Vaccination reshapes the virus-specific T cell repertoire in unexposed adults.

We examined how baseline CD4+ T cell repertoire and precursor states impact responses to pathogen infection in humans using primary immunization with yellow fever virus (YFV) vaccine. YFV-specific T cells in unexposed individuals were identified by peptide-MHC tetramer staining and tracked pre- and post-vaccination by tetramers and TCR sequencing. A substantial number of YFV-reactive T cells expressed memory phenotype markers and contained expanded clones in the absence of exposure to YFV. After vaccination, pre-existing YFV-specific T cell populations with low clonal diversity underwent limited expansion, but rare populations with a reservoir of unexpanded TCRs generated robust responses. These altered dynamics reorganized the immunodominance hierarchy and resulted in an overall increase in higher avidity T cells. Thus, instead of further increasing the representation of dominant clones, YFV vaccination recruits rare and more responsive T cells. Our findings illustrate the impact of vaccines in prioritizing T cell responses and reveal repertoire reorganization as a key component of effective vaccination.

When does humoral memory enhance infection?

Antibodies and humoral memory are key components of the adaptive immune system. We consider and computationally model mechanisms by which humoral memory present at baseline might increase rather than decrease infection load; we refer to this effect as EI-HM (enhancement of infection by humoral memory). We first consider antibody dependent enhancement (ADE) in which antibody enhances the growth of the pathogen, typically a virus, and typically at intermediate 'Goldilocks' levels of antibody. Our ADE model reproduces ADE in vitro and enhancement of infection in vivo from passive antibody transfer. But notably the simplest implementation of our ADE model never results in EI-HM. Adding complexity, by making the cross-reactive antibody much less neutralizing than the de novo generated antibody or by including a sufficiently strong non-antibody immune response, allows for ADE-mediated EI-HM. We next consider the possibility that cross-reactive memory causes EI-HM by crowding out a possibly superior de novo immune response. We show that, even without ADE, EI-HM can occur when the cross-reactive response is both less potent and 'directly' (i.e. independently of infection load) suppressive with regard to the de novo response. In this case adding a non-antibody immune response to our computational model greatly reduces or completely eliminates EI-HM, which suggests that 'crowding out' is unlikely to cause substantial EI-HM. Hence, our results provide examples in which simple models give qualitatively opposite results compared to models with plausible complexity. Our results may be helpful in interpreting and reconciling disparate experimental findings, especially from dengue, and for vaccination.

Estimating Waning of Vaccine Effectiveness: A Simulation Study.

BACKGROUND: Developing accurate and reliable methods to estimate vaccine protection is a key goal in immunology and public health. While several statistical methods have been proposed, their potential inaccuracy in capturing fast intraseasonal waning of vaccine-induced protection needs to be rigorously investigated. METHODS: To compare statistical methods for estimating vaccine effectiveness (VE), we generated simulated data using a multiscale, agent-based model of an epidemic with an acute viral infection and differing extents of VE waning. We apply a previously proposed framework for VE measures based on the observational data richness to assess changes of vaccine-induced protection over time. RESULTS: While VE measures based on hard-to-collect information (eg, the exact timing of exposures) were accurate, usually VE studies rely on time-to-infection data and the Cox proportional hazards model. We found that its extension using scaled Schoenfeld residuals, previously proposed for capturing VE waning, was unreliable in capturing both the degree of waning and its functional form and identified the mathematical factors contributing to this unreliability. We showed that partitioning time and including a time-vaccine interaction term in the Cox model significantly improved estimation of VE waning, even in the case of dramatic, rapid waning. We also proposed how to optimize the partitioning scheme. CONCLUSIONS: While appropriate for rejecting the null hypothesis of no waning, scaled Schoenfeld residuals are unreliable for estimating the degree of waning. We propose a Cox-model-based method with a time-vaccine interaction term and further optimization of partitioning time. These findings may guide future analysis of VE waning data.

The kinetics of E-selectin- and P-selectin-induced intermediate activation of integrin αLß2 on neutrophils.

Selectins and integrins are key players in the adhesion and signaling cascade that recruits leukocytes to inflamed tissues. Selectin binding induces ß2 integrin binding to slow leukocyte rolling. Here, a micropipette was used to characterize neutrophil adhesion to E-selectin and intercellular adhesion molecule-1 (ICAM-1) at room temperature. The time-dependent adhesion frequency displayed two-stage kinetics, with an E-selectin-mediated fast increase to a low plateau followed by a slow increase to a high plateau mediated by intermediate-affinity binding of integrin αLß2 to ICAM-1. The αLß2 activation required more than 5 s contact to E-selectin and spleen tyrosine kinase (Syk) activity. A multi-zone channel was used to analyze αLß2 activation by P-selectin in separate zones of receptors or antibodies, finding an inverse relationship between the rolling velocity on ICAM-1 and P-selectin dose, and a P-selectin dose-dependent change from bent to extended conformations with a closed headpiece that was faster at 37°C than at room temperature. Activation of αLß2 exhibited different levels of cooperativity and persistent times depending on the strength and duration of selectin stimulation. These results define the precise timing and kinetics of intermediate activation of αLß2 by E- and P-selectins.

Persistence of Virus-Specific Antibody after Depletion of Memory B Cells.

Humoral immunity is a major component of the adaptive immune response against viruses and other pathogens with pathogen-specific antibody acting as the first line of defense against infection. Virus-specific antibody levels are maintained by continual secretion of antibody by plasma cells residing in the bone marrow. This raises the important question of how the virus-specific plasma cell population is stably maintained and whether memory B cells are required to replenish plasma cells, balancing their loss arising from their intrinsic death rate. In this study, we examined the longevity of virus-specific antibody responses in the serum of mice following acute viral infection with three different viruses: lymphocytic choriomeningitis virus (LCMV), influenza virus, and vesicular stomatitis virus (VSV). To investigate the contribution of memory B cells to the maintenance of virus-specific antibody levels, we employed human CD20 transgenic mice, which allow for the efficient depletion of B cells with rituximab, a human CD20-specific monoclonal antibody. Mice that had resolved an acute infection with LCMV, influenza virus, or VSV were treated with rituximab starting at 2 months after infection, and the treatment was continued for up to a year postinfection. This treatment regimen with rituximab resulted in efficient depletion of B cells (>95%), with virus-specific memory B cells being undetectable. There was an early transient drop in the antibody levels after rituximab treatment followed by a plateauing of the curve with virus-specific antibody levels remaining relatively stable (half-life of 372 days) for up to a year after infection in the absence of memory B cells. The number of virus-specific plasma cells in the bone marrow were consistent with the changes seen in serum antibody levels. Overall, our data show that virus-specific plasma cells in the bone marrow are intrinsically long-lived and can maintain serum antibody titers for extended periods of time without requiring significant replenishment from memory B cells. These results provide insight into plasma cell longevity and have implications for B cell depletion regimens in cancer and autoimmune patients in the context of vaccination in general and especially for COVID-19 vaccines. IMPORTANCE Following vaccination or primary virus infection, virus-specific antibodies provide the first line of defense against reinfection. Plasma cells residing in the bone marrow constitutively secrete antibodies, are long-lived, and can thus maintain serum antibody levels over extended periods of time in the absence of antigen. Our data, in the murine model system, show that virus-specific plasma cells are intrinsically long-lived but that some reseeding by memory B cells might occur. Our findings demonstrate that, due to the longevity of plasma cells, virus-specific antibody levels remain relatively stable in the absence of memory B cells and have implications for vaccination.

Adjuvanted H5N1 influenza vaccine enhances both cross-reactive memory B cell and strain-specific naive B cell responses in humans.

There is a need for improved influenza vaccines. In this study we compared the antibody responses in humans after vaccination with an AS03-adjuvanted versus nonadjuvanted H5N1 avian influenza virus inactivated vaccine. Healthy young adults received two doses of either formulation 3 wk apart. We found that AS03 significantly enhanced H5 hemagglutinin (HA)-specific plasmablast and antibody responses compared to the nonadjuvanted vaccine. Plasmablast response after the first immunization was exclusively directed to the conserved HA stem region and came from memory B cells. Monoclonal antibodies (mAbs) derived from these plasmablasts had high levels of somatic hypermutation (SHM) and recognized the HA stem region of multiple influenza virus subtypes. Second immunization induced a plasmablast response to the highly variable HA head region. mAbs derived from these plasmablasts exhibited minimal SHM (naive B cell origin) and largely recognized the HA head region of the immunizing H5N1 strain. Interestingly, the antibody response to H5 HA stem region was much lower after the second immunization, and this suppression was most likely due to blocking of these epitopes by stem-specific antibodies induced by the first immunization. Taken together, these findings show that an adjuvanted influenza vaccine can substantially increase antibody responses in humans by effectively recruiting preexisting memory B cells as well as naive B cells into the response. In addition, we show that high levels of preexisting antibody can have a negative effect on boosting. These findings have implications toward the development of a universal influenza vaccine.

Dynamics and turnover of memory CD8 T cell responses following yellow fever vaccination.

Understanding how immunological memory lasts a lifetime requires quantifying changes in the number of memory cells as well as how their division and death rates change over time. We address these questions by using a statistically powerful mixed-effects differential equations framework to analyze data from two human studies that follow CD8 T cell responses to the yellow fever vaccine (YFV-17D). Models were first fit to the frequency of YFV-specific memory CD8 T cells and deuterium enrichment in those cells 42 days to 1 year post-vaccination. A different dataset, on the loss of YFV-specific CD8 T cells over three decades, was used to assess out of sample predictions of our models. The commonly used exponential and bi-exponential decline models performed relatively poorly. Models with the cell loss following a power law (exactly or approximately) were most predictive. Notably, using only the first year of data, these models accurately predicted T cell frequencies up to 30 years post-vaccination. Our analyses suggest that division rates of these cells drop and plateau at a low level (0.1% per day, ∼ double the estimated values for naive T cells) within one year following vaccination, whereas death rates continue to decline for much longer. Our results show that power laws can be predictive for T cell memory, a finding that may be useful for vaccine evaluation and epidemiological modeling. Moreover, since power laws asymptotically decline more slowly than any exponential decline, our results help explain the longevity of immune memory phenomenologically.

Why Are CD8 T Cell Epitopes of Human Influenza A Virus Conserved?

The high degree of conservation of CD8 T cell epitopes of influenza A virus (IAV) may allow for the development of T cell-inducing vaccines that provide protection across different strains and subtypes. This conservation is not fully explained by functional constraint, since an additional mutation(s) can compensate for the replicative fitness loss of IAV escape variants. Here, we propose three additional mechanisms that contribute to the conservation of CD8 T cell epitopes of IAV. First, influenza-specific CD8 T cells may protect predominantly against severe pathology rather than infection and may have only a modest effect on transmission. Second, polymorphism of the human major histocompatibility complex class I (MHC-I) gene restricts the advantage of an escape variant to only a small fraction of the human population who carry the relevant MHC-I alleles. Finally, infection with CD8 T cell escape variants may result in a compensatory increase in the responses to other epitopes of IAV. We use a combination of population genetics and epidemiological models to examine how the interplay between these mechanisms affects the rate of invasion of IAV escape variants. We conclude that for a wide range of biologically reasonable parameters, the invasion of an escape variant virus will be slow, with a timescale of a decade or more. The results suggest T cell-inducing vaccines do not engender the rapid evolution of IAV. Finally, we identify key parameters whose measurement will allow for more accurate quantification of the long-term effectiveness and impact of universal T cell-inducing influenza vaccines.IMPORTANCE Universal influenza vaccines against the conserved epitopes of influenza A virus have been proposed to minimize the burden of seasonal outbreaks and prepare for the pandemics. However, it is not clear how rapidly T cell-inducing vaccines will select for viruses that escape these T cell responses. Our mathematical models explore the factors that contribute to the conservation of CD8 T cell epitopes and how rapidly the virus will evolve in response to T cell-inducing vaccines. We identify the key biological parameters to be measured and questions that need to be addressed in future studies.

Exploring the impact of inoculum dose on host immunity and morbidity to inform model-based vaccine design.

Vaccination is an effective method to protect against infectious diseases. An important consideration in any vaccine formulation is the inoculum dose, i.e., amount of antigen or live attenuated pathogen that is used. Higher levels generally lead to better stimulation of the immune response but might cause more severe side effects and allow for less population coverage in the presence of vaccine shortages. Determining the optimal amount of inoculum dose is an important component of rational vaccine design. A combination of mathematical models with experimental data can help determine the impact of the inoculum dose. We illustrate the concept of using data and models to inform inoculum dose determination for vaccines, wby fitting a mathematical model to data from influenza A virus (IAV) infection of mice and human parainfluenza virus (HPIV) infection of cotton rats at different inoculum doses. We use the model to map inoculum dose to the level of immune protection and morbidity and to explore how such a framework might be used to determine an optimal inoculum dose. We show how a framework that combines mathematical models with experimental data can be used to study the impact of inoculum dose on important outcomes such as immune protection and morbidity. Our findings illustrate that the impact of inoculum dose on immune protection and morbidity can depend on the specific pathogen and that both protection and morbidity do not necessarily increase monotonically with increasing inoculum dose. Once vaccine design goals are specified with required levels of protection and acceptable levels of morbidity, our proposed framework can help in the rational design of vaccines and determination of the optimal amount of inoculum.

Multi-epitope Models Explain How Pre-existing Antibodies Affect the Generation of Broadly Protective Responses to Influenza.

The development of next-generation influenza vaccines that elicit strain-transcendent immunity against both seasonal and pandemic viruses is a key public health goal. Targeting the evolutionarily conserved epitopes on the stem of influenza's major surface molecule, hemagglutinin, is an appealing prospect, and novel vaccine formulations show promising results in animal model systems. However, studies in humans indicate that natural infection and vaccination result in limited boosting of antibodies to the stem of HA, and the level of stem-specific antibody elicited is insufficient to provide broad strain-transcendent immunity. Here, we use mathematical models of the humoral immune response to explore how pre-existing immunity affects the ability of vaccines to boost antibodies to the head and stem of HA in humans, and, in particular, how it leads to the apparent lack of boosting of broadly cross-reactive antibodies to the stem epitopes. We consider hypotheses where binding of antibody to an epitope: (i) results in more rapid clearance of the antigen; (ii) leads to the formation of antigen-antibody complexes which inhibit B cell activation through Fcγ receptor-mediated mechanism; and (iii) masks the epitope and prevents the stimulation and proliferation of specific B cells. We find that only epitope masking but not the former two mechanisms to be key in recapitulating patterns in data. We discuss the ramifications of our findings for the development of vaccines against both seasonal and pandemic influenza.

Regulatory and T Effector Cells Have Overlapping Low to High Ranges in TCR Affinities for Self during Demyelinating Disease.

Having regulatory T cells (Tregs) with the same Ag specificity as the responding conventional T cells is thought to be important in maintaining peripheral tolerance. It has been demonstrated that during experimental autoimmune encephalomyelitis there are myelin oligodendrocyte glycoprotein (MOG)--specific Tregs that infiltrate into the CNS. However, the affinity of naturally occurring polyclonal Tregs for any self-antigen, let alone MOG, has not been analyzed in the periphery or at the site of autoimmune disease. Utilizing the highly sensitive micropipette adhesion frequency assay, which allows one to determine on a single-cell basis the affinity and frequency of polyclonal Ag-specific T cells directly ex vivo, we demonstrate that at peak disease MOG-specific Tregs were progressively enriched in the draining cervical lymph nodes and CNS as compared with spleen. These frequencies were greater than the frequencies measured by tetramer analysis, indicative of the large fraction of lower affinity T cells that comprise the MOG-specific conventional T cell (Tconv) and Treg response. Of interest, the self-reactive CD4(+) Tconvs and Tregs displayed overlapping affinities for MOG in the periphery, yet in the CNS, the site of neuroinflammation, Tconvs skew toward higher affinities. Most of the MOG-specific Tregs in the CNS possessed the methylation signature associated with thymic-derived Tregs. These findings indicate that thymic-derived Treg affinity range matches that of their Tconvs in the periphery and suggest a change in TCR affinity as a potential mechanism for autoimmune progression and escape from immune regulation.

Insights from in situ analysis of TCR-pMHC recognition: response of an interaction network.

Recognition of peptide presented by the major histocompatibility complex (pMHC) molecule by the T-cell receptor (TCR) determines T-cell selection, development, differentiation, fate, and function. Despite intensive studies on the structures, thermodynamic properties, kinetic rates, and affinities of TCR-pMHC interactions in the past two decades, questions regarding the functional outcome of these interactions, i.e. how binding of the αß TCR heterodimer with distinct pMHCs triggers different intracellular signals via the adjacent CD3 components to produce different T-cell responses, remain unclear. Most kinetic measurements have used surface plasmon resonance, a three-dimensional (3D) technique in which fluid-phase receptors and ligands are removed from their cellular environment. Recently, several two-dimensional (2D) techniques have been developed to analyze molecular interactions on live T cells with pMHCs presented by surrogate antigen-presenting cells or supported planar lipid bilayers. The insights from these in situ analyses have provided a sharp contrast of the 2D network biology approach to the 3D reductionist approach and prompted rethinking of our current views of T-cell triggering. Based on these insights, we propose a mechanochemical coupled triggering hypothesis to explain why the in situ kinetic parameters differ so much from their 3D counterparts, yet correlate so much better with T-cell functional responses.

Accumulation of serial forces on TCR and CD8 frequently applied by agonist antigenic peptides embedded in MHC molecules triggers calcium in T cells.

T cell activation by Ag is one of the key events in adaptive immunity. It is triggered by interactions of the TCR and coreceptor (CD8 or CD4) with antigenic peptides embedded in MHC (pMHC) molecules expressed on APCs. The mechanism of how signal is initiated remains unclear. In this article, we complement our two-dimensional kinetic analysis of TCR-pMHC-CD8 interaction with concurrent calcium imaging to examine how ligand engagement of TCR with and without the coengagement of CD8 initiates signaling. We found that accumulation of frequently applied forces on the TCR via agonist pMHC triggered calcium, which was further enhanced by CD8 cooperative binding. Prolonging the intermission between sequential force applications impaired calcium signals. Our data support a model where rapid accumulation of serial forces on TCR-pMHC-CD8 bonds triggers calcium in T cells.

The kinetics of two-dimensional TCR and pMHC interactions determine T-cell responsiveness.

The T-cell receptor (TCR) interacts with peptide-major histocompatibility complexes (pMHC) to discriminate pathogens from self-antigens and trigger adaptive immune responses. Direct physical contact is required between the T cell and the antigen-presenting cell for cross-junctional binding where the TCR and pMHC are anchored on two-dimensional (2D) membranes of the apposing cells. Despite their 2D nature, TCR-pMHC binding kinetics have only been analysed three-dimensionally (3D) with a varying degree of correlation with the T-cell responsiveness. Here we use two mechanical assays to show high 2D affinities between a TCR and its antigenic pMHC driven by rapid on-rates. Compared to their 3D counterparts, 2D affinities and on-rates of the TCR for a panel of pMHC ligands possess far broader dynamic ranges that match that of their corresponding T-cell responses. The best 3D predictor of response is the off-rate, with agonist pMHC dissociating the slowest. In contrast, 2D off-rates are up to 8,300-fold faster, with the agonist pMHC dissociating the fastest. Our 2D data suggest rapid antigen sampling by T cells and serial engagement of a few agonist pMHCs by TCRs in a large self pMHC background. Thus, the cellular environment amplifies the intrinsic TCR-pMHC binding to generate broad affinities and rapid kinetics that determine T-cell responsiveness.

Preservation of naïve phenotype CD4+ T cells after vaccination contributes to durable immunity.

Memory T cells are conventionally associated with durable recall responses. In our longitudinal analyses of CD4+ T cell responses to the yellow fever virus (YFV) vaccine by peptide-MHC tetramers, we unexpectedly found CD45RO-CCR7+ virus-specific CD4+ T cells that expanded shortly after vaccination and persisted months to years after immunization. Further phenotypic analyses revealed the presence of stem-cell memory T cells (TSCM) within this subset. In addition, post-vaccine T cells lacking known memory markers and functionally resembling genuine naïve T cells were identified, referred to herein as marker-negative T cells (TMN). Single-cell TCR sequencing detected expanded clonotypes within the TMN subset and identified TMN TCRs shared with memory and effector T cells. Longitudinal tracking of YFV-specific responses over subsequent years revealed superior stability of TMN cells, which correlated with the longevity of the overall tetramer+ population. These findings uncovered additional complexity within the post-immune T cell compartment and implicate TMN cells in durable immune responses.

Differentiation marker-negative CD4+ T cells persist after yellow fever virus vaccination and contribute to durable memory.

Factors that contribute to durable immunological memory remain incompletely understood. In our longitudinal analyses of CD4+ T cell responses to the yellow fever virus (YFV) vaccine by peptide-MHC tetramers, we unexpectedly found naïve phenotype virus-specific CD4+ T cells that persisted months to years after immunization. These Marker negative T cells (TMN) lacked CD95, CXCR3, CD11a, and CD49d surface protein expression, distinguishing them from previously discovered stem-cell memory T cells. Functionally, they resembled genuine naïve T cells upon in vitro stimulation. Single-cell TCR sequencing detected expanded clonotypes within the TMN subset and identified a shared repertoire with memory and effector T cells. T cells expressing TMN-associated TCRs were rare before vaccination, suggesting their expansion following vaccination. Longitudinal tracking of YFV-specific responses over the subsequent years revealed superior stability of the TMN subset and their association with the longevity of the overall population. The identification of these long-lived, antigen-experienced T cells may inform the design of durable T cell-based vaccines and engineered T cell therapies.

A comparative immunological assessment of multiple clinical-stage adjuvants for the R21 malaria vaccine in nonhuman primates.

Authorization of the Matrix-M (MM)-adjuvanted R21 vaccine by three countries and its subsequent endorsement by the World Health Organization for malaria prevention in children are a milestone in the fight against malaria. Yet, our understanding of the innate and adaptive immune responses elicited by this vaccine remains limited. Here, we compared three clinically relevant adjuvants [3M-052 + aluminum hydroxide (Alum) (3M), a TLR7/8 agonist formulated in Alum; GLA-LSQ, a TLR4 agonist formulated in liposomes with QS-21; and MM, the now-approved adjuvant for R21] for their capacity to induce durable immune responses to R21 in macaques. R21 adjuvanted with 3M on a 0, 8, and 23-week schedule elicited anti-circumsporozoite antibody responses comparable in magnitude to the R21/MM vaccine administered using a 0-4-8-week regimen and persisted up to 72 weeks with a half-life of 337 days. A booster dose at 72 weeks induced a recall response similar to the R21/MM vaccination. In contrast, R21/GLA-LSQ immunization induced a lower, short-lived response at the dose used. Consistent with the durable serum antibody responses, MM and 3M induced long-lived plasma cells in the bone marrow and other tissues, including the spleen. Furthermore, whereas 3M stimulated potent and persistent antiviral transcriptional and cytokine signatures after primary and booster immunizations, MM induced enhanced expression of interferon- and TH2-related signatures more highly after the booster vaccination. Collectively, these findings provide a resource on the immune responses of three clinically relevant adjuvants with R21 and highlight the promise of 3M as another adjuvant for malarial vaccines.

Competing Heterogeneities in Vaccine Effectiveness Estimation.

Understanding the waning of vaccine-induced protection is important for both immunology and public health. Population heterogeneities in underlying (pre-vaccination) susceptibility and vaccine response can cause measured vaccine effectiveness (mVE) to change over time, even in the absence of pathogen evolution and any actual waning of immune responses. We use multi-scale agent-based models parameterized using epidemiological and immunological data, to investigate the effect of these heterogeneities on mVE as measured by the hazard ratio. Based on our previous work, we consider the waning of antibodies according to a power law and link it to protection in two ways: (1) motivated by correlates of risk data and (2) using a within-host model of stochastic viral extinction. The effect of the heterogeneities is given by concise and understandable formulas, one of which is essentially a generalization of Fisher's fundamental theorem of natural selection to include higher derivatives. Heterogeneity in underlying susceptibility accelerates apparent waning, whereas heterogeneity in vaccine response slows down apparent waning. Our models suggest that heterogeneity in underlying susceptibility is likely to dominate. However, heterogeneity in vaccine response offsets <10% to >100% (median of 29%) of this effect in our simulations. Our study suggests heterogeneity is more likely to 'bias' mVE downwards towards the faster waning of immunity but a subtle bias in the opposite direction is also plausible.

Competing Heterogeneities in Vaccine Effectiveness Estimation.

Understanding waning of vaccine-induced protection is important for both immunology and public health. Population heterogeneities in underlying (pre-vaccination) susceptibility and vaccine response can cause measured vaccine effectiveness (mVE) to change over time even in the absence of pathogen evolution and any actual waning of immune responses. We use a multi-scale agent-based models parameterized using epidemiological and immunological data, to investigate the effect of these heterogeneities on mVE as measured by the hazard ratio. Based on our previous work, we consider waning of antibodies according to a power law and link it to protection in two ways: 1) motivated by correlates of risk data and 2) using a within-host model of stochastic viral extinction. The effect of the heterogeneities is given by concise and understandable formulas, one of which is essentially a generalization of Fisher's fundamental theorem of natural selection to include higher derivatives. Heterogeneity in underlying susceptibility accelerates apparent waning, whereas heterogeneity in vaccine response slows down apparent waning. Our models suggest that heterogeneity in underlying susceptibility is likely to dominate. However, heterogeneity in vaccine response offsets <10% to >100% (median of 29%) of this effect in our simulations. Our methodology and results may be helpful in understanding competing heterogeneities and waning of immunity and vaccine-induced protection. Our study suggests heterogeneity is more likely to 'bias' mVE downwards towards faster waning of immunity but a subtle bias in the opposite direction is also plausible.