Fig 1.
Overview of the hemagglutination inhibition (HI) assay (top) and illustrative simulation results (bottom).
First step: patient serum is serially diluted and incubated with a constant amount of influenza virus. The model computes the amount of antibody-bound viral hemagglutinin (HA) for each serum dilution. Second step: red blood cells (RBCs) are added to each dilution and virus particles with free HA binding sites cross-link RBCs to cell aggregates. The model predicts a switch-like increase in agglutinated RBCs with decreasing antibody concentration. Third step: the plate is tilted by 90 degrees to detect full hemagglutination inhibition. If none/few RBCs are agglutinated, sedimented RBCs flow down to the rim. By definition, those wells show full hemagglutination inhibition. The reciprocal of the maximal inhibitory dilution is the HI titer. We classify our simulation results into inhibition and no inhibition by setting a threshold at 25% hemagglutination. Simulation results show median and interquartile range indicating the uncertainty due to experimental conditions (RBC concentration, virus concentration, readout time) and model parameters (summarized in Table 1) for an IgG serum concentration of 25 nM (4 μg/mL) and .
Table 1.
Model parameters and variables.
The assumed ranges of uncertainty and biological variability in model parameters and variables are defined by the distributions used in the sensitivity analysis. Abbreviations are: IgG, Immunoglobulin G; RBC, red blood cell; HA, hemagglutinin; HAU, HA unit; SA, sialic acid.
Fig 2.
Model sensitivity and resolution of the hemagglutination inhibition assay for influenza H1N1pdm09.
(A) Sensitivity analysis using Sobol indices. First-order effects show only the linear contribution to the total variance in hemagglutination degree (they sum up to 1), whereas total effects consider also interactions (see Methods for details). (B) Predicted degree of hemagglutination for different IgG concentrations and apparent dissociation constants . The red box indicates the usual assay range, bounded by the biological range of
, and the gray dashed line indicates
. (C) Predicted HI titers for the biological range of influenza-specific serum IgG and
. Colored areas correspond to titers shown on top.
Table 2.
Characteristics of allogeneic hematopoietic stem cell transplant patients (all patients and subset of patients with experimentally determined avidities for validation of inferred avidities).
Abbreviations are: IQR, interquartile range; GVHD, graft-versus-host disease.
Fig 3.
Inference of antibody avidities in HSCT patients.
(A) ELISA-detected anti-H1N1pmd09 serum IgG concentration, HI titers and corresponding inferred apparent dissociation constants from 197 serum samples from 43 HSCT patients. The dashed line indicates the seroprotection threshold (HI titer ≥ 40). (B) Correlation of inferred and experimentally determined avidities in 59 serum samples from 12 HSCT patients (Pearson’s ρ = 0.54, 95% CI = [0.31, 0.70]). Data show mean and standard deviation for avidity indices from two experiments (each performed in duplicates) and the median of the posterior distribution with the uncertainty range due to discretized HI titer measurements and ELISA measurement error for inferred
-values (see Methods for details on inference and S2 Fig for posterior distributions). Avidity indices correspond to the fraction of H1N1pmd09-specific serum IgG remaining bound after 4M urea treatment. Patient 11 was identified as an outlier, probably because ELISA detected non-neutralizing IgG; the patient showed no HI activity at any time point. For serum samples without detected HI activity (HI titer < 8; all five samples from patient 11 and three additional samples from in total two patients), the measured avidity index is plotted against the estimated upper bound for the inferred avidity and the uncertainty interval reflects the estimated uncertainty of the upper bound due to discretized HI titer measurements and ELISA measurement error. (C) Example patients with different types of responses to vaccination. In patient 3, we detected an increase in non-neutralizing IgG on d30. The predicted HI titer for the observed increase in IgG (shown in gray) is twice as high as the actually observed titer (green). For all 12 patients with experimentally determined avidities see S3 Fig.
Fig 4.
Response to influenza vaccination against H1N1pmd09 in HSCT patients.
(A) HI titers and ELISA-detected serum IgG concentrations in the investigated patient population. Patients were vaccinated on d0 and d30 with a non-adjuvanted trivalent influenza vaccine. Seroprotection corresponds to HI titer ≥ 40 and seroconversion to a four-fold HI titer increase compared to d0. (B) Fold changes in HI titer, serum IgG and inferred avidity () in all patients with a detectable increase in inferred avidity on d30 and/or d60. (C) Comparison of inferred avidities between patients with a detectable increase in avidity at any time point after vaccination (left), patients with no detectable increase (middle), and patients with a detectable increase in non-neutralizing IgG (right). We excluded 4/45 patients as they showed too large measurement uncertainty in IgG concentration on several time points. (D) Estimated effects on baseline levels of criteria for compromised immune response. Effects were estimated in a multivariable regression analysis on log2-transformed values controlling for sex and age. Time after HSCT was encoded as a binary variable (1 for HSCT ≤ 2 years and 0 for HSCT > 2 years). Immunosuppression grade and cGVHD grade ranging from 0 (no immunosuppression/cGVHD) to 3 (severe immunosuppression/cGVHD) were encoded as ordered categorical variables with grade 0 as reference (see Methods for details).