Tohoku
J. exp.
Med.,
1976,
Relationship Antigen
118, 289-296
between Weight
Precipitate
in
Volume
and
Immunodiffusion
SYUSAKU KATSURA, KENJI
TAKI and
KENJI
SUZUKI
Department of Legal Medicine, School of Medicine, Iwate M edical University, Morioka
KATSURA, and
S.,
Antigen
TAKI,
Weight
K.
in
and
Suzuxi,
289-296 •\Immunodiffusion various
sizes
was
affected
the
test
of
25
mg/ml,
In
this
the
and
weight
were
this
weight
case,
as
regression
(ƒÔ) and
weight
the
(ƒÔ) and follows:
for
times line
and
data
the
on
a
and
antigen
influences
the In
the
at
in
and
of
researches.
end
point
McKelvey
Onodera
linear wide between diameter radial
antigen et
at
antigen
(1965)
some
and
antigen
of
B the
area
were
s.D.=0.717, between
between
the
the
ring
concentration antigen
CA
from
ring
area
gave
diffusion
after
applying
precipitate
concluded
was
for publication,
and
in
no
a wide
from
the
his
semi-logarithmic reported
October
m=ƒÎƒÁ2.
27,
1975. 289
h. g
was
(ƒÁ, radius
and
of
that was
the
(m)
in
established
reported
that
mass
Fahey
immunodiffusion.
concentration
scale that
and
concentration
(1974)
antigen
in
a precipi
concentration
(1963),
relation
experiments
in
by
linear
of
antigen
radial
Berne
and
(1969)
given
in
utilized
area
antigen
ring
antigen. area
to
between
that
widely
the
Zigelbaum
precipitate
noticed
that
proportional
relation
of
is
reported
Tomasi
(1967)
Schmid
immunodiffusion 1965)
directly
linear
concentration
doubtful.
immunodiffusion
Received
was
diameter
time
he
radial (1963,
a
between but
was
and Ryan
constant
relationship range,
point
the and
relationship that
antigen
end
plates and
from
.104ƒÔ-1.251,
the in
medium,
the
diffusion.
obtained
scale
(1966)
by al.
agar
of
semi-logarithmic
only
an Mancini
antibody-containing
the
gel at
agar
respectively.
volume,
precipitation
in than
the
former
immunoassay
Quantitation
tate
linearity
from
and
concentration
obtained
y4=0
from
the
one,
to
one.
,
of
In 2
and
area
test
minimal
the
and
,
for
the
precipitate
of
weight
quantitation
range.•\immunodiffusion;
various
the
(y4)
clearer antigen
weight. antigen
of
s.D.=0.208,
was
volume
the
from
calculated
ring
of
precipitate weight .
volume
maximal
(3),
minimal
were
In the
deviation
(y3)
the
s .D.=0.092
times
standard data
standardized
There
precipitate
18.3
of
ranged
precipitation
B),
118 wells
shape antigen
precipitate
latter.
(CA
and
standardized
the
of
the
B
y3=0.146ƒÔ-1.754,
respectively.
and
16.7
(y2)
The the
(s .n.)
of
Volume
1976,
cylindrical
concentration was 15 .8 times
y1=0.006x-1.611,
anhydrase
was
and
(y1)
data
s.D.=0.295
B
. by
deviation
data
obtained:
anti-carbonic CA
standard
standardized
y2=0.005ƒÔ-1.546,
of
and
well
Precipitate Med.,
and
studied
, albumin weight
albumin
line
and
the
exp.
conic
was
of plate
standardized
J.
from
plate
size agar
maximal
(ƒÔ) and
results
containing weight
and
serum
regression
antigen following
shape
the
case, weight
In
by
gel
between
Tohoku
antigen
antiserum
anti-rabbit
antigen
and
thick
Relationship .
of
in
K.
Immunodiffusion
linear
a
ring
precipitate
precipitate
a
relation
precipitate of
the in
ring;
in h,
290
S. Katsura
thickness
of
antibody-containing
concentration In
the
tion
was
present was
linearly
report,
studied
and
agar correlated
relation
plate; g,
density
with ƒÁ2
between
compared
et al.
with
precipitate that
of
agar
h,
g
because
between
volume
plate),
and ƒÎ and
precipitate
and were
antigen area
antigen constant.
concentra and
antigen
weight.
MATERIALS AND METHODS Preparation
of antisera
Goat anti-rabbit-serum serum (anti-rabbit serum). Anti-rabbit serum was obtained from a goat immunized intravenously with rabbit serum diluted 10 times and subcutaneously with mixture of the serum and Freund's complete adjuvant. Only one precipitation line appeared in immunoelectrophoresis of rabbit albumin (Miles Lab., Inc.) with the anti-rabbit serum. Precipitin titer and precipitin content of the anti-rabbit serum by the ring test were 1: 64 and 1: 16, respectively. In the ring test, exactly 1 mg/ml albumin was prepared and defined as the original concentration of albumin solution. Anti-carbonic anhydrase B serum (anti-CA B serum). Carbonic anhydrase B (CA B) and anti-CA B serum were obtained as described by Matsuo (1972). In immunoelectro phoresis with anti-CA B serum, carbonic anhydrase solution containing CA A, CA B and CA C isozymes formed one precipitation line only at the location of CA B. Precipitin titer and content of the antiserum were 1: 3,200 and 1: 32, respectively. In the ring test, the original solution of CA B contained 2 mg/ml of CA B exactly. Preparation
of antiserum agar plate with wells
Six cylindrical
metal
blocks,
TABLE 1.
3 mm in diameter
TABLE 2.
and 3 mm in height , were pasted
The well forms and sizes in the anti-albumin
at equal
serum agar
The well forms and sizes in the serum agar plates containing anti -carbonic
Quantitation distance
on
glass
tray
tray. at
a
Agar 100•Ž,
serum
solution
was
prepared
one
volume
5 of
then
Various of
of
the
agar
were
dropped
manner
to
CA
B
18
to
to
23.1 ƒÊg.
B the
70 ƒÊl
in
they
were
from
under-side the
wells
Because precipitate the
antiserum
wells.
of and
normal
anti-rabbit
glass
tray
from
glass
mm
was
depth
the
saline
of
the
3
ml
A in
volume
cover
and
small. put
the
removed
were
formed
with
in in
from 2.
solution
the
wells
of
various
volumes
as
the
the to
CA
B
1
1,
sizes
from
anti-CA
mg/ml
and
varying
the
wells
in
the
(Nos.
to
prepared B
and
1
40
of
Besides,
made
Table
were
and
1).
were in
ranged
antigen
prepared, No.
forms wells
0.06
were
(Table
shown
wells
various
In
antigen
at
4•Ž.
above
as were
wells
surface
of
vertical
follows: drawn
were
growth
2-5)
630 ƒÊg.
in
serum
a
similar
agar
plate,
volumes ranged
Parallel on
the
lines photograph
with
plate
vertically
was
showed
from
from
1.26
of
vinyl
sheet
and
was
with
stopped,
oblique
through
light
the
center
photographed.
various 1
a
rings
agar
divided
precipitate
section
with
precipitation
antiserum
were
the
wrapped of
of
precipitates
section the
in After
the
The
in
plate
wells
Table
albumin
to
volumes
vertical
calculated agar
into
out
were
100
one
The
wells
plate.
in
of
applied
applied
with
shown
just
the
mg/ml
and
agar
plate.
precipitates was
poured
cut
blocks in
with
diameter
cylindrical
Albumin
chamber
the
25
concentrations as
photographed
to
or
serum
plates
moist
was
the
Bacto-Agar
filled.
mm
plate as
mixed
was
3
were
plates
of precipitate a
g
was
concentrations
varying
agar
2.5
conic
agar
applied
Antiserum allowed
with
anti-rabbit
were
with
solutions
various
these
in
Measurement
from
serum
solutions
2
tray
the
plate
was
mixture the
wells
albumin
in into
Anti-CA
The
of
glass
291
plate.
plates
solutions
corner
the
solution
until
cylindrical
a
dissolving
agar
55•Ž.
concentrations
antiserum
of
6
and with
by
the
glass
agar
each
albumin
at
cm) covered
of
cover
antiserum
21ƒÊl 4
times
the
gelling, the
(12x3 was
and
corner
after
plate cm)
diluted
cut
in
glass
(12 •~3•~1
of Antigen in Immunodiffusion
shapes,
mm
interval
a
precipitate
plates, the applied antigen weights and the sizes of the precipitates
anhydrase B, the applied antigen weights and the sizes of the precipitates
the to
volume
the in
surface the
vertical
of of
292
S. Katsura
et al.
section. The volume of precipitate was obtained from the sum of each volume discs with 1 mm thickness of the precipitate as shown in the following formula:
where m,
r
stands
for
magnifying
radius
power
of
of
the
the
disc;
h,
height
of
the
disc=l
mm; ƒÒ,
volume
of
of the
the
well;
photograph.
RESULTS
Shape of the precipitate In
the
diameter from
the
(Fig.
1).
solution
But
and
of Two
as
mm one
precipitate, 3
the
plate.
Fig.
mm
1.
in
shape
precipitates
ones
in
the
those
from
flattened
in
the
mg/ml
albumin
wells the
from
mm view
section
concentration
conic
precipitates
3 a
vertical
25
high
with in
the
and
to
to
wells
ring
mg/ml
from
The
of
Top:
Precipitation
agar
weight
in
plate the The
from In
solution was
of
the
5
mm
with
cylindrical
wells
30
lower
parts
various
in
wells same
was
the
in
a
in
,ƒÊl of 16 mg/ml which reached the
wells
420 ƒÊg,
210 ƒÊg, in
the
from of
to
of
various
3
mm
of
315 ƒÊg,
the
vertical
section.
wells
9
mm
the
diameter
upper
surface and
and
3 mm
525 ƒÊg,
were 3
In
mm,
the
mg/ml
wells
albumin
antiserum
agar
were (Table
with
in
diameter 105 ƒÊg
.
another
well
the
of
size
each;
plate
concentration
each
5
and
diameter
70 ƒÊl
shape with
form
agar
cylindrical
well
view
cylindrical
in
wells
hemispherical
from
precipitates
21
with
the
mm
antiserum
the
hold
from
rings
with
4).
nearly
precipitate
(3
the
volumes
appeared a
on
No.
albumin
showed the
1,
wells
wells
made
albumin
of
with
cylindrical
various
which
Also
plates
were
(Table
amount
serum
Bottom:
plates,
depth,
agar
depth)
volumes
definite
and
cylindrical
owing
precipitates
were
Three in
applied
various
The
20
tray
depth.
solution
of
glass
similar
mm
serum
the
were
a
were 3
the
showed
hemispherical
21 ƒÊl
the
in
1)
tray.
10 mm
of
solution
and
The
and
No.
from of
depth
follows:
and
plate,
mm
albumin
1,
plate
flattened.
albumin
the
the
bottom
anti-rabbit
prepared
of
diameter
mg/ml
bottom
and
5
plate,
(Table
precipitates
the were
3 mm 20
of
the
agar
depth
surface
and
with and
mm
reached
diameter
serum
3
upper
antigen,
5
anti-rabbit and
3
mm
vertical and
of
No.
5).
diameter section
3
the
mm
of depth
anti-rabbit
depth. from
applied, 1,
Albumin left
to
right.
Quantitation
Fig.
2.
Top:
the
antiserum
in
each
Bottom
The
precipitation agar
of :
the
of Antigen
rings
plate
of
though
the
in Immunodiffusion
various
sizes
definite
weight
were
293
tormed of
in
albumin
the
upper
(525 ƒÊg)
surface was
of
applied
wells.
The
vertical
section
of
was hemispherical. A trapezoid with 100 mm depth (Fig. 2).
the
precipitate
shown
precipitate
in
appeared
the
top.
from
the cylindrical
well
The shape of precipitates in the anti-rabbit serum agar plate was influenced by the shape and size of the well, and by antigen weight. In the sane way, the shape of precipitates in the anti-CA B agar plates corresponded to the shape and size of the well and to the applied antigen weight. Regression lines between the precipitate volume the precipitation ring area and the antigen The precipitate
volume
in the anti-rabbit column of Tables The relation be compared
serum 1 and
and the
the
with
antigen
that
because the unit of the volume which were not suitable for precipitate volume the computer:
and
where
standardized
y
tate
stands
volume
for or
ring
precipitation
and the anti-CA 2, respectively.
between
directly
ring
differs normal
plates
and
the
the
the
weight,
from
each
are shown precipitate
weight
and
of
with
precipitate
mean
of
y;
volume
S.D.
of
ring
can not
After the
area
the data data of
formula
area;
precipitate
wells lowest
ring
the following
or
between
of the
precipitation
volume a,
and
in the
from that of the ring area. distribution were discarded,
were standardized
data
area; y,
weight
the antigen
ring area
B agar
between
area
and
y,
by
precipi
volume
or
the
mean
ring
area. Since
variance
standardized In
the
and
experiments
obtained
from
volume,
and
standardized
influences
data
the with
antigen the data
standard were
upon variance the
weight
the of
and
deviation
a
fixed
serum
agar
standardized (S.D.)
as
of
were
anti-rabbit (ƒÔ)
calculated
tangent
then
follows
as
zero
the 3) :
line, and
plates, data
between (Fig.
regression
one, the
(y1)
of
regression
of
respectively. regression
the
line
precipitate line
and
the
294
Fig.
S. Katsura
3.
The
the
albumin
rings
Fig.
and
4.
The
the
weights
areas
(y4)
regression
lines
weights the
albumin
regression
of
the
weights
lines
(ƒÔ) of
between
(ƒÔ), and
the
precipitation
the
et al.
standardized
between
the
volumes
standardized
(y1) areas
of
the
(y2)
of
precipitates the
and
precipitation
(ƒÔ).
between
the
carbonic
standardized
anhydrase rings
and
volumes
B the
CA
(CA B
B), weights
(y3) and
of
between (ƒÔ).
the
precipitates the
standardized
and
Quantitation y1=
On
the
antigen
ring
area
and
the
standard
The
applied
ml;
in
in
other
In
(y3) data
of
the (y4)
with
the
as
0.005ƒÔ-1.546,
from
the
maximal
calculated
from volume,
precipitation the
former;
the
latter;
the and
CA from
ring
area
y3 y4
of
anti-CA
= =
of
=
albumin
was
regression
weight
15.8
B
line
weight (Fig.
0.146ƒÔ-1.754,
regression
line
S.D.
the
70 ƒÊl the and
of
9
minimal its
the
one.
standard
standardized
(ƒÔ) and
mg/
data
standardized
4):
S.D. ,
to
times
(ƒÔ) and
follows
0.104ƒÔ-1.251
the
precipitation
0.295.
mg/ml
the
CA
,
the
. 3) :
B,
the
of
plates
antigen
B
as
2
(y2)
agar
S.D.
20 ƒÊl
weight the
(Fig
295
0.092.
data
serum
follows
ranged
=
standardized
anti-rabbit
Y2 =
with
S.D.
the
antigen
precipitate of
the were
experiments were
(ƒÔ) and
deviation
words,
the
deviation
tests
in Immunodiffusion
0.006ƒÔ-1.611,
weight
the
of Antigen
= =
0.208, 0.717
.
DISCUSSION
Antigen in a well of antiserum gel plate diffuses physically into the gel. A ring precipitate is formed at a peripheral zone of the antigen diffusion at which antigen antibody ratio is optimal. When the antigen diffuses further from the well to the precipitate, the optimal proportion of antigen to antibody is broken and the precipitate disappears (Crowle 1961), and a new ring precipitate appears outside. It is considered that these procedures are repeated continuously and the precipitate grows gradually. When the antigen diffusion is completely finished, the antigen quantity in a precipitate is constant, because the antigen-antibody ratio is optimal and constant at the precipitate in the same antiserum gel plate. Therefore, antigen quantitation is considered to be unreliable while antigen is diffusing. Antigen diffusion in a gel column is related with the initial concentration of antigen as Oudin (1946, 1948) reported. However, the present studies revealed that the initial concentration and volume of antigen exert no influences upon quantitation of antigen weight as far as it is measured at the end point of antigen diffusion. Immunodiffusion of antigen from wells of various sizes and shapes in thick antiserum gel plates was studied. The shape of the precipitate varied with the shape and size of the well, and with the antigen weight. The relation between the precipitate volume and the antigen weight was compared with the relation between the precipitation ring area and the antigen weight. The results in the anti-rabbit serum agar plates and the anti-CA B agar plates showed that there was a clearer linearity in the relationship between the precipitate volume and the antigen weight than in the relation between the ring area and the antigen weight, as shown in Figs. 3 and 4. Hill (1968) reported that diffusion coefficient was extremely sensitive to the slightest variation in a thickness of an antiserum agarose plate. This suggests that the linear relationship between the precipitate volume and the antigen weight
296
is more
S. Katsura
accurate
than
that
between
the
et al.
ring
area
and
the
antigen
weight.
Acknowledgment We are grateful to Prof. T. Ichinohe, Department of Mathematics, Arts and Sciences, Iwate Medical University, for his cordial advice.
School
of Liberal
References
1) Berne, B.H. (1974) Differing methodology and equations used in quantitating im munoglobulins by radial immunodiffusion A comparative evaluation of reported and commercial techniques. Clin. Chem., 20, 61-69. 2) Crowle, A.J. (1961) Immunodiffusion. In: Dynamics of Immunodiffusion tests, Academic Press, New York & London, pp. 37-60. 3) Fahey, J.L. & McKelvey, E.M. (1965) Quantitative determination of serum im munoglobulins in antibody-agar plates. J. Immunol., 94, 84-90. 4) Hill, R.J. (1968) An evaluation of a method of quantitative radial immunodiffusion. Immunochemistry, 5, 185-202. 5) Mancini, G., Vaerman, J. -P., Carbonara, A. 0. & Heremans, J.F. (1963) A single radial-diffusion method for the immunological quantitation of proteins. Prot. biol. Fluid. Proc. Colloq., 11, 370-373. 6) Mancini, G., Carbonara, A.O. & Heremans, J.F. (1965) Immunochemical quantitation of antigens by single radial immunodiffusion. Immunochemistry, 2, 235-254. 7) Matsuo, W. (1972) Carbonic anhydrase quantity in the blood of newborns. Tohoku J. exp. Med., 107, 47-56. 8) Onodera, S. (1966) Quantitative determination of serum immunoglobulins in various diseases. Tohoku J. exp. Med., 89, 279-292. 9) Oudin, J. (1946) Methode d'analyse immunochimique par precipitation specifique en millieu gelifie. C. R. A. sci. (Paris), 222, 115-116. 10) Oudin, J. (1948) L'analyse immunochimique qualitative; methode par diffusion des antigenes au sein de l'immunserum precipitant gelose. Ann. Inst. Pasteur Lille, 75, 30-51. 11) Ryan, C.A. (1967) Quantitative determination of soluble cellular proteins by radial diffusion in agar gels containing antibodies. Analyt. Biochem., 19, 434-440. 12) Schmid, P. (1969) Quantitation of antigen in radial immunodiffusion plates. Clin. chim. Acta, 26, 181-182. 13) Tomasi, T.B. & Zigelbaum, S. (1963) The selective occurrence of y1A globulins in certain body fluids. J. clin. Invest., 42, 1552-1560.
J. exp.
Med.,
1976,
Relationship Antigen
118, 289-296
between Weight
Precipitate
in
Volume
and
Immunodiffusion
SYUSAKU KATSURA, KENJI
TAKI and
KENJI
SUZUKI
Department of Legal Medicine, School of Medicine, Iwate M edical University, Morioka
KATSURA, and
S.,
Antigen
TAKI,
Weight
K.
in
and
Suzuxi,
289-296 •\Immunodiffusion various
sizes
was
affected
the
test
of
25
mg/ml,
In
this
the
and
weight
were
this
weight
case,
as
regression
(ƒÔ) and
weight
the
(ƒÔ) and follows:
for
times line
and
data
the
on
a
and
antigen
influences
the In
the
at
in
and
of
researches.
end
point
McKelvey
Onodera
linear wide between diameter radial
antigen et
at
antigen
(1965)
some
and
antigen
of
B the
area
were
s.D.=0.717, between
between
the
the
ring
concentration antigen
CA
from
ring
area
gave
diffusion
after
applying
precipitate
concluded
was
for publication,
and
in
no
a wide
from
the
his
semi-logarithmic reported
October
m=ƒÎƒÁ2.
27,
1975. 289
h. g
was
(ƒÁ, radius
and
of
that was
the
(m)
in
established
reported
that
mass
Fahey
immunodiffusion.
concentration
scale that
and
concentration
(1974)
antigen
in
a precipi
concentration
(1963),
relation
experiments
in
by
linear
of
antigen
radial
Berne
and
(1969)
given
in
utilized
area
antigen
ring
antigen. area
to
between
that
widely
the
Zigelbaum
precipitate
noticed
that
proportional
relation
of
is
reported
Tomasi
(1967)
Schmid
immunodiffusion 1965)
directly
linear
concentration
doubtful.
immunodiffusion
Received
was
diameter
time
he
radial (1963,
a
between but
was
and Ryan
constant
relationship range,
point
the and
relationship that
antigen
end
plates and
from
.104ƒÔ-1.251,
the in
medium,
the
diffusion.
obtained
scale
(1966)
by al.
agar
of
semi-logarithmic
only
an Mancini
antibody-containing
the
gel at
agar
respectively.
volume,
precipitation
in than
the
former
immunoassay
Quantitation
tate
linearity
from
and
concentration
obtained
y4=0
from
the
one,
to
one.
,
of
In 2
and
area
test
minimal
the
and
,
for
the
precipitate
of
weight
quantitation
range.•\immunodiffusion;
various
the
(y4)
clearer antigen
weight. antigen
of
s.D.=0.208,
was
volume
the
from
calculated
ring
of
precipitate weight .
volume
maximal
(3),
minimal
were
In the
deviation
(y3)
the
s .D.=0.092
times
standard data
standardized
There
precipitate
18.3
of
ranged
precipitation
B),
118 wells
shape antigen
precipitate
latter.
(CA
and
standardized
the
of
the
B
y3=0.146ƒÔ-1.754,
respectively.
and
16.7
(y2)
The the
(s .n.)
of
Volume
1976,
cylindrical
concentration was 15 .8 times
y1=0.006x-1.611,
anhydrase
was
and
(y1)
data
s.D.=0.295
B
. by
deviation
data
obtained:
anti-carbonic CA
standard
standardized
y2=0.005ƒÔ-1.546,
of
and
well
Precipitate Med.,
and
studied
, albumin weight
albumin
line
and
the
exp.
conic
was
of plate
standardized
J.
from
plate
size agar
maximal
(ƒÔ) and
results
containing weight
and
serum
regression
antigen following
shape
the
case, weight
In
by
gel
between
Tohoku
antigen
antiserum
anti-rabbit
antigen
and
thick
Relationship .
of
in
K.
Immunodiffusion
linear
a
ring
precipitate
precipitate
a
relation
precipitate of
the in
ring;
in h,
290
S. Katsura
thickness
of
antibody-containing
concentration In
the
tion
was
present was
linearly
report,
studied
and
agar correlated
relation
plate; g,
density
with ƒÁ2
between
compared
et al.
with
precipitate that
of
agar
h,
g
because
between
volume
plate),
and ƒÎ and
precipitate
and were
antigen area
antigen constant.
concentra and
antigen
weight.
MATERIALS AND METHODS Preparation
of antisera
Goat anti-rabbit-serum serum (anti-rabbit serum). Anti-rabbit serum was obtained from a goat immunized intravenously with rabbit serum diluted 10 times and subcutaneously with mixture of the serum and Freund's complete adjuvant. Only one precipitation line appeared in immunoelectrophoresis of rabbit albumin (Miles Lab., Inc.) with the anti-rabbit serum. Precipitin titer and precipitin content of the anti-rabbit serum by the ring test were 1: 64 and 1: 16, respectively. In the ring test, exactly 1 mg/ml albumin was prepared and defined as the original concentration of albumin solution. Anti-carbonic anhydrase B serum (anti-CA B serum). Carbonic anhydrase B (CA B) and anti-CA B serum were obtained as described by Matsuo (1972). In immunoelectro phoresis with anti-CA B serum, carbonic anhydrase solution containing CA A, CA B and CA C isozymes formed one precipitation line only at the location of CA B. Precipitin titer and content of the antiserum were 1: 3,200 and 1: 32, respectively. In the ring test, the original solution of CA B contained 2 mg/ml of CA B exactly. Preparation
of antiserum agar plate with wells
Six cylindrical
metal
blocks,
TABLE 1.
3 mm in diameter
TABLE 2.
and 3 mm in height , were pasted
The well forms and sizes in the anti-albumin
at equal
serum agar
The well forms and sizes in the serum agar plates containing anti -carbonic
Quantitation distance
on
glass
tray
tray. at
a
Agar 100•Ž,
serum
solution
was
prepared
one
volume
5 of
then
Various of
of
the
agar
were
dropped
manner
to
CA
B
18
to
to
23.1 ƒÊg.
B the
70 ƒÊl
in
they
were
from
under-side the
wells
Because precipitate the
antiserum
wells.
of and
normal
anti-rabbit
glass
tray
from
glass
mm
was
depth
the
saline
of
the
3
ml
A in
volume
cover
and
small. put
the
removed
were
formed
with
in in
from 2.
solution
the
wells
of
various
volumes
as
the
the to
CA
B
1
1,
sizes
from
anti-CA
mg/ml
and
varying
the
wells
in
the
(Nos.
to
prepared B
and
1
40
of
Besides,
made
Table
were
and
1).
were in
ranged
antigen
prepared, No.
forms wells
0.06
were
(Table
shown
wells
various
In
antigen
at
4•Ž.
above
as were
wells
surface
of
vertical
follows: drawn
were
growth
2-5)
630 ƒÊg.
in
serum
a
similar
agar
plate,
volumes ranged
Parallel on
the
lines photograph
with
plate
vertically
was
showed
from
from
1.26
of
vinyl
sheet
and
was
with
stopped,
oblique
through
light
the
center
photographed.
various 1
a
rings
agar
divided
precipitate
section
with
precipitation
antiserum
were
the
wrapped of
of
precipitates
section the
in After
the
The
in
plate
wells
Table
albumin
to
volumes
vertical
calculated agar
into
out
were
100
one
The
wells
plate.
in
of
applied
applied
with
shown
just
the
mg/ml
and
agar
plate.
precipitates was
poured
cut
blocks in
with
diameter
cylindrical
Albumin
chamber
the
25
concentrations as
photographed
to
or
serum
plates
moist
was
the
Bacto-Agar
filled.
mm
plate as
mixed
was
3
were
plates
of precipitate a
g
was
concentrations
varying
agar
2.5
conic
agar
applied
Antiserum allowed
with
anti-rabbit
were
with
solutions
various
these
in
Measurement
from
serum
solutions
2
tray
the
plate
was
mixture the
wells
albumin
in into
Anti-CA
The
of
glass
291
plate.
plates
solutions
corner
the
solution
until
cylindrical
a
dissolving
agar
55•Ž.
concentrations
antiserum
of
6
and with
by
the
glass
agar
each
albumin
at
cm) covered
of
cover
antiserum
21ƒÊl 4
times
the
gelling, the
(12x3 was
and
corner
after
plate cm)
diluted
cut
in
glass
(12 •~3•~1
of Antigen in Immunodiffusion
shapes,
mm
interval
a
precipitate
plates, the applied antigen weights and the sizes of the precipitates
anhydrase B, the applied antigen weights and the sizes of the precipitates
the to
volume
the in
surface the
vertical
of of
292
S. Katsura
et al.
section. The volume of precipitate was obtained from the sum of each volume discs with 1 mm thickness of the precipitate as shown in the following formula:
where m,
r
stands
for
magnifying
radius
power
of
of
the
the
disc;
h,
height
of
the
disc=l
mm; ƒÒ,
volume
of
of the
the
well;
photograph.
RESULTS
Shape of the precipitate In
the
diameter from
the
(Fig.
1).
solution
But
and
of Two
as
mm one
precipitate, 3
the
plate.
Fig.
mm
1.
in
shape
precipitates
ones
in
the
those
from
flattened
in
the
mg/ml
albumin
wells the
from
mm view
section
concentration
conic
precipitates
3 a
vertical
25
high
with in
the
and
to
to
wells
ring
mg/ml
from
The
of
Top:
Precipitation
agar
weight
in
plate the The
from In
solution was
of
the
5
mm
with
cylindrical
wells
30
lower
parts
various
in
wells same
was
the
in
a
in
,ƒÊl of 16 mg/ml which reached the
wells
420 ƒÊg,
210 ƒÊg, in
the
from of
to
of
various
3
mm
of
315 ƒÊg,
the
vertical
section.
wells
9
mm
the
diameter
upper
surface and
and
3 mm
525 ƒÊg,
were 3
In
mm,
the
mg/ml
wells
albumin
antiserum
agar
were (Table
with
in
diameter 105 ƒÊg
.
another
well
the
of
size
each;
plate
concentration
each
5
and
diameter
70 ƒÊl
shape with
form
agar
cylindrical
well
view
cylindrical
in
wells
hemispherical
from
precipitates
21
with
the
mm
antiserum
the
hold
from
rings
with
4).
nearly
precipitate
(3
the
volumes
appeared a
on
No.
albumin
showed the
1,
wells
wells
made
albumin
of
with
cylindrical
various
which
Also
plates
were
(Table
amount
serum
Bottom:
plates,
depth,
agar
depth)
volumes
definite
and
cylindrical
owing
precipitates
were
Three in
applied
various
The
20
tray
depth.
solution
of
glass
similar
mm
serum
the
were
a
were 3
the
showed
hemispherical
21 ƒÊl
the
in
1)
tray.
10 mm
of
solution
and
The
and
No.
from of
depth
follows:
and
plate,
mm
albumin
1,
plate
flattened.
albumin
the
the
bottom
anti-rabbit
prepared
of
diameter
mg/ml
bottom
and
5
plate,
(Table
precipitates
the were
3 mm 20
of
the
agar
depth
surface
and
with and
mm
reached
diameter
serum
3
upper
antigen,
5
anti-rabbit and
3
mm
vertical and
of
No.
5).
diameter section
3
the
mm
of depth
anti-rabbit
depth. from
applied, 1,
Albumin left
to
right.
Quantitation
Fig.
2.
Top:
the
antiserum
in
each
Bottom
The
precipitation agar
of :
the
of Antigen
rings
plate
of
though
the
in Immunodiffusion
various
sizes
definite
weight
were
293
tormed of
in
albumin
the
upper
(525 ƒÊg)
surface was
of
applied
wells.
The
vertical
section
of
was hemispherical. A trapezoid with 100 mm depth (Fig. 2).
the
precipitate
shown
precipitate
in
appeared
the
top.
from
the cylindrical
well
The shape of precipitates in the anti-rabbit serum agar plate was influenced by the shape and size of the well, and by antigen weight. In the sane way, the shape of precipitates in the anti-CA B agar plates corresponded to the shape and size of the well and to the applied antigen weight. Regression lines between the precipitate volume the precipitation ring area and the antigen The precipitate
volume
in the anti-rabbit column of Tables The relation be compared
serum 1 and
and the
the
with
antigen
that
because the unit of the volume which were not suitable for precipitate volume the computer:
and
where
standardized
y
tate
stands
volume
for or
ring
precipitation
and the anti-CA 2, respectively.
between
directly
ring
differs normal
plates
and
the
the
the
weight,
from
each
are shown precipitate
weight
and
of
with
precipitate
mean
of
y;
volume
S.D.
of
ring
can not
After the
area
the data data of
formula
area;
precipitate
wells lowest
ring
the following
or
between
of the
precipitation
volume a,
and
in the
from that of the ring area. distribution were discarded,
were standardized
data
area; y,
weight
the antigen
ring area
B agar
between
area
and
y,
by
precipi
volume
or
the
mean
ring
area. Since
variance
standardized In
the
and
experiments
obtained
from
volume,
and
standardized
influences
data
the with
antigen the data
standard were
upon variance the
weight
the of
and
deviation
a
fixed
serum
agar
standardized (S.D.)
as
of
were
anti-rabbit (ƒÔ)
calculated
tangent
then
follows
as
zero
the 3) :
line, and
plates, data
between (Fig.
regression
one, the
(y1)
of
regression
of
respectively. regression
the
line
precipitate line
and
the
294
Fig.
S. Katsura
3.
The
the
albumin
rings
Fig.
and
4.
The
the
weights
areas
(y4)
regression
lines
weights the
albumin
regression
of
the
weights
lines
(ƒÔ) of
between
(ƒÔ), and
the
precipitation
the
et al.
standardized
between
the
volumes
standardized
(y1) areas
of
the
(y2)
of
precipitates the
and
precipitation
(ƒÔ).
between
the
carbonic
standardized
anhydrase rings
and
volumes
B the
CA
(CA B
B), weights
(y3) and
of
between (ƒÔ).
the
precipitates the
standardized
and
Quantitation y1=
On
the
antigen
ring
area
and
the
standard
The
applied
ml;
in
in
other
In
(y3) data
of
the (y4)
with
the
as
0.005ƒÔ-1.546,
from
the
maximal
calculated
from volume,
precipitation the
former;
the
latter;
the and
CA from
ring
area
y3 y4
of
anti-CA
= =
of
=
albumin
was
regression
weight
15.8
B
line
weight (Fig.
0.146ƒÔ-1.754,
regression
line
S.D.
the
70 ƒÊl the and
of
9
minimal its
the
one.
standard
standardized
(ƒÔ) and
mg/
data
standardized
4):
S.D. ,
to
times
(ƒÔ) and
follows
0.104ƒÔ-1.251
the
precipitation
0.295.
mg/ml
the
CA
,
the
. 3) :
B,
the
of
plates
antigen
B
as
2
(y2)
agar
S.D.
20 ƒÊl
weight the
(Fig
295
0.092.
data
serum
follows
ranged
=
standardized
anti-rabbit
Y2 =
with
S.D.
the
antigen
precipitate of
the were
experiments were
(ƒÔ) and
deviation
words,
the
deviation
tests
in Immunodiffusion
0.006ƒÔ-1.611,
weight
the
of Antigen
= =
0.208, 0.717
.
DISCUSSION
Antigen in a well of antiserum gel plate diffuses physically into the gel. A ring precipitate is formed at a peripheral zone of the antigen diffusion at which antigen antibody ratio is optimal. When the antigen diffuses further from the well to the precipitate, the optimal proportion of antigen to antibody is broken and the precipitate disappears (Crowle 1961), and a new ring precipitate appears outside. It is considered that these procedures are repeated continuously and the precipitate grows gradually. When the antigen diffusion is completely finished, the antigen quantity in a precipitate is constant, because the antigen-antibody ratio is optimal and constant at the precipitate in the same antiserum gel plate. Therefore, antigen quantitation is considered to be unreliable while antigen is diffusing. Antigen diffusion in a gel column is related with the initial concentration of antigen as Oudin (1946, 1948) reported. However, the present studies revealed that the initial concentration and volume of antigen exert no influences upon quantitation of antigen weight as far as it is measured at the end point of antigen diffusion. Immunodiffusion of antigen from wells of various sizes and shapes in thick antiserum gel plates was studied. The shape of the precipitate varied with the shape and size of the well, and with the antigen weight. The relation between the precipitate volume and the antigen weight was compared with the relation between the precipitation ring area and the antigen weight. The results in the anti-rabbit serum agar plates and the anti-CA B agar plates showed that there was a clearer linearity in the relationship between the precipitate volume and the antigen weight than in the relation between the ring area and the antigen weight, as shown in Figs. 3 and 4. Hill (1968) reported that diffusion coefficient was extremely sensitive to the slightest variation in a thickness of an antiserum agarose plate. This suggests that the linear relationship between the precipitate volume and the antigen weight
296
is more
S. Katsura
accurate
than
that
between
the
et al.
ring
area
and
the
antigen
weight.
Acknowledgment We are grateful to Prof. T. Ichinohe, Department of Mathematics, Arts and Sciences, Iwate Medical University, for his cordial advice.
School
of Liberal
References
1) Berne, B.H. (1974) Differing methodology and equations used in quantitating im munoglobulins by radial immunodiffusion A comparative evaluation of reported and commercial techniques. Clin. Chem., 20, 61-69. 2) Crowle, A.J. (1961) Immunodiffusion. In: Dynamics of Immunodiffusion tests, Academic Press, New York & London, pp. 37-60. 3) Fahey, J.L. & McKelvey, E.M. (1965) Quantitative determination of serum im munoglobulins in antibody-agar plates. J. Immunol., 94, 84-90. 4) Hill, R.J. (1968) An evaluation of a method of quantitative radial immunodiffusion. Immunochemistry, 5, 185-202. 5) Mancini, G., Vaerman, J. -P., Carbonara, A. 0. & Heremans, J.F. (1963) A single radial-diffusion method for the immunological quantitation of proteins. Prot. biol. Fluid. Proc. Colloq., 11, 370-373. 6) Mancini, G., Carbonara, A.O. & Heremans, J.F. (1965) Immunochemical quantitation of antigens by single radial immunodiffusion. Immunochemistry, 2, 235-254. 7) Matsuo, W. (1972) Carbonic anhydrase quantity in the blood of newborns. Tohoku J. exp. Med., 107, 47-56. 8) Onodera, S. (1966) Quantitative determination of serum immunoglobulins in various diseases. Tohoku J. exp. Med., 89, 279-292. 9) Oudin, J. (1946) Methode d'analyse immunochimique par precipitation specifique en millieu gelifie. C. R. A. sci. (Paris), 222, 115-116. 10) Oudin, J. (1948) L'analyse immunochimique qualitative; methode par diffusion des antigenes au sein de l'immunserum precipitant gelose. Ann. Inst. Pasteur Lille, 75, 30-51. 11) Ryan, C.A. (1967) Quantitative determination of soluble cellular proteins by radial diffusion in agar gels containing antibodies. Analyt. Biochem., 19, 434-440. 12) Schmid, P. (1969) Quantitation of antigen in radial immunodiffusion plates. Clin. chim. Acta, 26, 181-182. 13) Tomasi, T.B. & Zigelbaum, S. (1963) The selective occurrence of y1A globulins in certain body fluids. J. clin. Invest., 42, 1552-1560.
