Toward quantitative simulation of germinal center dynamics: Biological and modeling insights from experimental validation

As models of immune system dynamics are developed, it is important to validate them with specific experimental data in order to understand their shortcomings and guide them toward becoming predictive. In this paper, we examine whether a particular mathematical model of germinal center dynamics, proposed by Oprea and Perelson, can reproduce experimental data from two specific primary responses, namely those directed against the haptens 2-phenyl-5-oxazolone and (4-hydroxy-3-nitrophenyl)acetyl. We develop formulas for estimating response-specific model parameters, as well as constraints for validating the model. In addition, we outline a general methodology for translating a continuous/deterministic model, expressed as a set of ordinary differential equations, into a discrete/stochastic framework. This methodology is used to create a new implementation of the Oprea and Perelson model that enables comparison with data on individual germinal centers. We conclude that while the model can reproduce the average dynamics of splenic germinal centers, it is at best incomplete and does not reproduce the distribution of individual germinal center behaviors. In addition to suggesting possible extensions to the model which can reconcile the dynamics with some aspects of the experimental data, we make a number of specific predictions that can be tested by in vivo experiments to obtain further insights and validation.