40 Principles of Spectral Precision Distance Confocal ...€¦ · lar biology. He speculated that the chromosomes in the nucleus were ... (SPM) makes possible the measurement

40 Principles of Spectral PrecisionDistance Confocal Microscopy forthe Analysis of Molecular NuclearStructure

Christoph Cremer1,2, P. Edelmann1,2, H. Bornfleth1,2,G. Kreth1,2,3, H. Muench1, H. Luz1, M. Hausmann1

1Institut für Angewandte Physik2Interdisziplinäres Zentrum für Wissenschaftliches Rechnen3Graduiertenkolleg, Wissenschaftliches RechnenUniversität Heidelberg, Germany

40.1 The problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839

40.2 Principles of spectral precision distance microscopy . . . . . . 845

40.3 Determination of the resolution equivalent in situ . . . . . . . 852

40.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855

40.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855

40.1 The problem

Localization by light plays a fundamental role in many fields of science.In optics, during the last century, the development of high-performancelight microscopes was at the foundation of a revolution in biology andmedicine. In combination with appropriate staining techniques, lightmicroscopy allowed the discovery of the elementary unit of all organ-isms, the cell. Further light microscopical analysis of the cellular struc-ture soon resulted in the discovery of a main constituent of the cell,the cell nucleus, and of the chromosomes (“stained bodies”). At thattime, the latter were visible during cell division only but they had tobe present in some unknown form also in the nucleus. Today we knowthat the chromosomes contain (with very few exceptions) all the in-formation necessary for cellular metabolism and for the growth anddevelopment of every organism. Together, they form the genome thatin normal human cells is divided into 46 individual chromosomes.

839Handbook of Computer Vision and Applications Copyright © 1999 by Academic PressVolume 3 All rights of reproduction in any form reserved.Systems and Applications ISBN 0–12–379773-X/$30.00

840 40 Spectral Precision Distance Confocal Microscopy

a b

c d

Figure 40.1: Computer simulations of all chromosomes in the human inter-phase cell nucleus. Chromosomes were described by different models, whichapproximate the chromatin fiber by a polymer chain, folded in different ways.Corresponding to the different condensation levels, a nonterritorial (a Vogeland Schroeder-, b random-walk bead model) or a territorial (c random-walkgiant loop-, d spherical subdomain model) organization of chromosomes wasobtained. For visualization, in each case only four chromosomes are visualizedin a spherical nuclear envelope by ray tracing. For further details see Krethet al. [1]; (see also Plate 15).

The chromosomes are the most complex molecules found so far innature. For example, each human chromosome is formed from a sin-gle DNA-molecule with a specific sequence of base pairs carrying thehereditary information and consisting of several 109 atoms; the 50 to230 million base pairs of a human chromosome are further associatedin a specific way with about several million proteins, the histones. Thisenormous complexity, however, is not visible by conventional light mi-croscopical procedures. Thus, for more than a century discussions ofeven very fundamental questions concerning the structure of the chro-mosomes, especially in the cell nucleus, were controversial. For exam-ple, light and even electron microscopical observations as well as bio-

40.1 The problem 841

chemical data were compatible with models where DNA-protein-fibersof each of the chromosomes were stretched out through the entire nu-cleus but also with models where these fibers were folded in such away that the chromosome had an enveloping volume of a few percentof the entire nuclear volume only (for a review, see [2]). As an example,Fig. 40.1 shows visualizations of such models obtained by computersimulations of all chromosomes in the human interphase cell nucleus[1, 3, 4, 5, 6].

More than half a century ago, Erwin Schroedinger formulated a hy-pothesis that was to become decisive for the development of molecu-lar biology. He speculated that the chromosomes in the nucleus were“aperiodic solid bodies” with a complex 3-D structure, and that this wasthe key to their high informational content. Today, we know that thishypothesis was completely correct on the level of individual base pairsand of small clusters of so-called nucleosomes of 11-nm diameter (1 nm= 1 × 10−9 m), each with about 200 base pairs (including “linker” DNAto neighboring nucleosomes) associated with eight histone proteins ina very precise manner. Recently, it has become possible to unravelthe 3-D structure of the nucleosomes with almost atomic resolution bysynchrotron radiation diffraction experiments. From a formal point ofview, this reduced the problem of the molecular nuclear structure tothe problem of finding the relative 3-D positions for each nucleosomalDNA sequence. For a human cell nucleus, this would mean the topo-logical analysis of about 35 to 70 million different sites. Until recently,even partial solutions of this enormous problem (e.g., relative positionsof selected nucleosome clusters, or the morphology of still larger units)appeared to be impossible.

Since the 1970s, the progress of molecular biology opened an av-enue to the labeling of a variety of targets in the human cell nucleus ina specific way using fluorochrome molecules. For example, in principle,any known protein type or any known DNA sequence of the genome cannow be individually fluorescence labeled. In a simple, schematic formthis technique called “fluorescence in situ hybridization” (FISH) is basedon the binding of a fluorescence-labeled “probe” DNA to the comple-mentary sequence of the single-stranded (“denatured”) chromosomal“target” DNA “in situ,” that is, directly in the cell nuclei [7]. Using flu-orochromes of different spectral signature (characterized, e.g., by dif-ferent absorption or fluorescence emission spectra), the chromosomaltarget DNA sequences can be labelled in a spectrally distinct way.

As an example, Fig. 40.2 shows a 3-D reconstruction of a humanfemale cell nucleus where the two female sex chromosomes (the X)plus 2 genes, located on them, were FISH-labeled with different spec-tral signatures and registered by confocal laser scanning fluorescencemicroscopy (CLSM). For a quantitative image analysis of shape param-eters, both Voronoi and Cavalieri estimators have been successfully


Xr Xe

SF = 0.910 SF = 0.354

RF = 0.088 SF = 0.008

Volume = 18.94µm3 Volume = 16.39µm3

Surface area = 77.07µm3 Surface area = 154.84µm3

Figure 40.2: Reconstructed confocal 3-D dataset of a human female cell nucleusvisualized by ray tracing. The genes ANT2 (red)/ ANT3 (yellow) are representedby spheres with approximately the same volume as the registered signals in theconfocal image. The rounder shape of the inactive X-chromosome territory (Xi,red) and the more interior localization of the inactive ANT2 on Xi is clearlyvisible (SF = smoothness factor; SF converge against 0, elongated shape; SFconverge against 1, spherical shape; RF = roundness factor; see Bornfleth et al.,Chapter 41.2).

applied. It was even found that the same chromosome territory mayhave a distinctly different morphology according to its genetic activity[8, 9]. Compared with the extension of the entire nucleus, the individ-ual chromosome territories clearly have an enveloping volume of a fewpercent of the entire nuclear volume only. The “territoriality” of chro-mosomes has now been firmly established as a main feature of nuclearorganization of normal cells; it excludes a variety of models as generaldescriptions of chromosomal structure (compare Fig. 40.1).

Taken by itself, the territoriality of chromosomes in the cell nu-cleus (in the sense of a limited extension) may be quantitatively mod-eled by relatively simple polymer or “bead” models (compare Fig. 40.1;[1, 4, 6, 10]). Even light microscopically measured distances betweenindividual, FISH-labeled DNA target sequences within the same chromo-some territory were estimated by such models in a quantitatively satis-fying manner. An alternative view holds, however, that due to a “chro-matin folding code,” a functionally important degree of higher-orderstructures of the chromosome is obtained (for review, see [2, 4, 11]).To test such a hypothesis of considerable impact for our understandingof life, a much more detailed quantitative analysis of nuclear structure

40.1 The problem 843

is necessary; this appears to be especially meaningful for the molecu-lar genome structure below about 100,000 base pairs (100 kbp) of DNA(about 500 nucleosomes including “linker” DNA). From the microscop-ical point of view, this requires measuring 3-D geometric distances andspatial conformations of FISH-labeled target sequences located on thesame chromosomal fiber that have a linear genomic distance of lessthan about 100 kbp. Experimental evidence, however, indicates thatusing advanced far-field light microscopical methods such as confo-cal laser scanning microscopy (CLSM), geometrical target 3-D distancesin the nucleus below several hundred nanometers (corresponding togenomic distances below about 100 kbp) cannot be measured reliablyif both target sequences are labeled with the same spectral signature.This is due to the well-known limits of microscopical resolution (Vol-ume 1, Chapter 21; [12]).

Figure 40.3 shows an computed example for the limited resolutionof CLSM for conditions relevant in genome structure analysis. The sim-ulations made on the basis of scalar wave theory using point objectsof one spectral signature indicate that even under the (unrealistic) as-sumption of an ideal photon statistics and lack of detector noise, a 3-Dresolution of better than a few hundred nanometers is hardly feasi-ble. Under “practical” conditions of biological routine measurements,the 3-D resolution of CLSM (as determined from the axial full width athalf maximum (FWHM) of the confocal point-spread function (PSF)) wasfound to be on the order of 600 to 700 nm [13]. As an example of theconsequences of the limited resolution in genome structure research,Fig. 40.4a shows the simulated projection image of a 70-kbp long DNAsequence of a chromosomal fiber (calculated as a zig-zag random walkof nucleosomes) after labeling with one spectral signature and convo-lution with a PSF of 250 nm FWHM. As expected, even a rotation ofthe 70-kbp sequence by axial tomography [14] under these conditionswould not reveal any significant structural detail.

To increase the 3-D light optical resolution in the sense of point-spread function improvement, other microscopical far-field methodshave to be considered, such as 4Pi microscopy [15, 16], standing-wave-field microscopy [17]), spatially modulated excitation (SME) microscopy[18, 19], and other techniques of point-spread function engineering. Inthe following, the principles of an additional approach to reveal 3-Dgenome structure on a scale considerably lower than the classical reso-lution limit will be considered. Generally, this approach called spectralprecision distance microscopy (SPM) makes possible the measurementof distances well below the FWHM of the effective PSF that describes theoptical properties of the imaging system; SPM combines high-qualityoptics with advanced techniques of computer image analysis and re-construction. Because SPM can be used with any optical system hav-ing a well-defined PSF, it will greatly increase the possibilities of the


a

5

10

15

20

25

30

35

y

510

1520

2530

35

x

0

50

100

150

200 A

b

5

10

15

20

25

30

35

y

510

1520

2530

35

x

0

50

100

150

200

250A

c

5

10

15

20

25

30

35

y

510

1520

2530

35

x

0

50

100

150

200 A

d

5

10

15

20

25

30

35

y

510

1520

2530

35

x

0

50

100

150

200

250 A

Figure 40.3: Computer-generated example for the resolution of the CLSM us-ing two point-like targets of the same spectral signature of λ = 520 nm. The PSFwas sampled with stepwidths of 0.4 optical units (27 nm): a two point-like tar-gets with a lateral distance of 226 nm, corresponding to the Rayleigh criterion(∼ λ/NA) of optical resolution; b the same image after application of Poissonnoise. A maximum number of 12 detected photons per voxel was assumed; c,d two point-like targets with a spatial distance of 138 nm, corresponding to theFWHM criterion of optical resolution, before and after application of Poissonnoise as in b.

point-spread function engineered devices mentioned in the foregoing.In combination with digital microscopy and digital image analysis, SPMopens the possibility of measuring light microscopically 3-D positionsof fluorescence labeled targets on a scale several to many times smallerthan the nominal resolution of the system used. In combination withcomputer modeling of the regions studied and—where possible—with

40.2 Principles of spectral precision distance microscopy 845

ultrastructural procedures, this will eventually allow the unraveling ofthe 3-D structure and texture of the genome down to the molecularlevel in an analogous way as it has become possible for other biologicalmacromolecules such as large proteins.

40.2 Principles of spectral precision distance mi-croscopy (SPM)

It has been known for many years that “super resolution” of pointobjects situated within the Rayleigh distance (corresponding approxi-mately to 1 FWHM of the PSF) can be achieved if the two objects possessdifferent spectral characteristics. Strategies of deconvolution whereeach image associated with a particular wavelength is separately de-convoluted with the transfer function of that wavelength have beendescribed [20]. Even when the data were characterized by a moder-ate signal to noise ratio (SNR), simulated images of point-like objectswere correctly restored that were only 1/30–1/50 FWHM apart fromeach other. The SPM approach described here [21, 22] is based onthe same principle idea that using spectral information, the old res-olution limits such as those of Rayleigh or Abbé are no longer valid.That principal idea has been extended, however, to the special needs ofhigh-resolution fluorescence far-field microscopy and its application tothe 3-D analysis of the molecular nanostructure of the genome in themammalian cell nucleus.

The principle of SPM is shown schematically in Fig. 40.5: Let us as-sume three closely neighboring targets in a nucleus to be studied withdistances much smaller than 1 FWHM, where FWHM represents the fullwidth at half maximum of the effective PSF of the optical system used.The “point-like” (diameter much smaller than 1 FWHM) targets t1, t2

and t3 (e.g., three genes, or two genes and one protein) are assumed tohave been labeled with three different fluorescent spectral signaturesspecs1, specs2 and specs3. For example, t1 was labeled with specs1, t2

with specs2 and t3 with specs3. The registration of the images (using,e.g., CLSM) is performed in a spectrally discriminated way so that in afirst 3-D image stack IM1, a specs1 intensity value I1 is assigned to eachvoxel vk of the object space; in a second 3-D image stack IM2, a specs2

intensity value I2 is assigned to each voxel vk of the object space; andin a third 3-D image stack IM3, a specs3 intensity value I3 is assigned toeach voxel vk of the object space. So far, the strategy is very similar tothat described by Burns et al. [20] for one spatial dimension. Insteadof wavelength-discriminating deconvolution algorithms, however, theSPM approach is based on the direct evaluation of the spectrally sep-arated images. In ideal epifluorescent or 2Pi, 4Pi confocal images, forbasic optical reasons the absolute maximum max1 of the diffraction


Figure 40.4: a Zig-zag random-walk computer simulation of a 70-kb long nu-cleosome chain (beads) of chromosomal DNA after single color hybridization.In conventional fluorescence microscopy (corresponding to an assumed convo-lution with a PSF of 250-nm FWHM), even under various rotation angles noinner structures are detectable; b zig-zag random-walk computer simulation ofthe same 70-kb long nucleosome chain of chromosomal DNA after hybridiza-tion with seven spectrally different signatures (each color segment 10 kbp). Eachsegment is assumed to be detected by spectrally discriminated imaging. In spec-tral precision distance microscopy (SPM), the barycenters of the intensities canstill be localized after convolution with the PSF of the microscope, so that theirdistances can be measured. In combination with axial tomography for rotationof the labeled object, the 3-D conformation of the DNA segment can be revealed,although the barycenter distances were considerably below the resolution limitof the microscopy given by the FWHM of the PSF; (see also Plate 16).


a c e

0 100 200 300 400

[nm]

norm

aliz

ed

Inte

nsity

b d f

0 100 200 300 400

[ nm ]

no

rmaliz

ed

Inte

nsity

Figure 40.5: Example describing the principle of spectral precision distancemicroscopy (SPM). Three point-like objects are located within 50-nm distanceof each other. The three point-like objects are labeled with the same spectralsignature in a and with three different spectral signatures in b. The computedsystem responses of the objects in a and b for a confocal microscope with NA= 1.4/63× oil-immersion objective are shown in c and d. Linescanes throughthe objects in c and d are shown in e and f respectively (for details see text and[23]); (see also Plate 17).

pattern of the image of t1 (registered as a specs1 intensity distribution)gives the ideal (geometrical) image point i1 of t1; the absolute maximummax2 of the diffraction pattern of the image of t2 (registered as specs2

intensity distribution) gives the ideal (geometrical) image point i2 of t2;and the absolute maximum max3 of the diffraction pattern of the imaget3 (registered as specs3 intensity distribution) gives the ideal (geomet-rical) image point i3 of t3. From this, the positions (object points) o1,o2 and o3 of t1, t2 and t3 and their 3-D distances in the object spacecan be determined if the optical characteristics of the system (such asmagnification factors, aberration distortions) are known.

In principle, the minimum (real) distance that can be measured inthis way is independent of the FWHM of the PSF and varies only withuncorrected systematic errors and statistical errors affecting the lo-calization of the diffraction maxima. This minimum detectable dis-tance between two point-like objects of different spectral signaturesone may call the resolution equivalent (RE). It has to be distinguishedfrom the optical resolution (A) that usually refers to the capacity of an


optical system to transfer structural information (minimum distancedetectable) of any object structure. In general, A is given, for example,by the Abbe-, Rayleigh-, Sparrow (or similar) criterium, the FWHM ofthe PSF, or the limiting spatial frequency of the optical transfer func-tion (OTF). It is clear that the SPM strategy can be applied to more thantwo or three closely neighbored targets, if the neighboring targets t1, t2,t3, ..., tn have sufficiently different spectral signatures specs1, specs2,specs3, ..., specsn. Three or more spectral signatures allow true struc-tural conclusions. For example, already three targets with three dif-ferent spectral signatures allow us to define distance and angle rela-tionships between the targets; four targets with four different spectralsignatures allow a variety of 3-D structures.

Furthermore, it is clear that essentially the same SPM strategy can beapplied also in all cases where the distance between targets of the samespectral signature is larger than FWHM [24]. Computer simulationsperformed by Bornfleth et al. [21] indicated that a distance of about1.5 FWHM is sufficient. For example, in a nucleus with a volume ofabout 500µm3 and a confocal observation volume approximated byVobs = 4π/3 (FWHMxy)2 × (FWHMz) = 0.13µm3, this means that about103 different multispectral target sites can be evaluated in the samenucleus.

To realize local super-resolution strategies (RE much smaller than1 FWHM), using spectral characteristics as constraints in a microscopi-cally useful way, a variety of pitfalls have to be overcome. Here, basedon our present experience, some fundamental problems of the realiza-tion of confocal SPM methods will be discussed briefly:

1. As indicated in Fig. 40.5, the images of different spectral signatureshave to be registered independently of each other with the small-est amount of cross talk (reciprocal disturbance) possible. On onehand, this requires labeling of t1, t2, etc., with fluorochromes of well-distinguishable spectral signatures (e. g., spectrally clearly distinctfluorescence-emission maxima) as well as the possibility of excitingthem to fluorescence emission (e.g., using different laser lines andtypes). An additional important requirement is a sufficient fluores-cence photon yield of the fluorochromes used.

2. Detector systems are required that are capable of discriminating thedifferent spectral signatures (e.g., by appropriate optical filters) in aspatially highly resolved way (the FWHM required depending on theproblem to be solved); because in nuclear images the fluorescencephoton statistics usually is far below optimum, the quantum effi-ciency and the signal-to-noise relationship of the detector systemhas to be as good as possible.

3. The precision of localization of the diffraction-image maximaneeded for SPM super resolution has to be much better than the


voxel size. For example, a typical voxel size (object space scale)in confocal microscopy is 100 × 100 × 250 nm. This fulfills theNyquist theorem (ca. 1/2 FWHM lateral/axial) but is not sufficientfor the precision needed in SPM (e.g., 10 to 100 nm). This problemcan be overcome by appropriate image-evaluation algorithms basedon the barycentric calculus already introduced by Moebius [25]. Es-sentially, in its application to the maximum determination relevanthere, it means that for each diffraction pattern of an individual tar-get a fluorescence-intensity gravity center is calculated. In case ofsymmetrical PSFs, the barycenter positions in each spatial directionx, y , z coincide with the maximum positions of the diffraction pat-terns. Basic considerations show that in this case under the assump-tions of an appropriate photon statistics and detector noise, and forgeometrically stable relationships between the voxels, this makes itpossible to determine the positions of the diffraction pattern max-ima with any precision desired.

4. For the required high precision of fluorescence barycenter localiza-tion, fluorescence photon statistics (number of effective photonsregistered per voxel), detector noise and target noise (unspecific flu-orescence emission) play a decisive role. Such effects may not onlyconsiderably deteriorate the resolution equivalent, but even maycontribute to “limited-diffusion” phenomena. For example, com-puter simulations (Bornfleth et al. unpublished results) indicatedthat under the assumption of a small number of “effective” photonsper voxel typical for observations of small fluorescence labeled tar-gets in living cells, such “limited-diffusion” artifacts may be as largeas several hundred nanometer (mean squared distance obtained af-ter 12 evaluation steps) under the boundary conditions of standardconfocal microscopy. For an optimal solution of the problem, itis also important to define the voxels assigned to the target image.This may be done by appropriate segmentation algorithms with vari-able thresholding; see [21] and Chapter 41.

5. In all cases where the different spectral signatures are realized bydifferences in the fluorescence-emission spectra, a very significantsource of error is given by chromatic aberrations, especially in axialdirection [26]. Measurements using multispectral calibration beadsindicated that depending on the optical microconditions in confo-cal microscopy, axial chromatic shifts up to about 200 nm were ob-tained, whereas the lateral chromatic shifts were usually consider-ably smaller. The contribution of optical microconditions may in-volve, for example, refraction index variations between microscopefront lens and target and axial distance of the target relative to themicroscope front lens as well as spectral absorption characteristics


of the medium. Therefore, in situ calibration methods are requiredto more accurately determine 3-D chromatic shifts [27].

6. In addition to chromatic aberrations, the correction of monochro-matic deviations may be important. Even high-performance micro-scope lenses do not have a completely linear field of view. Thus, thesame physical distance of two fluorescing point objects located inthe object plane may result in spurious distance variations even un-der ideal signal-to-noise conditions. For a commercial high-aperturemicroscope lens, lateral distance variations greater than 50 nm havebeen measured (Heintzmann, unpublished results). In axial direc-tion, monochromatic distance variations also depend heavily onthe optical microconditions. Under conditions relevant for nuclearstructure analysis, such aberrations may be as large as 100 to sev-eral hundred nanometers (for example, compare [28]). By carefulmonochromatic calibration, it is experimentally possible to controlmonochromatic distance errors [21, 26].

7. In real optical systems, the PSF may show deviations from an ideallysymmetrical curve. Thus, the calculated barycenter coordinate maynot coincide exactly with the coordinate of the maximum (coordi-nate of the ideal image point). As the final goal is to measure smalldistances, that is, coordinate differences, in many cases such an er-ror may be eliminated if the PSF has the same kind of deviation forthe two targets located at slightly different positions in the objectspace.

8. Confocal laser scanning microscopes in some way or other use me-chanical scanning devices. Thus, mechanical stability and toler-ances may influence the correct voxel positioning that is of greatimportance for the precise subvoxel localization of fluorescence-intensity barycenters necessary for the SPM approach.

Figure 40.4b presents a computer visualization of the capacity ofSPM to allow a structural resolution far below the FWHM. On the upperleft, as in Fig. 40.4a, a simulated chromatin sequence and its 2-D projec-tions at different rotation angles (first row from above) are shown. Thesecond row then presents the 2-D projections after convolution with a250-nm PSF. Here, however, it was assumed that each piece of 10-kbplength was labeled with a different spectral signature. The visualiza-tion of the spectrally differentiated projections clearly suggests thatthese images contain structural information below the normal limit ofresolution. In the third row, the barycenters of the different spectralintensities were calculated according to the SPM method described inthe foregoing. In the end, this simulation example indicates that theSPM method should allow the topological analysis of relatively smallnucleosome configurations.


ab c

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

nearest-neighbor distance to otherlabel [nm]

cum

ulat

ive

frequ

ency

originaldata

afterimaging(n=42)

afterimaging(n=168)

d

e

f

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 400 800 1200 1600 2000

nearest-neighbor distance to otherlabel [nm]

cum

ulat

ive

frequ

ency

originaldata

after

imaging

(n=38)

afterimaging(n=152)

Figure 40.6: a Simulation dataset A; 500 FITC spots (i. e., spots carrying agreen spectral signature) and 500 CY5 spots (dark-red spectral signature) wererandomly distributed in a simulated nuclear volume with radii of 5.2 µm (xy)and 3.1 µm (z). The non-overlapping spots had a diameter of 440 nm; b thestandard deviation of nearest-neighbor distances (FITC to CY5) determined fordataset A from the true distances. The columns show the errors in distance de-termination with and without the ability to correct exactly for chromatic shifts; cthe distribution of nearest-neighbor distances between FITC and CY5 in datasetA. The systematic shift towards distances that are too high is due to the opti-cal merging of spots that are close to their neighbors in the same channel; dsimulation dataset B. 250 FITC spots and 250 CY5 spots were distributed in anuclear volume with radii of 9.6µm (xy) and 1.0µm (z). The minimum distancebetween spots was set to 1050 nm; e standard deviations of nearest-neighbordistances (FITC to CY5) determined for dataset B from the true distances. As allspots were found by the algorithm, the standard deviations give a true accountof the accuracies possible in lateral and axial direction; f the nearest-neighbordistance distribution of dataset B. A systematic shift is not detectable. (Reprintedfrom [21] with kind permission of the Royal Microscopical Society.)


As a second, more realistic example, Fig. 40.6 shows a computersimulation of the accuracy of distance measurements between differ-entially labeled targets in two-color confocal laser scanning microscopyconsidering experimental data for photon noise and error of chromaticshift determination [21]. Here, either a completely random distribu-tion of small targets with different spectral signatures within a nuclearvolume was assumed (Fig. 40.6a-c), or a random distribution was as-sumed with the boundary condition that the minimum distance be-tween any two pairs of the same spectral signature was at least oneFWHM (Fig. 40.6d-f). Under the assumptions used, the results of thesimulation indicated a standard deviation of 3-D distance determina-tion of about 50 nm, that is, about one-tenth the effective FWHM; 3-Ddistances far below the optical resolution can be determined correctlybetween targets of different spectral signature.

In analogous experimental high-precision measurements betweendifferentially labeled fluorescent targets, quartz glass beads of (mean± standard deviation (SD)) 1052 ± 19 nm with a green-yellow fluoresc-ing FITC core of 400 nm (target type I) were mixed with quartz glassbeads of 408 ± 22 nm with a red fluorescing RITC core of 200 nm indiameter (target type II), and attached to a cover slip. Besides clus-ters of beads of type I (FITC-fluorescence), clusters of beads of typeII (RITC-fluorescence) were obtained as well as pairs of a type-I beadand a type-II bead adjacent to each other. Three-dimensional imagingof FITC-fluorescence (specs1) and RITC-fluorescence (specs2) was per-formed with a commercial confocal laser scanning microscope. Theaxial chromatic shift (lateral chromatic shift was negligible comparedto the axial one) was measured using the two clusters of type-I andtype-II beads, respectively; the value obtained (225 ± 40 nm) was usedto perform the SPM-distance determinations for the barycenters of thetype-I type-II-pairs. For the experiment cited here, the mean 3-D dis-tance value determined by SPM was 732 ± 27 nm [29]; the value ex-pected was 734 ± 15 nm. More detailed SPM measurement using thesame types of quartz-glass beads with cores of different spectral sig-nature [21] indicated that in the range of 30 to 50 effective photonsper voxel (representing a biologically relevant photon statistics), thelateral distance error (SD) was around 20 nm whereas the axial errorwas between 50 to 75 nm.

40.3 Determination of the resolution equivalent in situ

The accuracy of the SPM method and thus the useful “resolution equiv-alent” (RE) is given by the capacity to control systematic errors such aschromatic and monochromatic aberrations and to control statistical er-rors such as deviations in positioning due to photon statistics, detector

40.3 Determination of the resolution equivalent in situ 853

noise, mechanical instabilities, unknown deviations in the optical mi-croconditions, etc. Besides the mechanical and optical parameters ofthe recording instruments, sophisticated computer-imaging algorithmsare of fundamental importance to obtain an optimal RE. For a direct insitu determination of the RE, let us in a thought experiment assume acell nucleus containing one “point-like” target tcal (for calibration); thistarget is simultaneously labeled with two spectral signatures specs1

(e.g., “green”), specs2 (e.g., “red”) in such a way that the barycenter co-ordinates of the fluorescence of specs1 and specs2 in the object spaceare identical, that is, “true” distances are much lower than the reso-lution equivalent envisaged. Experimentally, this can be realized withsufficient accuracy by molecular methods of fluorescence labeling, forexample, by multicolor FISH of the same genomic target sequence.

By spectrally discriminated registration with an optical system, forexample, a multichannel confocal laser scanning microscope, 3-D imagestacks for the intensities of specs1 and specs2 are obtained in the imageplane. If a system with negligible chromatic and monochromatic shiftsis used (or such deviations have been corrected for by independent cal-ibration measurements), the maxima of the image intensity curves I1for specs1 and I2 for specs2 (and hence their fluorescence barycenters)should coincide. Due to all kinds of errors (see the foregoing), however,the experimentally determined maxima (barycenter) positions for theintensity distributions I1 and I2 will be found at apparently differentlocations and hence indicate a spurious distance that does not exist inthe object space. Multiple measurements of this kind will eventuallygive a frequency distribution curve where the abscissa gives the (spuri-ous) distance measured and the ordinate the frequency of cases wherethis spurious distance was observed. Such a distance-error frequencycurve (“resolution equivalent (RE) curve”) will give a direct measure ofthe RE in situ, that is, under the relevant biological conditions to bestudied.

As an upper estimate of RE, we may take the full width at half max-imum of the distance-error curve (HW-DEC).

Figure 40.7 shows the result of a computer simulation of RE curvesassuming confocal 3-D imaging and a number of 6 and 30 effective pho-tons per voxel, respectively. The results indicate that using sufficientphoton statistics (realizable in biological labeling experiments) allow3-D REs much smaller than 100 nm. The HW-DEC using a maximum of30 photons/per voxel was 15 nm lateral and 45 nm axial. That gives a3-D RE of about 50 nm.


a

0

24

-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70

12

freq

uenc

y

distance [nm]

6 photonsin max.(x)

FWHM ~ 50nm

d

freq

uenc

y

in max.(x)

0

42

84

-30 -20 -10 0 10 20 30

distance [nm]

30 photons FWHM ~ 15nm

b

freq

uenc

y

distance [nm]

0

10.5

21

-120 -80 -40 0 40 80 120

6 photonsin max.(z)

FWHM ~ 160nm

e

freq

uenc

y

in max.(z)

distance [nm]

30 photons

0

18

36

-50 -40 -30 -20 -10 0 10 20 30 40 50

FWHM ~ 45nm

c

0

10

20

30

40

50

60

70

z-directionx-direction y-direction mean (nopreferencein direction)

erro

r (s

.d.)

[nm

]

FITC localization

TRITC localization

distance error

f

erro

r (s

.d.)

[nm

]

FITC localization

TRITC localization

distance error

0

10

20

30

50

60

z-directionx-direction y-direction mean (nopreferencein direction)

70

40

Figure 40.7: Computer simulation of the RE in situ; 250 simulated targets of160-nm diameter each were convoluted with a measured PSF of CLSM for afluorochrome with “green” spectral signature (FITC) and with “red” spectralsignature (TRITC), and noise was added. For each spot in the resulting FITC-image, the apparent distance to the nearest neighbor in the TRITC-image wascomputed after chromatic shift correction. The volume of a voxel was 80 × 80× 250nm3; a For the frequency of measured displacements between FITC- andTRITC- signals (distance-error frequency curve = RE-DEC curve) in x-directionassuming six photons in a voxel of maximum intensity, the values are distributedaround the true displacement zero. The full width at half maximum of thedistance-error frequency curve (HW-DEC)x is 50 nm; b the same as in a for thez-direction. The (HW-DEC)z is 160 nm; c error of localization and distance mea-surement (standard deviation) for FITC- and TRITC-images (6 photons in a voxelof maximum intensity); d the same dataset as in a,b,c was used, assuming 30photons in a voxel of maximum intensity. A (HW-DEC)x of 15 nm was obtainedfor the x-direction; e the same as in d for the z-direction. The (HW-DEC)z is45 nm; f error of localization and distance measurement (standard deviation)for FITC- and TRITC-images (30 photons in a voxel of maximum intensity).

40.4 Conclusions 855

40.4 Conclusions

Spectral precision distance microscopy (SPM) has opened the way to-wards an ultrastructural fluorescence far-field microscopy beyond thenormal limits of high-resolution microscopy. However, this was onlypossible because powerful computer hardware and sophisticated imageanalysis algorithms were available. Here, we highlighted the strong cor-relation between high-precision optics and high-end computing. Recentapplications in 3-D genome pathology have demonstrated the useful-ness of this approach using commercially available microscopes. Cal-ibrating and correcting the major parameters discussed in the forego-ing, which influence the localization accuracy and distance measure-ments, confocal laser scanning microscopy with lenses of high numer-ical aperture revealed a 3-D resolution equivalent of about 50 nm. Thisoffered a first glimpse into leukemia-relevant genome nanostructureson chromosome 9 and 22 (bcr-abl region; A. Esa, personal communica-tion) or chromosome 15 associated structures correlated to the Prader-Willi/Angelmann Syndrom (J. Rauch, personal communication). More-over, applying SPM to the recently developed SME microscope [19] ap-pears to make a resolution equivalent of less than 10 nm feasible be-cause a localization accuracy of 1 to 2 nm was reported [18]. Finally,it is anticipated that the general principle of SPM, that is, highly ac-curate localization of spectrally distinguishable targets in combinationwith sophisticated distance calibration and computer analysis, can beapplied to any optical micro- and macro-imaging technique.

Acknowledgments

The authors gratefully acknowledge the financial support of theDeutsche Forschungsgemeinschaft, the German Bundesminister for Ed-ucation, Science, Research and Technology (Human Genome Project)and the European Union (Biomed-Programme). For stimulating discus-sions the authors thank A. Esa, J. Rauch, Dr. L. Trakhtenbrot, Dr. Ch.Münkel, Prof. Dr. J. Langowski, and Prof. Dr. T. Cremer.

40.5 References

[1] Kreth, G., Muenkel, C., Langowski, J., Cremer, T., and Cremer, C., (1998).Chromatin structure and chromosome aberrations: modeling of damageinduced by isotropic and localized irradiation. Mut. Res. (in press).

[2] Cremer, T., Kurz, A., Zirbel, R., Dietzel, S., Rinke, B., Schroeck, E., Spe-icher, M. R., Mathieu, U., Jauch, A., Emmerich, P., Scherthan, H., Ried, T.,Cremer, C., and Lichter, P., (1993). Role of chromosome territories in thefunctional compartmentalization of the cell nucleus. Cold Spring Harb.Symp. Quant. Biol., 58:777–792.


[3] Comings, D. E., (1968). The rationale for an ordered arrangement of chro-matin in the interphase nucleus. Am. J. Hum. Genet., 20:440–460.

[4] Cremer, C., Muenkel, C., Granzow, M., Jauch, A., Dietzel, S., Eils, R.,Guan, X. Y., Meltzer, P. S., Trent, J. M., Langowski, J., and Cremer, T.,(1996b). Nuclear architecture and the induction of chromosomal aberra-tions. Mut. Res., 366:97–116.

[5] Muenkel, C., Eils, R., Imhoff, J., Dietzel, S., Cremer, C., and Cremer, T.,(1995). Simulation of the distribution of chromosome territories in cellnuclei under topological constraints. Bioimaging, 3:108–120.

[6] Sachs, R. K., van den Engh, G., Trask, B. J., Yokota, H., and Hearst, J. E.,(1995). A random-walk/giant loop model for interphase chromosomes.Proc. Natl. Acad. Sci. USA, 92:2710–2714.

[7] Lichter, P. and Cremer, T., (1992). Chromosome analysis by non-isotopicin situ hybridization. In Human Cytogenetics—a Practical Approach,D. Rooney and B. Czepulkowski, eds., pp. 157–192. Oxford: IRL-Press.

[8] Eils, R., Dietzel, S., Bertin, E., Schroeck, E., Speicher, M. R., Ried, T., Robert-Nicaud, M., Cremer, C., and Cremer, T., (1996). Three-dimensional recon-struction of painted human interphase chromosomes. Active and inactiveX chromosome territories have similar volumes but differ in shape andsurface structure. Jour. Cell Biol., 135:1427–1440.

[9] Rinke, B., Bischoff, A., Meffert, M. C., Scharschmidt, R., Hausmann, M.,Stelzer, E. H. K., Cremer, T., and Cremer, C., (1995). Volume ratios ofpainted chromosome territories 5, 7, and X in female human cell nu-clei studied with laser confocal microscopy and the Cavalieri estimator.Bioimaging, 3:1–11.

[10] Muenkel, C. and Langowski, J., (1998). Chromosome structure predictedby a polymer model. Phys. Rev. E, 57:5888–5896.

[11] Zirbel, R. M., Mathieu, U., Kurz, A., Cremer, T., and Lichter, P., (1993).Evidence for a nuclear compartment of transcription and splicing locatedat chromosome domain boundaries. Chromos. Res., 1:92–106.

[12] Stelzer, E. H. K., (1998). Contrast, resolution, pixelation, dynamic rangeand signal-to-noise ratio: fundamental limits to resolution in fluores-cence light microscopy. J. Microsc., 189:15–24.

[13] Rinke, B., Bradl, J., Schneider, B., Durm, M., Hausmann, M., Ludwig, H., andCremer, C., (1996a). in situ estimates of the spatial resolution for practicalfluorescence microscopy of cell nuclei. In Fluorescence Microscopy andFluorescent Probes, S. J, ed., pp. 169–173. New York Washington Boston:Plenum Press.

[14] Bradl, J., Rinke, B., Schneider, B., Edelmann, P., Krieger, H., Hausmann, M.,and Cremer, C., (1996a). Resolution improvement in 3D-microscopy byobject tilting. Microsc. Anal., 44(11):9–11.

[15] Cremer, C. and Cremer, T., (1978). Considerations on a laser-scanning-microscope with high resolution and depth of field. Microsc. Acta, 81:31–44.

40.5 References 857

[16] Hell, S., Lindek, S., Cremer, C., and Stelzer, E. H. K., (1994). Fundamentalimprovement of resolution by 4Pi-confocal microscopy. Appl. Phys., Lett.,64:1335–1337.

[17] Bailey, B., Farkas, D. L., Taylor, D. L., and Lanni, F., (1993). Enhancement ofaxial resolution in fluorescence microscopy by standing-wave excitation.Nature, 366:44–48.

[18] Hausmann, M., Schneider, B., Bradl, J., and Cremer, C., (1997). High-precision distance microscopy of 3D-nanostructures by a spatially mod-ulated excitation fluorescence microscope. Proc. SPIE, 3197:217–222.

[19] Schneider, B., Bradl, J., Kirsten, I., Hausmann, M., and Cremer, C., (1998).High precision localization of fluorescent targets in the nanometer rangeby spatially modulated excitation fluorescence microscopy. In Fluores-cence Microscopy and Fluorescent Probes, J. Slavik, ed., Vol. 2, pp. 71–76.New York: Plenum Press.

[20] Burns, D. H., Callis, J. B., Christian, G. D., and Davidson, E. R., (1985).Strategies for attaining superresolution using spectroscopic data as con-straints. Appl. Opt., 24(2):154–161.

[21] Bornfleth, H., Saetzler, K., Eils, R., and Cremer, C., (1998). High-precisiondistance measurements and volume-conserving segmentation of objectsnear and below the resolution limit in three-dimensional confocal fluo-rescence microscopy. Jour. Microsc., 189:118–136.

[22] Cremer, C., Hausmann, M., Bradl, J., and Rinke, B., (1996a). Verfahren zurmultispektralen Präzisionsdistanzmessung in biologischen Mikroobjek-ten. Vorläufige Patentanmeldung, Deutsches Patentamt.

[23] Cremer, C., Edelmann, P., Esa, A., Bornfleth, H., Schneider, B., Bradl, J.,Rinke, B., Trakhtenbrot, L., Dietzel, S., Hausmann, M., and Cremer, T.,(1998). Spektrale Präzisionsdistanzmikroskopie in der Genomforschung.Z. Med. Phys., submitted.

[24] Bradl, J., Rinke, B., Esa, A., Edelmann, P., Krieger, H., Schneider, B.,Hausmann, M., and Cremer, C., (1996b). Comparative study ofthree-dimensional localization accuracy in conventional, confocal-laser-scanning and axial tomographic fluorescence light microscopy. Proc. SPIE,2926:201–206.

[25] Moebius, A. E., (1827). Der barycentrische Calcul—ein neues Hülfsmittel.In Analytische Behandlung der Geometrie. Leipzig: J.A. Barth Verlag.

[26] Manders, E. M. M., (1997). Chromatic shift in multicolour confocal mi-croscopy. Jour. Microsc., 185:321–328.

[27] Edelmann, P., Esa, A., Hausmann, M., and Cremer, C., (1998). In situ deter-mination of the confocal point-spread function and the chromatic shiftsin intact cell nuclei. Optik (submitted).

[28] Rinke, B., Bradl, J., Edelmann, P., Schneider, B., Hausmann, M., and Cre-mer, C., (1996b). Image acquisition and calibration methods in quantita-tive confocal laser scanning microscopy. Proc. SPIE, 2926:190–199.

[29] Dietzel, S., Eils, R., Saetzler, K., Bornfleth, H., Jauch, A., Cremer, C., andCremer, T., (1998). Evidence against a looped structure of the inactivehuman X-chromosome territory. Exp. Cell. Res., in press.


Documents

40 Principles of Spectral Precision Distance Confocal ...€¦ · lar biology. He speculated that the chromosomes in the nucleus were ... (SPM) makes possible the measurement