Deconvolving single-molecule intensity distributions for quantitative microscopy measurements

Abstract

In fluorescence microscopy, images often contain puncta in which the fluorescent molecules are spatially clustered. This article describes a method that uses single-molecule intensity distributions to deconvolve the number of fluorophores present in fluorescent puncta as a way to "count" protein number. This method requires a determination of the correct statistical relationship between the single-molecule and single-puncta intensity distributions. Once the correct relationship has been determined, basis histograms can be generated from the single-molecule intensity distribution to fit the puncta distribution. Simulated data were used to demonstrate procedures to determine this relationship, and to test the methodology. This method has the advantages of single-molecule measurements, providing both the mean and variation in molecules per puncta. This methodology has been tested with the avidin-biocytin binding system for which the best-fit distribution of biocytins in the sample puncta was in good agreement with a bulk determination of the avidin-biocytin binding ratio.

FIGURE 1

Fluorescence intensity distributions of single molecules and particles. (A) Image of GAM labeled with multiple Alexa Fluor 488; the right panel shows each molecules being circled automatically by the imaging software to define a region of interest. The plots are intensity distributions of (B) single Alexa Fluor 488 carboxylic acid succinimidyl ester molecules, (C) single goat anti-mouse IgG molecules labeled with multiple Alexa Fluor 488, and (D) single synaptic vesicles tagged with anti-SV2 primary antibody and Alexa Fluor 488-labeled GAM secondary antibody. For B–D, the dashed line is the best fit lognormal distribution to the data, and the dash-dot line is the best fit normal distribution to the data. The distribution of the intensity data is better fit by a lognormal distribution in all cases, despite the increase in the number of fluorophores per ROI between B and D. The images of the single fluorophores were faint when collected at the same excitation power as used for C and D, and thus images of the single fluorophores were collected using a higher laser power, so that the shape of the intensity distribution in B could be more easily compared with those in C and D.

FIGURE 2

(A) MD basis histograms, , for c = 1–5. (B) Lognormal cumulative probability plots of for c = 1–5. The slope of the lognormal cumulative probability plot is proportional to the shape, . For a MD process, the slopes are independent of c, which indicates that the relative width of the MD basis histograms is the same regardless of the number of fluorophores in the puncta.

FIGURE 3

(A) RA basis histograms, , for c =1−5. (B) Lognormal cumulative probability plots of for c=1–5. The slope of the lognormal cumulative probability plot is proportional to the shape, . For a RA process, the slope decrease as c increases, which indicates that the relative width of the RA basis histograms decreases with increasing c.

FIGURE 4

Comparison of RA and MD basis histograms. (A) Probability plots of the basis histograms generated by the MD (solid curves) and RA (dashed curves) process for c = 2 and 3. (B) Ratio of of the MD and RA basis histograms for c = 1–8. The decrease in the ratio for RA basis histograms indicates a decrease in the relative width of the distribution.

FIGURE 5

Best-fit results for simulated distribution 3RA (see Tables 1 and 3; a Case I example) fitted with (A) MD basis histograms and (B) RA basis histograms. The vertical bars are the simulated data , the dashed line is a plot of the best-fit result, , the solid lines are plots of (see Table 3), and the dotted line is a plot of the residuals of the fit ().

FIGURE 6

Best-fit results for simulated distribution 5MD (see Tables 1 and 4; a Case II example) fitted with (A) MD basis histograms and (B) RA basis histograms. The vertical bars are the simulated data , the dashed line is a plot of the best fit result, , the solid lines are plots of (see Table 4); and the dotted line is a plot of the residuals of the fit ().

FIGURE 7

Distribution of coefficients from MD and RA fits of (A) 4MD and (B) 8MD (see Tables 1 and 5; a Case III example). The open bars are , the actual number of ROIs in the set with c fluorophores. The vertical bars are , the best-fit number of ROIs in the set with c fluorophores for the fit using MD basis histograms. The solid bars are , the best fit number of ROIs in the set with c fluorophores for the fit using RA basis histograms.

FIGURE 8

Single-molecule measurements of the binding of Alexa Fluor 488-tagged biocytin to avidin. (A) Results of fitting avidin/labeled-biocytin emission data using MD basis histograms. (B) Results of fitting avidin/labeled-biocytin emission data using RA basis histograms. (C) Histogram showing the percentage of avidin with c biocytins obtained from the fits using MD (solid vertical bars) and RA (open vertical bars) basis histograms. For A and B, the vertical bars are the simulated data , the dashed line is a plot of the best-fit result , the solid lines are plots of , and the dotted line is a plot of the residuals of the fit ().