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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Anal Chem. Author manuscript; available in PMC 2012 March 15.
Published in final edited form as:
Published online 2011 February 23. doi:  10.1021/ac103161b
PMCID: PMC3056883

Simultaneous Detection of Single Molecules and Singulated Ensembles of Molecules Enables Immunoassays with Broad Dynamic Range


We report a method for combining the detection of single molecules (digital) and an ensemble of molecules (analog) that is capable of detecting enzyme label from 10−19 M to 10−13 M, for use in high sensitivity enzyme-linked immunosorbent assays (ELISA). The approach works by capturing proteins on microscopic beads, labeling the proteins with enzymes using a conventional multi-step immunosandwich approach, isolating the beads in an array of 50-femtoliter wells (Single Molecule Array, SiMoA), and detecting bead-associated enzymatic activity using fluorescence imaging. At low concentrations of proteins, when the ratio of enzyme labels to beads is less than ~1.2, beads carry either zero or low numbers of enzymes, and protein concentration is quantified by counting the presence of “on” or “off” beads (digital regime)1. At higher protein concentrations, each bead typically carries multiple enzyme labels, and the average number of enzyme labels present on each bead is quantified from a measure of the average fluorescence intensity (analog regime). Both the digital and analog concentration ranges are quantified by a common unit, namely, average number of enzyme labels per bead (AEB). By combining digital and analog detection of singulated beads, a linear dynamic range of over 6 orders of magnitude to enzyme label was achieved. Using this approach, an immunoassay for prostate specific antigen (PSA) was developed. The combined digital and analog PSA assay provided linear response over approximately four logs of concentration ([PSA] from 8 fg/mL – 100 pg/mL or 250 aM – 3.3 pM). This approach extends the dynamic range of ELISA from picomolar levels down to sub-femtomolar levels in a single measurement.


The enzyme-linked immunosorbent assay (ELISA)2-4 has been the cornerstone of sensitive detection of proteins for almost 40 years. ELISA is based on the ensemble detection of many enzyme-labeled proteins in μL to mL volumes, and has typically been limited to detecting picomolar (pM) concentrations of proteins. We recently reported a method called digital ELISA1 based on single molecule arrays (SiMoA)5-8 that allows the detection of single enzyme-labeled immunocomplexes by confining them to fL volumes. This approach resulted in a dramatic improvement in immunoassay sensitivity using ELISA reagents, such that sub-femtomolar concentrations of proteins could be detected in serum1. In this paper, we extend this method to determining wider ranges of concentration by combining single molecule and ensemble detection in one straightforward measurement. This approach has allowed us to measure prostate specific antigen (PSA) in serum over a broad concentration range relevant to a particular clinical application. This paper makes use of several acronyms and symbols; for convenience, Table 1 provides a summary of their definitions. Many immunodiagnostic applications require both sensitive protein detection and broad analytical ranges (> 3 logs in concentration) in order to detect the target protein in the majority of samples. One such example is the detection of PSA in subjects who have undergone radical prostatectomy (RP). We have shown that digital ELISA can measure PSA levels in all men classified as undetectable by conventional immunoassay technology, the lowest being a patient with a PSA level of 14 fg/mL.1 Measurement of very low levels of PSA may lead to expedited detection of a cancer recurrence event when compared to a conventional ELISA measurement9. PSA levels in some RP patients, however, are known to reach 100 pg/mL shortly after surgery9, so PSA levels can span four logs of concentration in one group of patients. In another example, sensitive measurements of low levels of the serum biomarkers alpha fetoprotein and β-human chorionic gonadotropin10 could be used to monitor patients for recurrence of testicular cancer after retroperitoneal lymph node dissection. Pre-surgery levels of alpha fetoprotein and β-human chorionic gonadotropin are known to span >3-logs of concentration in these patients,10 with levels dropping below the detection limit of current assays post-surgery11, suggesting clinical utility for highly sensitive assays with wide dynamic ranges. In addition, the hormone estradiol is routinely measured to assess the reproductive function in pre-menopausal women where concentration ranges in serum are greater than five logs12. Immunoassays for estradiol have also been used to identify pre- and post-menopausal women at risk for breast cancer, and to monitor for breast cancer recurrence where the absolute concentration of circulating estradiol is much lower13,14. Again, a highly sensitive immunoassay with a broad dynamic range is needed to fulfill the clinical need.

Table 1
Definitions of some of the acronyms and symbols used in this paper.

New ultra-sensitive immunoassays1,15-17 are needed because the concentration of many biomarkers extend below the working range of currently used clinical assays, and its believed that most serum proteins are, in fact, currently undetectable18. Ultra-sensitive techniques are often capable of measuring low concentrations of a protein in a sample, but are not able to measure the high end of the concentration range without sample dilution and re-testing. It is often not possible, therefore, to measure the broad range of concentrations encountered in clinical samples in a single assay using ultra-sensitive methods. While diluting sample circumvents the insufficient working range of ultra-sensitive assays, in a clinical setting it is preferable to measure all samples in a single pass. By successfully quantitating the concentration of protein in the vast majority of samples in a single test, assay throughput and result turnaround time to the clinician will be improved.

Here, we present a technique for extending digital measurement of enzyme labels using SiMoA into the analog regime, enabling linear detection of enzyme label across six logs of concentration. With the goal of extending the working range of immunoassays, we applied this technique to digital ELISA for PSA. The working range of the combined digital and analog PSA assay was > 4 logs, detecting PSA in serum from 0.008 pg/mL to 100 pg/mL.

Experimental Section

Materials and Methods

The materials and procedures used for forming enzyme-labeled complexes on beads in the enzyme label and PSA assays, preparing femtoliter-volume well arrays, and loading beads into these arrays have been described elsewhere1 and are provided in the Supporting Experimental Section.

Imaging and analysis of beads and enzyme-associated beads in femtoliter-volume well arrays

A microscope-based imaging system, containing a mercury light source, filter cubes, objectives, and a CCD camera was used to image enzyme-associated beads in well arrays formed at the end of fiber bundles19,8. Strips of eight fiber bundles arrays were assembled by gluing the bundles into custom-made glass holders. A strip was clamped on the microscope stage using a custom fixture. A droplet of substrate to β-galactosidase (RGP) was placed on a silicone gasket material and placed in contact with the well arrays. A precision mechanical platform moved the silicone gasket into contact with the end of the fiber bundle, creating an array of isolated femtoliter-volume reaction vessels containing RGP. Fluorescence images were acquired (577 nm excitation; 620 nm emission) with an exposure time of 1011 ms to detect enzymatic activity in the wells. Five fluorescence images (at 30-s intervals) were taken for each femtoliter-volume well array. After acquiring the fluorescence images, the arrays were illuminated with white light and imaged on the CCD camera. The white light and fluorescence images were analyzed using customized software to determine the presence of beads and enzymatic activity, respectively. First, the white light image was analyzed to determine which wells contained a bead. Due to scattering of light by the beads, those wells that contained a bead appeared brighter in the image than wells without beads. Second, regardless of signal levels, all fluorescence images were analyzed the same way. The fluorescence intensities of each well in each array of all five fluorescent images were first determined. The digital signal (“on” or “off”) of each well containing a bead was assigned by determining whether or not the fluorescence intensity increased in each successive image, and by at least 20% over four images. Wells containing a bead that met these criteria were assigned as “on” or active; those that did not meet these criteria were assigned as “off”. The digital signal, i.e., the fraction of “on” beads for each array (fon), was then determined. The analog signal of each “on” bead was determined from the difference in its fluorescence intensity between the second and first fluorescence images (Ibead,F2–Ibead,F1). The analog signal of the array (Ībead) was the average of Ibead,F2–Ibead,F1 over all “on” beads.

Results and Discussion

Singulated Bead ELISA Format

In the first step of the singulated bead ELISA, microscopic beads coated in antibodies capture the target protein from serum, plasma, or another complex sample, followed by labeling the bound proteins with enzyme reporter molecules. Enzyme labeling of the proteins is achieved by the formation of an immunocomplex in two steps, using a biotinylated detection antibody and a streptavidin-enzyme conjugate. The capture beads are then loaded into an array of femtoliter-sized microwells and the loaded array is sealed against a silicone gasket in the presence of a droplet of fluorogenic enzyme substrate, isolating each bead in a femtoliter reaction chamber. Beads associated with bound enzyme label or labels generate a locally high concentration of fluorescent product in the 50-fL reaction chambers. By using standard fluorescence imaging, it is possible to image tens of thousands of enzyme-associated beads simultaneously (Figure S-1). Depending on the fraction of beads that have one or more enzymes associated with them, the assay signal is determined by either digital or analog analysis methods to quantify the number of enzyme labels per bead detected (Figure 1). Figure S-1 contains examples of fluorescence images that are represented schematically in Figure 1. At low ratios of enzyme labels to beads, where there are a significant number of beads that are associated with no enzyme (“off” beads), the number of active, enzyme-associated (or “on”) beads relative to the total number of beads detected are used to determine an average enzyme per bead (AEB) via Poisson statistics. As concentration is determined from counting “on” beads and is independent of the fluorescence intensity generated in the well, we refer to this approach as ‘digital’. At higher ratios of enzyme labels to beads, when most beads have one or more enzyme labels bound, the counting approach no longer works. In this situation, AEB (and, therefore, protein concentration) is determined from the average fluorescence intensity of wells containing a bead in the array (Ībead); we refer to this approach as ‘analog’. Currently, the analog approach is used to analyze images with >70% active beads. To convert Ībead to AEB in the analog regime, we make use of the digital measurements. First, images with <10% active beads are used to determine the average analog intensity of a single enzyme molecule (Īsingle). The ratio of Ībead to Īsingle over all beads provides the analog AEB. The digital and analog analytical regimes are described in detail below.

Figure 1
The signal output of SiMoA at different regimes of enzyme/bead ratios. (Left) At AEB = 0.1, active beads are statistically associated predominantly with single enzymes, and the SiMoA readout is “single molecule”. (Center) At AEB = 0.6, ...

Digital Determination of Protein Concentration

To determine protein concentration in samples, known standards are spiked into bovine serum or plasma, and SiMoA is used to generate a calibration curve of AEB versus concentration. SiMoA is then used to determine AEB for unknown samples that are compared to the calibration curve to determine concentration. At low ratios of enzymes to beads, when there are a statistically significant number of beads with no enzymes, by measuring the fraction of active beads in a population it is possible to determine the bulk analyte concentration because the binding probability of a population of analyte molecules to a population of beads is defined by the Poisson distribution. At very low ratios of labeled analyte to beads (less than about 0.1 enzyme labels per bead), most beads have either zero or one labeled analyte molecules and the percentage of active beads increases approximately linearly with increasing analyte concentration. As the fraction of active beads becomes larger (> 0.1), Poisson statistics show that there are a significant number of beads with multiple enzymes. If the fraction of active beads is plotted against concentration, linearity is lost at high target concentrations because active beads that have multiple enzyme molecules bound contribute the same ‘digital’ signal as an active bead that has one enzyme bound (Figure S-2). To quantitate the number of detected enzymes and to maintain linearity in the sub-populations of beads with multiple enzymes, we use Poisson statistics to convert the fraction of active beads to AEB.

The Poisson distribution (eq.1) describes the likelihood of a number of events occurring if the average number of events is known. If the expected average number of occurrences is μ, then the probability that there are exactly ν occurrences (ν being a non-negative integer, ν = 0, 1, 2, 3,…) is equal to:


In digital ELISA, μ is equal to the ratio of bound labeled proteins to the number of beads, and ν is the number of enzyme-labeled proteins carried by each sub-population of beads (i.e., 0, 1, 2, 3, etc.). The aim of the SiMoA experiment is to determine μ—which by definition is equal to AEB—and use it as the quantitative parameter to determine protein concentration. In the digital mode of analysis where beads are identified as being either “on” or “off”, then ν = 1, 2, 3 are indistinguishable and characterized as “on” beads. A bead associated with one enzyme is indistinguishable from a bead associated with two enzymes due to the static heterogeneity of enzyme activity, where populations of individual enzyme molecules have been shown to have up to a seven-fold distribution in enzymatic activity6,20-22. Due to this broad distribution, only occurrences of ν = 0 can by determined definitively as the fraction of “off” beads (Pμ(0)). Using eq.1 to determine Pμ(0), and the fact that the fraction of “off” beads is equal to one minus the fraction of “on” beads, it is possible to determine AEBdigital (the digitally-determined AEB) from fon (the fraction of “on” beads or % active) (eq.2):


Figure S-2 demonstrates the effectiveness of the Poisson distribution analysis in the digital range of a calibration curve using an assay for streptavidin-β-galactosidase (SβG) that creates beads with well-defined enzyme/bead ratios1. In brief, beads were functionalized with a biotinylated capture molecule, and these beads were used to capture various concentrations of the SβG enzyme conjugate that we use as a label in digital ELISA. The beads were loaded into the femtoliter arrays and, after sealing a solution of RGP into the wells of the array, fluorescence was generated from bound enzymes accumulated in the reaction chambers for 2.5 min, with fluorescent images acquired every 30 s. A white light image of the array was acquired at the end of the experiment. These images were analyzed to identify wells that contained beads (from the white light image) and determine which of those beads had associated bound enzyme molecules (from time-lapsed fluorescent images), as described previously1. Figure S-2 shows that AEBdigital determined from eq.2 maintained a linear response up to 50% active, despite non-linear variation in fon.

Analog Determination of Protein Concentration

While quantification of concentration using counting and Poisson statistics works well below 70% active beads, as the fraction of active beads exceeds about 70%, the change in AEB with concentration is reduced leading to greater imprecision of concentration determination (Figure 2A). The counting approach ultimately breaks down when every bead has at least one bound enzyme.

Figure 2
(A) Plot of fraction of active beads against the effective concentration—given by AEB—determined from digital counting using the Poisson distribution (eq. 2). As concentration increases, the slope of % active gets shallower and signal ...

We extend the dynamic range of the SiMoA assay beyond the digital regime by measuring the average fluorescence intensity of wells that contain beads to determine the number of enzymes associated with each bead detected. For this analysis, AEB can be determined from the average fluorescence intensity value of the active beads (Ībead) and the average fluorescence intensity generated by a single enzymesingle). The AEB of an array in the analog range (AEBanalog) is defined by eq. 3:


To determine Īsingle, we equate the digital (eq.2) and analog (eq.3) AEB terms at fractions of active beads where single enzymes dominate and substrate depletion is negligible (eq.4); we chose arrays with fractions of “on” beads <0.1 that meet these criteria:

I¯single=fon×I¯beadln[1fon],in arrays wherefon<0.1

AEB can then plotted for both the digital (AEBdigital (eq.2)) and analog (AEBanalog (eq.3)) ranges, and the two curves are seamlessly meshed into one calibration curve.

In order to combine digital and analog data, each experiment ideally requires arrays where the fraction of active beads is less than 10% (eq.4). This requirement is achieved using the calibration data points that cover this range, or specific control samples known to have this digital signal. With two or three concentrations in a calibration curve with fon < 0.1, the kinetic activities of thousands of individual enzyme molecules are averaged to determine Īsingle. Because the activities of thousands of molecules are averaged, the intrinsic variation associated with single enzyme molecule velocities described above does not add significant variation to the Īsingle measurement. The width parameter (σ Īslngle) of the mean single enzyme intensity (Īsingle) as a function of N measurements23 is given by σIsingle/N, where σIsingle is the width parameter of single enzyme molecule intensities. With a 30% CV in single enzyme molecule intensities6, the variation added to the CV of the calculated mean value Īsingle is 1% when averaging over 1000 single molecule measurements.

There is a significant range of fraction of active beads (10–99.98%) where theoretically digital counting and analog intensities could both be used to determine AEB. Below 10%, the contribution of beads associated with multiple enzymes is small and Ībead does not vary above measurement noise with % active, so the analog approach does not work. As fon approaches 100%, counting cannot be used to digitally determine AEB. Between these two extremes, imprecision considerations (manifested by the coefficient of variation (% CV) of AEB) determine the threshold of the fraction of active beads below which AEBdigital (eq.2) is used and above which AEBanalog (eq.3) is used. The choice of this threshold is illustrated by plotting the imprecision in AEB arising from the variation in digital and analog signals from 10–100% active beads (Figure 2C). Close to 10% active beads, changes in Ībead above single molecule values are small as AEB increases, leading to high imprecision in AEB. As the % active goes above 70% and the Poisson distribution curves deviates from linearity, the change in AEBdigital with % active decreases leading to greater imprecision in the AEBdigital determined. The balance of imprecision profiles in this overlap zone (Figure 2C) led us to choose the ‘digital-to-analog’ threshold as 70% active (around AEB = 1.2).

Combined digital and analog enzyme label detection

The SβG binding assay described in the Supporting Experimental Section and elsewhere1 was used to demonstrate the dynamic range to enzyme label that can be achieved by combining digital and analog determination of AEB. Figure 3 shows AEB determined from SiMoA images of populations of biotin-presenting beads that had been incubated with concentrations of SβG ranging from zeptomolar to picomolar. For images with % active beads < 70%, AEBdigital was determined using eq.2. All the arrays with <10% active beads were used to determine Īsingle, a total of 7566 beads; Īsingle was equal to 298 au. The average fluorescence intensities of beads in images with over 70% active were determined, and AEBanalog values were calculated using eq. 3. Because the 0 M SβG concentration yielded no active beads, the lower limit of detection in this experiment could not be calculated using the background plus 3 s.d. method. Using our previously established LOD of 220 zM1, and the highest concentration detected in the linear range of this curve, 316 fM, we determined a 6.2-log linear dynamic range for detecting enzyme label. The linear digital dynamic range was 4.7 logs; the analog linear dynamic range was 1.5 logs.

Figure 3
Broad dynamic range to enzyme label was achieved by combining digital and analog measurements in SiMoA. (A) Plot of AEB as a function of enzyme concentration. The error bars are standard deviations over three replicates. (B) % active and AEB values as ...

The dynamic range of the analog SiMoA measurement is affected by substrate depletion, timing of sealing and imaging by the system, and dynamic range of the camera. These issues are discussed in detail in the Supporting Text.

Combined digital and analog ELISA for measuring PSA in serum

We next sought to implement the combined digital and analog approach to develop a SiMoA ELISA for PSA with a wide dynamic range. Clinically, PSA is used to screen for prostate cancer and to monitor for biochemical recurrence of the disease in patients who have undergone surgery to remove the cancer. The PSA levels in the serum of patients who have undergone radical prostatectomy (RP) are known to range from 0.014 pg/mL1 to over 100 pg/mL9. To successfully measure the PSA levels in the majority of patients in a single test requires an assay with 4 logs of dynamic range. A SiMoA ELISA for PSA was developed and run as described in the Supporting Experimental Section. Figure 4 shows that by combining digital and analog analyses, the working range of the SiMoA PSA assay was from 0.008 pg/mL to 100 pg/mL, enabling precise quantification of PSA levels in the vast majority of RP patient samples in one pass.

Figure 4
The combined digital and analog SiMoA PSA assay with a 4-log working range and calculated LOD of 0.008 pg/mL. AEB is plotted as a function of PSA concentration in linear-linear space (left) and log-log space (right). Error bars are shown for all data ...

We used this assay to measure the concentration of PSA in the sera of 17 prostate cancer patients collected at 2 to 46 weeks (mean = 13.8 weeks) after radical prostatectomy surgery. These samples were collected closer to surgery than our previous study1 that—in order to push the lower limits of detection of digital ELISA—tested samples collected an average of 8 years post-surgery of patients whose cancer did not recur. Here, in order to evaluate the dynamic range of the assay across the intended clinical range, samples collected closer to surgery were tested to capture patients with higher PSA whose cancer could recur. PSA was, however, undetectable in all of these samples using a leading PSA diagnostic test (Siemens). Serum samples were diluted 1:4 in buffer and AEB was measured using SiMoA. The concentration of PSA for each sample was determined by reading the AEB off a simultaneously acquired calibration curve similar to Figure 4. Table 2 summarizes the AEB and PSA concentrations determined from these samples, along with the imprecision for signal and concentration given by % CV. PSA was quantified in all of the samples in one experiment. The average PSA concentration in these samples was 33 pg/mL, with a high of 136 pg/mL and a low of 0.4 pg/mL. When combined with our previous measurements of PSA in RP patients1, SiMoA has detected concentrations of PSA in clinical samples from 0.46 fM (0.014 pg/mL) to 4.5 pM (136 pg/mL), demonstrating the importance of an assay with good dynamic range. The PSA levels in Table 2 are significantly higher than from the set of samples that we previously tested1 that were collected from known, non-recurring patients, typically several years post-surgery. Presumably, the levels detected in this study are more indicative of patients soon after surgery, and will contain individuals whose cancer might recur.

Table 2
Summary of AEB and [PSA] determined for 17 serum samples from post-RP patients. Standard deviations and CVs were determined over triplicate tests. Sample S644 had an AEB value beyond the range of the calibration curve but its concentration was determined ...


The transition from extremely sensitive digital detection of single molecules to analog detection of ensembles of molecules was achieved with two enhancements to the SiMoA approach. First, a Poisson distribution analysis was applied to account for both single and multiple enzymes per bead from 0–70% active to determine the digital AEB value. Second, the average analog intensities of beads in images at over 70% active beads were converted to AEB using the average intensity for a single enzyme. These two analytical approaches permit linear measurement of AEB from 0.00005 to ~15. For PSA, combining the analog and digital analyses extended the working range to 4.1 logs of concentration from the original digital working range of 2.5 logs.

We are currently working on extending the working range of SiMoA an additional 1–2 orders of magnitude by improving the speed of the imaging system and minimizing the impact of substrate depletion. By further expanding the range of our assays, we hope to successfully measure all samples in a single assay cycle to improve assay throughput and reduce the cost of immunoassays.

Supplementary Material



The authors thank Dr. David Hanlon for helpful discussions. The project described was supported in part by Award Number R43CA133987 from the National Cancer Institute.


Supporting Information Available: This material is available free of charge via the Internet at


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