A Generalized Mathematical Model To Estimate T- and B-Cell Receptor Diversities Using AmpliCot

Abstract

The efficiency of the adaptive immune system is dependent on the diversity of T- and B-cell receptors, which is created by random rearrangement of receptor gene segments. AmpliCot is an experimental technique that allows the measurement of the diversity of the T- and B-cell repertoire. This procedure has the advantage over other cloning and sequencing techniques of being time- and expense-effective. In previous studies, receptor diversity, measured with AmpliCot, has been inferred assuming a second-order kinetics model. The latter implies that the relation between diversity and concentration × time (Cot) values is linear. We show that a more detailed model, involving heteroduplex and transient-duplex formation, leads to significantly better fits of experimental data and to nonlinear diversity-Cot relations. We propose an alternative fitting procedure, which is straightforward to apply and which gives an improved description of the relationship between Cot values and diversity.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

“… 2012 ; Baltcheva et al. 2012 ; Lythe et al. 2016 ), or the use of T cell receptor excision circles (TREC) to quantify thymic output (Dool and Boer 2006 ).…”

“… Baltcheva et al. ( 2012 ) developed two non-spatial mathematical models (of ODE type) and used them to understand the kinetics of the concentration of DNA molecules obtained via the AmpliCot technique, which measures the diversity of DNA samples through quantification of rehybridisation speed of polymerase chain reaction (PCR) products. The two models in Baltcheva et al.…”

“…The two models in Baltcheva et al. ( 2012 ) (a simple second-order kinetics for the formation of homoduplexes of complementary strands of DNA, and a more complex heteroduplex model for these DNA strands) were then used to fit the variable for the proportion of fluorescent material in the sample to available experimental data. Confidence intervals for the parameter values were also computed, using bootstrap replicates of the data.…”

“…However, the authors used the likelihood ratio test for nested models to show that the improved data fit observed with the heteroduplex model was significant for all three data sets used in model validation (Baltcheva et al. 2012 ). These types of results emphasise the usefulness of mathematical models on allowing us to discriminate between models/assumptions capable to fit or not the data [aspect considered important by Oreskes et al.…”