Kinetic modeling of Toxoplasma gondii invasion

The phylum Apicomplexa includes parasites responsible for global scourges such as malaria, cryptosporidiosis, and toxoplasmosis. Parasites in this phylum reproduce inside the cells of their hosts, making invasion of host cells an essential step of their life cycle. Characterizing the stages of host-cell invasion, has traditionally involved tedious microscopic observations of individual parasites over time. As an alternative, we introduce the use of compartment models for interpreting data collected from snapshots of synchronized populations of invading parasites. Parameters of the model are estimated via a maximum negative log-likelihood principle. Estimated parameter values and their 95% confidence intervals (95% CI), are consistent with reported observations of individual parasites. For RH strain parasites, our model yields that: (1) penetration of the host-cell plasma membrane takes 26s (95% CI: 22-30s); (2) parasites that ultimately invade, remain attached three times longer than parasites that eventually detach from the host cells, and (3) 25% (95% CI: 19-33%) of parasites invade while 75% (95% CI: 67-81%) eventually detach from their host cells without progressing to invasion. A key feature of the model is the incorporation of invasion stages that cannot be directly observed. This allows us to characterize the phenomenon of parasite detachment from host cells. The properties of this phenomenon would be difficult to quantify without a mathematical model. We conclude that mathematical modeling provides a powerful new tool for characterizing the stages of host-cell invasion by intracellular parasites.