Cytotechnology 6: 189-195, 1991. 9 1991 Kluwer Academic Publishers. Printed in the Netherlands.
An analysis of some batch and continuous kinetic data of specific monoclonal antibody production from hybridomas P.J. Phillips 1, C.P.Marquis 1, J.P. Barford 1 and C. Harbour 2 1Department of Chemical Engineering and 2Department o f Infectious Diseases, University of Sydney, N S W 2006, Australia
Received28 September 1990; accepted in revised form 13 May 1991
Abstract
An analysis of batch and continuous kinetic data obtained from hybridoma cell cultures has been performed with particular reference to the existence of specific antibody production profiles. The results presented by several groups, including our own, have been studied. Our analysis suggests that different interpretations of the data can be made to those previously presented in the literature. In view of the significance of these profiles, particularly in terms of production strategies designed to maximise antibody production, we believe that more consideration needs to be given to accuracy in reporting of kinetic studies in the future.
Introduction
The large quantity of research in the field of hybridoma cell growth and monoclonal antibody (MAb) production over the past fifteen years has provided a deal of batch experimental kinetic data (e.g. Fazekas de St.Groth, 1983; Miller et al., 1985; Reuveny et al., 1986; Emery et al., 1987; Merten, 1988; Dalili et al., 1990). From this data, there has been a trend to categorise specific antibody production (QAb) profiles and point to the existence of different profiles f o r different cell lines, since the determination of a consistent, general QAb profile would contribute greatly to our understanding of hybridoma cell metabolism, and may have considerable commercial significance. The variation of QAb profiles has been proposed to be as a result of major nutrient limitation (Dalili et al. 1990), inoculum size (Ozturk and Palsson, 1990) inherent differences in cell lines
(Merten, 1988) and recently, differences in the rate of degradation of MAb (A1-Rubeai and Emery, 1990). It is not the purpose of this correspondence to investigate the causes of the different profiles, but to demonstrate that statistically the differences between such profiles may not be valid and that much of the analysis of kinetic data from hybridoma cell growth rarely accounts for statistical error in measurement and may often have only a limited number of data points from which profiles are drawn. As an appendage to this work, an analysis of continuous kinetic studies is undertaken. Although the amount of available continuous culture kinetic data for hybridoma cell growth and MAb production is limited, a diverse range of Qab versus dilution rate profiles have been obtained to date (Harbour et al., 1989; Low et al., 1987; Miller et al., 1988; Ray et al., 1989). An analysis of four sets of continuous data has been
190 undertaken to investigate the possibility that the differences in QAb profiles are as the result of a lack of consideration of errors and their interpretation. In the collated batch and continuous experimental data we hope to illustrate that a careful consideration of potential errors should be undertaken before generalised categories are presented and that two important considerations, the limited number of data points and the lack of accountability of measurement error, can greatly affect the QAb profiles obtained.
20
Profde 1
P
g
0
0
10
20
30
112
r
-i
40
50
time (hr)
Fig. 1. First three data points from Fig. 1A of Merten (1988)
showing potentialvariabilityof Antlbodyprofiles.
Batch analysis An analysis of the batch data from four groups was undertaken. It could be said that more work should have been analysed but it is felt that the points at issue could be fully justified without further analysis. The data analysed included one work which had as its basis the compartmentation of QAb profiles into separate categories (Merten, 1988). It was this work inparticular that required some comment. Most noticeable in the data presented by Merten (1988) is the limited number of experimental data points. In the case of Fig. 1A and B only 4 and 5 experimental points can be found respectively, and by Merten's method of analysis this results in only 3 and 4 points for growth rate and specific antibody production rate. As a means of illustration of the effect of limited numbers of data points, we have constructed two plausible antibody profiles from the same initial points from Fig. 1A of merten (see Fig. 1). When the specific antibody production profiles are calculated from these (using the corresponding viable cell data), two very different profiles are obtained (Fig. 2). This illustrates very clearly the importance of obtaining as many experimental points as possible in the early stages of a batch run (i.e. in the 'lag' and 'log' phases of growth). Although all experiments were carried out in duplicate no mention is made of the potential variance of the data nor of the reproducibility of the results. We have found from our work that
4
x:
1
0
10
20
30
40
50
t i m e (hr)
Fig. 2. Data taken from Fig. 1. Comparison of the effect of
limitednumbers of initialpoints on QAb profiles. there are many sources of potential error in analysis (Marquis et al., unpublished results) most notably in obtaining consistent ELISA assays of antibody levels in the supematants. One estimate of the error in antibody determination is as high as 30% (McQueen and Bailey, 1990). To test whether this could be important in the production profiles, a conservative estimate of error was applied to both viable cells (+__5%) and antibody concentration (+ 10%). To calculate the resultant standard errors in growth rate (Ix) and specific antibody production rate (QAb) the following equations were used (Science Foundation Course Team, 1977): given tx
= Aln X / At
191 then
6
Error (IX)
= Error (Aln X)/At
Error (Ix)
- 0.05/At
5
or
(1) "2"
E
where Aln X and
= InX 1 -
At
=tl-t o
4 3
0
lnX o
t3~
E
~3 1 o
also, given
-1
QAb then Error (Qnb) where U V W
i
i
o
= X. 5 A b / f X
50
100
150
time(hr)
= QAb.x/U2+V2+W 2
(2)
Fig. 4, Alternative profiles of QAB from Merten (Fig. 2A and
Fig. 2B).
= Error (AAb)/AAb = Error (ZL~)/AX = Error (~t)/~t
4 3
and Error (AAb) = x/Error (Ab0) 2 + Error (Abl) 2 Error (ZL,Y) = x/Error (X0)2 + Error (X1) 2 Once these standard errors are placed on the data points for QAb, the potential for different profiles from those proposed by Merten becomes clearer. In Fig. 3 and 4 are presented the same data as M e r t e n ' s but with profiles encompassing the error estimated. The types 1 and 2 kinetics are
2
3 0
-1
~
i
50
100
1
150
time(hr)
Fig. 5. Plausible alternative QAB profile from experimental
3~
points of Merten (Fig. 3). T
~
I
Q-
o
0 l
0
50
100
lime(hr.)
Fig. 3. Profiles of QAB with calculated errors, taken from
Merten (Fig. 1A and Fig. 1B).
now no longer distinguishable. The type 3 kinetics (Fig. 5) may be considered tO have a different profile but this has been shown to be due to nutrient limitation (Dalili et al., 1990). The assertion that three distinct profiles exist can then be seriously questioned. F r o m this example we have attempted to illustrate why batch data (particularly after specific production rates are calculated) should be treated with some caution. Estimated errors based on duplicate (or triplicate) samples should be calculated and included as a matter o f course, and as many experimental points as possible should be
192 obtained (particularly in the 'lag/log' phases of growth). A more realistic interpretation of the resultant specific antibody production profiles may then be attempted. We analysed the batch data of two different cell lines from our own laboratory (Low et al., 1987; Marquis et al., unpublished results) with regard to specific growth rate and specific antibody production rate. The QAb data (with estimated errors) is shown in Fig. 6 and 7. Note that the possible specific antibody profiles from these experiments range from a straight line to a complex interpolation based on a polynomial. From this we may propose a likely general profile (Fig. 7), but is there enough evidence to support this? We think not. In the original paper (Low et al., 1987) no major comment is made concerning the QAb profile except to say that "these specific rates are not constant" and although there is a similarity between the kinetics of the two cell lines, to infer the same QA~ profiles would require more evidence.
Some typical batch growth curves are shown from Miller et al. (1988). The specific growth and production rates are also illustrated (Fig. 8). The curve for specific antibody production Shows a decrease that could probably be represented by a straight line but the authors make little comment except to say that it "declined somewhat before reaching a constant value of 22 x 106 g/cell/day". Given the potential error in calculation of QAb there is little more that can be inferred. Some of the batch hybridoma growth curves from Dalili et al. (1990) are shown (Fig. 9). These curves have a sudden cessation of antibody production upon glutamine depletion which resuits in zero specific antibody production rates after this time. This is similar to the type 3 kinetics of Merten (1988). The authors comment upon the "nearly step-function behavior" of the specific rates and provide a simulation which accommodates this. 5O e~
0.4
J::
40
,g o
o
0.2
30
20"
:i ~
0.0'
10-
..Q 0 -0.2
0
i
0
2Q
40
60
80
0 0
100
1
2
4
Fig. 6. QAB profile of Marquis et al. (unpublished data) with
O.OG
0.4
T
"C .t= o
0.2
%
6
Fig. 8. QAB profile from Miller et al. (1988) with error estimate.
error estimate. A simple straight line is probably adequate for this data.
-s
5
lime ( d a y s )
time (hr)
,T
0.04 "
l tq
o
E o.o
0.02
=t
0.00 " 0 0
-0.2
5'0
100
150
time (hr)
,0.02 20
Fig. 7. QAB profile of Low et al. (1987) with error estimate. A
simple straight line is just as adequate as the more complicated profile.
40
60
80
100
120
time (hr)
Fig. 9. QAB profile from Dalili et al. (1990) with error estimate.
193
250.
'~ 100
r'10
s
O
200
A
From Ray et al. (1989)
o
From Miller et al. (1988)
9
From Harbour et aL (1988)
-r" r
n-
150
0 --I
"~
50
0
"---- 1 0 0 E
E
C~
An analysis of some batch and continuous kinetic data of specific monoclonal antibody production from hybridomas P.J. Phillips 1, C.P.Marquis 1, J.P. Barford 1 and C. Harbour 2 1Department of Chemical Engineering and 2Department o f Infectious Diseases, University of Sydney, N S W 2006, Australia
Received28 September 1990; accepted in revised form 13 May 1991
Abstract
An analysis of batch and continuous kinetic data obtained from hybridoma cell cultures has been performed with particular reference to the existence of specific antibody production profiles. The results presented by several groups, including our own, have been studied. Our analysis suggests that different interpretations of the data can be made to those previously presented in the literature. In view of the significance of these profiles, particularly in terms of production strategies designed to maximise antibody production, we believe that more consideration needs to be given to accuracy in reporting of kinetic studies in the future.
Introduction
The large quantity of research in the field of hybridoma cell growth and monoclonal antibody (MAb) production over the past fifteen years has provided a deal of batch experimental kinetic data (e.g. Fazekas de St.Groth, 1983; Miller et al., 1985; Reuveny et al., 1986; Emery et al., 1987; Merten, 1988; Dalili et al., 1990). From this data, there has been a trend to categorise specific antibody production (QAb) profiles and point to the existence of different profiles f o r different cell lines, since the determination of a consistent, general QAb profile would contribute greatly to our understanding of hybridoma cell metabolism, and may have considerable commercial significance. The variation of QAb profiles has been proposed to be as a result of major nutrient limitation (Dalili et al. 1990), inoculum size (Ozturk and Palsson, 1990) inherent differences in cell lines
(Merten, 1988) and recently, differences in the rate of degradation of MAb (A1-Rubeai and Emery, 1990). It is not the purpose of this correspondence to investigate the causes of the different profiles, but to demonstrate that statistically the differences between such profiles may not be valid and that much of the analysis of kinetic data from hybridoma cell growth rarely accounts for statistical error in measurement and may often have only a limited number of data points from which profiles are drawn. As an appendage to this work, an analysis of continuous kinetic studies is undertaken. Although the amount of available continuous culture kinetic data for hybridoma cell growth and MAb production is limited, a diverse range of Qab versus dilution rate profiles have been obtained to date (Harbour et al., 1989; Low et al., 1987; Miller et al., 1988; Ray et al., 1989). An analysis of four sets of continuous data has been
190 undertaken to investigate the possibility that the differences in QAb profiles are as the result of a lack of consideration of errors and their interpretation. In the collated batch and continuous experimental data we hope to illustrate that a careful consideration of potential errors should be undertaken before generalised categories are presented and that two important considerations, the limited number of data points and the lack of accountability of measurement error, can greatly affect the QAb profiles obtained.
20
Profde 1
P
g
0
0
10
20
30
112
r
-i
40
50
time (hr)
Fig. 1. First three data points from Fig. 1A of Merten (1988)
showing potentialvariabilityof Antlbodyprofiles.
Batch analysis An analysis of the batch data from four groups was undertaken. It could be said that more work should have been analysed but it is felt that the points at issue could be fully justified without further analysis. The data analysed included one work which had as its basis the compartmentation of QAb profiles into separate categories (Merten, 1988). It was this work inparticular that required some comment. Most noticeable in the data presented by Merten (1988) is the limited number of experimental data points. In the case of Fig. 1A and B only 4 and 5 experimental points can be found respectively, and by Merten's method of analysis this results in only 3 and 4 points for growth rate and specific antibody production rate. As a means of illustration of the effect of limited numbers of data points, we have constructed two plausible antibody profiles from the same initial points from Fig. 1A of merten (see Fig. 1). When the specific antibody production profiles are calculated from these (using the corresponding viable cell data), two very different profiles are obtained (Fig. 2). This illustrates very clearly the importance of obtaining as many experimental points as possible in the early stages of a batch run (i.e. in the 'lag' and 'log' phases of growth). Although all experiments were carried out in duplicate no mention is made of the potential variance of the data nor of the reproducibility of the results. We have found from our work that
4
x:
1
0
10
20
30
40
50
t i m e (hr)
Fig. 2. Data taken from Fig. 1. Comparison of the effect of
limitednumbers of initialpoints on QAb profiles. there are many sources of potential error in analysis (Marquis et al., unpublished results) most notably in obtaining consistent ELISA assays of antibody levels in the supematants. One estimate of the error in antibody determination is as high as 30% (McQueen and Bailey, 1990). To test whether this could be important in the production profiles, a conservative estimate of error was applied to both viable cells (+__5%) and antibody concentration (+ 10%). To calculate the resultant standard errors in growth rate (Ix) and specific antibody production rate (QAb) the following equations were used (Science Foundation Course Team, 1977): given tx
= Aln X / At
191 then
6
Error (IX)
= Error (Aln X)/At
Error (Ix)
- 0.05/At
5
or
(1) "2"
E
where Aln X and
= InX 1 -
At
=tl-t o
4 3
0
lnX o
t3~
E
~3 1 o
also, given
-1
QAb then Error (Qnb) where U V W
i
i
o
= X. 5 A b / f X
50
100
150
time(hr)
= QAb.x/U2+V2+W 2
(2)
Fig. 4, Alternative profiles of QAB from Merten (Fig. 2A and
Fig. 2B).
= Error (AAb)/AAb = Error (ZL~)/AX = Error (~t)/~t
4 3
and Error (AAb) = x/Error (Ab0) 2 + Error (Abl) 2 Error (ZL,Y) = x/Error (X0)2 + Error (X1) 2 Once these standard errors are placed on the data points for QAb, the potential for different profiles from those proposed by Merten becomes clearer. In Fig. 3 and 4 are presented the same data as M e r t e n ' s but with profiles encompassing the error estimated. The types 1 and 2 kinetics are
2
3 0
-1
~
i
50
100
1
150
time(hr)
Fig. 5. Plausible alternative QAB profile from experimental
3~
points of Merten (Fig. 3). T
~
I
Q-
o
0 l
0
50
100
lime(hr.)
Fig. 3. Profiles of QAB with calculated errors, taken from
Merten (Fig. 1A and Fig. 1B).
now no longer distinguishable. The type 3 kinetics (Fig. 5) may be considered tO have a different profile but this has been shown to be due to nutrient limitation (Dalili et al., 1990). The assertion that three distinct profiles exist can then be seriously questioned. F r o m this example we have attempted to illustrate why batch data (particularly after specific production rates are calculated) should be treated with some caution. Estimated errors based on duplicate (or triplicate) samples should be calculated and included as a matter o f course, and as many experimental points as possible should be
192 obtained (particularly in the 'lag/log' phases of growth). A more realistic interpretation of the resultant specific antibody production profiles may then be attempted. We analysed the batch data of two different cell lines from our own laboratory (Low et al., 1987; Marquis et al., unpublished results) with regard to specific growth rate and specific antibody production rate. The QAb data (with estimated errors) is shown in Fig. 6 and 7. Note that the possible specific antibody profiles from these experiments range from a straight line to a complex interpolation based on a polynomial. From this we may propose a likely general profile (Fig. 7), but is there enough evidence to support this? We think not. In the original paper (Low et al., 1987) no major comment is made concerning the QAb profile except to say that "these specific rates are not constant" and although there is a similarity between the kinetics of the two cell lines, to infer the same QA~ profiles would require more evidence.
Some typical batch growth curves are shown from Miller et al. (1988). The specific growth and production rates are also illustrated (Fig. 8). The curve for specific antibody production Shows a decrease that could probably be represented by a straight line but the authors make little comment except to say that it "declined somewhat before reaching a constant value of 22 x 106 g/cell/day". Given the potential error in calculation of QAb there is little more that can be inferred. Some of the batch hybridoma growth curves from Dalili et al. (1990) are shown (Fig. 9). These curves have a sudden cessation of antibody production upon glutamine depletion which resuits in zero specific antibody production rates after this time. This is similar to the type 3 kinetics of Merten (1988). The authors comment upon the "nearly step-function behavior" of the specific rates and provide a simulation which accommodates this. 5O e~
0.4
J::
40
,g o
o
0.2
30
20"
:i ~
0.0'
10-
..Q 0 -0.2
0
i
0
2Q
40
60
80
0 0
100
1
2
4
Fig. 6. QAB profile of Marquis et al. (unpublished data) with
O.OG
0.4
T
"C .t= o
0.2
%
6
Fig. 8. QAB profile from Miller et al. (1988) with error estimate.
error estimate. A simple straight line is probably adequate for this data.
-s
5
lime ( d a y s )
time (hr)
,T
0.04 "
l tq
o
E o.o
0.02
=t
0.00 " 0 0
-0.2
5'0
100
150
time (hr)
,0.02 20
Fig. 7. QAB profile of Low et al. (1987) with error estimate. A
simple straight line is just as adequate as the more complicated profile.
40
60
80
100
120
time (hr)
Fig. 9. QAB profile from Dalili et al. (1990) with error estimate.
193
250.
'~ 100
r'10
s
O
200
A
From Ray et al. (1989)
o
From Miller et al. (1988)
9
From Harbour et aL (1988)
-r" r
n-
150
0 --I
"~
50
0
"---- 1 0 0 E
E
C~
