Minimal model reveals key features of vaccination protocols that optimally elicit broadly neutralizing antibodies*

During affinity maturation, B cell populations evolve in response to time-varying environments within germinal centers (GC). Recent simulations and experiments have shown that controlling the temporal application and degree of “frustration” (i.e. conflicting selection forces) within the GC crucially determines the successful production of broadly neutralizing antibodies (bnAbs). A one-dimensional fitness landscape enables us to quantify frustration as the change in entropy of the imposed fitness distribution as the selection forces change with time. Using a simple birth-death model, we then find that an optimal temporal profile of frustration maximizes bnAb production and determines the mechanisms underlying this result. The vaccination protocol requires a relatively low optimal level of frustration during GC priming to maintain the correct level of B cell diversity so that the surviving B cells have a high chance of evolving into bnAbs upon subsequently increasing the frustration by choosing appropriately designed vaccine immunogens. Our results also illustrate the importance of clonal interference in bnAb evolution due to time-varying environments.