Fig 1.
Schematic representation of a GC reaction.
Reticular stromal cells express CXCL12 chemokine in the DZ (blue gradient), and FDCs express CXCL13 chemokine in the LZ (red gradient). CBs which are more sensitive to CXCL12 proliferate and change their affinity for the Ag through SHM in the DZ. Subsequently, CBs differentiate to CCs that move to the LZ because of their sensitivity to CXCL13 and collect Ag from FDCs. CCs internalise, process, and present the Ag peptides through MHCII molecules on their surface to interact with Tfh cells. CCs that cannot collect Ag and or cannot receive Tfh help due to competition die by apoptosis. Positively selected CCs recycle back to DZ for further proliferation and mutation or differentiate to MBCs or PCs.
Table 1.
Initial affinity, association and dissociation rates of founder clones.
Fig 2.
Schematic of Ag collection scenarios.
Three mechanisms of Ag collection based on affinity and kinetic selection. The green rows denote the steps that the scenarios have in common. The starting point of each scenario is the event at which a free CC arrives at an Ag binding site. All scenarios end when the Ag collection phase is finished (last grey row), and the cell can engage in T-cell interactions. When no Ag is collected within 42 minutes, the CC will go into apoptosis. (A) Scenario-0: Competition for Ag depends on affinity directly. The CC’s probability of binding to Ag depends on the local Ag concentration (not shown in the figure) and CC’s affinity. After binding, the Ag extraction always starts directly. CC stays in bond until the Ag extraction process is finished after a period specified by a parameter ’Ag extraction time’ whereafter the CC captures the Ag. Subsequently, the CC may collect more Ag or engage in T-cell interactions. (B) Scenario-1: Competition for Ag collection depends on association (Pa) and dissociation (Pd) probabilities of CC that rely on the affinity. In this scenario, a CC associates to Ags presented on FDCs according to Ag concentration at the binding site and Pa. In the next time step, the bond dissociates with a probability of dissociation (Pd) or otherwise, CC initiates the Ag extraction process. During the Ag extraction process, the bond between CC and Ag still can get disrupted probabilistically (red arrow) at each time-step (dt = 0.002 h) with probability Pd that may lead to disruption of Ag extraction before it is fully complete, in which case the CC dissociates without obtaining Ag. Subsequently, if the bond between CC and Ag does not dissociate due to interruptions during the Ag extraction, CC collects the Ag and re-engages in another interaction. (C) Scenario-2: Similar to Scenario-1, only there are no interruptions after initiation of Ag extraction.
Fig 3.
Dynamics of population and Ag collection phase.
Results are obtained from 30 simulations. (A) The average of CB+CC counts for each clone in the reference scenario (Scenario-0). (B) Collected Ag for each clone during the GC reaction in the reference scenario. This consists of Ags collected by all CCs in each clone. Lines represent averages. The shaded area denotes the minimum and maximum values in all repeats. (C) Events during the Ag collection phase for CCs that attend the Tfh selection phase in the reference scenario. CC-FDC interactions denote the events at which the CC is located at an Ag binding site on a FDC. Boxplots are produced based on combined data of all simulations. Black dots represent average values per cell in each clone over all repeats. (D) The population of CCs that are positively selected by Tfh cells. Solid lines represent the average of all simulations. (E), (F), (G), and (H) represent the results of Scenario-1. (I), (J), (K) and (L) represent the results of Scenario-2. Panel descriptions are similar to that of the reference scenario.
Fig 4.
OCs production and affinity maturation.
Results are obtained from 30 simulations. (A), (B) and (C) represent produced OCs from each clone in the reference scenario, Scenario-1 and Scenario-2, respectively. Each dot represents OCs produced in a single simulation. Red lines denote the average. (D), (E) and (F) represent the average affinity of living GC B cells (dashed lines) and the cumulative average of produced OCs (solid lines) belonging to each clone in the reference scenario, Scenario-1 and Scenario-2, respectively. Shaded areas indicate the maximum and minimum of OC’s average affinity in 30 simulations.
Fig 5.
Correlation between Pa, Pd, affinity and Θ plotted for discrete affinity and Θ values.
(A) Schematic of correlation between distance d in the shape-space and the corresponding association and dissociation distances defined by Θ. The blue iso-affinity curves denote combinations of distances that result in identical affinities. (B) The correlation between Pa-Pd and affinity of CC in the shape-space. Red arrows represent the three clones defined by different Θ values. SHM moves cells from each clone along the lines that represent specific Θ values resulting in lower or higher affinities (represented by the points). Affinities below 0.0003 are considered as 0.