The fitness and structure of evolved libraries

Fig. shows how fitness scales with the library size A for the Gaussian distribution discussed above. As for the shape-space model, the evolved libraries attain a fitness that has a similar functional dependency on the library size as the random libraries. The dependency is sublogarithmic, that is, the fitness increases slower than linear as a function of the logarithm of the library size. The shape-space model, with a binomial distribution of bond strengths, is well approximated by the Gaussian distributed bond strengths, as we expected.

 

Let us analyze the structure of the evolved libraries. Given the fitness function that we used, we would expect that antibodies that have a high free energy in the unbound state would have the highest chance of lowering their free energy through intermolecular binding. It turns out that the evolved antibodies have higher than average energy. To assess the significance of this difference, we calculate the z-statistic for the evolved antibodies, that is $z = \frac{x - \mu}{\sigma},$ where x is the energy of an evolved antibody, $\mu$ is the mean energy of an antibody molecule, and $\sigma$ is the standard deviation of the energy of an antibody molecule. The evolved antibodies have a z-statistic centered around 2 standard deviations higher than the mean, clearly different from the mean. What this result tell us is that, as expected, the antibodies that were evolved are the equivalent of the "sticky" antibodies, of high interconnectivity and multispecificity, such as those commonly seen in the immune systems of newborns (see for example Kearney et al. (1992)). These antibodies bind not only to pathogens, but to many other molecules normally present in the body, including DNA and molecules on the surface of lymphoid cells. Thus, the evolutionary algorithm was able to evolve a property known to characterize the immune systems of newborns.