Mechanisms underlying vaccination protocols that may optimally elicit broadly neutralizing antibodies against highly mutable pathogens

Effective prophylactic vaccines usually induce the immune system to generate potent antibodies that can bind to an antigen and thus prevent it from infecting host cells. B cells produce antibodies by a Darwinian evolutionary process called affinity maturation (AM). During AM, the B cell population evolves in response to the antigen. Antibodies that bind specifically and strongly to the antigen are thus produced. Highly mutable pathogens pose a major challenge to the development of effective vaccines because antibodies that are effective against one strain of the virus may not protect against a mutant strain. Antibodies that can protect against diverse strains of a mutable pathogen are called broadly neutralizing antibodies (bnAbs). In spite of extensive experimental and computational studies that have led to important advances, an effective vaccination strategy that can generate bnAbs does not exist for any highly mutable pathogen. Here we study a minimal model of AM in different time-varying antigenic environments to explore the mechanisms underlying optimal vaccination protocols that maximize the production of bnAbs. We find that the characteristics of the time-varying Kullback-Leibler distance (KLD) between the B cell population distribution and the fitness landscape imposed by antigens is a key determinant of bnAb evolution. The optimal vaccination protocol requires a relatively low KLD in the beginning in order to increase the entropy (diversity) of the B cell population so that the surviving B cells have a high chance of evolving into bnAbs upon subsequently increasing the KLD. For a discretized two-step variation in antigenic environment, there are optimal values of the KLDs for the first and second steps. Phylogenetic tree analysis further reveals the evolutionary pathways that lead to bnAbs. The connections between our results and recent simulation studies of bnAb evolution and the general problem of evolution of generalists versus specialists are discussed.