Somatic generation of antibody diversity. Journal of Theoretical Biology, 141(2): 211-245 (1989) The NK Model of rugged fitness landscapes and its application to the maturation of the immune response. A single V gene segment encodes the immune response to phosphorylcholine: somatic mutation is correlated with the class of the antibody. Inter- and intraclonal diversity in the antibody response to influenza hemagglutin. In particular, their model suggests that typical epistasis in the CDR is on the order of 40 proteins (out of the total 112 proteins in the CDR).Ĭlark, S.H., Huppi, K., Ruezinsky, D., Staudt, L., Gerhard, W., & Weigert, M. Kauffman & Weinberger (1989) showed how this model can be used to study affinity maturation, and showed that to achieve a sudden leap we need high epistasis and low correlations between pointwise mutants. With a protein sequence on $N$ sites, we say that evolution is fast (and we have a sudden leap) if after our fitness landscape changes, we can get to a new local equilibrium in a number of generations that scales with $\log N$. The standard mathematical model for this is Kauffman's NK model. The length of this evolutionary process is very short, typically a local equilibrium is found after only 6-8 nucleotide changes in CDR (Crews et al., 1981 Tonegawa, 1983 Clark et al., 1985), so you need only a few point mutations to quickly develop a drastically better tuned antibody. Variability is introduced by a very high mutation rate in the complementarity determing region (CDR).
There is differential survival, with only antibodies with the highest affinity being able to survive. The cool part, is that the antigen produced is tuned via an evolutionary process! However, after some exposure time, your B cells will start to produce antibodies with much higher affinities for the antigen and thus you will be able to better fight off the disease. If it is your first exposure to the antigen then the antibodies produced will probably have very low binding affinity.
In the human immune system, when exposed to an antigen B cells produce antibodies. However, if you want to look at where this is the norm and try to build a mathematical theory then you need to look at something much smaller the prime candidate is affinity maturation. And provided you with a nice observational account of sudden leaps in large organisms.
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