In this paper we generalize the Linear Chain Trick (LCT; aka the Gamma Chain Trick) to help provide modelers more flexibility to incorporate appropriate dwell time assumptions into mean field ODEs, and help clarify connections between individual-level stochastic model assumptions and the structure of corresponding mean field ODEs. The LCT is a technique used to construct mean field ODE models from continuous-time stochastic state transition models where the time an individual spends in a given state (i.e., the dwell time) is Erlang distributed (i.e., gamma distributed with integer shape parameter). Despite the LCT’s widespread use, we lack general theory to facilitate the easy application of this technique, especially for complex models. Modelers must therefore choose between constructing ODE models using heuristics with oversimplified dwell time assumptions, using time consuming derivations from first principles, or to instead use non-ODE models (like integro-differential or delay differential equations) which can be cumbersome to derive and analyze. Here, we provide analytical results that enable modelers to more efficiently construct ODE models using the LCT or related extensions. Specifically, we provide (1) novel LCT extensions for various scenarios found in applications, including conditional dwell time distributions; (2) formulations of these LCT extensions that bypass the need to derive ODEs from integral equations; and (3) a novel Generalized Linear Chain Trick (GLCT) framework that extends the LCT to a much broader set of possible dwell time distribution assumptions, including the flexible phase-type distributions which can approximate distributions on and can be fit to data.

Burkholderia pseudomallei is the causative agent of melioidosis, a severe infection prominent in northern Australia and Southeast Asia. The “gold standard” for melioidosis diagnosis is bacterial isolation, which takes several days to complete. The resulting delay in diagnosis leads to delayed treatments, which could result in death. In an attempt to develop better methods for early diagnosis of melioidosis, B. pseudomallei capsular polysaccharide (CPS) was identified as an important diagnostic biomarker. A rapid lateral flow immunoassay utilizing CPS-specific monoclonal antibody was developed and tested in endemic regions worldwide. However, the in vivo fate and clearance of CPS has never been thoroughly investigated. Here, we injected mice with purified CPS intravenously and determined CPS concentrations in serum, urine, and major organs at various intervals. The results indicate that CPS is predominantly eliminated through urine and no CPS accumulation occurs in the major organs. Immunoblot analysis demonstrated that intact CPS was excreted through urine. To understand how a large molecule like CPS was eliminated without degradation, a 3-dimenational structure of CPS was modeled. The predicted CPS structure has a rod-like shape with a small diameter that could allow it to flow through the glomerulus of the kidney. CPS clearance was determined using exponential decay models and the corrected Akaike Information Criterion. The results show that CPS has a relatively short serum half-life of 2.9 to 4.4 hours. Therefore, the presence of CPS in the serum and/or urine suggests active melioidosis infection and provides a marker to monitor treatment of melioidosis.

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The CDC Tier 1 select agent Francisella tularensis is a small, Gram-negative bacterium and the causative agent of tularemia, a potentially life-threatening infection endemic in the United States, Europe and Asia. Currently, there is no licensed vaccine or rapid point-of-care diagnostic test for tularemia. The purpose of this research was to develop monoclonal antibodies (mAbs) specific to the F. tularensis surface-expressed lipopolysaccharide (LPS) for a potential use in a rapid diagnostic test. Our initial antigen capture ELISA was developed using murine IgG3 mAb 1A4. Due to the low sensitivity of the initial assay, IgG subclass switching, which is known to have an effect on the functional affinity of a mAb, was exploited for the purpose of enhancing assay sensitivity. The ELISA developed using the IgG1 or IgG2b mAbs from the subclass-switch family of 1A4 IgG3 yielded improved assay sensitivity. However, surface plasmon resonance (SPR) demonstrated that the functional affinity was decreased as a result of subclass switching. Further investigation using direct ELISA revealed the potential self-association of 1A4 IgG3, which could explain the higher functional affinity and higher assay background seen with this mAb. Additionally, the higher assay background was found to negatively affect assay sensitivity. Thus, enhancement of the assay sensitivity by subclass switching is likely due to the decrease in assay background, simply by avoiding the self-association of IgG3.

SARS–CoV–2–specific CD4+ T cells are likely important in immunity against COVID–19, but our understanding of CD4+ longitudinal dynamics following infection, and specific features that correlate with the maintenance of neutralizing antibodies, remains limited. We characterized SARS–CoV–2–specific CD4+ T cells in a longitudinal cohort of 109 COVID–19 outpatients. The quality of the SARS–CoV–2–specific CD4+ response shifted from cells producing IFNγ to TNFα from five days to four months post–enrollment, with IFNγ−IL21−TNFα+ CD4+ T cells the predominant population detected at later timepoints. Greater percentages of IFNγ−IL21−TNFα+ CD4+ T cells on day 28 correlated with SARS–CoV–2 neutralizing antibodies measured seven months post–infection (ρ=0.4, P=0.01). mRNA vaccination following SARS–CoV–2 infection boosted both IFNγ and TNFα producing, spike protein–specific CD4+ T cells. These data suggest that SARS–CoV–2–specific, TNFα–producing CD4+ T cells may play an important role in antibody maintenance following COVID–19.