Title:
A Novel Delay Differential Equation Model of the Germinal Center Reaction and an Algorithm for Minimum Length Surveillance Paths

dc.contributor.advisor Kang, Sung Ha
dc.contributor.author Ide, Benjamin
dc.contributor.committeeMember Short, Martin
dc.contributor.committeeMember Tao, Molei
dc.contributor.committeeMember Zarnitsyna, Veronika
dc.contributor.committeeMember Zhou, Haomin
dc.contributor.department Mathematics
dc.date.accessioned 2022-08-25T13:32:11Z
dc.date.available 2022-08-25T13:32:11Z
dc.date.created 2022-08
dc.date.issued 2022-05-19
dc.date.submitted August 2022
dc.date.updated 2022-08-25T13:32:11Z
dc.description.abstract The humoral adaptive immune system in vertebrates includes a process called the germinal center reaction in which B-cells rapidly increase their binding affinity to an antigen that is part of a pathogen. A fraction of germinal center B cells differentiates into plasma cells that secrete antibodies. Antibodies bind to the pathogen and neutralize it. In a secondary immune response to the same pathogen, memory B-cells and long-lived plasma cells generated during the primary immune response encode higher affinity antibodies and are able to fight the pathogen more efficiently. We develop a delay differential equation model of the germinal center reaction incorporating known physical mechanisms. We find that secondary immune responses including low affinity seeder B-cells outperform those seeded only with higher affinity. This helps to explain a recent laboratory observation that a high fraction of seeder B-cells in a secondary immune response are naive. Further, two mechanisms of antibody feedback are explored, where antibodies produced in the reaction interact with the reaction itself. Negative feedback occurs via epitope masking, which is consistent with experimental data. Positive feedback occurs via improved antigen presentation on follicular dendritic cells, which is a mechanism we propose. Additionally, we propose a novel path optimization algorithm. Given a path connected environment, our proposed algorithm finds the shortest paths from which surfaces in the environment are surveyed under a limited visibility constraint. We further explore how this is related to the inradius problem in classical geometry: What is the shortest curve whose convex hull includes the unit sphere? The solution is known for closed curves, but not for open curves. Our algorithm seems to converge numerically to the true solution for closed curves and to the best-known conjecture for open curves. This offers validation of our method and evidence for the open path conjecture.
dc.description.degree Ph.D.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/67205
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject Humoral immune system
dc.subject B-cells
dc.subject Affinity maturation
dc.subject Germinal center
dc.subject Path optimization
dc.subject Surveillance
dc.subject Inradius
dc.title A Novel Delay Differential Equation Model of the Germinal Center Reaction and an Algorithm for Minimum Length Surveillance Paths
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Kang, Sung Ha
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isAdvisorOfPublication 86e63bb1-4100-40ed-b6f8-bf3047b992cf
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
thesis.degree.level Doctoral
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