Role of t lymphocytes in the humoral immune response. II. T cell-mediated regulation of antibody avidity.

The effect of activated T lymphocytes (ATC) on the avidity distribution of PFC in the secondary response was studied in normal mice. The total PFC response was not significantly changed for either direct or indirect PFC by administration of ATC before secondary antigen challenge. However, marked suppression occurred of indirect PFC that secreted high avidity antibody; no suppression was seen of high avidity direct PFC. At the same time, significant stimulation was seen of relative and absolute frequencies of indirect PFC that secreted middle and low avidity antibody. These effects were dependent on Thy 1-bearing, nylon nonadherent cells which demonstrated carrier specificity. In further characterization of these effects, it was found that increasing the number of ATC transferred produced progressive loss of high avidity PFC and compensatory increase in lower avidity PFC. Moreover, in these experiments, suppression of the high avidity response was inducible with the administration of ATC 5 weeks before to 3 days after the secondary immunization. Thus, it is likely that the avidity-modifying effects are dependent on T lymphocytes which influence the late stages of B lymphocyte maturation.     

In vivo suppression of the primary immune response by a species of low density serum lipoprotein.

An apparent subspecies of normal human serum low density lipoprotein (LDL-In) has been identified with suppressive activity for early or facilitating events of human lymphocyte mitogen and allogenic cells stimulation in vitro. This report describes the effects of in vivo administration of LDL-In on the mouse anti-SRBC immune response. Human LDL-In is not species specific and was capable of suppressing the in vivo mouse anti-sheep erythrocyte (SRBC) hemagglutination response by 88% after the administration of 500 to 600 mug LDL-In IV, whereas human serum high density lipoproteins and fibrinogen had no effect. Maximal suppression occurred only when LDL-In was injected 24 to 48 hr before antigen administration. Simultaneous or subsequent injection of LDL-In had no effect. The activity of LDL-In was influenced by antigen dose and maximal at low antigen doses. The number of splenic plaque-forming cells was also reduced indicating a suppression of the clonal expansion of primary B cells to antibody-secreting cells rather than only suppression of antibody synthesis by differentiated B cells and their progeny. These observations suggest the hypothesis that endogenous LDL-In could play an important immunoregulatory role in the maintenance of immune homeostasis and the "natural" suppression of non-productive lymphocyte proliferation.     

Effects of carrageenan on immune responses. Studies on the macrophage dependency of various antigens after treatment with carrageenan.

Carrageenan, a sulfated polygalactose having macrophage toxic properties, elicited a marked suppression of IgM response to T cell-dependent antigens such as sheep red blood cells (SRBC), dinitrophenylated bovine serum gamma-globulin (DNP-BGG), and trinitrophenylated concanavalin A (TNP-Con A). In contrast, carrageenan did not inhibit antibody responses to such T cell-independent antigens as trinitrophenylated DEAE-dextran (TNP-DEAE-dextran), trinitrophenylated polyvinyl pyrrolidone(TNP-PVP), and trinitrophenylated Ficoll (TNP-Ficoll). Compared to total spleen cells, spleen cells from which macrophages had been removed by adhesion to plastic Petri dishes had less effect on the production of antibody against T cell-dependent antigens, but no change or a rather stimulated effect was observed in in vitro antibiody synthesis against T cell-independent antigens. These results strongly suggest that macrophages are involved in antibody responses to T cell-dependent antigens but not in those to T cell-independent antigens. However, the antibody response to trinitrophenylated lipopolysaccharide (TNP-LPS), a T cell-independent antigen, was inhibited by carrageenan treatment, suggesting that the response is macrophage dependent. Moreover, antibody response to higher doses of dinitrophenylated phytohemagglutinin (DNP-PHA), a T cell-dependent antigen, was shown to be macrophage independent by carrageenan treatment, although the antibody response to low doses of the antigen was macrophage dependent. Considering all these results, carrageenan treatment seems to be a very useful method to determine whether immune response to various antigens are macrophage dependent or not.     

Regulation of the secondary in vitro antibody response by endogenous natural killer cells: kinetics, isotype preference, and non-identity with T suppressor cells

Our previous studies had demonstrated that depletion of endogenous natural killer (NK) cells resulted in an augmented primary antibody response in vivo and in vitro. We have now examined the effect of NK cell depletion on the in vitro secondary response to antigen. Treatment of primed murine spleen cells with anti-NK-1.1 allo-antibody and complement before culture resulted in a significant increase in the magnitude of the antigen-specific plaque-forming cell (PFC) response. This treatment did not affect the proportions of Lyt-2+, L3T4+, or sIg+ cells in the population, however, indicating that the augmentation in PFC was not due to changes in the ratio of T to B cells. Removal of endogenous NK cells had a greater effect on the IgG (indirect) PFC response (100 to 200% increase) than on the IgM (direct) PFC response (25 to 50% increase). In contrast, removal of Lyt-2+ cells before culture affected the IgM and IgG responses similarly. Moreover, the kinetics of augmentation differed between cultures depleted of Lyt-2+ cells and those depleted of NK-1.1+ cells. NK cells appeared to act earlier in the response than did T suppressor cells. The NK-1.1+ cells involved in antibody regulation were not involved in the generation of the in vitro derived T suppressor cells. The conclusion that the regulation of the antibody response by NK-1.1+ cells is distinct from that involving T suppressor cells was confirmed in experiments in which removal of both regulatory cell populations resulted in an increase in PFC that was greater than in cultures depleted of either NK or T suppressor cells.     

Factors determining the effects of chronic protein-deficiency on antibody responses to sheep red blood cells and Brucella abortus vaccine in mice.

Chronic protein-deficiency in weanling mice caused variable suppression of the humoral plaque-forming cell (PFC) responses to sheep erythrocytes. This was most prominent at high antigen doses and did not increase when mice were maintained on the diets for longer periods. Antibody responses produced by deficient mice were often short-lived and involved high levels of IgM. Total PFC counts were depressed slightly more than were circulating antibodies. Antibody responses to Brucella abortus were slightly decreased by protein-deficiency at high antigen doses but were normal or elevated at lower doses, the proportion of IgM produced was increased and the splenomegaly response to B. abortus was severely depressed. These results suggest that the depression of antibody production by protein-deficiency is not simply due to an impairment of helper T cell function, but a reduction in the availability or effectiveness of macrophage and regulatory or suppressor T cells may be important.     

Studies on the control of antibody synthesis. XIV. Role of T cells in regulating antibody affinity.

The effect of limiting the number of helper T cells on the affinity of the primary antibody response to a T-dependent antigen (DNP-BGG) was evaluated in a cell transfer system. Lethally irradiated, thymectomized mice were reconstituted with either bone marrow or anti-brain θ antiserum plus complement-treated spleen as the source of B cells. In addition, they received various numbers of thymus cells as a source of helper T cells. The animals were immunized with DNP-BGG 1 day after cell transfer and their splenic anti-DNP PFC response was assayed for magnitude and affinity 3 weeks later. A marked restriction in helper T-cell activity resulted in a primary response which was of low magnitude, which lacked indirect PFC, and which had a very low affinity and restricted heterogeneity. When sufficient thymus cells were given to permit a switch to indirect plaque formation, a highly heterogeneous, high-affinity primary response was elicited. Further increase in the number of thymic cells resulted in a progressive increase in the magnitude of the primary response but had no effect on affinity. Thus, a reduction of 50% in the magnitude of the response as a consequence of limiting the number of T-helper cells had no effect on the affinity of the PFC. The results are consistent with the interpretation that the effect of restriction in T-cell help on antibody affinity is not due to a direct effect on precursors of high-affinity PFC but is secondary to inefficient selection for high-affinity cells when the degree of cell proliferation is markedly reduced.     

The effect of splenectomy on the immune responses of rabbits to a soluble protein antigen given parenterally or orally

Splenectomized and sham-operated rabbits were immunized with bovine serum albumin (BSA) intravenously, subcutaneously, or orally. Splenectomy caused a 2-to 4-day delay in antibody synthesis in animals immunized intravenously; this delay corresponded to the time that antibody-producing cells were found mainly in the spleen. By 14 days, the antibody response of the splenectomized intravenously immunized group was similar to that of the sham-operated group. Splenectomy did not diminish the antibody responses of rabbits immunized subcutaneously or orally.Splenectomy had no effect on the capacity of circulating lymphocytes to respond to phytohemagglutinin. Similarly, splenectomy did not alter the capacity of circulating lymphocytes from subcutaneously immunized rabbits to respond to BSA in vitro. In contrast, the presence of detectable circulating antigen-reactive lymphocytes in splenectomized animals was slightly reduced after intravenous immunization, and significantly enhanced after oral immunization.Thus, the spleen of the rabbit is important for the early antibody response to soluble protein antigens given intravenously. These studies suggest that the systemic immunity which follows local antigen stimulation at mucosal surfaces, i.e., oral immunization, may be secondary to the circulation of lymphoid cells sensitized in the lamina propria of the intestine.     

Trypanosoma cruzi: Early immune responses in infected mice

The influence of an active Trypanosoma (Schizotrypanum) cruzi infection in mice and the subsequent immune response to an administered unrelated, erythrocyte antigen was studied. When mice were infected with blood forms of the parasite, a depression of the humoral immune response to injected burro erythrocytes (BE), was observed. The suppression became evident at a time when the magnitude of parasitemia and tissue forms was increasing in the sensitized and infected mice. The immunosuppressive effect induced by the infection to BE was demonstrated by a diminished direct (19S) and indirect (7S) antibody-forming cell response. Additionally, a significant increase in phagocytic activity was observed in T. cruzi-infected mice using colloidal carbon uptake experiments. Probable mechanisms of suppression are discussed and related to accepted lymphocyte activities.     

Modification of immune reactions by antigen-immunosuppressive agent conjugates. V. Studies on antigen-specific activity of 6-mercaptopurine bovine gamma globulin conjugates on the humoral immune response in rabbits]

Rabbits treated daily and for seven consecutive days with 6-mercaptopurine bovine gamma globulin conjugates (MPI--n-BGG; 'I'--characterizes the king of chemical binding and 'n' the number of coupled MP-residues per one mole BGG) show an altered immunological reactivity. A following intradermal immunization with BGG alum adsorbate results in a suppressed anti BGG antibody production on the third day after antigen application (antibody titer 1:320, antibody titer of control animals--pretreated with BGG and uncoupled 6-MP equals 1:5120). Already three days later the antibody titers of the test groups show a significant increase and are two dilution stages higher than the titers of the controls. A suppressive effect on the third day is induced by MPI--13-BGG, MPI--26-BGG, MPI--36-BGG and MPI--46-BGG; the later adjuvant effect can only be seen in the MPI--26-BGG, MPI--36-BGG and MPI--46-BGG but not in the MPI--13-BGG pretreated animal group. While the short time suppression was antigen specific--the humoral immune response against a second unrelated antigen was not reduced--the adjuvans effect was not antigen specific. A pretreatment with the substances mentioned above results in an increased anti BGG and anti HSA serum antibody level. Comparing investigations on the unspecific immunosuppression in rabbits by 6-mercaptopurine shows that application of 10 mg 6-MP/kg/day for seven days at first leads to a suppression but later on to an enhancement of antibody production. Application of 10 mg 6-MP/kg/day for 10 days results in a long lasting suppression without enhancement effect. As a reason for these differences the different catabolism of immunosuppressive agent and antigen is discussed. For the phenomena following antigen specific immunosuppression, similar mechanisms can be responsible.     

Suppression of the responsiveness of lymphocytes from cancer patients triggered by co-culture with autologous tumor-derived cells

The question as to whether or not cancer patients have "tumor antigen"-induced suppressor T cells is of considerable interest and importance. As an approach to that question, the effect of addition of autologous irradiated tumor-derived cells (TDC) on the mixed lymphocyte response (MLR) of patients' lymphocytes (Ly) and of healthy donor Ly was tested. The rationale for these experiments was based on the fact that circulating antigen-responsive blood lymphocytes can be reactivated in vitro by exposure to the appropriate antigen. Thus, if there are circulating tumor "antigen"-reactive suppressor Ly, exposure to TDC as a source of the antigen should reactivate those cells. Reactivation of suppressor cells might result in diminished responsiveness to other stimuli such as alloantigens in the mixed leukocyte culture. We found that the addition of TDC to Ly cultures produced four distinct patterns of reaction. In 26 of the 74 different patient-tumor assays, the addition of autologous TDC to the patient cultures inhibited MLR, but the addition of the same TDC to cultures of Ly from healthy donors had no effect or increased their responsiveness (Specific Suppression). In 21 cases, the addition of autologous TDC to the patient cultures suppressed the MLR and the addition of the same TDC to control cultures suppressed the response of some but not all the healthy donors (Selective Suppression). In four cases, the addition of TDC to the cultures suppressed the MLR of the patients and all of the control donors (Nonspecific Suppression). In 23 cases, the addition of autologous TDC resulted in no suppression of the patient MLR or of any of the simultaneously tested normal donors (No Suppression). When TDC of patients with noninvasive bladder cancer were added to their own Ly cultures, only four of 11 produced specific or selective suppression compared to 11 of 12 when TDC came from patients with superficially invasive cancer. These data provide indirect evidence to support the hypothesis that human tumors induce circulating suppressor cells that may be reactivated in vitro by co-culture with TDC.     

Antibodies to nonpolymorphic determinants of the Thy-1 molecule inhibit T cell proliferation

The effect of anti-Thy-1 monoclonal antibodies on murine mixed lymphocyte reactions and concanavalin A-induced mitogenesis were investigated. It is demonstrated that rat antibodies against nonpolymorphic determinants of the murine Thy-1 antigen inhibited cell proliferation in the absence of complement. In contrast, antibodies against polymorphic determinants of Thy-1 had no effect on T cell activation. Inhibition of T cell proliferation did not depend on the isotype of the blocking antibody, because both IgM and IgG antibodies against monomorphic determinants were inhibitory, whereas IgM or IgG antibodies against allotypic determinants were inactive. In addition, the blocking activity could not be attributed to the xenogeneic (rat) origin of the antibodies to nonpolymorphic Thy-1 determinants, because rat anti-Thy-1.2 antibodies had no effect on cell activation. Thus, the efficacy of anti-Thy-1 antibodies as T cell inhibitors was determined by the antibody specificity. The suppressive mechanism of anti-Thy-1 antibodies was effective throughout the entire course of mixed lymphocyte reactions. Addition of antibodies at any time point during the first 90 hr of a 120-hr mixed lymphocyte culture resulted in significant suppression of the proliferative response. However, in some cases an early enhancement preceded suppression of the response. The modulation of proliferative responses by anti-Thy-1 did not result from a nonspecific mitogenic effect of the antibodies on T lymphocytes, because no effects were observed when antibodies were added to responder cells alone. These results suggest that the Thy-1 molecule, or a molecule that is located on the cell membrane in close proximity to the Thy-1 antigen, is involved in the activation of T lymphocytes.     

The suppressive effect of circulating specific antibody on the response to oral immunisation with Vibrio cholerae

Species IgG antibody given intravenously 3-4 hours prior to oral immunisation with Vibrio cholerae led to a specific depression of both the systemic and loca limmune response. One vibriocidal unit of IgG antibody, which itself would given undetectable levels of circulating specific antibody, was significantly immunosuppressive. The suppression is considered to be due to central repression of the antigen-reactive lymphocyte, rather than to antigen exclusion at the gut mucosal surface. The repression appeared less pronounced in some immunoglobulin classes than in others.     

Modulation of in vitro immune responses by monoclonal antibody to T200 antigen

The effects of monoclonal antibody to the T200 antigen on murine mixed-lymphocyte cultures (MLC) and on the generation of alloreactive cytotoxic T lymphocytes (CTL) are investigated. Addition of monoclonal anti-T200 without complement to MLC results in a late suppression of the proliferative response preceded in some cases by an early enhancement. These modulations require the presence of allogeneic stimulator cells; no effects are seen when antibody is added to responders alone. A similar effect is seen on the generation of CTL. Compared to controls without antibody, cultures carried out in the presence of anti-T200 show reduced levels of cytotoxicity measured against allogeneic targets by Day 5. The kinetics of the suppressive effects differ from those seen with anti-Lyt-2, and no suppressive effects are seen with monoclonal antibodies to other cell surface molecules.     

Studies on the control of antibody synthesis. XVI. Effect of immunodepression on antibody affinity

The relationship between depression in the magnitude of the immune response and a decrease in affinity of the antibody produced was examined in three different models of immuno-depression (B-cell clonal deletion tolerance, specific suppressor T-cell activity, and anti-genie competition). In B-cell clonal deletion tolerance and in antigen-specific, suppressor T-cell-mediated immunodepression, a small decrease in magnitude (50% or less) is associated with a marked decrease in high-affinity, plaque-forming cells. In contrast, with nonspecific immunodepression, due to antigenic competition, a depression in affinity is only seen when there is a marked (85%) reduction in the magnitude of the response. The results are consistent with the view that when the mechanism of immunodepression involves interaction of antigen with antigen-specific B cells there is a disproportionate loss of high-affinity, antibody-producing cells relative to the decrease in magnitude. In contrast, with nonspecific immuno-depression, where the decrease in affinity is presumably due to inefficient expansion of high-affinity clones, an effect on affinity is only observed in association with a marked depression in the magnitude of the response.     

Humoral factors and nonspecific immune suppression in Syrian hamsters infected with Leishmania donovani

Leishmania donovani produces progressive wasting and ultimately fatal visceral leishmaniasis in Syrian hamsters and provides an excellent model of progressive disease in humans. Experimentally infected hamsters were used to investigate the development of nonspecific immune suppression during visceral leishmaniasis and its association with humoral factors and wasting. At 2 wk all infected hamsters had developed antibody against a 59-kDa parasite antigen not recognized by sera of control hamsters. By 4 wk, strong antibody responses were noted against antigens of 26, 35, 46, 69, 107, and 120 kDa. No additional antigen was recognized at 6 or 8 wk or in hamsters treated with high doses of a pentavalent antimonial (stibogluconate sodium, 100 mg/kg/day for 5 days). Weight loss was first noted in infected hamsters at 8 wk. No difference in splenic lymphocyte proliferation in response to concanavalin A (Con A) was noted at 2 wk, but by 6 wk infected animals had only 20% of the Con A response of controls, and by 8 wk only 13%. Furthermore, incubation of splenic lymphocytes from uninfected control animals with 5% fetal calf serum and 5% serum from infected hamsters obtained at 4, 6, or 8 wk suppressed Con A responses by 50%, 99%, and 100%, respectively. Spleen cells from drug-treated animals exhibited no suppression of Con A responses when incubated with 5% autologous serum, but there was profound suppression when they were incubated with 5% autologous serum obtained during the acute phase of infection. Humoral factors, but not wasting, contributed to the suppression of lymphocyte responses.     

Regulation of antibody response in vitro. X. Biphasic effect of cyclic AMP on the secondary anti-hapten antibody response to anti-immunoglobulin and enhancing soluble factor.

The effect of elevation of an intracellular cyclic AMP level on in vitro anti-hapten antibody response was studied, by using mesenteric lymph node cells of rabbits which were primed with dinitrophenylated Ascaris antigen (DNP-Asc) or DNP-ragweed antigen (DNP-Rag). The anti-hapten antibody response was induced by stimulation of the primed B cells by either DNP-heterologous carrier conjugate or anti-immunoglobulin (anti-Ig) for 24 hr (first stage), followed by 6-day culture of the activated cells in the presence of nonspecific enhancing factor (second stage). The stimulation with anti-Ig induced IgG anti-hapten antibody response and enhanced the formation of total IgG. Addition of dibutyryl cyclic AMP or aminophylline with anti-Ig or DNP-heterologous carrier during the first stage enhanced IgG anti-hapten antibody response. The optimal concentration of these reagents for the enhancement was 5 x 10(-4) M to 10(-3) M. The presence of 5 x 10(-6) M prostaglandin E1 during the first stage also enhanced the antibody response. Similarly, the presence of dibutyryl cyclic AMP or aminophylline during the stimulation of DNP-Rag-primed cells with homologous antigen (first stage) enhanced the antibody response. If the same concentration of dibutyryl cyclic AMP or aminophylline was added together with enhancing soluble factor during the second stage after the stimulation of the primed cells with anti-Ig, both the antibody response and the formation of IgG were suppressed. The antibody response of DNP-Rag-primed cells stimulated with homologous antigen was also suppressed if dibutyryl cyclic AMP or aminophylline was added during the subsequent culture (second stage). Evidence was obtained that suppression of antibody response by cyclic AMP during the second stage is probably due to inhibition of the proliferation of B cells. Neither of these drugs suppressed the formation of enhancing soluble factor from the carrier-specific cells stimulated with the homologous carrier. The results obtained in the present experiments suggested that stimulation of hapten-primed B cells with anti-gamma chain in the presence of an optimal concentration of dibutyryl cyclic AMP resulted in the formation of a significant amount of IgG anti-DNP antibody without participation of T cells.     

The influence of TRPM8 ion channel activation on immune response at different temperature conditions

In experiments on rats it was shown that it is possible to modulate the immune response in a whole organism by activating cold-sensitive TRPM8 ion channel by its agonist menthol. The most pronounced changes in the conditions without external temperature stimulation were related to immune parameters for the spleen cells and immunoglobulin level in blood: the activation of TRPM8 ion channel by menthol enhances antigen binding and inhibits antibody formation in spleen, significantly reduces the level of IgG in blood. Activation of TRPM8 ion channel changes the effect of subsequent temperature exposure—cooling or heating. Preliminary application of menthol eliminates the inhibitory effect of deep cooling on immune response. Stimulation of the antigen binding in spleen at deep heating is inversed to suppression in case of heating on the background of TRPM8 activation by menthol. On the contrary, suppression of antibody formation caused by deep heating is eliminated if heating is carried out on the background of TRPM8 stimulation.     

Elicitation of antigen-induced primary and secondary murine IgE antibody responses in vitro

Described herein are methods for eliciting and quantitating primary and secondary murine IgE antibody responses in vitro, and the important role of antigen concentration in determining the level of IgE produced during an immune response. The methods for quantitating IgE antibody levels in culture supernatant fluids and in serum by ELISA are presented in detail. The specificity of such methods was confirmed in that (1) no other isotype of antibody registered in the IgE-ELISA, and (2) parallel determinations of IgE antibody concentrations could be obtained by independent analysis using Fc epsilon RI-dependent basophil degranulation. We examined various parameters of cell donor immunization and lymphoid cell culture which allow for optimal in vitro primary and secondary IgE responses. High relative antigen doses result in diminished IgE antibody responses in experimental animals, a finding confirmed herein. High antigen concentrations in vitro also result in relative suppression of IgE antibody synthesis. This was also true for in vitro production of IgG1 and IgA antibodies. Conversely, IgM and IgG2a responses were elicited at both low and high antigen concentrations; IgG2b and IgG3 were not produced under the conditions of priming and culture used herein. Finally, production of IgE in vitro depended on the presence of carrier-primed CD4+ T cells and hapten-specific B cells. Generation of maximal IgE antibody secretion, and hence elicitation of an allergic reaction, is thus dependent on the amount of antigen acting as stimulant for the immune response.     

Secretion rate independent evaluation of IgM antibody avidity at the level of single immunocytes.

The hemolytic plaque inhibition assay has been performed on spleen cells from mice immunized with TNP-HRBC to evaluate avidity of anti-TNP IgM antibodies. At different times after immunization direct plaques were inhibited by soluble TNP-EACA, TNP61-BGG, or anti-mu antiserum. Analysis of the inhibition data provided independent estimates of antibody avidity and secretion rate. Avidity was found to increase with time, to reach a maximum when the antibody response attained the peak value, and then to decline as the response was waning. There was a decrease followed by increase of the secretion rate concomitant with the rise and fall of the antibody response and avidity.     

Verification of immune response optimality through cybernetic modeling

An immune response cascade that is T cell independent begins with the stimulation of virgin lymphocytes by antigen to differentiate into large lymphocytes. These immune cells can either replicate themselves or differentiate into plasma cells or memory cells. Plasma cells produce antibody at a specific rate up to two orders of magnitude greater than large lymphocytes. However, plasma cells have short life-spans and cannot replicate. Memory cells produce only surface antibody, but in the event of a subsequent infection by the same antigen, memory cells revert rapidly to large lymphocytes. Immunologic memory is maintained throughout the organism's lifetime. Many immunologists believe that the optimal response strategy calls for large lymphocytes to replicate first, then differentiate into plasma cells and when the antigen has been nearly eliminated, they form memory cells. A mathematical model incorporating the concept of cybernetics has been developed to study the optimality of the immune response. Derived from the matching law of microeconomics, cybernetic variables control the allocation of large lymphocytes to maximize the instantaneous antibody production rate at any time during the response in order to most efficiently inactivate the antigen. A mouse is selected as the model organism and bacteria as the replicating antigen. In addition to verifying the optimal switching strategy, results showing how the immune response is affected by antigen growth rate, initial antigen concentration, and the number of antibodies required to eliminate an antigen are included.