Protecton Notes and Introduction:

Skip the blurb and jump in

The Protecton is in principle a unit of Protection and represents an attempt to deal with the equivalence of Protection as animals increasing size during development, and the vastly different sizes of adult, ranging from tadpoles to elephants. The computer program available here is a representation of the immunolgobulin-based Protecton. The concept is to think of the smallest sample of B cells that would provide a level of protection that is equivalent to the whole. This sample of cells would represent the protective repertoire.

Three key elements are needed to make the concept work.

Each of these elements is open to change depending on particular circumstances. For example: In short, there is no universal Protecton, but one for every pathogen under every different circumstance. One good way to think of the Protecton is as a unit of measure of protection, akin to milliliters as a measure of volume. To illustrate some of the consequences of using the concept of a Protecton it is illuminating to sketch out the limit case that provide the dominant selection pressure in evolution.

The limit case of an evolutionarily selective Protecton.

Based on a rough experimental overview, there are some pathogens that kill the host in less than 7-10 days post infection, and in these cases the antibody response is protective only if it is starting to lower the pathogenic load on or about day 5. This does not imply that all pathogens behave this way, but for the sake of illustration these are common observations of the kind that might well be expected to act as a coherent and reproducible selection pressure over many generations. In these cases the protective level of antibody is typical in the range of 10 - 100 ng/ml, and to emphasize the limit of selection, a concentration of 100 ng/ml of protective anybody is need on or before day 5 after infection.

Variables of the antibody-based Protecton

1. The first and most difficult variable to choose is the number of specificities that will form the functional paratopic repertoire. 2. The second variable concerns the number of functional V exons. This is given a single value even though there are heavy (H) and light (L) chains with V-segments. Given that selection operates on the VLVH pairs, and this maintains a certain number of V segments in the germline, it follows that there must be roughly the same number of V-segments for L and H chains, and hence the single number for this variable.

3. Another difficult variable is FIT, which sums the effects of the DH reading frame (one frame is strongly preferred), length matching of the DNJ region of the H chain for a given L chain, and any other factors that determine whether a given LH pair can act as a B cell receptor and transduce tolerance/induction signals upon binding antigen. The FIT factor would have to be fixed at unity in any model of B cell receptor function that required a simple antigen-driven aggregation signal to the B cell. This aggregation-only class of model treats the receptor as a pure binding device that is aggregated by forces outside the Ig molecule. ONLY if the antigen binding event causes the Ig receptor to undergo some change in order to generate the aggregation signal can the FIT factor be anything other than unity. Although the mouse does not seem to produce DH in both productive reading frames (one reading frame usually leads to termination codons in DH), in other species such as humans, chickens, and rabbits where there is some data, two reading frames appear in receptor Ig prior to antigenic selection and only one reading frame is used after selection, thereby implying some receptor Ig is non-functional in the signaling process. There is also the effect seen in all tested species, including mouse, that whenever an antibody uses a single light chain to produce a particular antibody, the length of the DNJ is constant even though the gene fusion process generates large length differences. This in not simply a repertoire problem because the sequence of amino acids can vary when the length does not, and when different VH pair with the same VL, the DNJ length is roughly the same and is determined by the L chain (kappa V-segments  vary up to 10 amino acids in length).

4. The mutation rate is calculated as a log base 10, and the requested parameter is the exponent base 10. The default value of 10-3 per base pair per cell division is close to the optimal number derived from an analysis of the number of CD codons (10 is the average per VLVH pair) and the probability that an amino acid replacement will wreck the molecule, either in CD or in the framework (FW). There is general agreement that in the mouse at least there is hyper mutation (the background normal mutation rate would be closer to 10-9 per base pair per division). This variable is applied only once after the first Ig is formed and one round of cell division and somatic hyper mutation before the B cell becomes a member of the recalculating newborn subset that represents the antigen unselected repertoire.

5. K is the probability a somatic mutation, or a germline one for that matter, will result in a change of antibody specificity and that change will produce anti-S. In effect this is the parameter that describes specificity of the Ig molecule. Any change in specificity that results in some anti-NS is weakly selected for, and the susceptibility of the Ig to changes in specificity by mutation is a basic property of the molecule and is common to all VLVH structures. In other words, the K for one VLVH cannot be very different from the K of all other VLVH pairs. The default value of 0.01 implies that the ratio of anti-S to anti-NS in the repertoire is 1 in 100. Values of 0.1 seem to be unrealistic even on experimental grounds, and values of 0.001 are barely selectable in evolution.

6. FL is a probability that an anti-F in the Ig repertoire will be engaged at any given time by antigen. Notice that there is a second parameter PL, which distinguishes the anti-F that is germline selected, and called anti-P to designate it's status as being likely directed at some common pathogen that maintains the N germline V segments. The remainder of the anti-NS that is not anti-P is called anti-F, and this is the repertoire that is unselected and simply generated somatically by random VLVH pairing and the gene fusion process. This probability of anti-F being engaged measures the strength of the antigenic load. In other words, the antibody system is under some roughly constant level of antigenic stimulation which is aside from rare massive pathogenic insults. Whatever the antibody repertoire, it has to be maintained by selection, and selection is by antigens. The default value of 5% if the repertoire is considered a lower limit on the grounds that over the lifetime of the individual, the majority of the repertoire should have been tested at least once. While in some long lived species the value of FL might be ten-fold less, evolution had to set the Protecton to function in the worst case setting and we assume that a set of seasonal pathogens will represent the majority of the antigenic load, meaning that there is not much more than 10 - 30 infectious episodes per year to test the load, making the default value of 5% on the lower side of reasonable.

7. PL is by analogy with FL the probability that the individual will engage the anti-P germline selected repertoire of N specificities, and because these are common pathogens the default value is again set at a low 10%.

8. This item, the concentration of antibody that is going to be protective. The results then compute how many days it will take on average to produce this concentration of antibody based on the rule of 3 or more different specificities with a combined concentration of this variable given the default value of 100 ng/ml

9. The minimum number of epitopes in the antigenic load is generally of no interest. However, if the calculations are adjusted to examine the effects of very small values of N, early during evolution perhaps, then the parameters FL and PL are unable to accurately reflect the antigenic selection, making this variable particularly useful for this highly specialized use of the calculation.

10. The total number of B cells per ml is apparently a constant for all species and we use 107 as a close round number. This is the total B cells and the total fluid volume into which the antibodies diffuse, not the number of B cells per ml of blood which is about ten fold less, and again constant. This variable is most useful when examining possible evolutionary choices governing why, perhaps this number of B cells per ml was not ten fold lower or higher than presently found.
Start choosing the variables and running the calculations
Return to CIG Home Page