Designing and Interpreting Limiting Dilution Assays: General Principles and Applications to the Latent Reservoir for Human Immunodeficiency Virus-1

Daniel I S Rosenbloom, Oliver Elliott, Alison L Hill, Timothy J Henrich, Janet M Siliciano, Robert F Siliciano, Daniel I S Rosenbloom, Oliver Elliott, Alison L Hill, Timothy J Henrich, Janet M Siliciano, Robert F Siliciano

Abstract

Limiting dilution assays are widely used in infectious disease research. These assays are crucial for current human immunodeficiency virus (HIV)-1 cure research in particular. In this study, we offer new tools to help investigators design and analyze dilution assays based on their specific research needs. Limiting dilution assays are commonly used to measure the extent of infection, and in the context of HIV they represent an essential tool for studying latency and potential curative strategies. Yet standard assay designs may not discern whether an intervention reduces an already miniscule latent infection. This review addresses challenges arising in this setting and in the general use of dilution assays. We illustrate the major statistical method for estimating frequency of infectious units from assay results, and we offer an online tool for computing this estimate. We recommend a procedure for customizing assay design to achieve desired sensitivity and precision goals, subject to experimental constraints. We consider experiments in which no viral outgrowth is observed and explain how using alternatives to viral outgrowth may make measurement of HIV latency more efficient. Finally, we discuss how biological complications, such as probabilistic growth of small infections, alter interpretations of experimental results.

Keywords: HIV; dilution assay; latent reservoir; maximum-likelihood statistics; viral outgrowth.

Figures

Figure 1.
Figure 1.
Precision of dilution assays increases with the number of wells into which a sample is divided. Consider two samples of the same size (total number of cells) collected from different donors. Sample A contains 2 latently infected cells, whereas Sample B contains 8 (ovals at left). Five possible assay setups are shown, distributing each sample into 1 to 5 equal wells (columns). Each assay results in a different pattern of possible outcomes for the samples, with the probability of each outcome shown in rows. The final row shows the probability that each assay yields the correct trend, ie, that more wells turn positive in Sample B than in Sample A. Positive wells (viral outgrowth) are shown in dark red. If all cells from a sample are deposited into a single well (first column), then it is impossible to distinguish between the two samples using a binary readout: the extra infected cells in Sample B are “redundant,” and each sample will show outgrowth. If the samples are divided among more wells (second through fifth columns), then the infected cells are less likely to appear redundantly in the same well, meaning that the two samples are more likely to show different outgrowth patterns. In this particular case, each sample must be divided into at least 4 equal wells to obtain the correct trend at least 95% of the time.
Figure 2.
Figure 2.
Schematic for describing quality of maximum-likelihood estimates of infected cell frequency. The thick blue line plots the typical value (median or geometric mean) of the measured infected cell frequency θ^ (y-axis) vs true frequency θ (x-axis), for an idealized experimental setup; this line is dashed outside the limits of detection for the assay. These limits are defined for a significance level α (eg, 0.05). Below the lower limit of detection (LLD), at least α of experiments result in all wells being negative. Above the upper limit of detection (ULD), at least α of experiments result in all wells being positive. In an accurate assay, the estimate tracks the diagonal line θ^=θ (light gray dashed line) between the limits of detection. The blue shaded region plots the confidence interval (CI), within which the middle (1 – α) of estimates fall. Between the lower and upper limits of quantification (LLQ, ULQ), the CI is smaller than a specified size, and a fraction less than α of experiments result in all-positive or all-negative wells. Note that it is possible for LLD = LLQ and/or ULD = ULQ.
Figure 3.
Figure 3.
Performance of the maximum likelihood estimator in simulations, using the two assay designs highlighted in Table 1. Left column: assay on row 4 (confidence interval [CI] θ^ and 95% CI plotted in blue; the diagonal line shows the case of a perfect unbiased estimator. Asymptotic CIs are reported, using likelihood of log-transformed θ. (B) Bias θ^/θ plotted in blue; the horizontal line at 1 shows the case of a perfect unbiased estimator. (C) Size of the estimated 95% CI plotted in black (note different y-axis scales). (D) Binomial probability expression used to estimate infection frequency, assuming n replicate wells of c cells apiece. According to this expression, the probability that all wells are negative equals e−Cθ, where C is the total number of cells across all replicate wells. A–C plot the actual infection frequency θ used in simulations on the x-axis. Each point on the curves is the geometric mean (A and B) or arithmetic mean (C) of 20 000 replicate simulations using the same θ (step size 0.025 logs). Curves are solid where <5% of simulated assays yield all-negative or all-positive results, dashed at 5%–50%, and not shown at >50%. Blue (A and B) or gray (C) shaded regions show the middle 95% of simulations; jaggedness results from the discrete nature of the dilution assay. Left to right in each panel, the thin vertical lines show the LLD, the LLQ, and the ULQ = ULD. Note that the assay shown at right is more sensitive (20-fold lower LLD), more precise (narrower shaded regions in A and B, smaller CI in C), and more accurate (curve in A better tracks the diagonal; curve in B better tracks the horizontal).

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