#### Rob Boer, Alan Perelson

Paper #: 90-017

The development of the immune repertoire during neonatal life involves a strong selection process among different clones. The immune system is genetically capable of producing a much more diverse set of lymphocyte receptors than are expressed in the actual repertoire. By means of a model we investigate the hypothesis that repertoire selection is carried out during early life by the immune network. We develop a model network in which possibly hundreds of B cell clones proliferate and produce antibodies following stimulation. Stimulation is viewed as occurring through receptor crosslinking and is modeled via a log bell-shaped dose-response function. Through secretion of free antibody B cell clones can stiulate one another if their receptors have complementary shapes. Receptor shapes are modeled as binary strings and complementarity is evaluated by a string matching algorithm. The dynamic behavior of our model is typically oscillatory and for some parameters chaotic. In the case of two complementary B cell clones, the chaotic attractor has a number of features in common with the Lorenz attractor. The networks we model do not have a predetermined size or topology. Rather, we model the bone marrow as a source which generates novel clones. These novel clones can either be incorporated into the network or remain isolated, mimicking the non-network portion of the immune system. Clones are removed from the network if they fail to expand. We invstigate the properties of the network as a function of “$P(match)$,” the probability that two randomly selected immunoglobulins have complementary shapes. As the model networks evolve they develop a number of self-regulatory features. Most importantly, networks attain a specific equilibrium size and generate a characteristic amount of “natural” antibody. Because the network reaches an asymptotic size even though the bone marrow keeps supplying novel clones, clones must compete for presence in the network, i.e., repertoire selection takes place. Networks comprised of cells with multireactive receptors remain small, whereas networks consisting of cells with specific receptors become much larger. We find an inverse relationship between $n$, the number of clones,in a network, and $P(match)$, and a linear relationship between $n$ and $M$, the rate at which novel clones are produced in the bone marrow. We present a simple phenomenological model for the number of clones in the network that accounts for the inverse relationship between $n$ and $P(match)$, and that can account for the relationshipo between $n$ and $M$. Additionally, the phenomenological model suggests that there are two qualitatively different network equilibria. The number of clones a given clone interacts with, its ‘connectivity,’ is another emergent property of these netowrks. During early ontogeny, before the network reaches its equilibrium size, the connectivity may become very high. Within a few months however, networks attain a degree of connectivity that is hardly dependent on the matching probability of the receptors. The networks appear to select for specificity: the average connectivity always remains lower than expected, and the selection process favors adding novel specific clones over maintaining established multireactive ones. We discuss the “dominance” of specificity, and the fact that the connectivity is lower than expected because clones tend to occupy similar regions in shape space. The rate at which antibodies in solution are removed from the system by forming idiotypic complexes, and the parameter in the dose-response curve determining the onset of suppression, turn out to be the most crucial parameters of the model. To summarize, we show how an immune network could select a limited actual repertoire from a seemingly infinite source of novelty from the bone marrow.