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Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy

Samuel T. Hess ^* , Thanu P. K. Girirajan   and Michael D. Mason 

^* Department of Physics and Astronomy, Institute for Molecular Biophysics, and Department of Chemical and Biological Engineering, University of Maine, Orono, Maine

Correspondence: Address reprint requests to Prof. Samuel T. Hess, Dept. of Physics and Astronomy, University of Maine, Orono, ME 04469. Tel.: 207-581-1036; Fax: 207 581-3410; E-mail: sam.hess{at}umit.maine.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION THEORY METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Biological structures span many orders of magnitude in size, but far-field visible light microscopy suffers from limited resolution. A new method for fluorescence imaging has been developed that can obtain spatial distributions of large numbers of fluorescent molecules on length scales shorter than the classical diffraction limit. Fluorescence photoactivation localization microscopy (FPALM) analyzes thousands of single fluorophores per acquisition, localizing small numbers of them at a time, at low excitation intensity. To control the number of visible fluorophores in the field of view and ensure that optically active molecules are separated by much more than the width of the point spread function, photoactivatable fluorescent molecules are used, in this case the photoactivatable green fluorescent protein (PA-GFP). For these photoactivatable molecules, the activation rate is controlled by the activation illumination intensity; nonfluorescent inactive molecules are activated by a high-frequency (405-nm) laser and are then fluorescent when excited at a lower frequency. The fluorescence is imaged by a CCD camera, and then the molecules are either reversibly inactivated or irreversibly photobleached to remove them from the field of view. The rate of photobleaching is controlled by the intensity of the laser used to excite the fluorescence, in this case an Ar+ ion laser. Because only a small number of molecules are visible at a given time, their positions can be determined precisely; with only 100 detected photons per molecule, the localization precision can be as much as 10-fold better than the resolution, depending on background levels. Heterogeneities on length scales of the order of tens of nanometers are observed by FPALM of PA-GFP on glass. FPALM images are compared with images of the same molecules by widefield fluorescence. FPALM images of PA-GFP on a terraced sapphire crystal surface were compared with atomic force microscopy and show that the full width at half-maximum of features 86 ± 4 nm is significantly better than the expected diffraction-limited optical resolution. The number of fluorescent molecules and their brightness distribution have also been determined using FPALM. This new method suggests a means to address a significant number of biological questions that had previously been limited by microscope resolution.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Although biological structures span many orders of magnitude in length scale (1), resolution in many types of biological light microscopy is limited. The limit on resolution of point sources imposed by the finite size of the diffraction-limited illumination volume in a far-field optical system (2) is quantified by the Rayleigh criterion (3):

where is the wavelength of the detected photons and NA is the numerical aperture of the lens system. To adequately visualize structure, most fluorescence imaging methods rely on observation of a large number of molecules simultaneously, which is inherently limited because the distance between observed molecules is much less than r_R. New imaging methods such as 4Pi microscopy (4–9), patterned illumination microscopy (10,11), stimulated emission depletion (STED) microscopy (12–14), and other types of reversible saturable optical fluorescence transition (RESOLFT) microscopies (15) can increase resolution by reducing the size of the observation volume or, correspondingly, by increasing the accessible Fourier space and therefore increasing the number of accessible spatial frequencies. 4Pi microscopy (6,9) provides a significant increase in axial resolution (100 nm), but its advantages are more difficult to apply toward examination of thick or scattering samples, or lateral molecular distributions such as in biological membranes. Although STED does not rely on image deconvolution as 4Pi and patterned illumination microscopy do, both STED and 4Pi depend on nonlinear excitation under high-intensity pulsed illumination. Furthermore, they typically derive their information from large numbers of molecules observed simultaneously, and therefore may obscure crucial behavior that is only discernable at the single-molecule level. Nonlinear structured illumination microscopy (10) has so far achieved resolution (full width at half-maximum (FWHM) of the point spread function (PSF)) of 50 nm and can in principle be improved further, but is limited by the photobleaching properties of the fluorophore, and uses excitation intensities near saturation, where photobleaching may be more pronounced than at low intensity (10). Near-field scanning optical microscopy is also capable of spatial resolution better than the classical diffraction limit, but is typically used to image surfaces and is difficult to use to image in aqueous solution (16). Fluorescence resonance energy transfer can access the molecular length scale, but has a limited range of distances over which it is sensitive and depends on a large number of variables, including molecular orientation and distance, dielectric constant, spectral overlap, and excited-state lifetime (17–19). Other single-molecule methods can resolve multiple fluorescent objects at distances longer than those accessible to fluorescence resonance energy transfer and closer than r_R, but only in limited numbers, and only if a very large number of photons is collected per object (e.g., 10⁴ photons to resolve two objects separated by 10 nm) (20). Thus, even the most advanced fluorescence microscopy and spectroscopy methods continue to be limited in their range of accessible length scales.

Fluorescent speckle microscopy (FSM) (21–24) provides an additional means to image subdiffraction objects such as actin and microtubules by localizing single molecules as they intermittently emit fluorescence. FSM also exploits (typically stochastic) intermittency of those single molecules, which allows large numbers of molecules (>10⁵) to be visualized, but does not allow direct control over the number of fluorescent molecules within the field of view. In FSM, the number of visible particles must be controlled by changing the concentration or density per unit area of the fluorophore-labeled molecules themselves, which in the case of green fluorescent protein (GFP)-transfected cells may not be a trivial proposition, especially if the desired density is low. Instead, in fluorescence photoactivation localization microscopy (FPALM), the number of active fluorophores, as will be explained, can be increased or decreased photophysically by changing the rates of photoactivation and photobleaching, even if the density of fluorophore-labeled molecules is much higher than one fluorophore per µm².

We present a novel method by which fluorescence microscopy may be performed to obtain an image with greatly enhanced ability to resolve large numbers of fluorescent molecules. Unlike previous approaches, this method does not suffer from the standard resolution limits because it does not exclusively rely on resolution for visualization of multiple molecules. Rather, single molecules are localized in modest numbers, allowing position localization, which is far more precise than the resolution limit. We demonstrate this principle using photoactivatable green fluorescent protein (PA-GFP) molecules that are initially found in a dark (weakly fluorescent) state, can be either reversibly or irreversibly activated by one excitation wavelength, and then can be visualized by excitation with a second wavelength. A small number of stochastically photoactivated molecules, which are spatially separated from each other (on average) by several times the resolution, are then localized using single-molecule detection methods, in this case a high-quantum efficiency charge-coupled device (see Fig. 1). After a (stochastically determined) number of photons has been collected from the molecule, the readout cycle ends by photobleaching of that particular molecule, and the process is repeated until the total number of localized molecules is very large. The positions of readout (observed and localized) molecules are then tabulated and plotted to construct a two-dimensional map (image). The acquisition of this single-molecule information also permits determination of the fluorescence brightness and mean molecular velocity during the acquisition time.

View larger version (44K): [in this window] [in a new window]   FIGURE 1  Fluorescence photoactivation localization microscopy (FPALM). An area containing photoactivatable molecules (here, PA-GFP) is illuminated simultaneously with two frequencies of light, one for readout (here, an Ar+ ion laser, its spatial illumination profile shown in A), and a second one for activation (here, a 405-nm diode laser, its profile superimposed in B). Within the region illuminated by the activation beam, inactive PA-GFPs (small dark blue circles) are activated (C) (small green circles) and then localized (D). After some time, the active PA-GFPs (E) photobleach (red Xs) and (F) become irreversibly dark (black circles). Additional molecules are then activated, localized, and bleached until a sufficient number of molecules have been analyzed to construct an image. (G) The experimental geometry shows the 405-nm activation laser (X405), which is reflected by a dichroic (DM1) to make it collinear with the Ar+ readout laser. A lens (L1) in the back port of an inverted fluorescence microscope is used to focus the lasers, which are reflected upward by a second dichroic mirror (DM2), onto the back aperture of the objective lens (OBJ). The sample, supported by a coverslip (CS), emits fluorescence which is collected by the objective, transmitted through DM2, filtered (F), and focused by the tube lens (TL) to form an image on a camera (CCD).

1. The spontaneous interconversion rates into and out of the activated (fluorescent) state must be low compared to the light-controlled activation rate.
   
2. For irreversible photoactivation, the photobleaching quantum yield must be finite and, when multiplied by the excitation rate at saturation, must give a photobleaching rate equal to or greater than the activation rate.
   
3. For reversible photoactivation, the light-controlled deactivation plus photobleaching rate must be equal to or greater than the activation rate.
   
4. The average number of detected photons per molecule before photobleaching must be large enough to provide the desired resolution enhancement.
   
5. The fluorescence of the inactive state must be low compared to that of the active state under the given detection conditions; that is, the contrast ratio (25) must be large.
   

	THEORY

TOP ABSTRACT INTRODUCTION THEORY METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
The spatial precision of localization of single fluorescent objects has been studied extensively (16,20,26–29). Thompson et al. calculate the localization precision _x for point-like objects imaged in two dimensions by fluorescence microscopy to be

(1)

where r₀ is the standard deviation of the point spread function, N is the total number of photons collected, q is the size of an image pixel, and b is the background noise per pixel. From Eq. 1, it is clear that molecular localization may be significantly more precise than the optical resolution by a factor of as much as . Thus, the number of detected photons will be crucial to the enhancement of localization precision compared to resolution, as stated by condition 4. For a single molecule capable of emitting 10⁵ visible photons (e.g., emission wavelength 500 nm) before photobleaching, the position localization could be as precise as 500 nm/(10⁵)^0.5 or a few nanometers. Considering the finite detection efficiency (typically <5%) of modern single-molecule fluorescence microscopes, an estimate of the number of collected photons is , where is the photobleaching quantum yield for the molecule and is the detection efficiency, and the two-dimensional localization precision becomes

(2)

Since an increased b will increase , it is crucial that background be minimized, including background from inactive protein molecules (condition 5). Consider, now, N photoactivatable molecules subdivided into inactive (I), active (A), and bleached (B) states, with interconversion rates as follows:

(3)

where k_A is the activation excitation rate, is the activation quantum yield, k₀ is the spontaneous activation rate, k_BC is the spontaneous and light-dependent inactivation rate, k_x is the fluorescence excitation rate, and is the photobleaching quantum yield. These rate equations are similar to those shown to describe reversible photoconversion kinetics in related GFP mutants in the absence of photobleaching (30). Here, considering photobleaching and photoactivation, three linear coupled first-order differential equations then describe A, B, and I, the numbers of molecules in each state, respectively:

(4A)

(4B)

(4C)

Alternatively, one of the three equations (4A–4C) could be replaced by the constraint that A + B + I = Const. Considering Eqs. (4A–4C), k_A and k_x can be chosen such that A, the number of active molecules within the illuminated region, is sufficiently sparse to allow simultaneous resolution and localization of those active molecules, and . The steady-state condition results in

(5)

where describes a characteristic ratio of photoactivation to (reversible and irreversible) photobleaching that should span as wide a range of values as possible for maximum control over molecular readout. It should be pointed out that performing FPALM does not strictly require dA/dt = 0, since it will be possible to localize molecules as long as they are sparse enough to not have overlap in their point spread functions, but estimation of the conditions that yield an appropriate density of molecules (i.e., a certain favorable value for A) will be easier if dA/dt 0 during the measurement. Typically, to control (limit) the number of active molecules at a given time (under irreversible photoactivation), the rate of photobleaching and spontaneous inactivation should be equal to or larger than the rate of activation, or << 1. At saturation, where k_x is at or near maximum, the denominator of will be maximum, and so will be at its minimum (at a given activation rate), and that minimum must be <1 (condition 2). Under this condition, if the number of inactive molecules I is approximately constant because (which should be satisfied anyway if dA/dt = 0), if k₀ << , and k_BC << (condition 1), the ratio A/I can be adjusted over a wide range of values. The value of k_BC is expected to be very small for PA-GFP, since its activation process is irreversible (25,31).

Considering reversible photoactivation, it will be necessary under some condition for k_BC >> k_x, so that the dominant path for limiting the number of activated molecules is by reversible deactivation rather than photobleaching. Also, to limit the number of active molecules, the deactivation plus photobleaching rate k_BC + k_x needs to be equal to or larger than the activation rate, which is again equivalent to << 1, or condition 3.

We may estimate the desired value of A (the number of active molecules) by considering the area/molecule in comparison to the expected area of the molecule given by the 1/e² radius of the point spread function () and the area covered by molecular (assuming nondirected) diffusion during the molecular readout time t_m:

(6)

where D is the diffusion coefficient, the FWHM of the PSF is f₀ (32), and , _m is the emission wavelength, NA is objective numerical aperture, and S is the area of the illuminated region.

To ensure that Eq. 6 is satisfied by a constant dimensionless factor >> 1, where is approximately the ratio of the area/molecule to the area of the PSF (e.g., 16 for molecules to be separated by approximately an average distance of four times the size of their image on the relevant timescale), let the limit for straightforward simultaneous resolution and localization of particles require that

(7)

or,

(8)

From Eqs. 5 and 8, it follows that

(9A)

and

(9B)

Similarly, an estimate of , the maximum range of , yields

(10)

which reflects the degree of control over the photoactivation readout and should be maximized experimentally. Thus, minimizing both k_BC and k₀ is essential for optimization of photoactivation readout. It also follows that in cases where and (i.e., the spontaneous rates are small compared to the light-induced rates), maximization of the quantum yield for activation is helpful for control of the number of active molecules. Furthermore, a nonzero photobleaching quantum yield is also necessary, since otherwise the number of active molecules will become too large for resolution and localization. However, a large photobleaching yield will also reduce the total number of photons that can be detected per molecule and therefore reduce localization precision.

Estimation of imaging requirements for 80-nm and 20-nm localization precision
Using the theoretical model described above, the desired properties for a candidate PA-GFP and the parameters of the imaging system can be summarized. Consider now two cases: 1), imaging immobilized molecules at the demonstrated localization precision of 80 nm, and 2), imaging molecules mobile in two dimensions with D 0.08 µm²/s such as for influenza hemagglutinin (33) with a goal of 20 nm precision.

Case 1. To have a representative sampling of molecules within a structure of size 80 nm, one would roughly require 100 molecules per 80 nm x 80 nm region within the image. For molecules uniformly distributed over a 10 µm x 10 µm area, this would require localization of 1.6 x 10⁶ molecules. However, typical confocal images of cells contain highly heterogeneous distributions of molecules, and in many cases large regions of the image do not contain significant concentrations of fluorophore. Thus, estimating that a fraction of the image (e.g., 10%) contains labeled features of interest, the number of molecules needed N_tot is effectively lower (N_tot 1.6 x 10⁵ molecules). Now, to estimate the acquisition timescale for such a number of immobile molecules, we employ the theory section derived previously in the text. Given that the image is 10 µm x 10 µm, but 10% of the image contains the majority of molecules, the area in which the molecules are effectively distributed is 0.1 x 100 µm² = 10 µm². To ensure that molecules are separated by 4 x r₀ on the average, we choose = 16 (Eqs. 7 and 8), which yields (from simulations) an 9.7% chance of having two molecules within r₀ of each other. Using Eq. 8, = 16, and r₀ = 0.281 µm, one estimates that A 8 molecules/frame within the 10 µm² area should be activated. If one is willing to discard any molecules that are within r₀ of each other, the number of frames then is equal to N_tot/A 2 x 10⁴ frames.
The next crucial factor determining time resolution is the imaging frame rate. The upper limit on frame rate is dictated by detected photon rate per molecule () and the photobleaching rate of molecules. The photobleaching rate should be optimized by using an excitation laser intensity where the photobleaching time is close to the image acquisition time (photobleaching times of <<1 s are achieved routinely using high-intensity laser beams). The most obvious limitation in this case would be laser power at the readout wavelength. Second, the value of at saturation for the fluorophore is crucial. Given a background noise estimated from measurements on coverslips to be b 1.02 photons/frame/pixel (including readout noise), and pixel size q = 0.121 µm, one can solve Eq. 2 to find that one needs N_coll 49 detected photons/molecule to achieve 80 nm localization precision. For EGFP, _EGFP 4 x 10⁴ photons/s/molecule detected is typical at saturation in fluorescence correlation spectroscopy measurements (S. Hess, unpublished). Using the detected for EGFP, it should be possible to detect 49 photons within a time of 1.2 ms. Allowing for PA-GFP to have even a 10-fold lower saturating emission rate (_PAGFP 4 x 10³ photons/s/molecule including average brightness reduction due to flicker), 12 ms/frame should be enough to collect sufficient photons for the desired localization precision. Thus, the total acquisition time for 2 x 10⁴ frames will be 240 s. In the case of the sapphire sample, estimating a twofold higher background yields a N_coll 90 photons, an acquisition frame time of 22.5 ms, and a total acquisition time of 450 s, which is the same order of magnitude as the actual acquisition time of 500 s. Note that this calculation assumes that the optimum (saturating) detected photon emission rate is achieved by the excitation (readout) laser. Thus, for a goal of 80 nm localization precision, the following parameters should be sufficient: q = 0.121 µm, > 4 x 10³ photons/s·molecule, b < 2 photons/s·pixel, frame acquisition time of >20 ms, and a total number of detected photons before photobleaching of N_coll = / > 100 (i.e., < 2 x 10^–4 using 2%). In practice, a number of parameters of the photoactivatable protein fluorophore, such as fluorescence quantum yield, extinction coefficient, fluorophore emission spectrum, flicker, and photobleaching properties, will affect the number of photons that are emitted. Detector quantum efficiency, objective numerical aperture, dichroic mirror and emission filters, and excitation laser intensity will also determine the number of emitted and detected photons.

Case 2. Now, to resolve features on 20 nm length scales (i.e., _x < 20 nm) in samples with molecules randomly diffusing in two dimensions with D = 0.08 µm²/s, N_tot increases to 2.5 x 10⁶ for 10% coverage of a 100 µm² area at a density of 100 activated molecules within each area of 20 nm x 20 nm. Reading out the same number of molecules per frame (8), the number of frames increases to 3 x 10⁵ frames. Given a background level of 2.0 photons/s·pixel, the required number of detected photons per molecule increases to N_coll 440, which will then require 110 ms/frame if the molecules are immobile, and an acquisition time of 3.3 x 10⁴ s, or >9 h. If the molecules are mobile, an acquisition time of 0.2 s will be required because the molecular image will be spread by diffusion at D 0.08 µm²/s such that 4Dt_m 0.064 µm² (from Eq. 6), which effectively blurs the image from a 1/e² radius of r₀ 0.281 µm to a larger radius = 0.38 µm, and requires an increase of N_coll to 800 photons, yielding a total acquisition time of 17 h. Thus, such measurements will require that the number of emitted photons before photobleaching (with detection efficiency 2%) to be 4 x 10⁴, which will require < 2.5 x 10^–5, not a trivial constraint.

	METHODS

TOP ABSTRACT INTRODUCTION THEORY METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Sample preparation
Samples of PA-GFP were prepared from stocks kindly provided by Dr. George Patterson (National Institute of Child Health and Human Development), by dilution 1:100, 1:400, or 1:1000 in high-purity water (HPLC grade, Sigma-Aldrich, St. Louis, MO) for a final concentration of 400 nanomolar. A single one-microliter droplet of diluted PA-GFP solution was deposited on a No. 1.5 glass coverslip (Corning Life Sciences, Corning, NY) and allowed to slowly evaporate. The sample was then placed on the microscope stage and illuminated from below by the objective lens.

Illumination, photoactivation, and detection
Fig. 1 illustrates the principle of the method. Photoactivatable molecules (initially in an inactive, nonfluorescent state) are illuminated continuously by the "readout light", in this case an Ar+ ion laser. Next, the "activation light", a 405-nm diode laser, is turned on, which causes some of the inactive molecules (presumably a stochastically determined subset) to become active, but only a small enough number that they can all be resolved from one another. After those active molecules have been imaged for some time, they will spontaneously photobleach and become (permanently) nonfluorescent (or, in the case of reversibly photoactivatable molecules, they will be inactivated by the readout light). Images taken of the molecules as a function of time are then used to individually localize each fluorescent molecule and, after sufficient numbers have been analyzed, to construct an image at higher resolution than diffraction would ordinarily allow.

Fig. 1 G shows the key features of the experimental geometry. An Argon ion laser (10 W Innova 310, Coherent, Santa Clara, CA) was directed by steering mirrors through a dichroic mirror DM1 (435 EFLP EM XF12, Omega Optical, Brattleboro, VT) and into a focusing lens L1 (f = 120 mm) which was located in the rear port of an inverted microscope (IX71, Olympus America, Melville, NY) at one focal length from the back aperture of a 60 x 1.2 NA infinity-corrected water-immersion objective (UPLAPO60XW, Olympus). A second beam from a diode-pumped solid-state laser at 405 nm (BCL-405-15, low noise model, Crystalaser, Reno, NV) was directed onto DM1 to (upon reflection) be approximately colinear with the Argon ion laser beam. After passing through L1, both laser beams struck a second dichroic mirror DM2 (Z488RDC, Chroma Technology, Rockingham, VT) and reached a focus at the objective back aperture. Measured (unattenuated) power levels at the sample were 3.50 ± 0.04 mW of total Ar+ ion laser power (24.8% at 476.5 nm, 72.0% at 496.5 nm, and 3.2% at <470 nm) and 0.197 ± 0.005 mW at 405 nm. Illumination by the 405-nm laser was controlled using a motorized filter wheel with RS232 interface and PC software (FW-102, Thorlabs, Newton, NJ), which was rotated into a completely transmitting (open) position for 10.0 ± 0.7 s, followed by return to a completely opaque position. The illumination intensity profile was approximately two-dimensional Gaussian with 1/e² radii 29.3 ± 0.5 µm and = 41.6 ± 0.5 µm for the 405-nm and Ar+ lasers, respectively. Emitted fluorescence was collected by the same objective, filtered by DM2 and an emission filter (HQ535/50, Chroma).

Spectroscopy
Fluorescence was focused by the tube lens and reflected out the left side port into an optical fiber with 1-mm diameter, then detected by a PC-controlled spectrometer (USB2000FL, Ocean Optics, Dunedin, FL). Raw spectra were recorded every 100 ms unless otherwise noted, without boxcar or averaging, background-subtracted using a blank spectrum determined under the same conditions, then smoothed by boxcar with full width 4 nm.

Photoactivation microscopy
Fluorescence was focused by the tube lens and reflected out the right side port onto a CCD camera (Quantifire, Indigo Scientific, Baldock, Herts, UK) interfaced by firewire to a PC. Images were collected by the CCD at 1.003 frames/s, gain of 11.4, and no binning (1 x 1) unless otherwise noted, then saved in raw (BMP or uncompressed TIF) format and analyzed using MATLAB scripts designed for particle recognition and localization. In brief, the algorithm searches for all pixels within the image above a threshold, assigning a single square region of interest (which in width is 3 times the FWHM of the measured PSF) for each such pixel above the threshold, excluding all pixels within any other region of interest (ROI) closer than 1.7 times the box half-width from any other ROI. The total number of pixels above a second threshold within each ROI is then determined. Those ROIs with at least 20 pixels above the second threshold are analyzed to determine the background-subtracted centroid. Only those pixels within the ROI that were above the second threshold are used to calculate the centroid. Because comparison of various algorithms for single-particle localization reveals that the centroid algorithm is susceptible to offset bias and degraded localization accuracy even at modest signal/noise ratios (S/N 5) (28), the center of mass coordinates are then used as the initial guess for a least-squares Gaussian fit of the image of the fluorescent object (26):

(11)

where B is the background pixel value, I₀ is the peak pixel value, x₀ and y₀ are estimated coordinates of the center of the fluorescent object, and r₀ is the 1/e² radius of the point spread function. Although the PSF of a high numerical aperture lens is not strictly Gaussian (34,35), for distances less than the 1/e² radius, a Gaussian is a reasonable approximation of the PSF, and is frequently used to fit the image of a point-like fluorescent object (16,26,27).

The overall magnification of the optical system results in a pixel size of 0.121 µm, which is within a factor of 2 of the standard deviation of the PSF (0.20 µm) recommended for optimal localization precision in the presence of background (27). Analysis of mean pixel value as a function of the variance of the pixel value under the binning (1 x 1) and gain (11.4) settings used to obtain images yielded a slope of 11.7 ± 0.4 pixel values per photon and an intercept of –1.8 ± 3.3 (i.e., zero within uncertainty).

In practice, when the sample is first visualized, a number of molecules may already be activated by exposure to room light or spontaneous activation processes. The density of molecules may be higher than is optimal for localization of individual molecules, but as photobleaching progressively decreases the number of active molecules (in the absence of the activation laser), the density approaches a more manageable level and acquired frames can be analyzed to determine molecular positions. As the density drops below the desired value (e.g., 0.8 molecules/µm²), the activation laser is pulsed at high intensity or turned on continuously at low intensity (such that the total dose per frame is between 4 and 40 J/cm²). From that point on, frames are acquired until the majority of activatable molecules have been read out and photobleached. The density of molecules that are already activated at the beginning of the experiment (i.e., accidentally activated) depends largely on the age of the PA-GFP sample and whether it has been exposed to room light or left in buffer at room temperature for a significant time (i.e., days). Frozen protein stocks appear to last for approximately months without significant spontaneous activation (data not shown).

Simulations
For simulations, molecules were positioned randomly (100 at a time) within a 512 x 512-pixel region by generating a floating-point random number for both x and y coordinates of the molecule (not rounded off to the nearest integer). The image of the molecules was generated to include shot noise by stochastically distributing 1000 photons/molecule using a random number generator to determine whether a given pixel would receive a photon. The probability of detecting a photon at a given position was given by the point spread function (in this case a Gaussian centered at the x,y coordinates of the molecule, with 1/e² radius of 1.6 pixels). Each pixel in the image then had a pixel value equal to the number of photons from the given distribution of molecules. Background of 10 ± 3 photons at each pixel was also added by a random number generator to the photons that form the image of the molecules.

Calibration sample
A 1 cm x 1 cm x 0.5-mm wafer of single-crystal sapphire (Princeton Scientific, Princeton, NJ) within 0.05° of R-cut was cleaned with acetone, isopropanol, then water, then annealed in air at 1700°C for 10 h, cooled to room temperature, then cleaned again by the same procedure. A 1-µL drop of PA-GFP (original stock diluted 1:100 in high-purity water) was then deposited on the surface and allowed to dry in air at room temperature in a darkened room. After drying, the sample was inverted and placed on top of a No. 1.5 coverslip (crystal surface with PA-GFP facing down) and was imaged from below by the objective. The sample was then imaged by FPALM as described above, using a Z496/10x laser cleanup filter (Chroma) to limit the excitation from the Ar+ ion laser to just the 496.5-nm line, yielding a power of 1.60 mW at the sample (496.5 nm line only), or an intensity of 105 W/cm². Activation was achieved by an initial 2-s pulse of illumination at 405 nm with intensity 40 W/cm² and by continuous illumination at 405 nm with 4 W/cm² after the molecular density had reduced due to photobleaching (500 s later); 1000 frames were acquired at 0.999 frames/s with an integration time of 0.983 s, gain of 11, and 2 x 2-pixel binning. The latter 500 frames were analyzed to determine the presented distribution of PA-GFP molecules.

Atomic force microscopy was performed using a JPSA (Manchester, NH) XE-100 microscope in contact mode on the same sapphire sample in various 1.5 µm x 1.5 µm areas of 256 x 256 pixels (not necessarily the same areas imaged by FPALM) with a stage with 50 µm travel, 1 line/s (256 s/image) rate, a new tip (radius <10 nm) with aluminum reflective coating (Budget Sensors, Sofia, Bulgaria), in air at room temperature.

	RESULTS

TOP ABSTRACT INTRODUCTION THEORY METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Fluorescence photoactivation and emission under 405 nm and Ar+ ion laser illumination
Fig. 2 shows emission spectra from PA-GFP molecules dried on a glass coverslip and illuminated continuously by 4.5 µW of power from the Ar+ ion laser and for brief (10-s) pulses of 197 µW of 405 nm illumination. Negligible fluorescence was observed on coverslips without PA-GFP illuminated under the same conditions. During and after 405 nm illumination, the fluorescence emission within the detected wavelength range 510–565 nm significantly increased (Fig. 2, C and D). The observed emission maximum at 518 ± 2 nm (not corrected for detection or filter transmission efficiency), matches the expected emission of PA-GFP of 517 nm (25). The increase in fluorescence after 405 nm illumination indicates that a significant fraction of previously inactive PA-GFP molecules were activated. Under continuous Ar+ illumination in the absence of 405 nm activation, the PA-GFP fluorescence photobleached at a rate of 0.046 ± 0.002 s^–1. Successive activation attempts became less effective as a larger fraction of the original molecules had already been activated or photobleached. The fluorescence visible before application of the first 405-nm pulse (Fig. 2 B) indicates that a small fraction of the PA-GFP had already been activated.

View larger version (20K): [in this window] [in a new window]   FIGURE 2  Fluorescence emission before and after photoactivation of PA-GFP. (A) Fluorescence emission spectra were measured as a function of time as PA-GFP molecules immobilized on a glass coverslip were illuminated continuously with an Ar+ ion laser (time dependence shown by long, light blue bar along time axis), and intermittently with a 405-nm laser (short, dark blue bars just above the axis). The background-subtracted integrated area under the fluorescence spectrum is plotted as a function of time (blue curve a). Downward red arrows indicate movement of the sample to a new area that had not been illuminated previously. Under continuous illumination at 488 nm, the fluorescence intensity increased significantly during illumination with the 405-nm laser. The emission spectra at various times before activation (b and c), during (d), and after (e–k) correspond to curves shown in B–D. The downward black arrow in D indicates that the emission intensity was decreasing with time.

View larger version (32K): [in this window] [in a new window]   FIGURE 3  Imaging single molecules of PA-GFP. (A) Single frame (1-s acquisition) from a time series of images of PA-GFP molecules at low density on a glass coverslip illuminated continuously by an Ar+ ion laser and activated by brief pulses from a 405-nm diode laser. Fluorescence was detected from 510–560 nm. (B–D) Three successive 1-s frames in the same series showing discrete on-off behavior expected for a single fluorophore. All images had the same constant offset subtracted and all pixels were multiplied by a second common constant for display purposes. (E) Collage of images from a longer time series of a 5 x 5-pixel region (0.6 µm x 0.6 µm) imaged at 0.998 frames/s for 200 s (images are arranged from left to right, in rows of 20 s each). (F) Count rate within the 5 x 5 region as a function of time shows discrete behavior. The dashed box in F highlights the time dependence of the count rate in the series of images in the white dashed box in E.

View larger version (33K): [in this window] [in a new window]   FIGURE 4  Single particle localization algorithm. Simulated images containing single particles were analyzed to compare the accuracy and precision of the centroid algorithm and Gaussian least-squares fit methods for particle localization. The simulated image (A) was processed to find pixels above a threshold and assign a nonoverlapping ROI for each one (minimum center-to-center ROI separation was 0.86 times the box full width). Centroid analysis was performed on ROIs with >20 pixels above a second threshold, and those coordinates (inset, dashed blue lines) were used as an initial guess for a Gaussian least-squares fit with the image using Eq. 11 (coordinates from the Gaussian best fit are shown in red). (B) Tabulation of the localization error for randomly positioned simulated molecules shows that the centroid algorithm has similar precision (curves shown are fits to a Gaussian distribution) but has a systematic bias. The Gaussian algorithm has less systematic bias and similar or better precision (particularly at low signal/noise ratio) (28) and was therefore used for subsequent analysis of the experimental images.

Fig. 5 shows the results of a simulated distribution of molecules placed along periodic vertical strips 60.5 nm wide separated by regions 60.5 nm wide without molecules. Although such a structure would be difficult to resolve using standard light microscopy, the periodicity is visible in the plot of localized molecular positions.

View larger version (72K): [in this window] [in a new window]   FIGURE 5  Simulated FPALM resolves a subdiffraction-scale structure. Simulated photoactivatable fluorescent molecules were distributed in periodic narrow vertical strips 60.5 nm wide, separated by 60.5-nm gaps. The molecules were activated stochastically in small numbers (50) per frame and simulated to emit photons, 1000 of which were detected. The simulated PSF was 200 nm wide (FWHM). Molecules were localized by the Gaussian algorithm described in Methods and in Fig. 4. A plot of 30,659 molecular positions determined by the algorithm demonstrates the ability of the technique to resolve structures smaller than the PSF. The histogram of particles observed within horizontally-spaced bins, each spanning a 10 nm range in x-coordinates only (shown directly below the plotted position), also reveals the subdiffraction periodicity of the simulated sample.

View larger version (94K): [in this window] [in a new window]   FIGURE 6  Measured FPALM images of PA-GFP on a glass coverslip. (A–D) Measured positions of 48,746 localized molecules are plotted in yellow, weighted by the peak intensity at the center of the molecule, obtained from a Gaussian fit of the image using Eq. 11. The molecular positions from FPALM are plotted on top of the sum of all the widefield fluorescence images obtained during the acquisition (sum image shown in green) to illustrate the significantly greater resolution of FPALM compared to widefield fluorescence microscopy. The sequence from A to D progresses toward higher zoom, where the dotted box shows the region being expanded (e.g., the dotted red box in B shows the same region as all of C). In C and D, heterogeneity on length scales shorter than the classical diffraction limit is clearly visible.

View larger version (50K): [in this window] [in a new window]   FIGURE 7  Second representation of measured molecular positions obtained by FPALM. (A–C) Blue dots indicate the location of a single PA-GFP molecule, determined by FPALM, of the same acquisition series shown in Fig. 6. (D) After zooming in >30-fold from A to C, the positions are replotted as yellow dots surrounded by a blue disk, approximating the lateral extent of the observation PSF, to emphasize the difficulty one would have in resolving these molecules simultaneously by standard widefield microscopy.

View larger version (36K): [in this window] [in a new window]   FIGURE 8  FPALM image of an R-cut single-crystal wafer of sapphire annealed at high temperature to produce atomic terraces, labeled with PA-GFP. (A) The positions of PA-GFP molecules localized over a period of 500 s are plotted (blue points) and compared with an atomic force microscope (AFM) image (inset) of the same sample (not necessarily the same area). Atomic step dislocations spaced laterally by 200–630 nm are visible by both techniques, because the PA-GFP has localized to those dislocations upon drying. Scale bar (1 µm) applies to both the FPALM and the AFM images. Note the gradient in particle density across the dislocations shown by FPALM. The red dotted box corresponds to the profile in B. (B) Analysis of the profile of a dislocation. The histogram of molecular positions (black points) as a function of distance perpendicular to the dislocation reveals the width of the feature as visualized by FPALM. Fitting the profile with a Gaussian (red line) yielded a 1/e2 half-width of 73 ± 3 nm, and an FWHM of 86 ± 4 nm.

In addition to high-resolution imaging of the molecular distribution, FPALM can be used to quantify other single-molecule properties of the fluorophores, which are inaccessible to standard widefield fluorescence microscopy. Fig. 9 shows the brightness distribution of localized molecules and the time dependence of the number of localized molecules. Under continuous Ar+ illumination, the number of fluorescent particles decayed as a single exponential with a 1/e time of 125 ± 3 s.

View larger version (20K): [in this window] [in a new window]   FIGURE 9  Additional information, not available to ensemble fluorescence microscopy methods that image large numbers of molecules (>>100) simultaneously, is obtained by FPALM. (A) The number of molecules fluctuates and decays with time as FPALM frames are acquired. The number of fluorescent molecules within the observation volume in a widefield or confocal fluorescence microscope is difficult to determine without a calibration standard, but is obtained for every image in FPALM. A single exponential time constant ( = 125 ± 3 s) described the decay of the number of molecules observed, consistent with depletion of a single reservoir of inactivated PA-GFP molecules. (B) The distribution of single-molecule fluorescence intensities is determined by FPALM and converted into the detected photon count rate at the center of the diffraction-limited image of the molecule. All amplitudes had a constant subtracted to account for background. Such information is useful in determining the degree of heterogeneity within a population of molecules and is typically difficult to obtain from measurements that sample large numbers of molecules simultaneously.

	DISCUSSION

TOP ABSTRACT INTRODUCTION THEORY METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

FPALM has been demonstrated as a means of imaging structures on subdiffraction length scales, which has been confirmed by atomic force microscopy. The distribution of molecular positions at the edge of a terrace shows a 1/e² width of 73 ± 3 nm, or a FWHM of 86 ± 4 nm, which is significantly less than the diffraction limit in normal widefield microscopy. AFM imaging revealed that the sharp side of the vertical steps from terrace to terrace occurred over a lateral distance of 79 ± 9 nm, in good agreement with the value determined by FPALM. Although the above FWHM shows that subdiffraction features can be resolved, the FWHM is also degraded by background from the sapphire, which was higher than in the samples of PA-GFP on coverslips, and therefore the ultimate resolution of FPALM may be much better than has been shown here. Nonetheless, the profile of the features and their spacing as determined by FPALM are consistent with AFM results, confirming that the method can be used to visualize structures on length scales shorter than the diffraction limit.

The time dependence of the fluorescence emission of single fluorophores can complicate localization analysis (26). Due to the relatively long (1-s) integration times in the FPALM results presented here, the flicker and blinking that occur on the microsecond and millisecond timescales is averaged over, and therefore not directly observed. However, some blinking on longer timescales (Fig. 3) is still observed. In addition, long integration times will allow for significant movement to occur if the molecules are mobile. When random molecular diffusion occurs on timescales shorter than the integration time per frame (here 1 s), the image of the molecule will be blurred, with fewer detected photons per pixel distributed over a larger number of pixels. Molecules moving in three dimensions during the acquisition time will be extremely difficult to localize by the current implementation of FPALM. On the other hand, consider molecules constrained to move in two dimensions (i.e., within the focal plane of the microscope). In this case, under random diffusion, the mean position of each molecule is expected to remain unchanged, whereas the variance is expected to increase according to , where r₀ is the 1/e² radius of the diffraction-limited PSF (see also Eqs. 6–8). Because of the larger variance and reduced signal/noise and signal/background ratios per pixel, the ability to determine the mean position will be significantly diminished. In the special case of random two-dimensional motion with a very small diffusion coefficient (D < 10^–10 cm²/s), localization may in principle still be possible.

If significant nonrandom motion occurs during the acquisition time, the image of a given molecule will no longer appear circular, also making analysis much more difficult; new methods of analysis will likely need to be developed. Although this complicates the determination of the mean position within a single image, successive images can be analyzed to determine molecular velocities (as is done in FSM), which is certainly of biological relevance (21–24). FPALM is particularly well-suited to the study of proteins and other structures in fixed cells, and is possibly applicable to a subset of membrane proteins in living cells, if their lateral mobilities are at least two orders of magnitude smaller (33) than those of soluble (i.e., cytosolic) GFP-tagged proteins (36–38). Successful examples of single-molecule total internal reflection fluorescence (TIRF) detection with high signal/noise ratio in agarose (39) and membranes (40) offer a promising complement to single-particle tracking measurements that have revealed time-dependent lateral heterogeneities in biological membranes (41,42).

The power offered by genetic manipulation of fluorescent proteins (43–46) is a significant advantage for FPALM, since any protein of interest can be labeled by splicing the gene for that protein into a PA-GFP or other photoactivatable fluorescent protein (PAFP) construct. Multiple labeling is possible using combinations of photoactivatable proteins with different activation and emission spectra. Labeling of other cellular species, such as lipids, will rely on development of conjugates with photoactivatable organic dyes, PAFP-tagged antibodies, or lipid binding proteins such as the pleckstrin homology domain that binds PIP₂ (47). As the variety of available PAFPs increases (31), multi-color labeling experiments using FPALM will become even more flexible. Mutagenesis of existing PAFPs can also be used to reduce blinking and undesirable types of spectral switching that complicate the use of many types of fluorophores, such as quantum dots, in single-molecule imaging. The quantum yield of PA-GFP (0.79) is already quite high in comparison to most other PAFPs (25,31). Comparison of fluorescence intermittency of PA-GFP mutants by fluorescence correlation spectroscopy has shown significant variation in the degree to which these proteins flicker, which can limit the number of photons emitted per second per molecule (S. Hess and G. Patterson, unpublished results). Improvement of the photophysical properties of PAFPs to reduce intermittency and increase photon emission rate will allow even greater localization precision to be achieved.

The irreversible photobleaching that fluorophores inevitably undergo is advantageous in FPALM since it helps control the number of fluorescent molecules in the field of view during each image frame (time point). Although it is expected that photobleaching will lead to the production of chemically reactive species that could be toxic to living cells, the number of bleached molecules produced is of the same order of magnitude as those produced in confocal microscopy experiments (it is not uncommon for a significant portion of the fluorophore to be bleached during the acquisition of a z-stack with frame averaging, for example).

The time required by a fluorophore to be photoactivated (the "settling time" mentioned by Hoffman et al.) can also limit imaging rate in scanning photoactivation microscopy (15) but is not as significant an impediment in FPALM because the entire field is imaged at once, and each frame is acquired over a timescale of seconds or fractions of a second, rather than the typical microsecond voxel dwell time in confocal and other scanning microscopies. Also, under some conditions in other types of photoactivation microscopy, it becomes difficult to increase the activation rate past a certain point (15). In comparison, activation rates for PA-GFP much larger than the frame rate (>10 s^–1) have been achieved with modest activation laser intensities (100 W/cm², data not shown) and since it is not anticipated that the frame rate would need to exceed 10² s^–1, the same kind of limitation for FPALM using PA-GFP may not exist. Further study of the activation rate as a function of activation laser intensity is needed, since the activation rate and photobleaching rate can limit the acquisition frame rate.

Although many fluorescent proteins are known to spontaneously aggregate, point mutations such as L221K can be introduced into PA-GFP (which is of the family of green fluorescent proteins and is less susceptible to aggregation, with K_d 0.11 mM) to raise (improve) the K_d to 9 mM (48).

Recent work in single-molecule fluorescence microscopy has focused on improving the ability to resolve multiple fluorophores by spectral separation (16); nanoparticles such as quantum dots offer somewhat narrower emission spectra and therefore can be "packed" in larger numbers into the same range of visible wavelengths (49). However, in comparison to fluorescent proteins, quantum dots have so far proven to be more difficult to target to some intracellular compartments, especially the nucleus (50). FPALM obviates the need for multiple detection channels by controlling the number of particles that are fluorescent at a given time, such that even at high inactive probe concentrations, the distance between active (fluorescent) molecules is on the average much larger than the resolution. It should be noted that extending this technique to multiple spectral channels is possible, and would result in a modest increase in the possible labeling density, proportional to the number of spectral channels, but a much more significant advantage of labeling with multiple, spectrally distinct photoactivatable species is simply to be able to visualize multiple species at high resolution.

Estimated signal/noise ratio
We use the definition of signal/noise ratio S/N = (I₀ – I_B)/, where is a representative noise level and I₀ – I_B is the difference in mean intensity between the object and the background (Cheezum et al.), to obtain for the molecule in Fig. 3 E: I₀ – I_B 161 photons and 25.6 photons, for S/N 6.3, which is high enough to allow localization with distance precision >100 nm using a Gaussian algorithm, but not necessarily with other algorithms (Cheezum et al.). The expected excitation rate k_x = I, where is the one-photon excitation cross section and I is the excitation intensity in photons/unit area/s, can be estimated theoretically considering the excitation laser (Ar+) power (6.7 mW) in the back aperture, the objective transmission coefficient (0.5) for the appropriate wavelengths (476.5 nm and 496.5 nm), the 1/e² radius of the illuminated area (41.6 ± 0.5 µm), the resulting intensity 46 W/cm² at 496.7 nm and 16 W/cm² at 476.5 nm, the energy per photon, and the estimated extinction coefficient at 476.5 nm