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The immune system task is to recognize and kill entities which do not belong to the organism ("self") [Atlan and Cohen 98].

The standard scheme describing the way the immune system does it is shown in FIG( 2 ).

Already at the very superficial level, one sees that the scheme in Fig 2 is very similar with the Figure (1) which describes the consequences of the autocatalysis equation 1 (or the reproduction of capital reaction 3.1 for that matter).

Let us describe in more detail what happens in Figure (2).

At the left of the diagram Fig (2), the immune system is producing (by iterated divisions) cells which are called B-cells and which (as opposed to all the other cells in the organism) undergo mutations in as far as their genetic information is concerned.

For instance, after 3 generations of divisions, one ends up with 2³ =8 B-cells in the middle of Figure 2. In reality, the B-cells carrying different genetic information are identified rather by a specific shape which each of them owns (as shown for the cells 1-8 in the Fig 2).

From now on the story of the B-cells is exactly like the one of the neutrons and the U235: whenever the a B-cell hits an entity which carries a shape complementary to its own specific shape (this is called and Antigen and it is denoted by Ag) 3 things happen:

1. The Ag entity is (eventually) destroyed
2. The B cell life is prolonged
3. New B cells with the same genes (and specific shape) are (eventually) produced

This is shown in Fig 2: an entity having shapes which fit the B-cells 2, 4, and 7 is present (around the center of the upper edge of Fig 2). Consequently, B-cells 2, 4 and 7 reproduce and the Ag is destroyed.

B+ Ag -----------> B+B + etc.              autocatalysis equation 2

The rest of the Fig 2 is not of interest for our purpose. We already have all the ingredients for our "B-bomb":

The B's resulting from autocatalysis equation 2 will "hit" other Ag's and generate new B's. As long as there are Ag's around, the B's will keep proliferating exponentially. This is the phase where the microscopic heterogeneity is amplified by auto-catalytic reactions to macroscopic coherent spatio-temporal features: in the present case the mounting of the macroscopic immune response by the organism. One should not consider auto-catalysis our exclusively our ally: after all is how the antigens act too in order to mount and localize ever-changing adaptive attacks on the integrity of our immune "self".

In conclusion: whenever a critical mass of a foreign entity Ag shows up, there will be always at least one of the 2ⁿ B-cells which fit it (is Idiotypic to it). The chain reaction autocatalysis equation 2 insures that, very fast, a large number of B-cells Idiotypic to Ag are produced and all the Ag destroyed.

Of course there are saturation mechanisms (B's competition for space / resources, repeated B - Ag encounters) as well as mutations of the Eigen –Schuster mutation ones. These additional effects, as well as the spatial distribution lead to equations of the type which introduce the additional terms corresponding to (spatially distributed logistic) or (diff eq logistic system ) with stochastic coefficients.

In fact those are responsible for the scaling behavior of the type described in JD Burgos, P Moreno-Tovar (1996), "Zipf-scaling behavior in the immune system", Biosystems, 39(3):227-232.

Fig 9

The left (yellow discs) part of the scheme insures (by repeated reproduction and mutations) that there are so many different types of B-cells, that for any Antigen presented to the body, there is at least one B-cell fitting (being Idiotypic to) it. This is the phase of creating microscopic inhomogeneity in the B genetic space.

The gray disks in the middle part of the diagram represent a particular Antigen Ag which fits the B-cells 2,4 and 7.

The multi-colored right part of the figure shows the subsequent proliferation of 2,4,7 cells (and other operations directed towards killing Ag). This is the auto-catalytic phase localizing (in the genetic space) the defense against Ag.

http://wsrv.clas.virginia.edu/~rjh9u/clsel.html - page maintained by Robert J. Huskey, last updated December 1, 1998.

JD Burgos, P Moreno-Tovar (1996), "Zipf-scaling behavior in the immune system", Biosystems, 39(3):227-232.

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