Lafayette, Indiana
(Received for publication, June 8, 1962)
and it is absolutely essential to make correction for such binding
in the calculation of 2. Unfortunately,
however, data on chloride binding are somewhat limited and uncertain, particularly at
low pH. Perhaps the most important objection is raised by the
studies of Aoki and Foster (6, 7), which indicate that the isoelectric points calculated at various ionic strengths from the
known hydrogen ion binding data and the best available chloride
binding data do not agree with those determined
by electrophoresis. The discrepancy amounted to as much as 8 to 9 charge
units in experiments at 0.1 ionic strength in chloride.
Barnett
and Bull (11) have confirmed a similar discrepancy with several
other proteins.
These findings appear to be very important and
indicate that either (a) chloride binding data are in serious error,
or (5) the effective surface charge is not obtained by simple summation of hydrogen and anion binding data. Barnett and Bull
arrived at the second conclusion and suggested that some of the
positive charges on the protein are in valleys and are not effective
insofar as the surface potential is concerned.
In any event,
whatever the correct interpretation,
the results give cause for
concern as to the validity of calculations in which a calculated
net charge is employed.
An alternative approach was suggested by Hartley and Roe
(12)) namely, the experimental evaluation of the surface potential
from measurements of electrophoretic
mobility and application
of the Henry equation.
This approach has been utilized by
Chattoraj and Bull (13) in a study of the titration behavior of
stearic acid and of octadecylamine
adsorbed on the surface of
Nujol particles.
By this appraoch they were able to compute,
for the adsorbed acids or bases, effective values of pKi,t that
agree well with known values. Beychok and Warner (14) have
also utilized this approach in a study of the titration behavior of
a protein, lysozyme.
A detailed study of the electrophoretic
behavior of human
mercaptalbumin
in acid solution has been reported (15). In the
present study, the titration curve of this protein has been redetermined with the same protein preparation
and the same experimental conditions
as those employed in the electrophoretic
studies. The combined data on hydrogen ion binding, electrophoretic mobility, and N-F composition as a function of pH have
been subjected to extensive analysis.
The results show clearly
that the titration anomaly is associated primarily with the N-F
reaction and not with expansion.
In addition, the results suggest
that the isomerization
leads to an unmasking or normalization
of a large number of carboxylate groups, possibly as many as
50, that are essentially masked in the native form.
3163
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It is now well known that the titration curves of the plasma
albumins, both human and bovine, cannot be fitted satisfactorily
The
through the classical Linderstrom-Lang
titration equation.
observed anomaly is an abnormal steepening of the binding curve
near the midpoint of the carboxyl titration region, i.e. near pH 4.
This anomaly was first pointed out by Tanford (I), who suggested
that the abnormality is due to expansion of the protein molecule
with consequent reduction of the electrostatic interaction
parameter, w. In the years since this suggestion was made, the
reversible expansion of albumin at pH below 4 has been well
established (2-5).
Now, it is also well established, however,
that the expansion is preceded by another important transformation, the N-F transformation,
which does not involve any important increase in the hydrodynamic
volume of the protein but
does lead to other important changes in properties (5). It was
pointed out by Aoki and Foster (6, 7) that the major part of the
anomaly in the titration
curve is in all probability
associated
The
with the N-F transformation
rather than with expansion.
most compelling argument for this hypothesis is the fact that
most of the anomaly occurs in the pH range 4.5 to 4.0, a range in
which essentially no expansion occurs but in which isomerization
does take place. It was shown that to a reasonable approximation the titration curve of bovine plasma albumin could be explained on the basis that in the native or N form all of the carboxy1 groups are abnormal with pKi,t of approximately
3.7,
whereas in the isomerized or F form they are essentially normal
4.4). Loeb and Scheraga (8) have also
(PKint, approximately
concluded that the titration
anomaly cannot be explained in
terms of expansion and have suggested certain hydrogen-bonded
structures that might explain the observed results.
All such arguments are somewhat tenuous, however, in that
they are based on application of the Debye-Hiickel
theory, which
assumes the protein to be a rigid, spherical molecule with homogeneous distribution
of charges on the surface. Elaborations
of the theory that include various assumed positionings of charges
have been considered by Tanford and Kirkwood
(9). Perhaps
an even more pertinent objection is the uncertainty
as to the
precise net charge, 2. It is well known that the albumins have
an unusual propensity to bind anions, even chloride ions (10)
* This paper, taken from the Ph.D. thesis of Patricia Clark
(Purdue University, 1962), was presented in part before the First
International
Congress of Biophysics, Stockholm, August 1961.
The work was supported by Grant C-2248 of the National Cancer
Institute, United States Public Health Service.
t Present address, Gerontology Branch, National Institutes of
Health, Baltimore City Hospital, Baltimore, Maryland.
Amphoteric
Properties
and N-F
Transformation
Vol. 237, No.
10
RESULTS
FIG.
strength
obtained
(17).
1. Titration
curve of human mercaptalbumin,
0.10 ionic
(chloride), 0”. Shown for comparison are four points
at this same temperature in 0.15 M chloride by Tanford
EXPERIMENTAL
PROCEDURE
Xateriuls-Human
mercaptalbumin
was prepared from human
plasma Fraction V’ through its mercury dimer essentially by the
Dintzis method (16). Isoionic solutions of the monomer were
prepared by passage of concentrated
solutions of the dimer
through the thioglycolate and mixed bed ion exchange columns
specified by Dintzis.
To defat the monomer the pH was lowered to 2.5 or 3.0 for 48
hours and the fatty acid-like material was removed from the
turbid solution by centrifugation
or filtration.
The monomer
was tested for the presence of dimer by ultracentrifugal
analysis
of a 0.8 to 1 y0 solution of the isoionic monomer.
Usually about
5% of dimer was present in each stock solution of monomer prepared.
An electrophoresis determination
with 0.2% protein at
pH 4.0 in 0.02 ionic strength chloride was run on each freshly
prepared solution of monomer (15). The ratio of the areas of the
two peaks was checked against previous data to determine
whether the protein had the normal properties.
Reagent grade potassium chloride and hydrochloric
acid were
employed.
All water used in the preparation of protein solutions
and reagents was distilled and deionized by passage through a
demineralizing
column.2
1 Obtained through the courtesy of Dr. J. N. Ashworth of the
American National Red Cross. We are indebted to Dr. H. Saroff
of the National Institutes of Health for suggested modifications
of the Dintzis procedure for crystallization
of the mercury dimer.
2 Barnstead Bantam, Barnstead Still and Sterilizer Company,
Boston, Massachusetts.
The titration results, in the usual form of equivalents of hydrogen ions bound plotted against pH and measured relative to
the isoionic pH, are shown graphically in Fig. 1. The few previously published experimental
data at 0’ on human mercaptalbumin in this pH range, those of Tanford (17), are given for
comparison.
Tanford’s data were obtained in 0.15 M chloride
rather than in 0.1 M, as employed in the present experiments,
but otherwise the conditions were probably comparable.
The
most striking difference is clearly in the isoionic pH, which is 5.78
in the present experiments as compared to Tanford’s 5.17. This
difference is doubtless mostly due to the fact that in the much
earlier experiments the protein preparations
were deionized by
electrodialysis rather than by the Dintzis column.
Dintzis (16)
has reported an isoionic pH of 5.72 for human mercaptalbumin
at 2.5” and 0.1 M KCl.
It will be noted that the increment in
bound hydrogen ions over the range covered by Tanford’s data
is almost exactly the same as ours over the same pH range.
In Table I are collated the data employed in the calculations
to be summarized in the “Discussion.”
Since titration and electrophoretic data were not obtained at the same pH values, the
data employed were obtained only from smoothed curves of the
titration,
mobility,
and N-F composition
data. As a consequence, the calculated points in all cases formed smooth curves,
and it was not necessary to include them in subsequent graphs.
DISCUSSION
Theory-The
standard free energy of ionization
of a proton
from a particular acid site on a protein depends on both the intrinsic standard free energy change and on the over-all change in
free energy resulting from the change in charge on the macromolecule.
Thus formally
3 Type Al534 supplied byMicrochemica1
California.
Specialties, Berkeley 3,
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Preparationof SolutionsAll
solutions of protein were prepared
from the concentrated isoionic stock solutions previously mentioned.
The protein solutions were diluted to 0.98% protein in
0.10 N potassium chloride before titration with 0.104 N hydrochloric acid. The hydrochloric
acid solution was standardized
against 0.0832 N potassium hydroxide that had previoulsy been
standardized
with dried potassium acid phthalate.
Titration Xtudies-The
titration studies \yere carried out on the
B or expanded scale of a Beckman Model GS pH meter with a
glass electrode and a silver-silver chloride reference electrode
with ground glass junction.
Fisher standard buffer, pH 4.00,
was used to standardize the pH meter at the beginning and end
of the titration.
The concentration
of the protein solutions was
measured in a Beckman model DU spectrophotometer;
E:&
was assumed to be 5.30 at 280 rnp.
Once the protein solution had been prepared with the proper
amount of potassium chloride, it and the tips of the electrodes
were chilled in an ice bath before the titration was started.
The
titration was performed by the continuous method with a microburette3 that was calibrated just before the titration studies were
begun.
Total dilution of the protein solution at the lowest pH
did not exceed 15%. Blank corrections were determined and
applied in the usual fashion whenever they were significant.
The
calculations of equivalents of hydrogen ions bound per mole
were based on an assumed molecular weight of 69,000.
October
J. F. Foster and P. Clark
1962
AF”
=
AFiat
If $J is the surface potential and E the elementary charge on the
proton, it follows that (dF)/(dZ)
= Neti. Also remembering
that AZ is -1 for loss of a proton,
0
AF” = AFi,t
-
NC*
(2)
In terms of ionization constants K and Kint and the corresponding values of pK, equivalent forms of Equation 2 are
K = Kinter+lkT
(3a)
and
pK = pKi,t
Assuming
n equivalent
- 0.434&kT
(3b)
sites, v of which are protonated,
pK = pH - log--
n--u
”
TABLE
(1)
+
= PKint - 0.434.$/kT
(4)
22
$ = - (l/b - ~/l + Ka)
D
(5)
where D is the dielectric constant.
As was pointed out in the
introduction,
this treatment demands knowledge of 2, a parameter that is in fact very uncertain.
Hartley and Roe (12) pointed out that the surface potential,
#, can be approximated
through measurement of the electrophoretic mobility, EL,and use of the Henry equation.
The Henry
equation (19) strictly yields a “{ potential,”
the potential at an
imaginary surface of shear that must be somewhat outside the
true surface of the molecule.
Assuming the difference between
the { and the true surface potential to be negligible, the potential
is given by
Here 77 is the solvent viscosity in poise. The limitations
and
merits of this treatment
have been discussed adequately
by
Chattoraj and Bull (13) and by Beychek and Warner (14) and
need not be further elaborated here. It is worth re-emphasizing,
however, that Equation 6 makes minimal demands on knowledge
of the size and shape of the protein.
For a sphere, the radius a
enters only through I,
which is a slowly varying function
of a. Although the equation is strictly applicable only to spherical molecules, mathematical
relationships
have been suggested
(19) for relating the mobility of a cylinder to that of an equivalent
sphere. Aoki and Foster (6, 7) utilized these relationships
and
concluded that the mobility of bovine plasma albumin with an
assumed axial ratio of 4: 1 should be equivalent
to that
of a spherical molecule with a radius 100/67 times that of the
effective radius of the molecule considered as a sphere. Thus,
many considerations lead to an estimate of about 30 A for the
radius of the plasma albumin molecule, whereas correction of the
mobility for the nonspherical shape would lead to an estimate of
about 45 A for the effective radius to be employed in Equation
6. At 0.1 ionic strength, the corresponding
I
values are
I
Smoothed data employed in calculations
PH
p x
UFl
5.68
5.60
5.47
5.31
5.17
5.00
4.80
4.70
4.60
4.50
4.40
4.30
4.20
4.10
4.00
3.90
3.80
3.70
3.60
3.50
3.10
i
0.7
1.5
2.9
5.1
7.2
10.5
15.0
18.0
21.0
24.5
28.5
33.5
39.0
45.5
51.5
57.0
62.0
67.0
72.0
76.5
91.5
Fraction
Ft
lo-
_-
--4.73
-4.53
-4.36
-4.06
-3.77
-3.35
-2.75
-2.40
-1.90
-1.20
-0.15
+0.65
1.55
2.65
3.60
4.45
5.20
5.95
6.65
7.40
7.85
i
-0.601
-0.576
-0.555
-0.516
-0.480
-0.426
-0.350
-0.305
-0.242
-0.153
-0.019
+0.083
0.197
0.337
0.458
0.566
0.661
0.756
0.845
0.940
0.997
0.549
0.563
0.575
0.598
0.620
0.654
0.705
0.738
0.786
0.859
0.981
1.09
1.23
1.40
1.58
1.76
1.93
2.13
2.33
2.56
2.71
0
0
0
0
0
0
0
0
0
0
0.03
0.08
0.17
0.41
0.59
0.68
0.77
0.86
0.94
1.00
1.00
*h is the average of ascending and descending mobilities,
weighted for composition in cases where both N and F boundaries
appear (14).
t e)/kT = 1.27 X lo4 /.L.
$ N-F Composition
(14).
1.10 and 1.13, and there is a difference of only about 3% in the
calculated potential.
Throughout
the calculations that follow a radius of 30 A has
been assumed. The factor employed for converting mobility in
centigrade-gram-second
units to the dimensionless
parameter
qb/kT, namely, 6 qc/DkTf(Ka),
was taken as 1.27 X lo4 for
the conditions of the experiments.
Before proceeding with the mathematical
analysis of the data,
it is essential to make some assumption about the state of protonation of the protein at the isoionic pH, the reference pH in
these studies. Tanford, Swanson, and Shore (20) have concluded that the imidazolium
groups of bovine plasma albumin
(16 or 17 in number) have a reasonably normal pKi,t of 6.9. It
is assumed that this is also the case for human mercaptalbumin,
from which it follows, with due consideration for the electrostatic
term, which is substantial at the isoionic pH, that less than 1.0
imidazole group per molecule is unprotonated
in the reference
state. This assumption has been made, and a small correction
has been applied to the observed u values to allow for protonation
of imidazole sites. (The correction ranges from -0.2 at pH
5.68 to -0.9 at pH 4.7 and below.)
It is assumed that all of the
remaining protons are taken up by carboxylate sites. If this is
so, and if approximately
100 carboxylate groups are assumed, it
can be calculated that approximately
three such sites must be
protonated
at the isoionic pH. The actual number of sites,
however, depends upon the interpretation
given to the titration
curve, as will be considered below.
In all of the calculations to
be reported it has been assumed that 3.4 carboxylates are protonated at the isoionic pH; this number seems most reasonable
on the basis of the various interpretations
of the binding cu.rve
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In the usual Linderstrem-Lang
(18) treatment, the surface
potential is evaluated according to the Debye-Hiickel
theory,
which assumes the protein molecule to be a sphere with radius
b and radius of exclusion a, through
3165
Amphoteric Properties and N-F Transformation
3166
FIG. 2. Plot
parameter,
-1.40.
parison.
The
of pK
= pH
-
The
0.434 qb/kT.
region of the N-F
E V/kT
log %I-!!
versus
slope :f the
transformation
the
electrostatic
initial
dashed line is
is shown for com-
PH
for two extreme
models
of the
FIG. 3. Results of calculations
carboxvlate
sites in the native
human
mercantalbumin
molecule.
Curve a, equivalent
abnormal
site model,
showing
effective
pKi,t
as function
of pH (left-hand
ordinate).
Curve
b, masked
site
model,
showing
number
of titratable
sites as function
of pH
(right-hand ordinate).
The region
of the N-F
transformation
is
shown for comparison.
For further
explanation
of calculations,
see the text.
10
(see below).
Only in the case of Fig. 5 and the associated discussion is this assumed number critical, and in that case calculations have been repeated for other assumed states of protonation
at the reference pH. In all other cases the graphs and conclusions would not be materially altered by any reasonable change
from the number 3.4.
Plot of pK against Potential-A
standard method of treating
protein titration data for the purpose of evaluation of pKi,t has
been to plot pK, i.e. (pH - log (n - u)/u), against the electrostatic potential.
Usually when the Linderstrom-Lang
treatment is followed, such a plot has the calculated charge Z as abscissa; then pKi,t is obtained from the intercept at Z = 0, and
the electrostatic interaction
parameter w, from the slope (20).
In the present case, the appropriate plot by Equation 4 is of pH log (n - LJ)/LJ versus 0.434 qb/kT.
In this case, assuming all
groups equivalent, a straight line of slope - 1.00 is to be expected,
provided that the use of the $J obtained from electrophoretic
mobility is in fact justified.
In Fig. 2, the data are plotted in this fashion.
The most
striking result is the flatness of the curve in the region of the N-F
transformation.
Since in this region there is relatively little
expansion, it does not seem reasonable that there should be any
essential alteration in the constant that relates # and electrophoretic mobility.
The only reasonable interpretation
is that
this flatness is an artifact of the cooperative transition, and it
follows that the slope in this region has no physical signijicance.
This being so, it also follows that the parameter w, which would
be obtained from the conventional plot in this range, can have
no real significance.
It can also be concluded that the procedure
of obtaining pKi,t by extrapolation
to zero potential (charge)
cannot yield a meaningful value in this case. Thus, if the curve
is extrapolated from the low pH side, a pKi,t of approximately
4.02 is obtained, whereas if extrapolation
is made from the high
pH side, the value is only 3.90.
The slope of the initial linear portion of the curve is -1.40,
not -1.00, as theory would predict.
At first thought this discrepancy might be taken as indicative of a deficiency in the
method of evaluation of the potential #. However, as will be
seen below, the effective number of titratable groups in the native
form of the protein is probably much less than the 105 assumed
in this calculation.
If that is the case, the function plotted and
the slope obtained can have no physical significance.
It is found,
in fact, that if n is taken as 55 instead of 105,4 the curve is again
linear and of slope very close to - 1.0 down to pH 4.8. This suggests the possibility that, to a first approximation,
almost half of
the carboxylate sites may be effectively masked in the N form.
Calculation of pKcnt as Function of pH, Assuming All Sites
EqGvaZent-This
is the type of calculation performed by Aoki
and Foster (6, 7), who concluded that the mean value of pKi,t
changes from approximately
3.7 for the N form to approximately
4.4 for F. In Fig. 3 (Curve a) are shown results of similar calculations made when 105 binding sites, all equivalent, were assumed. In substantial agreement with the previous calculations,
which were based on the Debye-Htickel
equation and are hence
4 The
any type
limiting
ford (17)
molecular
indicates,
number
107.
value
105 was used here because
of the fact that almost
of analysis
applied
to our titration
data suggests
a
binding
of 100 to 110 protons
at extreme
acid pH.
Tanfound
a binding
limit
of 100 based on the same assumed
weight
of 69,000 that we have employed.
As Fig, 1
approximately
7 protons
would
have to be added to his
to correct
for the error in isoionic
pH, giving
a limit
of
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0.434
Vol. 237, No.
October
1962
J. F. Foster and P. Clark
&
= k (n - u)
(7)
In the presentcasethe electrostaticinteraction canbe introduced
through Equation 3a, which yields
u eryC/kT
=
tH+l
Thus the appropriate plot is (v/H+)e”‘LT versusu. Such a plot
I
I
1
I
I
I
I
,
I
IOO-
n
-4.0
f
,
I,
0
Fraction
I
0.5
I
I
I
I,
1.0
F Form
FIG. 4. Plot of the sameparametersas those in Fig. 3 versus
the fraction of the F form as obtained from electrophoresis
Curve a, equivalent abnormal site model (right-hand ordinate)
Curveb, maskedsite model (left-handor&nate).
shouldyield a straight line of slope- 1/Ki,t and intercept on the
abscissaequal to n, provided that all groupsare equivalent and
do not changetheir propertiesthroughout the titration, and provided, of course, that the electrostatic parameter is correctly
determined. In the caseof nonequivalent sites, a progressive
decreasein slope is expected; i.e. the curve will be monotonic
and concave upwards with no inflections. The procedure for
handling suchcurves in the caseof nonequivalent siteshas been
discussed
by Scatchard, Coleman,and Shen (10).
In Fig. 5 are shown examplesof Scatchard plots for human
mercaptalbuminbasedon three different assumptionsregarding
the state of protonation of carboxylate groupsat the isoionicpH.
The full curve is basedon the assumptionmadein all previous
calculations,namely, that there are 3.4 protonated carboxyls at
the isoionicpoint. Consideringonly this curve for the moment,
the initial portion, from pH 5.7 to 4.6, is strongly suggestiveof
the presenceof some55 equivalent sites of reasonably normal
pKi,t (4.3), the rest of the sites being effectively masked
(pKi,t
