CELLULAR
IMMUNOLOGY
l&324-331
(1992)
Behavior of the ldiotypic Network in Conventional Immune Responses II. Affinity and Heterogeneity of ldiotypic and Anti-idiotypic Antibodies Following Immunization with T-Independent and T-Dependent Antigens MARIANGELASEGRE,‘RONALDM.
WEIGEL,ANNETTE
J. SCHLUETER,
ANDDIEGOSEGRE Department of Veterinary Pathobiology, University of Illinois, 2001 South Lincoln Avenue, Urbana, Illinois 61801 Received April 13, 1992; accepted July 6, 1992
The relative affinity and heterogeneity of affinity of idiotypic and anti-idiotypic antibodies in mice immunized with the T-independent antigen DNP-Ficoll and the T-dependent antigen DNPHGG were measured by a plaque inhibition assay. Idiotypic plaque-forming cells (PFC) were detected by a conventional assayutilizing DNP-coated SRBC. Anti-idiotypic PFC were detected with SRBC coated with affinity-purified anti-DNP antibody of rabbit origin. It was found that both idiotypic and anti-idiotypic antibodies elicited by immunization with the T-independent antigen had lower alhnity and were lessheterogeneousthan the correspondingantibodies originating in mice immunized with the T-dependent antigen, In addition, the affinity and heterogeneity values of the idiotypic antibodies were correlated with the affinity and heterogeneity values of the anti-idiotypic antibodies from the same mice. This finding indicates that idiotypic and anti-idiotypic antibodies mutually regulate each other, thus pointing to internal immunoregulatory effects of the idiotypic network with respect to these parameters. o 1992 Academic PUSS, h.
INTRODUCTION In the companion paper (1) we have describeda technique which allows the detection and enumeration of anti-idiotypic plaque-forming cells (PFC)2 in mice immunized with the T-independent antigen DNP-Ficoll and with the T-dependent antigen DNPhuman y-globulin (HGG). This methodology appears particularly suitable for investigations of the immunoregulatory functions that have been attributed to the idiotypic network in its original formulation (2), but whose existence has not been unequivocally confirmed experimentally (3). In the companion paper (1) we have reported that mice which received a secondary immunization at a time when anti-idiotypic PFC were still detectable had a depressed secondary idiotypic (Abl) response, suggesting that ’ To whom correspondence and reprint requests should be addressed. * Abbreviations used: Abl , idiotypic antibody; Ab2, anti-idiotypic antibody; Ab2& anti-idiotypic antibody with idiotope that is bound by the idiotypic antibody’s paratope (aka the internal image of the antigen); DNP, dinitrophenyl hapten; Is,,, free hapten concentration that inhibits 50% of the hemolytic plaques; PFC, plaque-forming cell(s). 324 0008-8749192$5.00 Copyright 0 1992 by Academic Press, Inc. All fights of reproduction in WY form reszved.
IMMUNOREGULATION
VIA THE IDIOTYPIC NETWORK, II
325
the secondary Abl response was downregulated by anti-idiotypic (Ab2) antibody. In this report, we address the issue of affinity and heterogeneity of the Abl and Ab2 responsesof mice to immunization with a T-independent and a T-dependent antigen. We found a correlation between Abl and Ab2 with regard to these parameters, suggesting that the two complementary antibodies mutually regulate one another. MATERIALS AND METHODS Mice. Two to three-month-old female BALB/c mice were purchased from HarlanSprague-Dawley (Indianapolis, IN). Immunizations. Mice were immunized with 100 pg of DNPbO-Ficoll (Biosearch, San Rafael, CA) ip. Some of the mice were rested for 3 weeks, after which the immunization was repeated. Spleen cells for the hemolytic plaque assay and for the plaque inhibition assaywere obtained 5 days after primary or secondary immunization, at the time of peak Ab 1 and Ab2 responses( 1). Mice receiving primary immunizations with DNP,,-HGG were injected ip with 100 pg of the antigen adsorbed on bentonite (4). Secondary immunizations were given in a similar manner 3 weeks after primary immunization. Spleen cells were assayed 13 days after primary immunization, at the time of maximal Ab2 response but several days after peak Abl response, or 5 days after secondary immunization, when both the Abl and Ab2 responsespeaked (1). Hemolytic plaque assay and plaque inhibition assay. The hemolytic plaque assay for the detection of Ab 1 PFC was performed utilizing SRBC coated with DNP-derivatized F(ab’)2 from rabbit anti-SRBC antibody, as previously described (5-7). For the detection of Ab2 PFC the indicator SRBC were coated with affinity-purified F(ab’h fragments of rabbit anti-DNP antibodies to which dipalmitoyl phosphatidylethanolamine was covalently attached as described in the companion paper (1). For the plaque inhibition assayidentical aliquots of spleen cells were plated in duplicate in agar containing various concentrations of the hapten DNP-lysine or no hapten (5). The percentage of plaque inhibition was calculated for each hapten concentration. Statistical methods. When the affinities of the PFC are normally distributed, a plot of the percentage of plaque inhibition versus inhibitor concentration would result in a sigmoid curve. By logit transformation of the percentage of inhibition values, the sigmoid curve is converted into a straight line. We determined the least-squareslinear regressionequation for the relationship between inhibitor concentration and both Ab 1 and Ab2 plaque inhibition for each mouse. We took into consideration only the data points spanning the interval between 100% inhibition (all inhibitor concentrations greater than that resulting in 100% inhibition would also result in 100% inhibition) and 0% inhibition (all lower inhibitor concentrations would also result in 0% inhibition), and calculated the line of best fit for these data points. The outcome analyzed was the logit transformation of the percentage of inhibition values (= 0.5 ln[p/l - p], where p = percentage of inhibition) with the logarithm (to base 10) of inhibitor molar concentration as the predictor variable. For each set of data, the regression line intercept provided the value of the inhibitor concentration at the 50% inhibition point (Iso), a measure of PFC affinity, and the regression line slope provided an estimate of heterogeneity of affinity. Classically, the affinity of anti-hapten antibodies has been expressed as the average association constant (Z&J,and the heterogeneity of affinity by a heterogeneity index (a or a) based on the assumption that affinities of antibody molecules follow a Gaussian (8) or Sipsian (9) distribution. It has been shown that the distribution
326
SEGRE ET AL.
of antibody affinities is often skewed, and that the K, and LYvalues do not faithfully representthe binding data ( 10). Alternative methods of calculating the binding constant and heterogeneity index have been proposed (lo), but have not gained wide acceptance. When these parameters are estimated from plaque inhibition data, the 50% inhibition points have been shown to be correlated with K, values and have been usedto indicate the relative affinity of PFC (5). The distribution of affinities has been generally described by a histogram (1 l), but has not been given a numerical value, although a heterogeneity index based on information theory has been used by some authors (12). In the current study, heterogeneity of affinity is estimated from the slope of line from the regression of (logit transform of) the percentage of inhibition on (log,,) inhibitor concentration. A gradual slope indicates little change in inhibition across concentrations, and thus heterogeneity of affinity, whereas a steep slope indicates substantial change across concentrations, and thus high homogeneity of affinities. Although the statistical model requires normality of residuals for proper statistical inference, this is not required for parameter estimation (I 3). Likewise estimation of heterogeneity does not require an underlying normal distribution of affinities. The effectof T-dependent vs T-independent antigen and of primary vs secondary response on affinity and heterogeneity was ascertained for both the Abl and Ab2 responsesusing a two-way analysis of variance. RESULTS An example of the Abl and Ab2 plots for a mouse undergoing a primary response to DNP-Ficoll is shown in Fig. 1. The numbers of mice employed for the plaque inhibition experiments and their mean Ab 1 and Ab2 PFC responsesare reported in Table 1. The secondary Ab 1 response to DNP-Ficoll was significantly (P < 0.001) lower than the corresponding primary response,confirming our previous observation (1). No similar statement can be made for the Abl response to DNP-HGG, since the mice were not assayedat the time of peak primary response. In examining the data of the hapten inhibition experiments, we found that at times there were more PFC in the assayplates containing low inhibitor concentrations than were found in plates with no inhibitor. This phenomenon is known as hapten augmentation, and it has been shown to result from the displacement by hapten of antiidiotypic antibody that was bound to idiotypic antibody on the surface of the antibodyproducing cell, thus blocking antibody secretion and preventing plaque formation (14, 15). We encountered this phenomenon not only in inhibition assaysof Ab 1 PFC, but also in inhibition assaysof Ab2 PFC. In the latter case,evidently it was the idiotypic antibody that was blocking the release of anti-idiotypic antibody by potential Ab2 PFC. Whenever hapten augmentation occurred, the number of PFC in the haptenaugmented plates, rather than the number of PFC in the plates containing no inhibitor, was taken as 0% inhibition, and the percentage of inhibition for each inhibitor concentration was calculated accordingly. Hapten augmentation was seen sporadically, but was especially prevalent in inhibition assayswith spleen cells from mice undergoing a secondary response to DNP-Ficoll (Table 2). Results of statistical comparisons of ZsO(affinity) and slope (heterogeneity) values derived from plaque inhibition assayson various groups of mice are summarized in Table 3. The mean Z50value of Abl PFC for the T-dependent antigen DNP-HGG was significantly lower (P < 0.00 1) than the corresponding value for the T-independent
IMMUNOREGULATION
327
VIA THE IDIOTYPIC NETWORK, II
I
i
-1.2
4
-1.41
I
,
I
-k
-5
(
-3
LOG INHIBITOR MOLARITY 3 ,
-1.5
i
I
I
-2 I -10
-9
-6
-5
LOG INHIBtOR MOL-;RITY FIG. 1. Plots of lo&-transformed percentage of inhibition vs inhibitor concentration for PFC obtained from mouse No. 104 5 days after immunization with DNP-Ficoll. Top, Abl PFC: 1,, = 10-4.‘4,slope = 1.22. Bottom, Ab2 PFC: I,, = 10-8.47,slope = 0.80.
antigen DNP-Ficoll, indicating greater affinity for the former antibodies than for the latter. Similarly, the mean slope value of Abl PFC for DNP-HGG was significantly lower (P < 0.01) than that for DNP-Ficoll, indicating greater heterogeneity for the
TABLE 1 Abl and Ab2 PFC Responsesfollowing Immunization with DNP-Ficoll and DNP-HGG Mean PFC/spleen + SE Immunogen DNP-Ficoll DNP-HGG
Type of response
Day of assay
Primary Secondary Primary Secondary
5
No. of mice
13
3 6 3
5
7
5
Abl 83,215 15,706 9,142 211,625
f 2,025 t 1,300 + 1,003 ?I 49,694
Ab2 267,661 k 42,141 141,075 f 40,530 1,633 iz224 12,925 + 2,33 1
328
SEGRE ET AL. TABLE 2 Hapten Augmentation in Abl and Ab2 Plaque-Inhibition Assays with Spleen Cells of Mice Undergoing a Secondary Responseto DNP-Ficoll Maximal No. PFC with inhibitor: No. PFC without inhibitor Mouse no.
Abl
Ab2
94 95 96 111 113 114
1.37 1.32 2.17 0.88 1.26 1.46
2.37 6.32 1.24 1.06 1.16 3.26
former than for the latter antibodies. In the Ab2 plaque inhibition assays,the mean Z,, value was higher for the T-dependent than for the T-independent antigen (P < 0.0 1). In contrast to the Ab 1 plaque inhibition assay,in this case,becauseof the nature of the assay, higher Z,, values correspond to high-affinity antibodies and vice versa. Thus, as was the case for the Abl response, the Ab2 response to DNP-HGG also resulted in higher affinity PFC than did the Ab2 response to DNP-Ficoll. There was also a greater mean slope value for the Ab2 response to DNP-Ficoll than for the corresponding response to DNP-HGG, indicating greater heterogeneity for the latter than for the former antibodies (P < 0.01). Finally, the mean Is,, value for the secondary Abl responseto DNP-HGG was lower than the corresponding value for the primary response, indicating, as expected, an increase in affinity from the primary to the sec-
TABLE 3 Plaque Inhibition Analysis: Comparison of Z,, and Slope Values Treatment grow
No. of mice
Abl, Tdb Abl, Ti Ab2, Td Ab2, Ti Abl 3 1”’ >Td Abl, 2”, Td Ab2, l”, Td Ab2,2”, Td Abl, l”, Ti Abl, 2”, Ti Ab2, I”, Ti Ab2, 2”, Ti
10 9 10 9 3 7 3 7 3 6 3 6
Mean Zs0” -6.201 -4.39 -5.803 -8.194 -5.820 -6.583 -5.827 -5.780 -4.467 -4.317 -8.720 -7.668
P value
Mean slope
P value
IMMUNOLOGY
l&324-331
(1992)
Behavior of the ldiotypic Network in Conventional Immune Responses II. Affinity and Heterogeneity of ldiotypic and Anti-idiotypic Antibodies Following Immunization with T-Independent and T-Dependent Antigens MARIANGELASEGRE,‘RONALDM.
WEIGEL,ANNETTE
J. SCHLUETER,
ANDDIEGOSEGRE Department of Veterinary Pathobiology, University of Illinois, 2001 South Lincoln Avenue, Urbana, Illinois 61801 Received April 13, 1992; accepted July 6, 1992
The relative affinity and heterogeneity of affinity of idiotypic and anti-idiotypic antibodies in mice immunized with the T-independent antigen DNP-Ficoll and the T-dependent antigen DNPHGG were measured by a plaque inhibition assay. Idiotypic plaque-forming cells (PFC) were detected by a conventional assayutilizing DNP-coated SRBC. Anti-idiotypic PFC were detected with SRBC coated with affinity-purified anti-DNP antibody of rabbit origin. It was found that both idiotypic and anti-idiotypic antibodies elicited by immunization with the T-independent antigen had lower alhnity and were lessheterogeneousthan the correspondingantibodies originating in mice immunized with the T-dependent antigen, In addition, the affinity and heterogeneity values of the idiotypic antibodies were correlated with the affinity and heterogeneity values of the anti-idiotypic antibodies from the same mice. This finding indicates that idiotypic and anti-idiotypic antibodies mutually regulate each other, thus pointing to internal immunoregulatory effects of the idiotypic network with respect to these parameters. o 1992 Academic PUSS, h.
INTRODUCTION In the companion paper (1) we have describeda technique which allows the detection and enumeration of anti-idiotypic plaque-forming cells (PFC)2 in mice immunized with the T-independent antigen DNP-Ficoll and with the T-dependent antigen DNPhuman y-globulin (HGG). This methodology appears particularly suitable for investigations of the immunoregulatory functions that have been attributed to the idiotypic network in its original formulation (2), but whose existence has not been unequivocally confirmed experimentally (3). In the companion paper (1) we have reported that mice which received a secondary immunization at a time when anti-idiotypic PFC were still detectable had a depressed secondary idiotypic (Abl) response, suggesting that ’ To whom correspondence and reprint requests should be addressed. * Abbreviations used: Abl , idiotypic antibody; Ab2, anti-idiotypic antibody; Ab2& anti-idiotypic antibody with idiotope that is bound by the idiotypic antibody’s paratope (aka the internal image of the antigen); DNP, dinitrophenyl hapten; Is,,, free hapten concentration that inhibits 50% of the hemolytic plaques; PFC, plaque-forming cell(s). 324 0008-8749192$5.00 Copyright 0 1992 by Academic Press, Inc. All fights of reproduction in WY form reszved.
IMMUNOREGULATION
VIA THE IDIOTYPIC NETWORK, II
325
the secondary Abl response was downregulated by anti-idiotypic (Ab2) antibody. In this report, we address the issue of affinity and heterogeneity of the Abl and Ab2 responsesof mice to immunization with a T-independent and a T-dependent antigen. We found a correlation between Abl and Ab2 with regard to these parameters, suggesting that the two complementary antibodies mutually regulate one another. MATERIALS AND METHODS Mice. Two to three-month-old female BALB/c mice were purchased from HarlanSprague-Dawley (Indianapolis, IN). Immunizations. Mice were immunized with 100 pg of DNPbO-Ficoll (Biosearch, San Rafael, CA) ip. Some of the mice were rested for 3 weeks, after which the immunization was repeated. Spleen cells for the hemolytic plaque assay and for the plaque inhibition assaywere obtained 5 days after primary or secondary immunization, at the time of peak Ab 1 and Ab2 responses( 1). Mice receiving primary immunizations with DNP,,-HGG were injected ip with 100 pg of the antigen adsorbed on bentonite (4). Secondary immunizations were given in a similar manner 3 weeks after primary immunization. Spleen cells were assayed 13 days after primary immunization, at the time of maximal Ab2 response but several days after peak Abl response, or 5 days after secondary immunization, when both the Abl and Ab2 responsespeaked (1). Hemolytic plaque assay and plaque inhibition assay. The hemolytic plaque assay for the detection of Ab 1 PFC was performed utilizing SRBC coated with DNP-derivatized F(ab’)2 from rabbit anti-SRBC antibody, as previously described (5-7). For the detection of Ab2 PFC the indicator SRBC were coated with affinity-purified F(ab’h fragments of rabbit anti-DNP antibodies to which dipalmitoyl phosphatidylethanolamine was covalently attached as described in the companion paper (1). For the plaque inhibition assayidentical aliquots of spleen cells were plated in duplicate in agar containing various concentrations of the hapten DNP-lysine or no hapten (5). The percentage of plaque inhibition was calculated for each hapten concentration. Statistical methods. When the affinities of the PFC are normally distributed, a plot of the percentage of plaque inhibition versus inhibitor concentration would result in a sigmoid curve. By logit transformation of the percentage of inhibition values, the sigmoid curve is converted into a straight line. We determined the least-squareslinear regressionequation for the relationship between inhibitor concentration and both Ab 1 and Ab2 plaque inhibition for each mouse. We took into consideration only the data points spanning the interval between 100% inhibition (all inhibitor concentrations greater than that resulting in 100% inhibition would also result in 100% inhibition) and 0% inhibition (all lower inhibitor concentrations would also result in 0% inhibition), and calculated the line of best fit for these data points. The outcome analyzed was the logit transformation of the percentage of inhibition values (= 0.5 ln[p/l - p], where p = percentage of inhibition) with the logarithm (to base 10) of inhibitor molar concentration as the predictor variable. For each set of data, the regression line intercept provided the value of the inhibitor concentration at the 50% inhibition point (Iso), a measure of PFC affinity, and the regression line slope provided an estimate of heterogeneity of affinity. Classically, the affinity of anti-hapten antibodies has been expressed as the average association constant (Z&J,and the heterogeneity of affinity by a heterogeneity index (a or a) based on the assumption that affinities of antibody molecules follow a Gaussian (8) or Sipsian (9) distribution. It has been shown that the distribution
326
SEGRE ET AL.
of antibody affinities is often skewed, and that the K, and LYvalues do not faithfully representthe binding data ( 10). Alternative methods of calculating the binding constant and heterogeneity index have been proposed (lo), but have not gained wide acceptance. When these parameters are estimated from plaque inhibition data, the 50% inhibition points have been shown to be correlated with K, values and have been usedto indicate the relative affinity of PFC (5). The distribution of affinities has been generally described by a histogram (1 l), but has not been given a numerical value, although a heterogeneity index based on information theory has been used by some authors (12). In the current study, heterogeneity of affinity is estimated from the slope of line from the regression of (logit transform of) the percentage of inhibition on (log,,) inhibitor concentration. A gradual slope indicates little change in inhibition across concentrations, and thus heterogeneity of affinity, whereas a steep slope indicates substantial change across concentrations, and thus high homogeneity of affinities. Although the statistical model requires normality of residuals for proper statistical inference, this is not required for parameter estimation (I 3). Likewise estimation of heterogeneity does not require an underlying normal distribution of affinities. The effectof T-dependent vs T-independent antigen and of primary vs secondary response on affinity and heterogeneity was ascertained for both the Abl and Ab2 responsesusing a two-way analysis of variance. RESULTS An example of the Abl and Ab2 plots for a mouse undergoing a primary response to DNP-Ficoll is shown in Fig. 1. The numbers of mice employed for the plaque inhibition experiments and their mean Ab 1 and Ab2 PFC responsesare reported in Table 1. The secondary Ab 1 response to DNP-Ficoll was significantly (P < 0.001) lower than the corresponding primary response,confirming our previous observation (1). No similar statement can be made for the Abl response to DNP-HGG, since the mice were not assayedat the time of peak primary response. In examining the data of the hapten inhibition experiments, we found that at times there were more PFC in the assayplates containing low inhibitor concentrations than were found in plates with no inhibitor. This phenomenon is known as hapten augmentation, and it has been shown to result from the displacement by hapten of antiidiotypic antibody that was bound to idiotypic antibody on the surface of the antibodyproducing cell, thus blocking antibody secretion and preventing plaque formation (14, 15). We encountered this phenomenon not only in inhibition assaysof Ab 1 PFC, but also in inhibition assaysof Ab2 PFC. In the latter case,evidently it was the idiotypic antibody that was blocking the release of anti-idiotypic antibody by potential Ab2 PFC. Whenever hapten augmentation occurred, the number of PFC in the haptenaugmented plates, rather than the number of PFC in the plates containing no inhibitor, was taken as 0% inhibition, and the percentage of inhibition for each inhibitor concentration was calculated accordingly. Hapten augmentation was seen sporadically, but was especially prevalent in inhibition assayswith spleen cells from mice undergoing a secondary response to DNP-Ficoll (Table 2). Results of statistical comparisons of ZsO(affinity) and slope (heterogeneity) values derived from plaque inhibition assayson various groups of mice are summarized in Table 3. The mean Z50value of Abl PFC for the T-dependent antigen DNP-HGG was significantly lower (P < 0.00 1) than the corresponding value for the T-independent
IMMUNOREGULATION
327
VIA THE IDIOTYPIC NETWORK, II
I
i
-1.2
4
-1.41
I
,
I
-k
-5
(
-3
LOG INHIBITOR MOLARITY 3 ,
-1.5
i
I
I
-2 I -10
-9
-6
-5
LOG INHIBtOR MOL-;RITY FIG. 1. Plots of lo&-transformed percentage of inhibition vs inhibitor concentration for PFC obtained from mouse No. 104 5 days after immunization with DNP-Ficoll. Top, Abl PFC: 1,, = 10-4.‘4,slope = 1.22. Bottom, Ab2 PFC: I,, = 10-8.47,slope = 0.80.
antigen DNP-Ficoll, indicating greater affinity for the former antibodies than for the latter. Similarly, the mean slope value of Abl PFC for DNP-HGG was significantly lower (P < 0.01) than that for DNP-Ficoll, indicating greater heterogeneity for the
TABLE 1 Abl and Ab2 PFC Responsesfollowing Immunization with DNP-Ficoll and DNP-HGG Mean PFC/spleen + SE Immunogen DNP-Ficoll DNP-HGG
Type of response
Day of assay
Primary Secondary Primary Secondary
5
No. of mice
13
3 6 3
5
7
5
Abl 83,215 15,706 9,142 211,625
f 2,025 t 1,300 + 1,003 ?I 49,694
Ab2 267,661 k 42,141 141,075 f 40,530 1,633 iz224 12,925 + 2,33 1
328
SEGRE ET AL. TABLE 2 Hapten Augmentation in Abl and Ab2 Plaque-Inhibition Assays with Spleen Cells of Mice Undergoing a Secondary Responseto DNP-Ficoll Maximal No. PFC with inhibitor: No. PFC without inhibitor Mouse no.
Abl
Ab2
94 95 96 111 113 114
1.37 1.32 2.17 0.88 1.26 1.46
2.37 6.32 1.24 1.06 1.16 3.26
former than for the latter antibodies. In the Ab2 plaque inhibition assays,the mean Z,, value was higher for the T-dependent than for the T-independent antigen (P < 0.0 1). In contrast to the Ab 1 plaque inhibition assay,in this case,becauseof the nature of the assay, higher Z,, values correspond to high-affinity antibodies and vice versa. Thus, as was the case for the Abl response, the Ab2 response to DNP-HGG also resulted in higher affinity PFC than did the Ab2 response to DNP-Ficoll. There was also a greater mean slope value for the Ab2 response to DNP-Ficoll than for the corresponding response to DNP-HGG, indicating greater heterogeneity for the latter than for the former antibodies (P < 0.01). Finally, the mean Is,, value for the secondary Abl responseto DNP-HGG was lower than the corresponding value for the primary response, indicating, as expected, an increase in affinity from the primary to the sec-
TABLE 3 Plaque Inhibition Analysis: Comparison of Z,, and Slope Values Treatment grow
No. of mice
Abl, Tdb Abl, Ti Ab2, Td Ab2, Ti Abl 3 1”’ >Td Abl, 2”, Td Ab2, l”, Td Ab2,2”, Td Abl, l”, Ti Abl, 2”, Ti Ab2, I”, Ti Ab2, 2”, Ti
10 9 10 9 3 7 3 7 3 6 3 6
Mean Zs0” -6.201 -4.39 -5.803 -8.194 -5.820 -6.583 -5.827 -5.780 -4.467 -4.317 -8.720 -7.668
P value
Mean slope
P value
