Abstract
Germinal centers (GC) are dynamic, short-lived anatomical structures generated within lymphoid follicles during immune responses to protein-containing antigens. There, follicular dendritic cells, antigen-specific B cells, and follicular T helper cells engage with each other in an antigen dependent way, setting into play a mini-evolutionary ecosystem that ultimately lead to antibody affinity maturation, with the resulting GC reaction following a rise-and-fall dynamics. The complexity of the cell-to-cell interaction processes makes very difficult to mechanistically understand the GC dynamics. Different mathematical or computational models have been or can be developed to help clarify the mechanisms driving and regulating the GC dynamics. However, the very important question of which are the dominant model parameters is not frequently studied for most of those models. Here we describe in detail one method to perform such a parameter analysis—known as parameter sensitivity analysis—which can be applied to many models of the GC dynamics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Jacob J, Przylepa J, Miller C, Kelsoe G (1993) In situ studies of the primary immune response to (4-hydroxy-3-nitrophenyl)acetyl III The kinetics of V region mutation and selection in germinal center B cells. J Exp Med 178:1293–1307
McHeyzer-Williams MG, McLean MJ, Lalor PA, Nossal GJ (1993) Antigen-driven B cell differentiation in vivo. J Exp Med 178:295–307
Ziegner M, Berek C (1994) Analysis of germinal centres in the immune response to oxazolone. Adv Exp Med Biol 355:201–205
Moreira JS, Faro J (2006) Modelling two possible mechanisms for the regulation of the germinal center dynamics. J Immunol 177:3705–3710
Keşmir C, De Boer RJ (1999) A mathematical model on germinal center kinetics and termination. J Immunol 163:2463–9
Faro J, von Haeften B, Gardner R, Faro E (2019) A sensitivity analysis comparison of three models for the dynamics of germinal centers. Front Immunol 10:2038
Blower SM, Dowlatabadi H (1994) Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. Int Stat Rev 229–243
Ellner SP, Guckenheimer J (2011) Dynamic models in biology. Princeton University Press, Princeton
Rabitz H, Kramer M, Dacol D (1983) Sensitivity analysis in chemical kinetics. Ann Rev Phys Chem 34:419–461
Vassiliadis VS, Canto EB, Banga JR (1999) Second-order sensitivities of general dynamic systems with application to optimal control problems. Chem Eng Sci 54:3851–3860
McKay MD, Beckman RJ, Conover WJ (1979) Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245
Bai P, Banks HT, Dediu S, Govan AY, Last M, Lloyd AL, Nguyen HK, Olufsen MS, Rempala G, Slenning BD (2007) Stochastic and deterministic models for agricultural production networks. Math Biosci Eng 4:373–402
Acknowledgements
This work has received financial support from the European Union 7th Framework Program under grant agreement PIRSES-GA-2012-317893 (INDOEUROPEAN-MATHDS), the Xunta de Galicia (Centro singular de investigación de Galicia accreditation 2019-2022), and the European Union (European Regional Development Fund—ERDF) Ref. ED431G2019/06.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Science+Business Media, LLC, part of Springer Nature
About this protocol
Cite this protocol
Faro, J., Faro, E. (2022). A Method to Analyze Models of the Dynamics of Germinal Centers. In: Graca, L. (eds) T-Follicular Helper Cells. Methods in Molecular Biology, vol 2380. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-1736-6_10
Download citation
DOI: https://doi.org/10.1007/978-1-0716-1736-6_10
Published:
Publisher Name: Humana, New York, NY
Print ISBN: 978-1-0716-1735-9
Online ISBN: 978-1-0716-1736-6
eBook Packages: Springer Protocols