We found a minor implementation error in the NK cell education process of our agent-based model. Fortunately, this hardly affected our main results and conclusions. The main difference lies in the polymorphism of iNKRs, as our new results show that it increases substantially over time similar to that of aNKRs. For reasons of accuracy and reproducibility, we here provide the corrected Figures and paragraphs (underlined).
Populations Having Only aNKRs Evolve a Larger NKR Polymorphism than Populations with Only iNKRs
Our probabilistic model predicts that the protection by iNKRs and aNKRs increases with the number of receptors per individual (Figure 2), because a large receptor number increases the chance of a host carrying very specific NKRs to have licensed receptors. This observation suggests that heterozygous hosts should have an advantage over homozygotes. We therefore hypothesized that heterozygous advantage must be selecting novel NKRs in our agent-based model, driving polymorphism of NKRs in the population.
To measure the polymorphism at population level, we use the Simpson’s reciprocal index (SRI, see Material and Methods). The SRI is a diversity measure that is equal to the total number of NKRs if they are equally distributed in the population, whereas the SRI is lower than that in a population where some alleles dominate (34).
The initial polymorphism of aNKRs (i.e., SRI = 10) increases over time (Figure 4G black line), reflecting that a high number of aNKRs provides indeed an advantage. Similarly, the SRI score of iNKRs increases over time. Because each evolved iNKRs recognizes on average one MHC molecule in the population, there is selection for haplotypes that do not overlap in the MHC molecules they recognize. Thus, the heterozygote advantage is large in these populations, driving the diversity of iNKRs.
Figure 4
Figure 5
Protection Depends on the Number of MHC Loci
To confirm our results concerning the dependency on MHC loci number, we also perform simulations with individuals having two MHC loci. An increasing number of MHC loci has a large effect on the protection provided by aNKRs. Although these populations are initialized with intermediate specific NKRs, the initial protection is lower than in the population carrying only one MHC locus (Figure 4D). For better protection, a higher specificity is required, and the selection for more specific aNKRs is stronger in these simulations (Figure 4F). As a result of the higher specificity, a larger number of receptors per haplotype is necessary to become licensed and to recognize the foreign decoy molecules. Therefore, the advantage of heterozygotes over homozygotes is larger in these populations, resulting in a higher degree of polymorphism (Figure 4H).
The protection and evolution of iNKRs is also sensitive to the number of MHC loci per individual. Like in the simulations considering one MHC locus, we observe a recovery of the population as more specific receptors are evolving (Figures 4D,F). Hereby, the specificity evolved to even higher values, as the evolved iNKRs recognize on average <5% of all the MHC alleles in the population. Because of this high specificity and the larger number of MHC alleles in populations having two MHC loci, more iNKRs per haplotype are necessary to have at least one licensed receptor. Hence, the total SRI score is higher in these simulations, than in the case of single MHC locus (Figures 4G,H red line).
Statements
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Summary
Keywords
agent-based modeling, NK cell receptors, evolution, CMV infection, models, theoretical
Citation
Carrillo-Bustamante P, Keşmir C and De Boer RJ (2015) Corrigendum: Quantifying the Protection of Activating and Inhibiting NK Cell Receptors during Infection with a CMV-Like Virus. Front. Immunol. 5:663. doi: 10.3389/fimmu.2014.00663
Received
29 October 2014
Accepted
10 December 2014
Published
05 January 2015
Volume
5 - 2014
Edited by
Ramit Mehr, Bar-Ilan University, Israel
Reviewed by
Becca Asquith, Imperial College London, UK; Jayajit Das, The Ohio State University, USA
Copyright
© 2015 Carrillo-Bustamante, Keşmir and De Boer.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: p.carrillobustamante@uu.nl
This article was submitted to T Cell Biology, a section of the journal Frontiers in Immunology.
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