Minding the margins: Evaluating the impact of COVID-19 among Latinx and Black communities with optimal qualitative serological assessment tools.

COVID-19 disproportionately affected minorities, while research barriers to engage underserved communities persist. Serological studies reveal infection and vaccination histories within these communities, however lack of consensus on downstream evaluation methods impede meta-analyses and dampen the broader public health impact. To reveal the impact of COVID-19 and vaccine uptake among diverse communities and to develop rigorous serological downstream evaluation methods, we engaged racial and ethnic minorities in Massachusetts in a cross-sectional study (April - July 2022), screened blood and saliva for SARS-CoV-2 and human endemic coronavirus (hCoV) antibodies by bead-based multiplex assay and point-of-care (POC) test and developed across-plate normalization and classification boundary methods for optimal qualitative serological assessments. Among 290 participants, 91.4 % reported receiving at least one dose of a COVID-19 vaccine, while 41.7 % reported past SARS-CoV-2 infections, which was confirmed by POC- and multiplex-based saliva and blood IgG seroprevalences. We found significant differences in antigen-specific IgA and IgG antibody outcomes and indication of cross-reactivity with hCoV OC43. Finally, 26.5 % of participants reported lingering COVID-19 symptoms, mostly middle-aged Latinas. Hence, prolonged COVID-19 symptoms were common among our underserved population and require public health attention, despite high COVID-19 vaccine uptake. Saliva served as a less-invasive sample-type for IgG-based serosurveys and hCoV cross-reactivity needed to be evaluated for reliable SARS-CoV-2 serosurvey results. Using the developed rigorous downstream qualitative serological assessment methods will help standardize serosurvey outcomes and meta-analyses for future serosurveys beyond SARS-CoV-2.

Spatially-dependent model for rods and cones in the retina.

We develop a mathematical model for photoreceptors in the retina. We focus on rod and cone outer segment dynamics and interactions with a nutrient source associated with the retinal pigment epithelium cells. Rod and cone densities (number per unit area of retinal surface) are known to have significant spatial dependence in the retina with cones located primarily near the fovea and the rods located primarily away from the fovea. Our model accounts for this spatial dependence of the rod and cone photoreceptor density as well as for the possibility of nutrient diffusion. We present equilibrium and dynamic solutions, discuss their relation to existing models, and estimate model parameters through comparisons with available experimental measurements of both spatial and temporal photoreceptor characteristics. Our model compares well with existing data on spatially-dependent regrowth of photoreceptor outer segments in the macular region of Rhesus Monkeys. Our predictions are also consistent with existing data on the spatial dependence of photoreceptor outer segment length near the fovea in healthy human subjects. We focus primarily on the healthy eye but our model could be the basis for future efforts designed to explore various retinal pathologies, eye-related injuries, and treatments of these conditions.

Reproducibility in cytometry: Signals analysis and its connection to uncertainty quantification.

Signals analysis for cytometry remains a challenging task that has a significant impact on uncertainty. Conventional cytometers assume that individual measurements are well characterized by simple properties such as the signal area, width, and height. However, these approaches have difficulty distinguishing inherent biological variability from instrument artifacts and operating conditions. As a result, it is challenging to quantify uncertainty in the properties of individual cells and perform tasks such as doublet deconvolution. We address these problems via signals analysis techniques that use scale transformations to: (I) separate variation in biomarker expression from effects due to flow conditions and particle size; (II) quantify reproducibility associated with a given laser interrogation region; (III) estimate uncertainty in measurement values on a per-event basis; and (IV) extract the singlets that make up a multiplet. The key idea behind this approach is to model how variable operating conditions deform the signal shape and then use constrained optimization to "undo" these deformations for measured signals; residuals to this process characterize reproducibility. Using a recently developed microfluidic cytometer, we demonstrate that these techniques can account for instrument and measurand induced variability with a residual uncertainty of less than 2.5% in the signal shape and less than 1% in integrated area.

Monoclonal Antibodies as SARS-CoV-2 Serology Standards: Experimental Validation and Broader Implications for Correlates of Protection.

COVID-19 has highlighted challenges in the measurement quality and comparability of serological binding and neutralization assays. Due to many different assay formats and reagents, these measurements are known to be highly variable with large uncertainties. The development of the WHO international standard (WHO IS) and other pool standards have facilitated assay comparability through normalization to a common material but does not provide assay harmonization nor uncertainty quantification. In this paper, we present the results from an interlaboratory study that led to the development of (1) a novel hierarchy of data analyses based on the thermodynamics of antibody binding and (2) a modeling framework that quantifies the probability of neutralization potential for a given binding measurement. Importantly, we introduced a precise, mathematical definition of harmonization that separates the sources of quantitative uncertainties, some of which can be corrected to enable, for the first time, assay comparability. Both the theory and experimental data confirmed that mAbs and WHO IS performed identically as a primary standard for establishing traceability and bridging across different assay platforms. The metrological anchoring of complex serological binding and neuralization assays and fast turn-around production of an mAb reference control can enable the unprecedented comparability and traceability of serological binding assay results for new variants of SARS-CoV-2 and immune responses to other viruses.

Inferring the Nominal Molecular Mass of an Analyte from Its Electron Ionization Mass Spectrum.

The performance of three algorithms for predicting nominal molecular mass from an analyte's electron ionization mass spectrum is presented. The Peak Interpretation Method (PIM) attempts to quantify the likelihood that a molecular ion peak is contained in the mass spectrum, whereas the Simple Search Hitlist Method (SS-HM) and iterative Hybrid Search Hitlist Method (iHS-HM) leverage results from mass spectral library searching. These predictions can be employed in combination (recommended) or independently. The methods were tested on two sets of query mass spectra searched against libraries that did not contain the reference mass spectra of the same compounds: 19,074 spectra of various organic molecules searched against the NIST17 mass spectral library and 162 spectra of small molecule drugs searched against SWGDRUG version 3.3. Individually, each molecular mass prediction method had computed precisions (the fraction of positive predictions that were correct) of 91, 89, and 74%, respectively. The methods become more valuable when predictions are taken together. When all three predictions were identical, which occurred in 33% of the test cases, the predicted molecular mass was almost always correct (>99%).

Reducing Bias and Quantifying Uncertainty in Fluorescence Produced by PCR.

We present a new approach for relating nucleic-acid content to fluorescence in a real-time Polymerase Chain Reaction (PCR) assay. By coupling a two-type branching process for PCR with a fluorescence analog of Beer's Law, the approach reduces bias and quantifies uncertainty in fluorescence. As the two-type branching process distinguishes between complementary strands of DNA, it allows for a stoichiometric description of reactions between fluorescent probes and DNA and can capture the initial conditions encountered in assays targeting RNA. Analysis of the expected copy-number identifies additional dynamics that occur at short times (or, equivalently, low cycle numbers), while investigation of the variance reveals the contributions from liquid volume transfer, imperfect amplification, and strand-specific amplification (i.e., if one strand is synthesized more efficiently than its complement). Linking the branching process to fluorescence by the Beer's Law analog allows for an a priori description of background fluorescence. It also enables uncertainty quantification (UQ) in fluorescence which, in turn, leads to analytical relationships between amplification efficiency (probability) and limit of detection. This work sets the stage for UQ-PCR, where both the input copy-number and its uncertainty are quantified from fluorescence kinetics.

On the challenge of unambiguous identification of fentanyl analogs: Exploring measurement diversity using standard reference mass spectral libraries.

Fentanyl analogs are a class of designer drugs that are particularly challenging to unambiguously identify due to the mass spectral and retention time similarities of unique compounds. In this paper, we use agglomerative hierarchical clustering to explore the measurement diversity of fentanyl analogs and better understand the challenge of unambiguous identifications using analytical techniques traditionally available to drug chemists. We consider four measurements in particular: gas chromatography retention indices, electron ionization mass spectra, electrospray ionization tandem mass spectra, and direct analysis in real time mass spectra. Our analysis demonstrates how simultaneously considering data from multiple measurement techniques increases the observable measurement diversity of fentanyl analogs, which can reduce identification ambiguity. This paper further supports the use of multiple analytical techniques to identify fentanyl analogs (among other substances), as is recommended by the Scientific Working Group for the Analysis of Seized Drugs (SWGDRUG).

Modeling in higher dimensions to improve diagnostic testing accuracy: Theory and examples for multiplex saliva-based SARS-CoV-2 antibody assays.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has emphasized the importance and challenges of correctly interpreting antibody test results. Identification of positive and negative samples requires a classification strategy with low error rates, which is hard to achieve when the corresponding measurement values overlap. Additional uncertainty arises when classification schemes fail to account for complicated structure in data. We address these problems through a mathematical framework that combines high dimensional data modeling and optimal decision theory. Specifically, we show that appropriately increasing the dimension of data better separates positive and negative populations and reveals nuanced structure that can be described in terms of mathematical models. We combine these models with optimal decision theory to yield a classification scheme that better separates positive and negative samples relative to traditional methods such as confidence intervals (CIs) and receiver operating characteristics. We validate the usefulness of this approach in the context of a multiplex salivary SARS-CoV-2 immunoglobulin G assay dataset. This example illustrates how our analysis: (i) improves the assay accuracy, (e.g. lowers classification errors by up to 42% compared to CI methods); (ii) reduces the number of indeterminate samples when an inconclusive class is permissible, (e.g. by 40% compared to the original analysis of the example multiplex dataset) and (iii) decreases the number of antigens needed to classify samples. Our work showcases the power of mathematical modeling in diagnostic classification and highlights a method that can be adopted broadly in public health and clinical settings.

Binding, brightness, or noise? Extracting temperature-dependent properties of dye bound to DNA.

We present a method for extracting temperature-dependent thermodynamic and photophysical properties of SYTO-13 dye bound to DNA from fluorescence measurements. Together, mathematical modeling, control experiments, and numerical optimization enable dye binding strength, dye brightness, and experimental noise (or error) to be discriminated from one another. By focusing on the low-dye-coverage regime, the model avoids bias and can simplify quantification. Utilizing the temperature-cycling capabilities and multi-reaction chambers of a real-time PCR machine increases throughput. Significant well-to-well and plate-to-plate variation is quantified by using total least squares to account for error in both fluorescence and nominal dye concentration. Properties computed independently for single-stranded DNA and double-stranded DNA by numerical optimization are consistent with intuition and explain the advantageous performance of SYTO-13 in high-resolution melting and real-time PCR assays. Distinguishing between binding, brightness, and noise also clarifies the mechanism for the increased fluorescence of dye in a solution of double-stranded DNA compared to single-stranded DNA; in fact, the explanation changes with temperature.

Optimal classification and generalized prevalence estimates for diagnostic settings with more than two classes.

An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two classes. We address this problem by developing a multiclass classification based on probabilistic modeling and optimal decision theory that minimizes the convex combination of false classification rates. The classification process is challenging when the relative fraction of the population in each class, or generalized prevalence, is unknown. Thus, we also develop a method for estimating the generalized prevalence of test data that is independent of classification of the test data. We validate our approach on serological data with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) naïve, previously infected, and vaccinated classes. Synthetic data are used to demonstrate that (i) prevalence estimates are unbiased and converge to true values and (ii) our procedure applies to arbitrary measurement dimensions. In contrast to the binary problem, the multiclass setting offers wide-reaching utility as the most general framework and provides new insight into prevalence estimation best practices.

Prevalence estimation and optimal classification methods to account for time dependence in antibody levels.

Serology testing can identify past infection by quantifying the immune response of an infected individual providing important public health guidance. Individual immune responses are time-dependent, which is reflected in antibody measurements. Moreover, the probability of obtaining a particular measurement from a random sample changes due to changing prevalence (i.e., seroprevalence, or fraction of individuals exhibiting an immune response) of the disease in the population. Taking into account these personal and population-level effects, we develop a mathematical model that suggests a natural adaptive scheme for estimating prevalence as a function of time. We then combine the estimated prevalence with optimal decision theory to develop a time-dependent probabilistic classification scheme that minimizes the error associated with classifying a value as positive (history of infection) or negative (no such history) on a given day since the start of the pandemic. We validate this analysis by using a combination of real-world and synthetic SARS-CoV-2 data and discuss the type of longitudinal studies needed to execute this scheme in real-world settings.

Incorporating measurement variability when comparing sets of high-resolution mass spectra.

Mass spectra are an important signature by which compounds can be identified. We recently formulated a mathematical approach for incorporating measurement variability when comparing sets of high-resolution mass spectra. Leveraging replicate mass spectra, we construct high-dimensional consensus mass spectra-representing each of the compared analytes-and compute the similarity between these data structures. In this paper, we present this approach and discuss its applications and limitations when trying to discriminate methamphetamine and phentermine using in-source collision induced dissociation mass spectra collected with direct analysis in real time mass spectrometry.

Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 antibody assays.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has emphasized the importance and challenges of correctly interpreting antibody test results. Identification of positive and negative samples requires a classification strategy with low error rates, which is hard to achieve when the corresponding measurement values overlap. Additional uncertainty arises when classification schemes fail to account for complicated structure in data. We address these problems through a mathematical framework that combines high dimensional data modeling and optimal decision theory. Specifically, we show that appropriately increasing the dimension of data better separates positive and negative populations and reveals nuanced structure that can be described in terms of mathematical models. We combine these models with optimal decision theory to yield a classification scheme that better separates positive and negative samples relative to traditional methods such as confidence intervals (CIs) and receiver operating characteristics. We validate the usefulness of this approach in the context of a multiplex salivary SARS-CoV-2 immunoglobulin G assay dataset. This example illustrates how our analysis: (i) improves the assay accuracy (e.g. lowers classification errors by up to 42 % compared to CI methods); (ii) reduces the number of indeterminate samples when an inconclusive class is permissible (e.g. by 40 % compared to the original analysis of the example multiplex dataset); and (iii) decreases the number of antigens needed to classify samples. Our work showcases the power of mathematical modeling in diagnostic classification and highlights a method that can be adopted broadly in public health and clinical settings.

Serial flow cytometry in an inertial focusing optofluidic microchip for direct assessment of measurement variations.

Flow cytometry is an invaluable technology in biomedical research, but confidence in single-cell measurements remains limited due to a lack of appropriate techniques for uncertainty quantification (UQ). It is particularly challenging to evaluate the potential for different instrumentation designs or operating parameters to influence the measurement physics in ways that change measurement repeatability. Here, we report a direct experimental approach to UQ using a serial flow cytometer that measured each particle more than once along a flow path. The instrument was automated for real-time characterization of measurement precision and operated with particle velocities exceeding 1 m s-1, throughputs above 100 s-1, and analysis yields better than 99.9%. These achievements were enabled by a novel hybrid inertial and hydrodynamic particle focuser to tightly control particle positions and velocities. The cytometer identified ideal flow conditions with fluorescence area measurement precision on the order of 1% and characterized tradeoffs between precision, throughput, and analysis yield. The serial cytometer is anticipated to improve single-cell measurements through estimation (and subsequent control) of uncertainty contributions from various other instrument parameters leading to overall improvements in the ability to better classify sample composition and to find rare events.

Optimal decision theory for diagnostic testing: Minimizing indeterminate classes with applications to saliva-based SARS-CoV-2 antibody assays.

In diagnostic testing, establishing an indeterminate class is an effective way to identify samples that cannot be accurately classified. However, such approaches also make testing less efficient and must be balanced against overall assay performance. We address this problem by reformulating data classification in terms of a constrained optimization problem that (i) minimizes the probability of labeling samples as indeterminate while (ii) ensuring that the remaining ones are classified with an average target accuracy X. We show that the solution to this problem is expressed in terms of a bathtub-type principle that holds out those samples with the lowest local accuracy up to an X-dependent threshold. To illustrate the usefulness of this analysis, we apply it to a multiplex, saliva-based SARS-CoV-2 antibody assay and demonstrate up to a 30 % reduction in the number of indeterminate samples relative to more traditional approaches.

Graph convolutional neural network applied to the prediction of normal boiling point.

In this article, we describe training and validation of a machine learning model for the prediction of organic compound normal boiling points. Data are drawn from the experimental literature as captured in the NIST Thermodynamics Research Center (TRC) SOURCE Data Archival System. The machine learning model is based on a graph neural network approach, a methodology that has proven powerful when applied to a variety of chemical problems. Model input is extracted from a 2D sketch of the molecule, making the methodology suitable for rapid prediction of normal boiling points in a wide variety of scenarios. Our final model predicts normal boiling points within 6 K (corresponding to a mean absolute percent error of 1.32%) with sample standard deviation less than 8 K. Additionally, we found that our model robustly identifies errors in the input data set during the model training phase, thereby further motivating the utility of systematic data exploration approaches for data-related efforts.

Optimal Decision Theory for Diagnostic Testing: Minimizing Indeterminate Classes with Applications to Saliva-Based SARS-CoV-2 Antibody Assays.

In diagnostic testing, establishing an indeterminate class is an effective way to identify samples that cannot be accurately classified. However, such approaches also make testing less efficient and must be balanced against overall assay performance. We address this problem by reformulating data classification in terms of a constrained optimization problem that (i) minimizes the probability of labeling samples as indeterminate while (ii) ensuring that the remaining ones are classified with an average target accuracy X. We show that the solution to this problem is expressed in terms of a bathtub principle that holds out those samples with the lowest local accuracy up to an X-dependent threshold. To illustrate the usefulness of this analysis, we apply it to a multiplex, saliva-based SARS-CoV-2 antibody assay and demonstrate up to a 30 % reduction in the number of indeterminate samples relative to more traditional approaches.

Optofluidic flow meter for sub-nanoliter per minute flow measurements.

SIGNIFICANCE: Performance improvements in microfluidic systems depend on accurate measurement and fluid control on the micro- and nanoscales. New applications are continuously leading to lower volumetric flow rates. AIM: We focus on improving an optofluidic system for measuring and calibrating microflows to the sub-nanoliter per minute range. APPROACH: Measurements rely on an optofluidic system that delivers excitation light and records fluorescence in a precise interrogation region of a microfluidic channel. Exploiting a scaling relationship between the flow rate and fluorescence emission after photobleaching, the system enables real-time determination of flow rates. RESULTS: Here, we demonstrate improved calibration of a flow controller to 1% uncertainty. Further, the resolution of the optofluidic flow meter improved to less than 1 nL / min with 5% uncertainty using a molecule with a 14-fold smaller diffusion coefficient than our previous report. CONCLUSIONS: We demonstrate new capabilities in sub-nanoliter per minute flow control and measurement that are generalizable to cutting-edge light-material interaction and molecular diffusion for chemical and biomedical industries.

Classification under uncertainty: data analysis for diagnostic antibody testing.

Formulating accurate and robust classification strategies is a key challenge of developing diagnostic and antibody tests. Methods that do not explicitly account for disease prevalence and uncertainty therein can lead to significant classification errors. We present a novel method that leverages optimal decision theory to address this problem. As a preliminary step, we develop an analysis that uses an assumed prevalence and conditional probability models of diagnostic measurement outcomes to define optimal (in the sense of minimizing rates of false positives and false negatives) classification domains. Critically, we demonstrate how this strategy can be generalized to a setting in which the prevalence is unknown by either (i) defining a third class of hold-out samples that require further testing or (ii) using an adaptive algorithm to estimate prevalence prior to defining classification domains. We also provide examples for a recently published SARS-CoV-2 serology test and discuss how measurement uncertainty (e.g. associated with instrumentation) can be incorporated into the analysis. We find that our new strategy decreases classification error by up to a decade relative to more traditional methods based on confidence intervals. Moreover, it establishes a theoretical foundation for generalizing techniques such as receiver operating characteristics by connecting them to the broader field of optimization.

Towards Quantitative and Standardized Serological and Neutralization Assays for COVID-19.

Quantitative and robust serology assays are critical measurements underpinning global COVID-19 response to diagnostic, surveillance, and vaccine development. Here, we report a proof-of-concept approach for the development of quantitative, multiplexed flow cytometry-based serological and neutralization assays. The serology assays test the IgG and IgM against both the full-length spike antigens and the receptor binding domain (RBD) of the spike antigen. Benchmarking against an RBD-specific SARS-CoV IgG reference standard, the anti-SARS-CoV-2 RBD antibody titer was quantified in the range of 37.6 µg/mL to 31.0 ng/mL. The quantitative assays are highly specific with no correlative cross-reactivity with the spike proteins of MERS, SARS1, OC43 and HKU1 viruses. We further demonstrated good correlation between anti-RBD antibody titers and neutralizing antibody titers. The suite of serology and neutralization assays help to improve measurement confidence and are complementary and foundational for clinical and epidemiologic studies.