2.1.

Reagents

Ribonuclease A (RNase), propidium iodide (PI), chromomycin A3 $\left({\mathrm{CA}}_3\right)$ , and N-propyl gallate (NPG) were all from Sigma-Aldrich (Poznan, Poland); formaldehyde [16% EM (electron microscopy) grade] was from Electron Microscopy Sciences (Fort Washington, Pennsylvania). Stocks of PI and ${\mathrm{CA}}_3$ were made in phosphate-buffered saline (PBS) and kept at $4°\mathrm{C}$ ; stocks of RNase were kept frozen. Compressed argon (99.998% pure) from BOC Gazy (Poland) was delivered to an imaged sample through copper and steel tubes.

2.2.

Cell Culture and Labeling

MSU 1.1 human fibroblasts were cultured, fixed with formaldehyde, and treated using RNAse as described previously.²¹ Nuclei of MSU 1.1 cells were stained by incubating $30\min$ with a solution of PI $(5\mu \mathrm{g}∕\mathrm{ml})$ or $25\min$ with ${\mathrm{CA}}_3$ $(100\mu \mathrm{g}∕\mathrm{ml})$ in PBS. Following incubation with PI, the dye solution was removed and the preparation was incubated $45\min$ in fresh PBS prior to photobleaching. The rapid exchange of ${\mathrm{CA}}_3$ ( $t_{1∕2}$ approximately $3\min$ ) made it impossible to maintain a stable level of fluorescence in the absence of dye in the incubation solution. Thus, ${\mathrm{CA}}_3$ was present in the sample throughout the experiment. Fluorescent labeling procedures and photobleaching experiments were carried out at room temperature. Cells incubated in PBS (without ${\mathrm{CA}}_3$ or PI) were used to estimate contingent autofluorescence.

2.3.

Confocal Microscopy

Fluorescence of PI (excitation $488\mathrm{nm}$ , emission $590\text{to}630\mathrm{nm}$ ) or ${\mathrm{CA}}_3$ (excitation $457\mathrm{nm}$ , emission $490\text{to}550\mathrm{nm}$ ) and transmitted light $\left(647\mathrm{nm}\right)$ were detected using a BioRad MRC1024 (Carl Zeiss Incorporated) confocal system equipped with a Nikon Diaphot 300 microscope, $60\times$ PlanApo oil-immersion objective lens (NA 1.4), a $15\text{‐}\mathrm{mW}$ krypton-argon laser (ALC, Salt Lake City, Utah), and a $100\text{‐}\mathrm{mW}$ argon-ion laser (ILT, Salt Lake City, Utah). Time series of fluorescent confocal images of equatorial sections through nuclei (thickness of approximately $1.1\mu \mathrm{m}$ ) were collected using alternately a low-intensity probing beam and a high-intensity bleaching beam. No measurable bleaching occurred when labels were excited using the probing beam alone. At the end of each time series, single transmitted-light images were registered. Images ( $512\times 512\text{pixels}$ ; 256 gray levels) were collected using LaserSharp 3.2 software (Carl Zeiss Incorporated). A final image was a sum of 20 (PI), 45 $\left({\mathrm{CA}}_3\right)$ , or 10 (transmitted light) consecutive scans. The number of scans was chosen so that the total number of detector counts at the onset of a photobleaching series was similar in the PI and ${\mathrm{CA}}_3$ images and sufficient to fill the $8\text{‐}\text{bit}$ dynamic range when images were registered using the probing beam. One should note that these two dyes have different absorption coefficients at their respective excitation wavelengths and different quantum efficiencies. Fluorescence in the control cells (incubated in the absence of PI or ${\mathrm{CA}}_3$ ) was not detectable. Fluorescence was detected using photomultipliers in photon-counting (low signal) mode. Transmitted light was collected using the standard MRC1024 TLD detector. The intensity of excitation light was adjusted using neutral density filters.

2.4.

Image Processing

2.4.1.

Actual resolution distance

Performance of an optical imaging system is determined by its optical transfer function (OTF).²² The modulus of the OTF (which is a complex function) characterizes the amplitude (maximum to minimum intensity contrast) of a spatial frequency transferred by the system. The OTF modulus [modulation transfer function (MTF)] of a confocal microscope used in further calculations is given (at the focal plane, $xy$ ) by an approximate formula²³:

1.

$$\mathrm{MTF}\left(s\right)=1-0.69s+0.0076s^2+0.043s^3,$$

$$s=\frac{\lambda }{n\sin \left(\alpha \right)}{f}_r,$$

where $\lambda$ is the emission wavelength; $\alpha$ is the objective aperture angle; $f_r$ is the radial spatial frequency; $s$ is the normalized $f_r$ (expressed in optical units); and $n$ is the light refraction coefficient.

The MTF intensity (representing contrast) is plotted versus the normalized spatial frequency $\left(s\right)$ in Fig. 1 . The resolution distance of the confocal microscope is determined by the maximum spatial frequency that can propagate through the system (i.e., the cutoff frequency $f_c$ ). In the absence of noise [or when the signal-to-noise ratio (SNR) is infinite], the cutoff frequency is the point at which the MTF crosses the zero-intensity contrast line (Fig. 1). Hence, the nominal (minimal) resolution distance $\left(d\right)$ is achieved:

Eq. 2

$$d=\frac{1}{f_c}=0.5\frac{\lambda }{\mathrm{NA}}=0.5\frac{\lambda }{n\sin \left(\alpha \right)},$$

where $f_c$ is the cutoff frequency, and NA is the objective numerical aperture.

Fig. 1

Influence of noise on the cutoff frequency of the microscope MTF (continuous black line). The nominal cutoff frequency ( $s=2$ in normalized optical units) is estimated in the absence of noise at zero contrast level. Frequency-independent noise (20%, gray dashed line) is introduced by imposing a lowest limit to the contrast. The practical cutoff frequency is calculated at the point where the MTF crosses this minimum contrast level.

In practice, the effective intensity contrast in microscope images is reduced by noise. Consequently, the actual cutoff frequency is lower than the nominal.⁴ This frequency was estimated from the intersection of the line determined by the noise-to-signal ratio (1∕SNR, calculated as described further) and the MTF, as illustrated in Fig. 1.

The noise level was calculated using the algorithm described in Ref. 24. First, eight directional high-pass filters were applied to an image. The eight resulting images were added, and five pixels having the smallest sums were chosen to represent the most homogeneous image regions. The choice was restricted to the regions in which fluorescence intensity was at least 75% of the image maximum. The signal and noise were estimated using the following formulas:

3.

$$S_W=\frac{{\sum }_{i,j∊W}I(i,j)}{N_W}$$

$${\sigma }_W={\left\{\frac{{\sum }_{i,j∊W}{[I(i,j)-S_w]}^2}{N_W}\right\}}^{1∕2},$$

where $S_w$ is the average intensity (signal) in the region $W$ ; $N_w$ is the number of pixels in the region; $I(i,j)$ is the intensity at the spatial coordinate $(i,j)$ ; and ${\sigma }_w$ is the standard deviation (noise) in the region $W$ . Hence, the noise-to-signal ratio (1∕SNR) was calculated using the formula²⁴:

Eq. 4

$$1∕\mathrm{SNR}=1∕\text{median}\left(\frac{S_w}{{\sigma }_W}\right),$$

where SNR is the signal-to-noise ratio.

The ratio was used as an estimator of the minimum intensity contrast for a spatial frequency to propagate through the microscope. Hence, the actual cutoff frequency was determined at the point of intersection of the contrast line and the MTF, as illustrated in Fig. 1. The actual resolution distance $\left(d\right)$ was then determined using Eq. 2 ( $f_c$ set to the the actual cutoff frequency) and plotted against average signal intensity calculated over the whole image using the formula:

5.

$$I_{\mathrm{avg}}=\frac{{\sum }_{i,j}I(i,j)}{N}$$

$$i,j∊\{I(i,j)>0.75\max \left[I(i,j)\right]\},$$

where $I_{\mathrm{avg}}$ is the average intensity in the regions where the intensity was at least 0.75 image maximum; and $N$ is the number of pixels.

2.4.4.

Photobleaching kinetics

Loss of fluorescence intensity was analyzed as described previously.²¹ Briefly, the grayscale was subdivided into 25 consecutive intervals (i.e., from 6 to 15, 16 to 25, etc.) using binary masks. Average intensities of pixels comprising each brightness class were calculated for each of the images in the stack before background (the mean intensity of signal in an area without cells, as determined from the transmitted light image) was subtracted. These corrected values were plotted against the total dose $(\mathrm{J}∕{\mathrm{cm}}^2)$ of the incident light and the number of scans (Fig. 2 ).

Fig. 2

Kinetics of photobleaching of PI [(a) triangles up] and ${\mathrm{CA}}_3$ [(b), circles] bound to DNA. Equatorial sections of fixed cells were scanned with the laser in a confocal microscope. 20 (PI) or 45 $\left({\mathrm{CA}}_3\right)$ successive scans were accumulated to form one image, and the average intensity (arbitrary units, au) of pixels of different initial brightness in images was plotted relative to the accumulated dose of incident light.

3.1.

Photobleaching Kinetics

Excitation of ${\mathrm{CA}}_3$ and PI during fluorescence microscopy imaging of cell nuclei resulted in loss of fluorescence intensity of these dyes. Examples of the fluorescence-loss kinetic curves are shown in Fig. 2. The photobleaching rates were affected by excitation light flux and concentration of oxygen as described by Bernas ²¹ We studied the influence of such fluorescence intensity loss on image quality. This parameter is assessed using the three measures discussed in the following paragraphs.

3.2.

Increase of Actual Resolution Distance

Loss of fluorescence intensity due to photobleaching was followed by an increase in actual resolution distance of the images of cell nuclei stained with PI [Fig. 3(a) ] and ${\mathrm{CA}}_3$ [Fig. 3(b)]. This decrease for images registered with PI may be described using a square root function of average fluorescence intensity. No such inference could be made for ${\mathrm{CA}}_3$ due to significant variation in the results. Nonetheless, the relative increase of resolution distance was significantly smaller than the corresponding decrease of fluorescence intensity for both fluorochromes. The actual resolution distance in the images registered using PI and ${\mathrm{CA}}_3$ was similar. Furthermore, this actual resolution distance was significantly lower than the nominal for PI $(d=0.192\mu \mathrm{m})$ and ${\mathrm{CA}}_3$ $(d=0.175\mu \mathrm{m})$ as well. One should note, however, that SNR in the former case was higher than in the latter.

Fig. 3

Increase of actual resolution distance (left $y$ axis) and decrease of SNR (right $y$ axis) in photobleaching in images of nuclei stained with PI [(a), triangles up] and ${\mathrm{CA}}_3$ [(b), circles]. Fluorescence intensity ( $x$ axis) represents the mean image brightness in the areas where SNR was calculated. Note that SNR values (represented on the linear scale) are approximates within $\pm 2\%$ error margin, owing to the fact that the MTF (and thus the actual resolution distance) is a nonlinear function of fluorescence intensity (see Materials and Methods in Sec. 2 and Fig. 1).

3.3.

Loss of Information

Photobleaching resulted in a loss of relative information entropy in the images of cell nuclei stained with PI [Fig. 4(a) ] and ${\mathrm{CA}}_3$ [Fig. 4(b)]. The entropy loss was proportional to the corresponding fluorescence decrease and similar for different image series (each registered at one field of view; see Materials and Methods in Sec. 2). Nonetheless, the entropy varied slightly from series to series. On the other hand, one should note that the entropy of the images of nuclei stained with PI and ${\mathrm{CA}}_3$ is comparable for any given fluorescence level.

Fig. 4

Change of the relative information entropy in photobleaching of (a) PI and (b) ${\mathrm{CA}}_3$ in cell nuclei. The individual images are depicted as black dots. Image series (each registered at a different region) are indicated with grey lines.

3.4.

Decrease of Wavelet Signal-to-Noise Ratio

Loss of fluorescence intensity was also accompanied by a decrease of SNR estimated using wavelet shrinkage [Figs. 5(a) and 5(b) ]. The SNR was similar for these two fluorochromes and was proportional to the square root of the fluorescence intensity. One should note, however, that the data variation was higher in the images registered using ${\mathrm{CA}}_3$ [Fig. 5(a)], than in those using PI (Fig. 5(b)). The noise estimated with the wavelet shrinkage was lower than predicted from the number of detected photons and Poisson statistics [Figs. 5(c) and 5(d); see also Materials and Methods in Sec. 2]. This error increased slightly as the fluorescence intensity dropped.

Fig. 5

Decrease in SNR in the images of nuclei labeled using (a) PI and (b) ${\mathrm{CA}}_3$ as estimated using the wavelet shrinkage algorithm. The noise expressed as the fraction of the theoretical value is plotted against the respective fluorescence intensity for (c) PI and (d) ${\mathrm{CA}}_3$ .

3.5.

Influence of Nominal Optical Resolution

One may hypothesize that the adverse effects of photobleaching on image quality (defined using the three proposed measures) are influenced by the size of the objects which may be resolved under ideal imaging conditions. For biological specimens, this parameter is determined by the nominal resolution distance of a microscope. Therefore, the effects of the intensity loss were studied using cell nuclei stained with PI and imaged with large ( $d=0.360\mu \mathrm{m}$ , $\mathrm{NA}=0.75$ ) and small ( $d=0.192\mu \mathrm{m}$ , $\mathrm{NA}=1.4$ ) resolution distance. The decrease in relative fluorescence intensity was followed by a loss in relative image quality measured using the actual resolution distance [Fig. 6(a) ], information entropy [Fig. 6(b)], and wavelet SNR [Fig. 6(c)]. The impact of photobleaching on the actual resolution distance was greater for the low-NA objective than for the high-NA objective. A similar pattern was found for information entropy. The decrease of wavelet SNR was, however, similar for images registered with small and large nominal resolution distance.

Fig. 6

Effect of photobleaching on the quality of images of nuclei stained with PI and registered with low (gray triangles) and high (black squares) nominal resolution. The quality was estimated using (a) the actual resolution distance, (b) entropy, and (c) wavelet SNR. These parameters are expressed as fractions of the respective values for the nonbleached images. Similarly, the fluorescence intensities were normalized to the respective values for the initial (nonbleached) images.

4.1.

Actual Resolution Distance

The relative increase of the actual resolution distance was significantly lower than the corresponding change in fluorescence of ${\mathrm{CA}}_3$ and PI. Since the resolution distance was nearly proportional to the SNR, it seems plausible that the noise was dependent on the signal in a nonlinear manner. The resolution distance could be described using the square-root function of PI fluorescence intensity. Thus, one may hypothesize that the majority of the noise obeyed Poisson statistics. The images of nuclei stained with ${\mathrm{CA}}_3$ and PI were registered using a similar number of photons. Thus, one might expect smaller actual resolution distance in the former, as ${\mathrm{CA}}_3$ was excited at and fluoresced at a shorter wavelength than PI. However, no such difference in actual resolution distance was observed. It should be noted that images of ${\mathrm{CA}}_3$ fluorescence were constructed from 45 summed scans, whereas only 20 were accumulated for PI (see Materials and Methods in Sec. 2). Consequently, it is likely that detector noise was higher in ${\mathrm{CA}}_3$ images than in PI images. The higher variability of the points in the ${\mathrm{CA}}_3$ plot [compare Figs. 3(a) and 3(b)] is in agreement with this hypothesis.

4.2.

Information Entropy

The relative decrease in entropy was very low compared to the corresponding loss of fluorescence intensity of ${\mathrm{CA}}_3$ and PI. Therefore, one may postulate that only a small information loss occurred due to photobleaching. Hence, it seems possible to restore a faded image efficiently by correcting for photobleaching, provided that the kinetics of this process is well characterized. An example of such restoration is demonstrated in Fig. 7 . The images of PI and ${\mathrm{CA}}_3$ fluorescence were characterized by similar values of information entropy. However, one may note differences in initial entropy between different series of images (experiments) registered using the same flurochrome (i.e., ${\mathrm{CA}}_3$ or PI). This is not surprising as the entropy is calculated in the frequency (Fourier) domain, and the spectrum depends on the number of nuclei in the image. It would be reasonable to assume that the information content increased with the number of acquisitions of relevant objects (nuclei, in this case).

Fig. 7

Structural information preservation in photobleaching of PI-stained nuclei: (a) initial (nonbleached) image, (b) image after bleaching, (c) corrected (bleached) image, and (d) the difference between the corrected and the initial image.

4.3.

Wavelet Signal-to-Noise Ratio

The wavelet SNR followed a square-root dependence on fluorescence intensity in a pattern similar to that of the actual resolution distance. However, the SNR values estimated using the wavelet algorithm are higher (lower noise) than the values obtained using the spatial domain method (see Materials and Methods in Sec. 2). While the former method estimates only Poisson noise, the latter gives the total value. On the other hand, the SNR in the wavelet domain is calculated using all the pixels, whereas only a fraction of the pixels is used for calculations in the spatial domain (see Materials and Methods in Sec. 2). Therefore, the wavelet-based algorithm is more precise from a statistical point of view. This notion is in agreement with the fact that the SNR obtained with this method exhibited smaller variability compared to the SNR computed in the spatial domain.

4.4.

Influence of Nominal Optical Resolution

The relationship between the image quality and the number of registered fluorescence photons was affected by the nominal optical resolution of the microscope. The calculation of actual resolution distance depends on the MTF shape (in particular the cutoff frequency; see Materials and Methods in Sec. 2). Thus, it seems reasonable that a similar drop in SNR would result in a more pronounced increase of the actual resolution distance in the case of low NA (more steep MTF, see Fig. 1) compared with high NA (less steep MTF). The decrease in SNR narrows the range of spatial frequencies that contribute to the imaged structure of the nuclei. As with the actual resolution distance, the photobleaching caused a greater loss of information entropy in the images registered with large nominal resolution distance in comparison to these registered with small distance. On the other hand, the wavelet SNR is computed on a pixel-to-pixel basis and therefore was not affected by the optical properties of the imaging system. Hence, the effect of photobleaching measured using this method is similar for images registered with small and large nominal resolution distance. An overview of variables affecting the three quality measures is given in Table 1 .

Table 1

Overview of variables influencing the three image-quality measures: actual resolution, information entropy, and wavelet SNR.

4.5.

Autofluorescence and Image Quality

No signal was detected if the cells were not labeled with PI or ${\mathrm{CA}}_3$ , indicating that endogenous fluorescence (autofluorescence) did not interfere with image registration in our experiments. Therefore, one may assume that the same biological structure (fluorescently labeled chromatin) was registered at the onset and at the end of photobleaching. In other words, the subsequent images of the same field of view differed with respect to the total number of detected photons but not the subcellular fluorescence distribution. However, autofluorescence of biological specimens is not always negligible. Possible sources of autofluorescence include endogenous fluorophores, such as flavins and flavoproteins,^{29, 30} lipopigments and phospholipids,^{31, 32} or putative endogenous Schiff-base compounds.^{33, 34} Another source of nonspecific fluorescence signal might lie in the fixation procedure itself.^{35, 36} The presence of autofluorescence may reduce the effective dynamic range of the light detector available for registration of specific fluorescence signal. Consequently, the presence of autofluorescence can be a precision-limiting factor in the measurement of concentration (amount) of a fluorophore of interest. Moreover, if autofluorescence is nonuniform within a cell, it can obscure cellular distribution of the specific fluorescent label. To the authors' knowledge, no detailed studies of the photobleaching kinetics of compounds that contribute to autofluorescence have been reported. However, one may expect that differences in photobleaching kinetics between the endogenous fluorochromes and exogenous fluorescent labels could further complicate microscopic imaging. If such differences occur, the intensity ratio between the autofluorescence and the specific fluorescence would depend on the intensity of excitation light and the image registration time. Consequently, spatial distribution of total cell fluorescence could change in the course of imaging due to different photobleaching of the autofluorescence and the specific fluorescence. Since autofluorescence did not contribute to the signal in our experiments, image quality was a monotonic (and smooth) function of fluorescence intensity. However, if the distribution of the total fluorescence changed in the course of sample illumination, the image quality might not depend on the fluorescence intensity in monotonic fashion.

4.6.

Practical Applications

The quality measures proposed here make it possible to estimate the fundamental limits of measurement precision in the spatial and intensity domains. Hence, using these measures one may establish reliability of measurement of a given concentration of fluorophore (and thus the labeled molecule of interest). Furthermore, the reliability of detection of an object of a given size (and thus precision of structural studies) may be verified as well. To summarize, using these quality measures one may estimate the amount of syntactic information present in biological images. However, it is up to the researcher to decide whether the spatial distribution of fluorescence registered with a microscope conveys any biological information. Thus, the suitability of a quality measure depends on the semantic information to be extracted from an image. In other words, the choice of the proper measure is a function of the biological question to be answered.

Utility of the proposed quality measures may be extended beyond image analysis. The following notions indicate some image-processing applications.