Mathematical Modeling to Guide Experimental Design: T Cell Clustering as a Case Study.

Area of Science:

• Immunology
• Computational Biology
• Mathematical Modeling

Background:

• Mathematical models quantify immunological processes and test hypotheses.
• Experimental data collection often precedes model development, with insufficient data for parameter estimation or model discrimination.
• Previous models for CD8 T cell clustering around Plasmodium liver stages include density-dependent recruitment (DDR) and density-independent exit (DIE) models.

Purpose of the Study:

• To conduct power analyses for optimal sample sizes in immunological modeling.
• To determine sample sizes for accurate parameter estimation and discrimination between alternative models.
• To guide experimental design for studying CD8 T cell clustering around Plasmodium liver stages.

Main Methods:

• Developed power analyses to assess sample size requirements.
• Compared longitudinal (LT) and cross-sectional (CS) data collection methods.
• Evaluated the impact of the number of parasites imaged and time points on model parameter estimation.

Main Results:

• Discriminating between DDR and DIE models requires imaging approximately 50 parasites at 2, 4, and 8 hours post-T cell transfer for >95% accuracy.
• Longitudinal imaging provides more precise and less biased parameter estimates for the DDR model than cross-sectional imaging.
• Estimating all DDR model parameters accurately requires measurements at multiple time points, not just one.

Conclusions:

• Mathematical modeling and power analyses are crucial for optimizing experimental design in immunology.
• Optimal sample sizes and data collection strategies (LT vs. CS) enhance the reliability of immunological models.
• This framework can guide experimental design for complex biological processes.