The regular lines of antigen-antibody

interactions in vitro

Antibodies are bound irreversibly to their antigenic determinants under physiological conditions
t

An analytical review

Viggo Bitsch

viggo.bitsch@gmail.com

Published Oct. 26, 2017

ISBN 978-87-994685-2-2

© 2017 Viggo Bitsch

Abstract

Viggo Bitsch: The regular lines of antigen-antibody interactions in vitro. Antibodies are bound irreversibly to their antigenic determinants under physiological conditions.

This analytical review aims to clarify antigen-antibody interactions in vitro. Aspects of the antigen-antibody binding reactions are evaluated, and important conclusions are made. All are summarized in Section 3 at the end of each subsection. Results related to the performance of sensitive and standardized tests for demonstrating antigens and antibodies are overviewed in a final section. Only the most important relations will be mentioned in this abstract.

Antibodies are bound firmly and irreversibly to their antigenic determinants on a virus. The binding reaction does not lead to an equilibrium state. The sensitivity of antigen-antibody tests may consequently be variable and adjustable.

Neutralization of virus by antibody in a virus-antibody mixture and in the dilutions of a neutralization test proceeds as two separate reactions, i.e., 1) a first-order reaction caused by neutralizing antibodies being bound monovalently to their antigenic neutralization determinant on virions and 2) a supplementary “over-neutralization” reaction that can be attributed to the formation of virus aggregates by the di- and polyvalent antibodies which predominantly are non-neutralizing. The aggregation reaction is prompt and short-lasting. In contrast, the first-order neutralization reaction is slowly progressing but enduring, and the test sensitivity is temperature-dependent and directly proportional to the reaction time.

The neutralizing effect of antibodies by aggregating virions is enhanced by complement. The binding of an antibody to its antigenic determinant will sensitize that antibody for binding to the polyvalent complement component C1q, after which the virus will be inactivated by the inclusion in virus-antibody aggregates. If complement in optimal amounts is added to mixtures of virus and specific antibody in the dilutions of neutralization test, two different reaction rates will be observed. Practically instantly, the complement will aggregate all pre-formed virus-antibody complexes and the reaction will subsequently be of first-order, following the first-order binding of non-neutralizing antibodies to their antigenic determinants.

The huge virus-neutralizing potential of the non-neutralizing antibodies in a joint action with complement indicates the fundamental role of these antibodies in preventing and combatting infectious diseases.

The antigen-antibody interaction formula expresses the regular lines of antigen-antibody interactions not comprising aggregation. Sensitive and specific antigen-antibody tests elaborated based on the relationships documented have been used in the veterinary field for a long time.

1. Introduction.

The aim of this analytical review is to clarify and document the regular lines of antigen-antibody interactions in vitro.

An antibody neutralizing a virion by attachment to its antigenic determinant is a neutralizing antibody, and the corresponding epitope on the virion will be termed the antigenic neutralization determinant. Antibodies not neutralizing a virion by being bound to their antigenic determinant are non-neutralizing antibodies.

The lines of antigen-antibody interactions are significant for elaborating adequate tests for demonstrating antigens or antibodies. These tests are usually performed in the way that test material is allowed to react for an appropriate time with a specific reactant, antigen or antibody, after which a detection system is used to confirm if a reaction has taken place. Reaction conditions used in such tests have commonly been chosen empirically, rather than from knowledge of regular lines of antigen-antibody reactions.

In the following, using a herpesvirus model, the influence of the various variables on neutralization in a virus-antibody mixture and in the serial dilutions of neutralization tests are analyzed and the implications of the relationships demonstrated for the elaboration of appropriately sensitive antigen-antibody tests are evaluated. Figs. 1-6 and 7-8 are from Bitsch 1978 [1] and Bitsch and Eskildsen 1982 [2], while Fig. 9 shows unpublished data.

2. The regular virus-antibody neutralization reactions in vitro.

2.1. The regular neutralization reactions without interaction by complement.

In very early in vitro investigations performed with bacteriophages and animal viruses, the neutralization rate in a virus-antibody mixture was found to be semi-logarithmically linear with the reaction time (Andrewes and Elford 1933) [3], proportional to the antibody concentration (Burnet et al. 1937) [4], temperature-dependent (Dulbecco et al. 1956) [5], and independent of the virus concentration (the percentage law) [3]. Despite these findings related to interactions in a virus-antibody mixture, it became generally acknowledged that the reaction in a conventional neutralization test would lead to a state of equilibrium in compliance with the law of mass action, most likely because no substantial progression of the reaction was achieved in a neutralization test over the first couple of hours.

The 1978 study [1] became significant for understanding the neutralization reactions, being the only investigation of antigen-antibody interactions comprising the short- and long-term influence of all relevant variables, i.e., antigen and antibody titers (concentrations of reactants measured), the reaction temperature, and the reaction time.

Figs. 1, 2, and 3 are from the 1978 study [1]. Fig.1 shows the semi-logarithmic progression of neutralization of the virus in a mixture of virus and an appropriate amount of antibody, which is linear following Eq. 1 below. The initial virus concentration corresponds to what is ordinarily used in a conventional neutralization test (100 TCID₅₀ per inoculation dose). In Fig. 6b an identical linear progression is recorded with a much higher virus dose with serum diluted 1:4. In Fig. 2 the kinetics of neutralization in neutralization tests at 37 ^oC are shown after very short reaction periods using a traditional low virus dose, whereas Fig. 3 shows the log-log kinetics in tests also at 37 ^oC for reaction periods up to 24 hours with varying virus concentrations. Here, with reaction periods from approx. 2-3 hours onwards, the log-log neutralization lines for all virus concentrations show a slope coefficient of 1, demonstrating a first-order progression of neutralization, whereas with shorter reaction periods a supplementary “over-neutralization” phenomenon is observed. Over-neutralization could not be immediately explained.

          Figure 1. Kinetics of virus neutralization in two virus-antibody mixtures with different low                      antibody concentrations. From Bitsch 1978 [1]

Virus: BoHV1. When plotted semi-logarithmically, the progression of virus neutralization is linear with the neutralization rate being 4 times higher for the stronger antibody mixture.

          Figure 2. Kinetics of neutralization for 3 sera in neutralization tests with very short
          reaction periods for the virus-serum mixtures. From Bitsch 1978 [1].

Virus: BoHV-1. VNA: virus-neutralizing antibody. Preincubation: reaction time for virus-serum mixtures before inoculation of cultures. Virus concentration was approx. 100 TCID₅₀ per 0.1 ml. After incubation of virus-serum mixtures at 37 ^oC for the indicated periods, 0.2 ml was inoculated from each mixture into each of 4 tissue culture roller tubes containing maintenance medium, implying that the mixtures were diluted 1:10 immediately on inoculation. Serum B₃ was tested in parallel by inoculation of cultures without medium but with the addition of medium after 3 hours. Results were plotted logarithmically. The dotted line shows the results from the testing of Serum B₃ on cultures without medium.

Figure 3. Kinetics of neutralization in neutralization tests at 37 ^oC with relatively long periods of virus-serum incubation and varying virus concentrations. From Bitsch 1978 [1].

Virus and definitions: see Fig. 2. Results were plotted logarithmically. The neutralization lines are seen to be identical, although varying with the virus concentrations. From approx. 2-3 hours onwards, they can be considered to be linear with a slope coefficient of 1.

The linear progression of virus inactivation in a neutralization test with a log-log slope coefficient of 1 was seen also in Figure 4 with the reaction temperature of 4 ^oC for up to 8 days of reaction, and in Figure 5 at 37, 26, 15 and 4 ^oC for up to 2, 4, 8, and 8 days, respectively.

        Figure 4. Kinetics of neutralization in a cv/v neutralization test at low temperature (4 ^oC)
        with varying virus doses and long-term incubation periods for virus-serum mixtures from 12
        to 192 hours. From Bitsch 1978 [1] .

          Virus and definitions: see Fig. 2. The log-log neutralization lines show the same slope coefficient of 1.

        Figure 5. The influence of the reaction temperature on the progression of neutralization in
        neutralization tests. From Bitsch 1978 [1].
  
           The virus dose was approx. 1000 TCID₅₀ and incubation of virus-serum mixtures were made at 37,
           26, 15, and  4  ^oC from  12 to 48, 96, 192, and 192 hours, respectively. The log-log neutralization
            lines were all linear with a slope coefficient of 1, and a semi-logarithmic direct proportionality was
           found over the temperature range between the temperature and antibody titer.

In Figs. 3, 4, and 5, the log-log progression of neutralization is recorded. All reaction lines show a slope coefficient of 1 from approx. 2-3 hours onwards at 37 ^oC, and at least from 12 hours onwards at 15 and 26 ^oC, and from 24 hours onwards at 4 ^oC. A log-log slope coefficient of 1 is indicative of a first-order reaction (from log y = log x + log a, follows y=ax). Fig. 5 furthermore demonstrates a semi-logarithmically linear relationship between the antibody titer and reaction temperature. 

It is unquestionable that the inactivation of the virus in a conventional neutralization test results from two completely different reactions. With extended reaction times, the neutralization proceeds as a slowly progressing, enduring reaction of first order, consistent with the lines found in the early investigations apart from the percentage law [3,4,5], while a prompt and short-lasting “over-neutralization” dominates with short reaction periods.

Addendum
When one particular serum was tested in the same way as Serum A (Fig. 3), a somewhat irregular course of neutralization was observed, as the highest virus dose after long reaction periods in mixtures with low antibody concentrations gave reduced neutralization (Figs.6a and 6b). The rates of neutralization for this virus dose by the serum in dilutions 1:4 and 1:16 demonstrated that the deviation was associated with a residual fraction of the virus being neutralized at a lower rate.

Figures 6a (left) and 6b (right). Irregular progression of neutralization for a certain serum sample in a cv/va neutralization test with high virus doses and long incubation periods. From Bitsch 1978 [1].

Virus and definitions: see Fig. 2. Fig. 6a shows that the neutralization curve for the serum, when tested with the highest virus dose and incubation for 6 to 24 hours, drops out. Furthermore, Fig. 6b confirms that the high virus dose is linearly neutralized in dilution 1:4 within 2 hours, while in dilution 1:16 a residual fraction is neutralized at a lower rate.

2.2. The supplementary complement-dependent neutralization reaction.

The investigations were performed with Suid herpesvirus 1 (SuHV-1) with extended reactions at 37 ^oC [2]. First, the effect of complement on the progression of virus inactivation in a neutralization test was investigated (Fig. 7), using serum from a pig 13 days after nasal infection containing predominantly specific IgM but also a low level of IgG antibodies, cf. Fig. 8. The optimal effect of complement was not obtained if added at the start of the virus-serum incubation (neutralization line 1-1). The extended reaction periods gave neutralization lines with a log-log slope coefficient of 1, indicating a first-order reaction with increasing reaction times.

Figure 7. The effect of complement on the progression of neutralization in a convalescent-phase serum. From Bitsch and Eskildsen 1982 [2]

Virus: SuHV-1. Serum was taken 13 days after nasal infection. Virus-serum mixtures were incubated at 37 ^oC, and titers were recorded by inoculation of cultures after 3, 6, 12, and 24 hours. K₀ and K₁: no complement (K₀) or heat-inactivated complement (K₁) was added at the start of virus-serum incubation. For the reactions 1-1, 2-2, 3-3, and 4 complement was added at the start of incubation and after 5, 11, and 23 hours, respectively.

Fig. 8 shows results obtained in neutralization tests with serum from a nasally infected pig during the first 21 days after infection. Tests were performed with reaction at 37 ^oC for 24 hours. Sera were treated with 2-mercaptoethanol to inactivate IgM antibodies, and both treated and non-treated samples were tested with and without the addition of complement. Regarding the virus-inactivation titers of the non-neutralizing and neutralizing IgM and IgG antibodies visualized by the action of complement, see the legend in Fig. 8. Titers are determined by the reacting antibodies in the highest concentrations, which in conventional tests will be neutralizing and in complement-dependent tests will be non-neutralizing antibodies.

Figure 8. Effect of complement on reactions in conventional and complement-enriched neutralization tests for sera collected from an animal during the first 21 days after nasal infection. From Bitsch and Eskildsen 1982 [2].

Virus: SuHV-1. The sera were inactivated at 56 ^oC for 30 min. and tested, either untreated (N) or treated with 2-mercaptoethanol (2-MC), which will inhibit the neutralizing effect of IgM antibodies, but leave IgG antibodies unchanged. In both cases, they were tested with and without the addition of complement (C´). The virus-serum mixtures were incubated at 37 ^oC for 24 hours, and where used complement was added after 23 hours of reaction. Results from a complement fixation test are also shown (CF).
Titers measured for antibodies are indicated by the symbols as follows:
N+C':              non-neutralizing IgM antibodies;
N:                    neutralizing IgM antibodies;
2-MC +C':      non-neutralizing IgG antibodies;
2-MC:             neutralizing IgG antibodies.

2.3. Major findings regarding regular lines of virus-antibody interactions in vitro.

Viruses are neutralized under natural conditions in neutralization tests by antibodies in three different ways following certain lines. These reactions are the first-order neutralization test, the “over-neutralization” reaction, and the supplementary complement-dependent neutralization [1,2].

Only the first-order reaction will be seen with extended reaction periods. The first-order neutralization is slowly progressing and enduring with increasing reaction periods. The titer and the test sensitivity are proportional to the reaction period. The reacting antibodies are neutralizing. 

The over-neutralization is rapid and short-lasting.  

The supplementary complement-dependent neutralization is caused by non-neutralizing antibodies in a joint action with the complement component C1q. The reaction is prompt immediately after the addition of complement but otherwise of first order with increasing reaction periods, following the first-order binding of non-neutralizing antibodies to antigenic determinants.

3. Discussion and conclusions on specific items.

3.1. The over-neutralization reaction in a conventional neutralization test.

In the 1978 study [1], over-neutralization was defined as the early and regular neutralization reaction in virus-antibody mixtures of neutralization test, being more advanced than expected from a linear progression of neutralization following Eq.2. Over-neutralization is rapid and short-lasting and could in tests with herpesviruses not be observed with reaction periods exceeding 2-3 hours at 37 ^oC, implying that it will not appear at all in mixtures with low antibody concentrations.

In 1983, Brioen et al. [14] reported that aggregation of virions by di- and polyvalent antibodies resulted in the inactivation of the virus (see also Thomas et al. 1985 [15], Thomas et al. 1986 [16], and reviews by Klasse and Sattentau 2001 [17], and Reading and Dimmock 2007 [6]).

Over-neutralization could, therefore, immediately be explained by this second method of neutralization. In other words, the initial over-neutralization reaction observed in Fig. 3 is the united aggregation effect of the di- and polyvalent antibodies, but predominantly the non-neutralizing ones. A reason for this speedy reaction is that the many different antibodies aggregate synergistically. The second reaction identified in the 1978 study [1] was the slowly progressing, first-order inactivation by neutralizing antibodies being bound monovalently to their antigenic neutralization determinant.

The complex pattern of neutralization disclosed by the reactions in a conventional neutralization test indicates that also non-neutralizing antibodies may have important functions in fighting viral infections.

The aggregation reaction had not been seen in measurements of neutralization rates. A likely explanation is that the antibody samples used had high antibody concentrations, because of which it will have been diluted away.

Conclusions summarized.

1. Over-neutralization was defined as neutralization exceeding what should be expected from
    the first-order neutralization reaction and is a regular feature of a neutralization reaction.
2. The reaction can be attributed to a particular ability of IgG and IgM antibodies, due 
    to their di- or polyvalency, to aggregate virions.
3. Over-neutralization is seen with moderate to high antibody concentrations. In a
    neutralization test, it will be negligible in dilutions with antibody concentrations below a
    certain level.
4. Over-neutralization will be negligible in neutralization tests with reaction periods beyond a
    given length.

3.2. The first-order progression of neutralization in a conventional neutralization test.

The binding of neutralizing antibodies to their antigenic neutralization determinant on a virion will abolish its ability to adhere to and infect susceptible cells. Neutralization of a virus in vivo may be more complicated (cf. reviews by Reading and Dimmock 2007 [6] and Klasse 2014 [7]), but only in vitro conditions are relevant here.

The simple neutralization reaction in a virus-antibody mixture [3] (see also [1]) follows the formula

(Eq. 1)       ,

and the simple reaction in the serial dilutions of a neutralization test with a fixed virus dose follows the formula

(Eq. 2)       ,

where r is the neutralization rate, V₀ and V_T are titers of infective virus after 0 and T hours of reaction, k is the neutralization rate factor, and D is the titer of the antibody medium, i.e., the dilution factor for that dilution of the antibody medium where the virus dose has been reduced to 1 TCID₅₀ after T hours of reaction. If for a first-order reaction, D₁ and D_T are the titers obtained in a neutralization test after 1 and T hours of reaction, this titer-time relationship can be expressed as follows:

(Eq. 3)       or .

In Figs. 3 to 7, the log-log reaction lines with extended reaction periods are linear with a slope coefficient of 1, confirming that the neutralization is proceeding as a first-order reaction.

The results shown in Fig. 5 demonstrate the semi-logarithmic linear relationship between the progression of neutralization and the reaction temperature as documented by Dulbecco et al. (1956)[5]. A decrease in temperature by 10 ^oC within the interval examined will reduce the test sensitivity approximately by a factor of 2.3, and the antibody titer or test sensitivity obtained at 37 ^oC after 24 hours of reaction will not be achieved in tests at room temperature or 4 ^oC until after 4 and 16 days of reaction, respectively. This underlines that the reaction temperature in sensitive antigen-antibody tests should not be below 37 ^oC.

Conclusions summarized.

1. The antibody reaction in a neutralization test with extended reaction is enduring and of
    first order.
2. The sensitivity of a test following a first-order antibody reaction is proportional to the
    reaction time.
3. The sensitivity of a first-order neutralization test is temperature-dependent to such an extent
     that 37 ^oC should be the standard reaction temperature for laboratory tests.
4. A standard neutralization test should be performed with a reaction at 37 ^oC for 24 hours.

3.3. The supplementary complement-dependent virus neutralization.

Yoshino and Taniguchi (1964) [8], see also Yoshino and Morishima (1971) [9], observed an enhanced neutralizing effect in vitro of convalescent-phase antibodies to herpes simplex virus by the addition of complement. Complement-dependent neutralization by antibodies has been found also for other viruses. IgM and IgG antibodies are the significant immunoglobulins involved in neutralization, being deca- and divalent, respectively, cf. reviews by Oldstone 1975 [10], Cooper and Nemerow 1986 [11], and Goldsby et al. 2000 [12]. The complement component C1q has six globular heads capable of binding to the Fc region of antibody molecules that have been sensitized by being coupled with its antigenic determinant. As soon as antibody-virus complexes have been caught by complement, they will be included in non-infectious aggregates.

The supplementary neutralization by non-neutralizing IgM antibodies in association with C1q is huge (Bitsch and Eskildsen (1982) [2]. A maximal neutralization titer increase of 8-9 base-2 log units was obtained 9-11 days after infection (Fig. 8). Also for IgG antibodies a considerable effect, a titer increase of 3 base-2 log units could be noted. Consistently, an investigation of 24 naturally infected animals a long time after natural infection had shown a titer improvement of 3 base-2 log units, cf. Bitsch and Eskildsen 1976 [13].

The effect of complement was found somewhat reduced if added to the virus-antibody mixtures at the start of the reaction (Fig. 7, neutralization line 1-1). A full effect is achieved if the complement is added as late as 15 min. before inoculation of cultures. The results (2-2, 3-3. and 4 in Fig. 7) illustrate that the reaction immediately after the addition of complement is rapid and that it thereafter is of first order, following a first-order binding of non-neutralizing antibodies to their antigenic determinants.

The extremely high neutralization titers for non-neutralizing IgG but not least for non-neutralizing IgM antibodies caused by complement indicate an important role of these antibodies in the prevention and control of viral infections.

Conclusions summarized.

1. The complement component C1q is hexavalent and will bind to the Fc region of antibodies
    that have been bound to their antigenic determinant on a virion, Because of the polyvalency
    of C1q, antibody-virus complexes will thereafter be included in non-infectious aggregates.
2. The supplementary neutralizing effect is caused by a reaction with non-neutralizing antibodies.
3. The complement effect is biphasic. After the addition, C1q will react immediately with
    pre-formed antibody-virus complexes, but thereafter the reaction will continue as a
    first-order reaction, following the first-order binding of non-neutralizing antibodies to their
    antigenic determinants.
4. Complement raised IgG antibody titers by a factor of 8 for herpesviruses but for IgM
    antibodies, the improvement was considerably higher.
5. A standard complement-enriched neutralization test is ideally performed with a reaction at
    37 ^oC for 24 hours. Complement should be added late to achieve optimal sensitivity.

3.4. The factor q, a temperature-dependent co-determiner of the regular virus-antibody neutralization rate.

Considering the linear progression of neutralization with reaction periods exceeding 3 hours as seen in Fig. 3, it will be seen that 1) for any given reaction period, a certain log increase in virus titer will require a log increase in antibody titer of a certain size to have this higher virus dose neutralized to 1 TCID₅₀, and 2) for any antibody concentration this same log increase in virus titer will require a
log increase in reaction period of exactly that same size to neutralize the virus dose to 1 TCID₅₀. This is a consequence of the fact that the slope coefficient of the neutralization lines is 1. This particular log increase per 1 base-10 log unit of virus, a log antibody/log virus ratio, is a characteristic of the first-order neutralization reaction and was in the 1978 study designated the factor q or the log antibody/log virus equivalence factor of neutralization [1].

The relations above 1) between antibody and virus titers, when the reaction time is the same and 2) virus dose and reaction period, when antibody titers are the same, can be expressed by the equations:

(Eq. 4)         , or , and

(Eq. 5)        , or ,

where D expresses the antibody titer, lim D is the limit of D as V approaches 1, and V₁ is the value of V corresponding to T=1 (the factor q is independent of the log base used in the equations).

By comparing the results in Fig. 3 with those in Fig. 4, it will be seen that the factor q at 4 ^oC is almost 50% higher than at 37 ^oC. This reduced effect of antibodies at lower temperatures may be explained simply by a reduced number of hits between the reactants due to reduced molecular movements.

Conclusions summarized.

1. The concentration (titer) of both antigen and antibody determines the rate of neutralization in
    virus-antibody mixtures.
2. The antibody-virus equivalence factor of neutralization or the factor q (a particular log 
    antibody/log virus ratio) is a central characteristic of the first-order antigen-antibody
    reaction.
3. This factor is dependent on the reaction temperature.

3.5. On dissociability of antigen-antibody complexes and the law of mass action.

The stability of the binding between antigens and antibodies has been a matter of debate since the beginning of interaction studies. The forces connecting the reactants have been hypothesized to be weak and to be caused by electrostatic forces, hydrogen bonds, van der Waals forces, and hydrophobic forces, cf. Male et al. 2012 [21], Murphy 2012 [22]. If these concepts should be correct or not is presently unimportant, because they do not explain the question concerning the mechanisms of specificity: the specific attraction and binding between epitopes and their paratopes.

In immunology textbooks (Goldsby et al. 2000 [12], Male et al.2012 [21], Murphy 2012 [22]) and review articles (Svehag (1968) [23], Parren and Burton (2001) [24], Klasse and Sattentau (2002) [17], Reading and Dimmock (2007) [6], Klasse 2014 [7] ) it is generally stated that the antigen-antibody reaction follows, at least principally, the law of mass action (the law of chemical equilibrium) according to which the reaction will lead to an equilibrium state. Conflicting results have in literature been explained in different ways, for example by varying affinity of antibodies. Some authors demonstrated a somewhat higher sensitivity by increasing the reaction time and concluded that bindings might become more stable over time, e.g., Gard 1955 [32], 1957)[33], Svehag 1963 [34], Svehag and Mandel 1964 [35].

When the progression of neutralization in a virus-antibody mixture is measured in samples taken at regular intervals, a semi-logarithmically linear relationship is found [3], cf. Figs. 1 and 6b, and Eq. 1. The dilution procedure used in such cases to disclose the actual advancement of neutralization in the samples can be taken to indicate that the neutralization observed is caused by the formation of antigen-antibody complexes that are not readily dissociable under physiological conditions. A steady, linear progression of a monovalent reaction must be the maximal rate and significant dissociation should give a diminishing rate.

In the 1978 study, the progression of neutralization in a cv/va test was investigated at varying temperatures for reaction periods up to 48 hours at 37 ^oC and 8 days at 4 ^oC (Figs. 3 and 4). After an initial phase characterized by over-neutralization due to the aggregation of virus particles created mainly by non-neutralizing antibodies, the reaction proceeded strictly following the linear relationship seen in individual antigen-antibody mixtures (Eqs. 1 and 2). The investigations were performed with samples collected long after infection. This allows one definite conclusion: the complexes formed between IgG-neutralizing antibodies and the virus are stable and do not dissociate under physiological conditions. Even after extremely long reaction periods, the neutralization rate is constant. The binding of the non-neutralizing IgM antibodies to their epitopes also is a first-order reaction as shown by the addition of complement (Fig. 7).

The neutralization process in vitro of the non-enveloped poliovirus and enveloped herpesviruses directed by antibodies seems to have been most extensively studied, and results appear to be similar. This may not be surprising after all, since significant antigenic neutralization determinants seem predominantly to be glycoproteins, and since immunoglobulins basically are identical, varying only with specificity. Mandel (1961) [25] found no reversibility of neutralized poliovirus-antibody complexes after reaction at 37 ^oC for 2 hours. Jerne and Avegno (1956) [26] stated that only one report (Andrewes and Elford (1933) [27] out of 14 cited had found reactivation of neutralized phages. Andrews and Elford had found for one serum, but not for others, that if a diluted virus-antibody mixture was allowed to stand for some hours before being tested for infectivity, the number of infective particles would be higher than when tested immediately on dilution. Jerne and Avegno found differences among sera collected early and late after immunization, as a late sample was found to neutralize phages irreversibly, whereas neutralization by an early serum taken 8 days after the first immunizing injection appeared to be reversible on dilution. It is obvious that the effect of the early serum was related to IgM antibody, but, unfortunately, serum was used undiluted in the phage-antibody mixture tested and had not been heated to inactivate complement, so the importance of their observation appears to be unclear.

In investigations of dissociability, no attention seems to have been paid to the possibility that the neutralization process might not be mono-factorial. It must be concluded that antigen-antibody complexes as seen with herpesviruses are generally stable under ordinary physiologic conditions. No results contradicting that could be found. Both neutralizing and non-neutralizing IgG and IgM antibodies can be concluded to be firmly bound to their antigenic determinants.

Conclusions summarized.

1. The widely acknowledged concept that neutralization follows the lines of the law of mass
    action, leading to an equilibrium state, does not seem to have been substantiated by results
    from the literature.
2. No evidence of reversibility of virus-antibody bindings under physiologic conditions could 
    be found either.
3. The mechanisms of the specific binding between antigenic determinants and their paratopes 
    haven't been explained.
4. A first-order antigen-antibody reaction at extended reaction periods in a neutralization
    test correlates with monovalent binding and proceeds at a constant rate. Significant 
    dissociation should give a diminishing rate.
5. Both neutralizing and non-neutralizing herpesvirus antibodies were found to be firmly bound
    to their antigenic determinants, following the lines of the antigen-antibody interaction formula
    with extended reaction periods.

3.6. The percentage law.

Andrewes and Elford 1933 [3] presented the so-called percentage law, implying that the percentage of virus neutralized in a virus-antibody mixture is independent of the virus concentration. Burnet et al. 1937 [4] and Dulbecco et al. 1956 [5] accepted their conclusion, which seems to have been widely recognized thereafter, although it was not clearly documented or logically explained.

As shown above, the first-order progression of neutralization found in a neutralization test with reaction periods long enough to make over-neutralization negligible, is in agreement with Eq. 2. However, when this regular reaction was investigated with varying virus doses (Fig. 3), the neutralization rate was found dependent on the virus concentration. This appears from Eq. 6, which follows directly from Eqs. 3, 4, and 5. In Eq. 6, the neutralization rate is shown to depend on the virus concentration to a degree further dependent on the antibody-antigen equivalence factor of neutralization (the factor q).

In consequence of the demonstrated invalidity of the percentage law, the neutralization rate factor given in Eq.2 is not a constant characteristic of the antibody concentration (titer) as usually claimed, but a variable factor further depending on the virus concentration to a degree determined by the factor q. The term neutralization rate factor is, therefore, to be preferred to the neutralization rate constant.

Conclusions summarized.

1. The rate of neutralization in a virus-antibody mixture depends on the concentration of
    antigen as well as the concentration of antibody and the reaction temperature.
2. The hypothetical percentage law is invalid.
3. The term neutralization rate factor should be preferred to neutralization rate constant.

3.7. A residual fraction of virus neutralized at a lower rate (a persistent fraction).

Andrewes and Elford 1933 [3] observed in their investigations on neutralization that a fraction of the virus was refractory to neutralization. Burnet et al. 1937 suggested that it was the result of an equilibrium state of neutralization, while Dulbecco et al. 1956 objected to that, as the fraction was not proportional to the antibody concentration. Various theories have been presented to explain this phenomenon, among these that it is caused by the interaction of non-neutralizing antibodies leading to a sterical hindrance for neutralizing antibodies (Ashe and Notkins 1966 [20], Massey and Schochetman 1981 [28], see also reviews by Parren and Burton 2001 [24], Klasse and Sattentau 2002 [17], and Reading and Dimmock 2007 [6]).

The 1978 study demonstrated that neutralization in a neutralization test with extended reaction proceeds as a first-order reaction but initially is complicated by the rapid and short-lasting aggregation reaction. Both reactions were concluded to be regular. One serum sample, however, showed a deviation with the highest virus dose and long reaction periods, as a residual fraction of the virus was neutralized at a lower rate (Figs. 6a and 6b). Several other sera had been examined in pilot studies, but only this serum showed that complication.

The question was, in which way that particular serum was differing. It had been selected because it originated from a bull at an artificial insemination center, where it had become naturally infected several years before the blood collection. As that animal was a champion bull, his semen was allowed for routine inseminations after the infection had been diagnosed, but preconditioned virological examination with a negative result of a preputial washing collected immediately before semen collection. The virus was demonstrated later occasionally, and at one time it was decided to clarify if a booster injection of culture virus could reduce the risk of re-shedding the virus. So, although the serum originated from a naturally infected animal, it was in fact from an experimental animal having been further immunized by the injection of the virus.

The reduced neutralization observed in the 1978 study in antibody dilutions can logically be explained by the action of non-neutralizing antibodies. In virus-antibody mixtures, virions will literally be coated with antibodies on their surface. This means that the virus particles to be neutralized very late in the course of the process already before the neutralization takes place, or should take place, will have been coated with a variety of non-neutralizing antibodies, which thereby to a degree depending on the reaction time will block for the binding of neutralizing antibodies to their epitopes. The particular circumstances related to the problem observed for this bull point to the possibility that the parenteral immunization had significantly changed the relative concentrations of non-neutralizing and neutralizing antibodies from what is seen in natural antibody media. The antibody samples used by authors having demonstrated a reduced neutralization rate or a persistent fraction of virus had in fact regularly been artificial hyper-immune sera, cf. Andrewes and Elford 1933 [3], Burnet et al. 1937 [4], Dulbecco et al. 1956 [5], Isenogle et al. 1983 [29], had in fact regularly been artificial hyper-immune sera.

A persistent fraction of the virus, or a residual fraction of the virus being neutralized at a lower rate, may therefore very well be considered to be an artifact.

Conclusions summarized.

1. Reduced neutralization - a persistent fraction of virus - is a complication, which has been
    seen in experiments with hyper-immune sera. This phenomenon might be considered an artifact,
    as it is questionable if it will be encountered in vitro with natural immune media.
2. The effect is logically explained simply by overcrowding over time of the surface of
    virions, still remaining to be neutralized, with non-neutralizing antibodies being bound to
    their antigenic determinants. This will in the end create a blockage for the neutralizing 
    antibodies, thereby preventing the neutralization of such virions.
3. Virions overcoated with non-neutralizing antibodies remain infective, as long as they
    have not been included in a virus-antibody aggregate or caught by a neutralizing antibody.

3.8. The formula for the regular in vitro antigen-antibody interactions.

The in vitro virus-antibody neutralization reaction proceeds as two elementary processes: 1) the regular and uncomplicated first-order reaction by binding of antibodies to antigenic neutralization determinants on the virions and 2) an ”over-neutralization” caused by virus aggregation by predominating non-neutralizing antibodies. Over-neutralization can be observed in a neutralization test only with antibody concentrations over a certain moderate level and will be negligible with reaction periods exceeding a certain limit.

For IgM antibodies, the reaction by neutralizing antibodies and the binding of non-neutralizing antibodies to their antigenic determinants were found to proceed as first-order reactions with extended reaction periods. The first-order process is therefore the fundamental antibody reaction in vitro.

In the 1978 article [1], the following formula for this basic neutralization reaction, including also the antigen as a variable, was deduced from the relationships presented in Eqs. 3, 4, and 5 above:

(Eq. 6)               .

where k_st is the standard neutralization rate factor, V₀ is the virus titer (virus dose), T is the reaction time, D is the antibody titer, which in a neutralization test is the dilution factor of that particular dilution of the antibody medium that neutralizes V₀ to 1 TCID₅₀ after a reaction period of T, and q is the log antibody/log antigen equivalence factor of neutralization.

It will be understood that k_st, the neutralization rate factor, is a characteristic expressing the neutralizing potency of an antibody medium. It is proportional to the antibody titer and dependent on the virus concentration to a degree determined by the factor q. It follows from the formula that the antibody titer obtained in a neutralization test, but also the test sensitivity will be proportional to the length of the reaction period. The relationship between the antibody titer and reaction time is of first order, while the relationship between the virus titer and reaction time is exponential.

The temperature is an important variable, which is not shown directly in the formula, but it is included because the values of the factor q are temperature-dependent. In the 1978 study, q was found to be approx. 0.15 at 37 but 0.24 at 4 oC [1].

The character and significance of Eq. 6 might justify a more easily accessible version of the:antigen-antibody interaction formula:

(Eq. 7)             ,
where the symbols D and V0 are substituted with Ab and Ag (antibody and antigen titer). It should be noted that while the virus titer and virus concentration are identical terms, the antibody titer and antibody concentration are not because of multiple antigenic determinants on a virion giving rise to a variety of n especially non-neutralizing antibodies.

Conclusions summarized.

1. The basic antigen-antibody interactions in a neutralization test, where the aggregation is
    eliminated, can be expressed in a relatively simple formula comprising all variables.
2. The neutralization rate factor and the antibody titer for an antibody medium, and
    correspondingly the sensitivity of the antibody test, are directly proportional to the reaction
    time.
3. A linear neutralization rate in a virus-antibody mixture confirms that neutralization is
    of first order, is non-reversible under physiological conditions, and consequently will 
    follow the lines of the formula.

3.9 Implications of the regular lines of antigen-antibody interactions for the elaboration and performance of antigen-antibody tests.

Neutralization tests.

Neutralization of virus by antibody in a neutralization test is the combined effect of two separate reactions, i.e., 1) the regular first-order neutralization reaction, and 2) the over-neutralization that will be seen with moderate to high antibody concentrations and relatively short reaction times.

The level of sensitivity obtained in a neutralization test performed at 37 ^oC and with a reaction period of 24 hours will not be obtained in tests at 22 or 4 ^oC until after a reaction for 4 or 16 days, respectively, cf. Fig. 5. The reaction time should be long enough to ensure that over-neutralization will be negligible. Neutralization will then follow the lines of the regular, first-order reaction, implying that the sensitivity of the test will be strictly proportional to the reaction time. In the herpesvirus studies, an increase of the reaction time at 37 ^oC from 1 to 24 hours raised the sensitivity of a neutralization test by a factor of 16-18 and not by a factor of 24 because of a remaining aggregation reaction recorded after 1 hour of reaction.

A 37^oC/24h neutralization test will be the ideal standard test. In 2008, the World Organization for Animal Health approved the 37^oC/24h neutralization test as a reference standard test in controlling BoHV-1 infections [31].

ELISA modifications.

The conventional antibody ELISA

In a conventional antibody ELISA, the antigen is coated on the wells of microtiter plates, and the reaction to be visualized by the detecting reagent is the progressive binding of antibodies to the antigens. In titrations, titers will show the highest levels of the reacting antibodies to the antigenic determinants fixed to the plates. Aggregation is excluded, so the reaction between antigen and antibody in a dilution series of an antibody sample will be of first order right from the start of the reaction, involving that the sensitivity of an antibody ELISA will be directly proportional to the reaction time.

For herpesvirus 37^oC/24h test modifications, the conventional antibody ELISA is 8 times more sensitive than the first-order neutralization test.

The advantage of an adjustable sensitivity can be illustrated by the following. In 1988, the EU Commission issued a directive (88/406) committing member countries to test their cattle herds twice at an interval from 4 to 12 months for the presence of infection with the bovine leukemia virus, a retrovirus. Dairy herds could be tested for antibodies on pooled milk samples twice with a specified interval, conditioned that not more than 20 cows were represented in a test sample. The sensitivity requirements were indicated by a reference standard sample distributed. In collaboration with G. Florent, Norden Laboratories, the sensitivity of an antibody ELISA as described by Portetelle et al. 1983 [37] was increased by changing the reaction conditions to 37 ^oC for a long period, implying that Danish dairy herds could be controlled on bulk tank milk samples.

The blocking antibody ELISA

Sørensen and Lei 1986 [38] found that the reaction in a blocking antibody ELISA depended on both the reaction temperature and period. The reaction characteristics of a simple test version used with late-infection serum are illustrated in Fig. 9. A log-log linear relationship exists between the antibody titer and reaction time, but the reaction is not of first order but decelerating. An increase in the reaction time by a factor of 16 raised the antibody titer by a factor of approximately 4.

Figure 9. The kinetics of antigen-antibody binding in a serum dilution series as seen in a blocking ELISA for demonstration of SuHV1 antibodies. Bitsch, unpublished.

A twofold dilution series of a natural antibody-positive serum containing predominantly IgG antibody was allowed to react for 1.5, 3, 6, 12, and 24 hours. In the next steps, (1) a specific BoHV1 antibody preparation conjugated to biotin, (2) peroxidase conjugated to avidin, and (3) a suitable substrate were added. Steps 1, 2, and 3 were preceded by thorough washings. Negative samples will show an identical full-color development in the enzyme-substrate, while positive samples will show full or partial blocking of color development. A titer can be recorded by the dilution factor of the dilution showing e.g. 50% of the optic density measured for negative samples. A linear relationship is seen to exist between the logarithmic values of antibody titer and reaction time, (decelerating rate).

The change in reaction from full blocking to no blocking occurs over an antibody titer interval of 5-6 log base-2 units. A log-log linear relationship exists between antibody titer and reaction time. An increase in the reaction time from 1 to 24 hours will raise the antibody titer by a factor of approximately 4 (decelerating rate).

In connection with the eradication of the three widespread respiratory viral SuHV-1, BoHV-1, and bovine viral diarrhea infections in Denmark after 1980, the blocking antibody ELISA was selected for routine testing of undiluted serum/plasma and bulk tank milk samples with reaction at 37 oC for close to 24 hours because of its simplicity and applicability for large-scale examinations.

For herpesvirus 37oC/24h test modifications, the sensitivity of the blocking ELISA was 2 times higher than that of the first-order neutralization test, although 4 times lower than that of the conventional antibody ELISA. This last-mentioned test was used for follow-up examinations or whenever a higher sensitivity was desirable.

The conventional antigen ELISA.

Antigen ELISA versions, where specific capture antibodies are coated to the wells of the microtiter plates, are widely used for the diagnosis of viral infections. The sensitivity will be determined by the frequency of hits between capture antibodies and antigens, or actually the lines of the antigen-antibody interaction formula, indicating an exponential increase of the sensitivity by increasing reaction time. From the data with extended reactions in Fig. 3, it can be seen that 1) if for a constant concentration of the reacting antibody the reaction time i increased by a factor of 2. the amount of virus neutralized will be increased by approx. a factor of 100, and 2) if for a constant reaction period, the concentration of the reaction antibody is increased by a factor of 2, the concentration of virus neutralized is increased by a factor of approx. 100. From the early 1980s, routine examinations for various viral agents were performed in the veterinary field in Denmark with antigen ELISA versions with reaction at 37 oC for close to 24 hours. The test sensitivity was extremely high.

NB:
Rapid and sensitive antigen and antibody ELISAs can be configured by including appropriate aggregation reactions.

Conclusions summarized.

1. The neutralization in a conventional neutralization test proceeds as two separate reactions,
    i.e., a first-order enduring reaction and an aggregation reaction (”over-neutralization”) of
    short duration.
2. Highest sensitivity will always be obtained at a temperature not below 37 ^oC.
3. The conditions for an optimal neutralization test should be selected accordingly:
    over-neutralization should be negligible, the reaction temperature should be 37 ^oC, and the
    reaction period should be extended appropriately.
4. A standard neutralization test for comparative examinations, showing exclusively the reaction
    with neutralizing antibodies being bound to their antigenic neutralization determinant, will be
    an assay with reaction at 37 ^oC for 24 hours.
5. A conventional antibody ELISA is of first order and the sensitivity is proportional to the
   reaction time.
6. The sensitivity of an antigen ELISA will be raised exponentially with increased reaction
    periods.

4. Concluding considerations regarding virus-antibody interactions.

The findings and conclusions from the analyses of antigen-antibody interactions in vitro in this review article are conflict with general concepts of antigen-antibody interactions in vitro, including also the relatively new so-called occupancy theory of neutralization (Parren and Burton 2001 [24], Burton et al.2001 [30]).

In Denmark, the control of the BoHV-1 infection was introduced in the artificial insemination bull centers in 1970 immediately after the eradication of the infection in these centers. A sufficiently high sensitivity of the antibody test used for control was crucial, so comprehensive analyses of the antigen-antibody interactions were conducted [1].

First, the neutralization test was found to be bi-factorial, consisting of an early regular over-neutralization reaction and a neutralization reaction of first order. Second, virus-antibody bindings were found to be irreversible under physiological conditions. Third, the percentage law [3] was found invalid. Fourth, a particular temperature-dependent factor (q) was found to be an important co-determinator of the reaction rate and a central factor in virus-antibody interactions. Fifth, the relationships demonstrated made it possible to present the formula for the regular interactions, not comprising aggregation, between viruses and antibodies (Eqs. 6 and 7).

The implications were of the greatest importance. From the formula, it will be seen that the reaction in a constant-virus/varying-antibody test for demonstration of antibody will be of first order. A titer obtained, or the test sensitivity, will be proportional to the reaction time. As mentioned above, the increase in reaction time from 1 to 24 hours did not increase the sensitivity of a herpesvirus neutralization test by a factor of 24, but by a factor of 16-18 because of a residual over-neutralization by virus aggregation still being recorded after a reaction for 1 hour. Also, IgM antibodies, neutralizing and non-neutralizing, followed a first-order binding reaction with extended reaction times.

The huge neutralizing potency demonstrated for the non-neutralizing antibodies in a joint action with complement indicates a very important role of these antibodies in preventing and combating infectious diseases.

A varying-virus/constant-serum test will be of no practical use for the demonstration of antibodies because an antibody sample of relatively low titer can easily neutralize virus in high concentrations, cf. Fig.3. Inversely, however, for a test where a fixed quantity of antibody is used to catch antigen from a test sample and where this reaction can be visualized as in an antigen ELISA, the test sensitivity will be raised exponentially with increased reaction time, because the value of the factor q is considerably lower than 1, cf. Eq. 7. It should be recalled that the purpose of the use of a test of high sensitivity is not to obtain very high titers but to demonstrate a reactant in low concentrations.

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