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 Antibody Maturation

by the

Natural Selection

of

Randomly Generated Mutants .

Naive B Lymphocytes are formed by gene re-arrangement so that their antibody genes contain random combinations drawn from a repertoire of more than 30,000,000 different possibilities.  Those which bind weakly to an antigen form a Quasi-Species with considerable "mountaineering"  capabilities.  The fitness landscape for these B Lymphocytes is determined by the strength of their ability to bind to the antigen. The high mutation rates characteristic of a Quasi-Species  are provided by Hypermutation.

This animation presents the results of a simple simulation designed to illustrate the adaptive power of Evolution by the Natural Selection of random mutations. In this, the "Target" antibody gene is represented uniquely by the following 12 digit decimal number chosen at random:

829472749371

The fitness landscape is a "Stepped Pyramid" .  Antibodies with gene combinations represented by numbers of the form: 8XXXXXXXXXXX bind weakly to the antigen and other forms don't bind at all. Antibodies represented by numbers of the form 82XXXXXXXXX all bind more strongly and 829XXXXXXXXX stronger still and so on. This is represented by the following table:

The simulation starts at T=0 with all of the Lymphocytes at fitness level 1. As mutants with greater fitness appear at random they compete with lower fitness variants and drive them extinct. This causes the mean of the distribution to move towards the peak in the fitness landscape. This peak corresponds to the antibody form that gives the strongest available binding to the antigen.

The animation shows that the Lymphocytes find the target value in a Sequence Space of 10^12 possible values with a total population size of < 10 ^ 6.