Bayesian Diallel Analysis Reveals Mx1-Dependent and Mx1-Independent Effects on Response to Influenza A Virus in Mice

Influenza A virus (IAV) is a respiratory pathogen that causes substantial morbidity and mortality during both seasonal and pandemic outbreaks. Infection outcomes in unexposed populations are affected by host genetics, but the host genetic architecture is not well understood. Here, we obtain a broad view of how heritable factors affect a mouse model of response to IAV infection using an 8 × 8 diallel of the eight inbred founder strains of the Collaborative Cross (CC). Expanding on a prior statistical framework for modeling treatment response in diallels, we explore how a range of heritable effects modify acute host response to IAV through 4 d postinfection. Heritable effects in aggregate explained ∼57% of the variance in IAV-induced weight loss. Much of this was attributable to a pattern of additive effects that became more prominent through day 4 postinfection and was consistent with previous reports of antiinfluenza myxovirus resistance 1 (Mx1) polymorphisms segregating between these strains; these additive effects largely recapitulated haplotype effects observed at the Mx1 locus in a previous study of the incipient CC, and are also replicated here in a CC recombinant intercross population. Genetic dominance of protective Mx1 haplotypes was observed to differ by subspecies of origin: relative to the domesticus null Mx1 allele, musculus acts dominantly whereas castaneus acts additively. After controlling for Mx1, heritable effects, though less distinct, accounted for ∼34% of the phenotypic variance. Implications for future mapping studies are discussed.


Paternal Strain
Diallel crossing design for the influenza diallel experiment. (A) Eight inbred Mus musculus strains were crossed in both directions to generate animals used in this experiment. All of the animals were followed from D0 through D2. Approximately half of the animals were followed through D4, and the remaining half of the mice were sacrificed on D2 (for analysis not included in this manuscript). (B) Of the 1,043 mice in this experiment, 268 received mock treatment, and 775 received influenza (flu) inoculation, or approximately 1 mock for every 2.9 infected mice within each category. There were one hundred twenty-nine inbred mice and 914 heterozygous (hybrid F1) mice used in this study. Crosses that were not observed (marked with a "-") include NZO×CAST and NZO×PWK, for which viable offspring cannot be produced.
Volume X November 2017 | Host genetics of influenza A virus | 23 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q   37  57  52  14  59  65  72  63  02  21  32  17  04  11  42  19  27  45  44  60  06  39  20  08  10  15  18  09  40  03  51  05  01  74  62  46  68  35  71  58  22  24  23  25  28  30  61  26  34  16  38  13  41  12  07  29  33  36  43  49  53  55  56  70  CC-RIX crossing design for the influenza infection experiment. As part of a larger CC-RIX QTL mapping experiment, 65 Collaborative Cross (CC) RI strains were crossed, approximately once as dam and once as sire in a round robin breeding scheme, to generate female animals in 105 CC-RIX lines, aged 8-12 weeks, that were sacrificed on day 7 (D7) post-infection, and used in this experiment. Weights for all of the animals were measured from D0 through D7. There were 1,402 heterozygous (hybrid F1) mice used in this study. weight loss on D4 p.i. (as pct D0 weight) individual infected mice (ordered by weight loss severity) weight loss on D4 p.i.
(as pct D0 weight) The panel of raw weights for the 62 possible diallel categories. In (C) and (D), y-axes indicate percent of D0 weight, and x-axes indicate day(s) post-infection, while grey lines indicate individual weight change trajectories; colored lines indicate mean male (blue) and mean female (red) weight trajectories, and among these means, colored line styles indicate mock (dashed) and influenza (solid) treatment means within each group. In (D), the large X's in EF and EG indicate non-productive F1 matings. Inbred mouse lines AJ, B6, 129, NOD, NZO, CAST, PWK, and WSB are indicated by letters A through H, respectively, with the first letter indicating maternal parentage and the second letter indicating paternal parentage.                    Figure S6 Diallel effects on D0 body weight in a diallel cross of inbred mice. (A) Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in grams) for adult baseline body weight in 8-12 week old mice (n=1,043). Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall mean, µ, (not shown) is 23.97 (23.56, 24.41) grams. (B) Posterior mean model inclusion probabilities (MIPs) are given for effect parameter classes. (C) Variance projection (VarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).          Figure S7 Diallel effects on host infection response (weight change) at D1 post-infection, using multiple imputation matched quartets. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=1,042). Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -0.131% (-0.484%,0.223%). (B) Model inclusion probabilities (MIPs) are given (posterior mean ± 1 s.d.) for effect parameter classes. (C) Treatment response variance projections (TReVarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).

Figure S8
Diallel effects on host infection response (weight change) at D2 post-infection, using multiple imputation matched quartets. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=1,042). Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -0.833% (-1.328%,-0.318%). (B) Model inclusion probabilities (MIPs) are given (posterior mean ± 1 s.d.) for effect parameter classes. (C) Treatment response variance projections (TReVarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).

Figure S9
Diallel effects on host infection response (weight change) at D3 post-infection, using multiple imputation matched quartets. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=514). Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -5.594% (-6.470%, -4.729%). (B) Model inclusion probabilities (MIPs) are given (posterior mean ± 1 s.d.) for effect parameter classes. (C) Treatment response variance projections (TReVarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).

MIP TReVarP
Figure S10 Diallel effects on host infection response (weight change) at D4 post-infection, using multiple imputation matched quartets. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=513). Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -8.849% (-9.920%, -7.779%). (B) Model inclusion probabilities (MIPs) are given (posterior mean ± 1 s.d.) for effect parameter classes. (C) Treatment response variance projections (TReVarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).

MIP TReVarP
Figure S11 Diallel effects on host infection response (weight change) at D1 post-infection, using multiple imputation matched quartets and accounting for Mx1. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=1,042) after including random effect u (Mx1 diplo) . Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -0.193% (

MIP TReVarP
Figure S12 Diallel effects on host infection response (weight change) at D2 post-infection, using multiple imputation matched quartets and accounting for Mx1. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=1,042) after including random effect u (Mx1 diplo) . Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -0.925% (-1.991%, 0.113%). (B) Model inclusion probabilities (MIPs) are given (posterior mean ± 1 s.d.) for effect parameter classes. (C) Treatment response variance projections (TReVarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).

MIP TReVarP
Figure S13 Diallel effects on host infection response (weight change) at D3 post-infection, using multiple imputation matched quartets and accounting for Mx1. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=514) after including random effect u (Mx1 diplo) . Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -5.429% (-7.675%, -3.102%). (B) Model inclusion probabilities (MIPs) are given (posterior mean ± 1 s.d.) for effect parameter classes. (C) Treatment response variance projections (TReVarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).

MIP TReVarP
Figure S14 Diallel effects on host infection response (weight change) at D4 post-infection, using multiple imputation matched quartets and accounting for Mx1. Effect estimates for additive, maternal, inbred, and epistatic effects, including sex-specific effects, are presented as highest posterior density intervals (in percent starting weight) in 8-12 week old mice (n=513) after including random effect u (Mx1 diplo) . Parameters are labeled according to the methods, and intervals are presented as in Figure 4A. Symmetric epistatic, asymmetric epistatic, and sex-specific parameters are indicated by "v:", "w:", and "f:", respectively. The overall treatment effect θ is -7.986% (-11.202%, -4.147%). (B) Model inclusion probabilities (MIPs) are given (posterior mean ± 1 s.d.) for effect parameter classes. (C) Treatment response variance projections (TReVarPs), a generalization of heritability to the diallel effects classes, are shown for three overall effects, five random effects classes, and five corresponding sex-specific random effects classes (with posterior median and 95% HPDs).
I Table S1 Proportion of variance in IAV-induced weight loss attributable to diallel effect classes across 4 days post-infection. Part C of Figure S7 through Figure S10 show Bayesian confidence interval plots of treatment response variance projection (TReVarP) values presented here. a To indicate the relative contribution of different diallel effects on host response to IAV, TreVarPs are given for overall effects (female, inbred, female inbred) and strain/strainpair-specific effects (additive, maternal, inbred, symmetric epistatic, asymmetric epistatic) on D1delta through D4delta (median and 95% HPD intervals).

Effect Class
I I Table S7 Summary of overall, additive, and Mx1 effects from Figures S11A, S12A, S13A, and S14A.