detect a change in the conformation of the antibody upon binding antigen
     detect a change in the "concentration" via aggregation of antibody bound to antigen

Any conformational change is a thermodynamic equilibrium and even in the absence of antigen there will be some finite amount of the two conformations - all that antigen binding could do is change the equilibrium in favor of the "bound" conformation. So, if free antibody is present at around 10 mg/ml and if antigen-bound antibody is around 1 ng/ml, there is a 10⁷-fold difference in concentration and so big that the thermal noise would be enough to push a significant amount of unbound Ig to the bound conformation, and it would be needlessly eliminated, and far faster than it could be synthesized. Moreover, it is hard to have a system of detection of conformations that would detect single molecules of antibody.

An aggregate of several antibodies bound to an antigen quickly increases the local concentration of antibody and, moreover, if several different antibodies could bind to the same antigen, all would act equivalently in the aggregation-detection reaction. Once a threshold for detection of aggregates is reached here is no advantage to detecting one or one hundred aggregates, meaning that single antigen molecules or bacteria etc. are just as effectively recognized when antibody is bound. We will see later that this mechanism is in fact used, and that the concept of specificity at the level of effector function has to include the recognition of antigens with many antibody binding sites and that antigens with a single antibody binding site could not engage the antigen elimination mechanisms that depend on forming antibody aggregates. This is a key concept and will crop up several times again. Thus, clear thinking for the simple problems will make thinking about the complicated ones much more productive.

The moral to this story is to take each solution and ask the kinds of questions that would reveal why it is impossible. Remember that evolution actively functions to eliminate the bad, not to select for the good.

Antigens:
 

In the beginning there were antigens, then came antibodies, and now there are immunogens, epitopes, paratopes, antigenic determinants, immunoglobulins, and the list grows. Many names are sales gimmicks, though some are ultimately useful.

I tend to think of pathogens as real antigens, and all else as an attempt to mimic a pathogen. Experimentalists like to avoid pathogens because they are hard to handle, particularly if you are a little sloppy. For many years sheep erythrocytes were a favorite along with proteins such as serum albumins and even gamma globulins from all kinds of barnyard sources (including human proteins when working with mouse immune systems). Then came the real chemical era when proteins could be synthesized chemically and all manner of bizarre structures were made. But, what does the immune system think about antigens?

Real anti-gens are patho-gens and thus not studied directly very often; instead we use substitutes that also allow us to forget that a real immune response has to result in the ridding of a growing infectious agent.

It was clear from the earliest days that there were vast numbers of antigens, even as pathogens,  and certainly vastly more than there could possibly be genes to encode one antibody for every antigen. So, if evolution had to get by with less than one, we might ask how few. Imagine an antibody that recognized peptide bonds that are common to all proteins, in this case one antibody would just about be enough. However, if these antibodies are to do their job of protecting against infection by eliminating antigen, then self and nonself peptide bonds would be indistinguishable and thus such an antibody would not have sufficient specificity. Antibodies must recognize a big enough "chunk" of antigen to be able to gather enough information to tell a self antigen from a nonself antigen. This chunk is best described as an epitope, and the corresponding complementary site on the antibody is called a paratope. But, be very careful to remember it is the paratopes of the antibodies that carve antigens into epitopes; in other words, epitopes do not exist without paratopes to define them.

From a knowledge of the chemistry of the antibody molecule we have a good idea of it's surface area of contact. And, if we take the smallest proteins that the immune system has to effectively recognize and rid (around 20 amino acids or 20,000 molecular weight) then the suffice of the antigen can fit around 10 antibodies simultaneously. This gives an important number, roughly the number of epitopes per antigen. There is no way for evolution to select for an immune repertoire that would recognize 100 epitopes per antigen.

Recall that antibody does not eliminate antigen by merely binding - antibody has to be aggregated in order to initiate the immune elimination mechanisms. We also know that antibody is a dimer and has two identical binding sites per molecule and so one antibody can link monomers into dimers, but no more because the antibody can only find one exemplar of each epitope per antigen. Two different specificities of antibody could aggregate a monomer into linear chains, and three could cross-link these into a tangled web of the type that initiates the immune eliminate mechanisms. Thus, if three different antibodies must bind and an average of 10 binds, then the probability according to the Poisson distribution that an antigen will be seen in less than three ways is around 1 in 10³. To miss 1 in 10² seems like an immune system that would miss too many antigens and not protect us well whereas to miss 1 in 10⁴ sounds like an immune specificity that is too good to be true - i.e., evolution could not select for such superb precision because there are too many other ways for individuals to be killed. See below for some interesting calculations that show how specificity is dramatically increased by the combinatorial effect of requiring three or more different antibodies to bind in order to elicit the bio-destructive effector reaction.

The paratope is what evolution selected on to be sufficiently specific and epitopes are simply a convenient way of describing what antibodies recognize. Although the paratope is considered to be the complement of the epitope, it is the paratope that defines the epitope. For example, an experimentor could find many different chemicals that bind to a particular antibody and yet it could not be argued that the antibody contained many different paratopes. Just as evolution selected one antibody per cell so there is only one specificity (paratope) per antibody. From the immune system's point of view all of the different chemicals that bind a particular paratope are a single epitope. From the pathogen's point of view making new epitopes that are not recognized by a particular paratope is of great importance in the survival of the pathogen.

The immune system is at one level rather simple. It reacts to antigens only when it is exposed to them - seemingly self-evident, but often ignored. For example, most antigens inside of cells cannot be "seen" by the antibody system - they are simply not extracellular antigens, yet when these antigens are taken out purified and injected into the serum there is widespread surprise that the animal responds to an antigen that can be labeled (genetically and by the experimentor) as "self."  In the same vein the immune system reacts above some threshold concentration. In other words it is not able to detect and respond to single molecules, there have to be enough of them to hit the threshold. And, finally there is the self-nonself distinction to be made. The immune system cannot respond to self antigens in the sense that the response cannot be to cause the elimination of self. There may be some antibodies to self antigens and these antibodies may have full access to these antigens, but if this reaction does not lead to self destruction, the immune system does not care one whit.

Immunogenicity: If there was an immune response in the forest and nobody was there to measure it...?? The point to remember in this context is that an immune response to some nonpathogenic protein has to be measure by some experimentor, and depending on how good the tools are, an immune reaction might or might not be measured. In other words, the magnitude of the immune response is going to be an important parameter, depending on how it is measured. So, some antigenic insults may result in small immune responses, too small to be measured by the tools available, and the compound is said to be nonimmunogenic - or the experimentor is incompetent. There may be a huge immune response, but in a class that was not assayed - more incompetence not nonimmunogenicity. And, of course, there may indeed be no immune response. What we can say is that the same antigen in two different contexts can produce dramatically different magnitudes of immune response. One of the classic terms describing such contextual differences is Adjuvant. Typically adjuvants are irritants and aggregative, they initiate powerful inflammatory reactions and make huge lumps of antigen that are easily hauled off into lymph nodes etc. For vaccines these Adjuvants can be very important, especially when small bits of the pathogen are used for safety reasons and the immune system has to work hard to find epitopes on the fragment of the pathogen.

    We understand that antibodies had to be dimeric in order to participate in aggregation reactions. The biochemical name for antibodies is Immunoglobulin (Ig). When talking about the chemistry object I like to use the word Immunoglobulin or Ig, and when talking about the biological defense mechanism I tend to talk about antibodies - for the most part these two terms are interchangeable.

    We also know that the number of different antibody specificities should be as large as possible, and this has to be almost certainly larger than the number of genes available to code for each different specificity. The question is, how to use a small number of genes and get a large number of different products. Evolution reverts to the classic combinatorial rule, just as it did when using 4 nucleotides taken 3 at a time to make the genetic code for 20+ amino acids (albeit with a little overkill). In the case of Ig there are two subunits needed to make a single antigen binding site (i.e., paratope). One subunit was found to have a molecular mass of around 20,000 D while the other was 40,000+. Naturally in the golden day these were designated light and heavy chains (today they would have more likely been labeled alpha and beta - Greek being the popular source of biologists jargon to differentiate them from the Latinized medical profession). The terms L and H are used extensively and should be treated with a reverence equal to T and B cells.

    Recall that the antibody had to be dimeric (a homodimer) to be able to aggregate antigen. The (LH)₂ dimer is the basic structure for Ig. It will not surprise you to know that there are several different kinds of Ig that deal with several different kinds of extracellular pathogen. In fact there are 7 distinct different Igs, for humans these are IgM, IgG1, 2, 3, 4, IgE, and IgA. These are usually called isotypes, or classes of antibody. There is one further class termed IgD, which is predominantly found on the surface of B cells and only trace amounts in serum that are generally thought to be from B cell breakdown. The IgD class has no known function. All the other 7 isotypes have distinct functions.

    The IgM and IgA molecules are polymers of the (LH)₂. IgM has five of these dimers and IgA has two dimers of the (LH)2 form. IgA is special because it is found predominantly in mucosal secretions and it is well documented that this form of Ig can pass through epithelial cells in order to reached the outside of the body. IgA is found in saliva. tears, and gut secretions. The odd thing from out point of view is that IgM is an aggregated pentamer and should most likely stimulate immune elimination reactions - yet it obviously does not. Is the aggregation principle violated? Yes, in the special case of IgM because the demonstration of direct plaques in a sheep erythrocyte (SRBC) assay is unique to IgM because IgG antibodies of the same specificity do not give plaques unless anti-Ig is added in order to further capture and aggregate the Ig around the SRBC. Thus it would seem that IgM can undergo a conformational change within the pentamer when two sites are occupied causing strain on the pentamer that is detected by immune elimination mechanisms.

    The reason for LH pairs is the ancient problem of getting the biggest bang possible from the genes. There are obviously vastly more pathogenic epitopes than there are genes to encode antibody paratopes. The solution is the normal combinatorial rule. Recall how 4 nucleotide pairs had to specify 20+ amino acids.  Evolution simply did it my multiples of 4 nucleotides taken 3 at a time to get 64 possible codons. The immune system went the same way. It took about 10² different L chain genes and 10² different H chain genes and made 10⁴ different LH pairs. For the moment we will just accept 100 as a magic number. Another magic number is 10⁶, which represents  close to the maximum size of the immediately functional antibody repertoire. Recall that pathogens grow and the immune system has a strict time limit on how long it can take to reach an effective concentration of antibody. The smaller the repertoire the larger the number of copies of each specificity and the shorter the time taken to reach an effective concentration. But, the smaller the repertoire the fewer pathogens can be recognized and ridded. The question is how to optimize these two boundary conditions. For reasons that will be easier understood later, a smallish repertoire at high copy number (e.g., the germline repertoire of 10⁴) is used to generate a mutant repertoire of about 100 total possible single step mutants per L or H, and thus a single copy repertoire of around 10⁶. When we get to the genetics the reasons for all of these magic numbers will be more easily understood.

Calculation of some probabilities that the antibody repertoire will not recognize and antigen in at least three ways as a function of the number of epitopes per antigen.

    The above table was calculated to illustrate how the average number of epitopes per antigen affects survival in an immune system that used a particular value. The Poisson distribution is used to compute the sum of the probabilities of 0, 1, and 2 epitopes actually being recognized for the indicated average number of epitopes recognized per antigen. Results are expressed both as a probability and as a rate to better indicate the proportions of antigens that would be missed should evolution have adopted a particular average number of epitopes per antigen.

    It is assumed that the limiting case for evolution is a monomeric toxin that has to be eliminated by bio-destructive effector mechanisms that recognize aggregates of antibody. The reaction of a monomer with a single specificity of antibody results in dimers (the antibody is a dimer of two identical paratopes). Two antibodies would lead to the formation of linear chains, and only when three or more different antibodies are present can tangled webs form the aggregates needed to induce immune elimination.

    It is worth noting that most descriptions of antibodies at work equate binding of antibody to antigen as synonymous with ridding the antigen. This is a typical experimental blind spot. Most of the antigens used are non pathogenic and rather simple proteins or cells and to assay the presence and amount of antibody a simple binding assay is most commonly used - the radio immune, or enzyme linked (ELISA) assays, where labeled antigen or antibody is added to antibody or antigen that is stuck to plastic. By doing these non biological assays for so long it is generally forgotten that aggregates have to form in order to rid the antigen.

    In this whole section we are thinking about a relatively large repertoire of antibodies (i.e., paratopes) of random specificity reacting with a narrowly defined antigen (i.e., epitopes). That is to say a large random paratope repertoire is smaller than the total epitopic repertoire and that antigens represent a small sample of the epitopic set, and the size of this sample is what is termed the number of epitopes per antigen. Evolution selected on the structure of the paratopic site to set the size of an epitope and hence the average number of epitopes per antigen.

    One final thought. Consider the case of polymers where a single antibody could cause crosslinking. If mere aggregation was sufficient to induce elimination then there would be no need for antibody because most pathogens are already aggregated. Indeed most of the so-called innate "immune" reactions are reactions against aggregates. It is the aggregation of antibody that is key to initiating the immune elimination mechanisms that detect lumps of antibody in particular. Thus, the average pathogen has evolved to spread it's epitopes on it's surface so as to avoid having a single antibody present at high enough density to initiate immune elimination. After careful though it seems that even polymers need to react with three or more different antibodies to make aggregates of antibody because aggregates of antigen are inadequate. In the overall battle of host-parasite relationships there is always a bug that escapes whatever defense mechanism is present, whether in a bacterium of man, and yet such parasites are not evolutionarily selectable because they quickly kill all of their hosts and run out of "food."

Chapter 5, up; to monoclonal antibodies pg 131.

Chapter 6 can be read, though most of it is not examinable. Treat it as a novel remembering the kinds of material covered so you can find it later when it is referred to.