A model for establishment, maintenance and reactivation of the immune response after vaccination against Ebola virus.

The 2014-2016 Ebola outbreak in West Africa has triggered accelerated development of several preventive vaccines against Ebola virus. Under the EBOVAC1 consortium, three phase I studies were carried out to assess safety and immunogenicity of a two-dose heterologous vaccination regimen developed by Janssen Vaccines and Prevention in collaboration with Bavarian Nordic. To describe the immune response induced by the two-dose heterologous vaccine regimen, we propose a mechanistic ODE based model, which takes into account the role of immunological memory. We perform identifiability and sensitivity analysis of the proposed model to establish which kind of biological data are ideally needed in order to accurately estimate parameters, and additionally, which of those are non-identifiable based on the available data. Antibody concentrations data from phase I studies have been used to calibrate the model and show its ability in reproducing the observed antibody dynamics. Together with other factors, the establishment of an effective and reactive immunological memory is of pivotal importance for several prophylactic vaccines. We show that introducing a memory compartment in our calibrated model allows to evaluate the magnitude of the immune response induced by a booster dose and its long-term persistence afterwards.

Dynamics of the Humoral Immune Response to a Prime-Boost Ebola Vaccine: Quantification and Sources of Variation.

The Ebola vaccine based on Ad26.ZEBOV/MVA-BN-Filo prime-boost regimens is being evaluated in multiple clinical trials. The long-term immune response to the vaccine is unknown, including factors associated with the response and variability around the response. We analyzed data from three phase 1 trials performed by the EBOVAC1 Consortium in four countries: the United Kingdom, Kenya, Tanzania, and Uganda. Participants were randomized into four groups based on the interval between prime and boost immunizations (28 or 56 days) and the sequence in which Ad26.ZEBOV and MVA-BN-Filo were administered. Consecutive enzyme-linked immunosorbent assay (ELISA) measurements of the IgG binding antibody concentrations against the Kikwit glycoprotein (GP) were available for 177 participants to assess the humoral immune response up to 1 year postprime. Using a mathematical model for the dynamics of the humoral response, from 7 days after the boost immunization up to 1 year after the prime immunization, we estimated the durability of the antibody response and the influence of different factors on the dynamics of the humoral response. Ordinary differential equations (ODEs) described the dynamics of antibody response and two populations of antibody-secreting cells (ASCs), short-lived (SL) and long-lived (LL). Parameters of the ODEs were estimated using a population approach. We estimated that half of the LL ASCs could persist for at least 5 years. The vaccine regimen significantly affected the SL ASCs and the antibody peak but not the long-term response. The LL ASC compartment dynamics differed significantly by geographic regions analyzed, with a higher long-term antibody persistence in European subjects. These differences could not be explained by the observed differences in cellular immune response.IMPORTANCE With no available licensed vaccines or therapies, the West African Ebola virus disease epidemic of 2014 to 2016 caused 11,310 deaths. Following this outbreak, the development of vaccines has been accelerated. Combining different vector-based vaccines as heterologous regimens could induce a durable immune response, assessed through antibody concentrations. Based on data from phase 1 trials in East Africa and Europe, the dynamics of the humoral immune response from 7 days after the boost immunization onwards were modeled to estimate the durability of the response and understand its variability. Antibody production is maintained by a population of long-lived cells. Estimation suggests that half of these cells can persist for at least 5 years in humans. Differences in prime-boost vaccine regimens affect only the short-term immune response. Geographical differences in long-lived cell dynamics were inferred, with higher long-term antibody concentrations induced in European participants.

Multi-type Galton-Watson Processes with Affinity-Dependent Selection Applied to Antibody Affinity Maturation.

We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is motivated by the modeling of antibody affinity maturation of B-cells in germinal centers during an immune response. This is a key process in adaptive immunity leading to the production of high-affinity antibodies against a presented antigen. Our aim is to understand how the different biological parameters affect the system's functionality. We identify the existence of an optimal value of the selection rate, able to maximize the number of selected B-cells for a given generation.

Random walks on binary strings applied to the somatic hypermutation of B-cells.

Within the germinal center in follicles, B-cells proliferate, mutate and differentiate, while being submitted to a powerful selection: a micro-evolutionary mechanism at the heart of adaptive immunity. A new foreign pathogen is confronted to our immune system, the mutation mechanism that allows B-cells to adapt to it is called somatic hypermutation: a programmed process of mutation affecting B-cell receptors at extremely high rate. By considering random walks on graphs, we introduce and analyze a simplified mathematical model in order to understand this extremely efficient learning process. The structure of the graph reflects the choice of the mutation rule. We focus on the impact of this choice on typical time-scales of the graphs' exploration. We derive explicit formulas to evaluate the expected hitting time to cover a given Hamming distance on the graphs under consideration. This characterizes the efficiency of these processes in driving antibody affinity maturation. In a further step we present a biologically more involved model and discuss its numerical outputs within our mathematical framework. We provide as well limitations and possible extensions of our approach.