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

As models of immune system dynamics are developed, it is important to valid ate them with specific experimental data in order to understand their short comings and guide them toward becoming predictive. In this paper, we examin e whether a particular mathematical model of germinal center dynamics, prop osed by Oprea and Perelson, can reproduce experimental data from two specif ic primary responses, namely those directed against the haptens 2-phenyl-5- oxazolone and (4-hydroxy-3-nitrophenyl)acetyl. We develop formulas for esti mating response-specific model parameters, as well as constraints for valid ating the model. In addition, we outline a general methodology for translat ing a continuous/deterministic model, expressed as a set of ordinary differ ential equations, into a discrete/stochastic framework. This methodology is used to create a new implementation of the Oprea and Perelson model that e nables comparison with data on individual germinal centers. We conclude tha t while the model can reproduce the average dynamics of splenic germinal ce nters, it is at best incomplete and does not reproduce the distribution of individual germinal center behaviors. In addition to suggesting possible ex tensions to the model which can reconcile the dynamics with some aspects of the experimental data, we make a number of specific predictions that can b e tested by in vivo experiments to obtain further insights and validation. (C) 2001 Academic Press.