Ph.D Thesis Colloquium: Akshay Tiwari

Mathematical modelling of antibody responses for vaccine design and assessment of vaccine efficacies.

Designing vaccines that generate potent immune responses is often a challenge, especially against rapidly evolving pathogens like HIV. B cells, which produce antibodies, are the primary mediators of protective responses induced by most licensed human vaccines. In recent studies, the use of vaccines carrying ‘multivalent’ antigen has shown promise in improving B cell responses. High valency antigens amplify the magnitude of the B cell response. However, they often reduce the specificity of the response, raising a critical question: Is there a valency at which the B cell response is optimal? Here, we address this question by developing a mathematical model of the germinal center, where B cell responses mature. Germinal centers are microstructures in secondary lymphoid organs where B cells evolve to increase their affinity towards their target antigen. B cell selection in GCs depends on the ability of the B cells to acquire antigen presented on the surfaces of dendritic cells in the GCs. Antigen valency modulates this process. We developed a biophysical theory to predict the probability of antigen acquisition by B cells depending on the affinity of its receptors for the antigen and the antigen valency. The theory also accounts for the mechanical pulling force applied by the B cell to extract antigen. We employed the theory in a model of repeated cycles of selection of B cells in the GC, predicting the antibody response. Model predictions recapitulate experimental observations of the quality-quantity trade-off in the antibody response with increasing antigen valency. We identify the valency that optimizes the response. Our findings have implications for vaccine design and immunotherapies.

An important outcome of COVID-19 vaccines was to render potentially symptomatic infections asymptomatic. Assessment of vaccine efficacies thus require accurate estimation of the prevalence of asymptomatic SARS-CoV-2 infections, 𝜓, in clinical trials. Two-part population-based surveys, combining infection testing with symptom assessment, have been the primary method for estimating 𝜓. We identified a major confounding factor in these surveys that leads to a systematic underestimation of 𝜓: many symptoms associated with COVID-19, such as fever and cough, are nonspecific and can arise from other conditions, including influenza and circulating coronaviruses. This nonspecificity misclassifies individuals experiencing symptoms from other causes as symptomatic for SARS-CoV-2, skewing prevalence estimates downward. To correct for this bias, we developed a rigorous formalism that adjusts for the nonspecificity of symptoms while simultaneously accounting for the sensitivity and specificity of the SARS-CoV-2 tests used in the surveys. The adjustment resulted in a facile formula for the corrected prevalence, 𝜓. We applied this formalism to data from 50 published serosurveys conducted across 28 countries. Our analysis revealed that 𝜓 was significantly higher than previously reported (P = 3 × 10⁻⁸), with several instances where the estimates had to be revised upward by over 100%. These findings suggest that asymptomatic infections have been far more prevalent than previously recognized. By enabling accurate estimation of 𝜓, our formalism helps better assess vaccine efficacies. The formalism is also applicable to other pathogens that can cause asymptomatic infections.