The probability ofkor more events occurring
inthetimeintervalisthen
PðX≥kÞ¼ 1 Qðk;lÞwhich can be solved forlnumerically using
the inverse incomplete regularized gamma
function,
l¼Q^1 ½ 1 PðX≥kÞ;kThe total time to acquirekor more mu-
tations is thenlΤ.
The probability of acquiring at leastk=4
improbable mutations given a rate parameter
of 1 improbable mutation every 12 weeks is
plotted as a function of time in fig. S19C. For
P(X≥4) = 0.99, the number of 12-week inter-
vals is 10.05 to acquire at least four improbable
mutations. Thus, mice would need to be im-
munized biweekly for ~120 weeks in order to
achieve 99% probability of acquiring at least
four improbable mutations.
Quantification and statistical analysis
The statistical analyses for this paper were per-
formed in SAS 9.4 to calculate exact Wilcoxon
tests for group comparisons. Due to the ex-
ploratorynatureofthisresearchandthesmall
sample size, we are using an alpha level of
0.05 as a descriptive level for significance
and have not made any adjustments to con-
trol for multiple testing. For group sizes less
than 5, no paired-sample comparisons were
performed due to the small sample size; only
descriptive statistics are provided in these
instances.
REFERENCES AND NOTES
- B. F. Haynes, D. R. Burton, Developing an HIV vaccine.
Science 355 , 1129–1130 (2017). doi:10.1126/science.aan0662;
pmid: 28302812 - B. F. Haynes, J. R. Mascola, The quest for an antibody-based
HIV vaccine.Immunol. Rev. 275 ,5–10 (2017). doi:10.1111/
imr.12517; pmid: 28133795 - B. F. Hayneset al., Cardiolipin polyspecific autoreactivity in two
broadly neutralizing HIV-1 antibodies.Science 308 , 1906– 1908
(2005). doi:10.1126/science.1111781; pmid: 15860590 - B. F. Hayneset al., HIV-Host Interactions: Implications for
Vaccine Design.Cell Host Microbe 19 , 292–303 (2016).
doi:10.1016/j.chom.2016.02.002; pmid: 26922989 - F. Kleinet al., Somatic mutations of the immunoglobulin
framework are generally required for broad and potent
HIV-1 neutralization.Cell 153 , 126–138 (2013). doi:10.1016/
j.cell.2013.03.018; pmid: 23540694 - H. X. Liaoet al., Co-evolution of a broadly neutralizing
HIV-1 antibody and founder virus.Nature 496 , 469– 476
(2013). doi:10.1038/nature12053; pmid: 23552890 - X. Wuet al., Maturation and Diversity of the VRC01-Antibody
Lineage over 15 Years of Chronic HIV-1 Infection.Cell 161 ,
470 – 485 (2015). doi:10.1016/j.cell.2015.03.004;pmid:25865483 - J. M. Di Noia, M. S. Neuberger, Molecular mechanisms of
antibody somatic hypermutation.Annu. Rev. Biochem. 76 ,1– 22
(2007). doi:10.1146/annurev.biochem.76.061705.090740;
pmid: 17328676 - A. G. Betz, C. Rada, R. Pannell, C. Milstein, M. S. Neuberger,
Passenger transgenes reveal intrinsic specificity of the
antibody hypermutation mechanism: Clustering, polarity, and
specific hotspots.Proc. Natl. Acad. Sci. U.S.A. 90 , 2385– 2388
(1993). doi:10.1073/pnas.90.6.2385; pmid: 8460148 - K. Wieheet al., Functional Relevance of Improbable Antibody
Mutations for HIV Broadly Neutralizing Antibody Development.
Cell Host Microbe 23 , 759–765.e6 (2018). doi:10.1016/
j.chom.2018.04.018; pmid: 29861171- C. A. Schramm, D. C. Douek, Beyond Hot Spots: Biases in
Antibody Somatic Hypermutation and Implications for Vaccine
Design.Front. Immunol. 9 , 1876 (2018). doi:10.3389/
fimmu.2018.01876; pmid: 30154794 - J. K. Hwanget al., Sequence intrinsic somatic mutation
mechanisms contribute to affinity maturation of VRC01-class
HIV-1 broadly neutralizing antibodies.Proc. Natl. Acad. Sci. U.S.A.
114 ,8614–8619 (2017). doi:10.1073/pnas.1709203114;
pmid: 28747530 - B. F. Haynes, G. Kelsoe, S. C. Harrison, T. B. Kepler,
B-cell-lineage immunogen design in vaccine development with
HIV-1 as a case study.Nat. Biotechnol. 30 , 423–433 (2012).
doi:10.1038/nbt.2197; pmid: 22565972 - A. Escolanoet al., Sequential Immunization Elicits Broadly
Neutralizing Anti-HIV-1 Antibodies in Ig Knockin Mice.Cell
166 , 1445–1458.e12 (2016). doi:10.1016/j.cell.2016.07.030;
pmid: 27610569 - A. Escolanoet al., Immunization expands B cells specific to
HIV-1 V3 glycan in mice and macaques.Nature 570 , 468– 473
(2019). doi:10.1038/s41586-019-1250-z; pmid: 31142836 - R. N. Germain, The art of the probable: System control in
the adaptive immune system.Science 293 , 240–245 (2001).
doi:10.1126/science.1062946; pmid: 11452112 - A. Ribas, J. D. Wolchok, Cancer immunotherapy using
checkpoint blockade.Science 359 , 1350–1355 (2018).
doi: 10 .1126/science.aar4060; pmid:^29567705 - M. Bonsignoriet al., Staged induction of HIV-1 glycan-dependent
broadly neutralizing antibodies.Sci. Transl. Med. 9 , eaai7514
(2017). doi:10.1126/scitranslmed.aai7514;pmid:28298420 - L. M. Walkeret al., Broad neutralization coverage of HIV by
multiple highly potent antibodies.Nature 477 , 466–470 (2011).
doi:10.1038/nature10373; pmid: 21849977 - C. N. Daniels, K. O. Saunders, Antibody responses to the
HIV-1 envelope high mannose patch.Adv. Immunol. 143 ,11– 73
(2019). doi:10.1016/bs.ai.2019.08.002; pmid: 31607367 - L. Konget al., Supersite of immune vulnerability on the
glycosylated face of HIV-1 envelope glycoprotein gp120.
Nat. Struct. Mol. Biol. 20 , 796–803 (2013). doi:10.1038/
nsmb.2594; pmid: 23708606 - F. Gaoet al., Cooperation of B cell lineages in induction of
HIV-1-broadly neutralizing antibodies.Cell 158 , 481–491 (2014).
doi:10.1016/j.cell.2014.06.022; pmid: 25065977 - M. Bonsignoriet al., Maturation Pathway from Germline to
Broad HIV-1 Neutralizer of a CD4-Mimic Antibody.Cell 165 ,
449 – 463 (2016). doi:10.1016/j.cell.2016.02.022;pmid:26949186 - Y. D. Kwonet al., Crystal structure, conformational fixation and
entry-related interactions of mature ligand-free HIV-1 Env.
Nat. Struct. Mol. Biol. 22 , 522–531 (2015). doi:10.1038/
nsmb.3051; pmid: 26098315 - S. W. de Taeyeet al., Immunogenicity of Stabilized HIV-1 Envelope
Trimers with Reduced Exposure of Non-neutralizing Epitopes.
Cell 163 ,1702–1715 (2015). doi:10.1016/j.cell.2015.11.056;
pmid: 26687358 - A. Torrents de la Peñaet al., Improving the Immunogenicity
of Native-like HIV-1 Envelope Trimers by Hyperstabilization.
Cell Rep. 20 , 1805–1817 (2017). doi:10.1016/
j.celrep.2017.07.077; pmid: 28834745 - D. Jung, C. Giallourakis, R. Mostoslavsky, F. W. Alt, Mechanism
and control of V(D)J recombination at the immunoglobulin
heavy chain locus.Annu. Rev. Immunol. 24 , 541– 570
(2006). doi:10.1146/annurev.immunol.23.021704.115830;
pmid: 16551259 - L. R. Covey, P. Ferrier, F. W. Alt, VH to VHDJH rearrangement is
mediated by the internal VH heptamer.Int. Immunol. 2 ,
579 – 583 (1990). doi:10.1093/intimm/2.6.579; pmid: 2085492 - R. Kleinfieldet al., Recombination between an expressed
immunoglobulin heavy-chain gene and a germline variable
gene segment in a Ly 1+ B-cell lymphoma.Nature 322 ,
843 – 846 (1986). doi:10.1038/322843a0; pmid: 3092106 - R. W. Kleinfield, M. G. Weigert, Analysis of VH gene
replacement events in a B cell lymphoma.J. Immunol. 142 ,
4475 – 4482 (1989). pmid: 2498430 - C. Chen, Z. Nagy, E. L. Prak, M. Weigert, Immunoglobulin heavy
chain gene replacement: A mechanism of receptor editing.
Immunity 3 , 747–755 (1995). doi:10.1016/1074-7613(95)
90064-0; pmid: 8777720 - S. L. Tiegs, D. M. Russell, D. Nemazee, Receptor editing in self-
reactive bone marrow B cells.J. Exp. Med. 177 , 1009– 1020
(1993). doi:10.1084/jem.177.4.1009; pmid: 8459201 - D. Gay, T. Saunders, S. Camper, M. Weigert, Receptor editing:
An approach by autoreactive B cells to escape tolerance.
J. Exp. Med. 177 , 999–1008 (1993). doi:10.1084/
jem.177.4.999; pmid: 8459227- E. L. Prak, M. Weigert, Light chain replacement: A new model
for antibody gene rearrangement.J. Exp. Med. 182 , 541– 548
(1995). doi: 10 .1084/jem.182.2.541; pmid: 7629511 - G. Kelsoe, L. Verkoczy, B. F. Haynes, Immune System
Regulation in the Induction of Broadly Neutralizing
HIV-1 Antibodies.Vaccines 2 ,1–14 (2014). doi:10.3390/
vaccines2010001; pmid: 24932410 - L. Verkoczyet al., Autoreactivity in an HIV-1 broadly reactive
neutralizing antibody variable region heavy chain induces
immunologic tolerance.Proc. Natl. Acad. Sci. U.S.A. 107 ,181– 186
(2010). doi:10.1073/pnas.0912914107;pmid: 20018688 - C. Doyle-Cooperet al., Immune tolerance negatively regulates
B cells in knock-in mice expressing broadly neutralizing
HIV antibody 4E10.J. Immunol. 191 , 3186–3191 (2013).
doi:10.4049/jimmunol.1301285; pmid: 23940276 - Y. Chenet al., Common tolerance mechanisms, but distinct
cross-reactivities associated with gp41 and lipids, limit
production of HIV-1 broad neutralizing antibodies 2F5 and
4E10.J. Immunol. 191 , 1260–1275 (2013). doi:10.4049/
jimmunol.1300770; pmid: 23825311 - P. Martinez-Murilloet al., Particulate Array of Well-Ordered
HIV Clade C Env Trimers Elicits Neutralizing Antibodies that
Display a Unique V2 Cap Approach.Immunity 46 , 804–817.e7
(2017). doi:10.1016/j.immuni.2017.04.021; pmid: 28514687 - C. D. Morriset al., Differential Antibody Responses to
Conserved HIV-1 Neutralizing Epitopes in the Context of
Multivalent Scaffolds and Native-Like gp140 Trimers.mBio 8 ,
e00036-17 (2017). doi:10.1128/mBio.00036-17; pmid: 28246356 - J. Ingaleet al., High-Density Array of Well-Ordered HIV-1 Spikes
on Synthetic Liposomal Nanoparticles Efficiently Activate B
Cells.Cell Rep. 15 , 1986–1999 (2016). doi:10.1016/
j.celrep.2016.04.078; pmid: 27210756 - L. Heet al., Presenting native-like trimeric HIV-1 antigens with
self-assembling nanoparticles.Nat. Commun. 7 , 12041
(2016). doi:10.1038/ncomms12041; pmid: 27349934 - M. Kanekiyoet al., Self-assembling influenza nanoparticle
vaccines elicit broadly neutralizing H1N1 antibodies.Nature
499 , 102–106 (2013). doi:10.1038/nature12202;pmid:23698367 - F. D. Batista, M. S. Neuberger, B cells extract and present
immobilized antigen: Implications for affinity discrimination.
EMBO J. 19 , 513–520 (2000). doi:10.1093/emboj/19.4.513;
pmid: 10675320 - K. Sliepenet al., Presenting native-like HIV-1 envelope trimers
on ferritin nanoparticles improves their immunogenicity.
Retrovirology 12 , 82 (2015). doi:10.1186/s12977-015-0210-4;
pmid: 26410741 - T. Tokatlianet al., Innate immune recognition of glycans
targets HIV nanoparticle immunogens to germinal centers.
Science 363 , 649–654 (2019). doi:10.1126/science.aat9120;
pmid: 30573546 - D. Feraet al., HIV envelope V3 region mimic embodies key
features of a broadly neutralizing antibody lineage epitope.
Nat. Commun. 9 , 1111 (2018). doi:10.1038/s41467-018-03565-6;
pmid: 29549260 - S. Dutta, P. Sengupta, Men and mice: Relating their ages.
Life Sci. 152 , 244–248 (2016). doi:10.1016/j.lfs.2015.10.025;
pmid: 26596563 - Z. Shenget al., Effects of Darwinian Selection and Mutability on
Rate of Broadly Neutralizing Antibody Evolution during
HIV-1 Infection.PLOS Comput. Biol. 12 , e1004940 (2016).
doi:10.1371/journal.pcbi.1004940; pmid: 27191167 - M. Tianet al., Induction of HIV Neutralizing Antibody Lineages
in Mice with Diverse Precursor Repertoires.Cell 166 ,
1471 – 1484.e18 (2016). doi:10.1016/j.cell.2016.07.029;
pmid: 27610571 - R.K. Abbottet al., Precursor Frequency and Affinity Determine
B Cell Competitive Fitness in Germinal Centers, Tested
with Germline-Targeting HIV Vaccine Immunogens.Immunity
48 , 133–146.e6 (2018). doi:10.1016/j.immuni.2017.11.023;
pmid: 29287996 - C. C. LaBrancheet al., Neutralization-guided design of
HIV-1 envelope trimers with high affinity for the unmutated
common ancestor of CH235 lineage CD4bs broadly
neutralizing antibodies.PLOS Pathog. 15 , e1008026 (2019).
doi:10.1371/journal.ppat.1008026; pmid: 31527908 - K. M. Cirelliet al., Slow Delivery Immunization Enhances HIV
Neutralizing Antibody and Germinal Center Responses via
Modulation of Immunodominance.Cell 177 , 1153–1171.e28
(2019). doi:10.1016/j.cell.2019.04.012; pmid: 31080066 - M. Pauthneret al., Elicitation of Robust Tier 2 Neutralizing
Antibody Responses in Nonhuman Primates by HIV Envelope
Saunderset al.,Science 366 , eaay7199 (2019) 6 December 2019 16 of 17
RESEARCH | RESEARCH ARTICLE
on December 12, 2019^http://science.sciencemag.org/Downloaded from