Single Molecule Fluorescence Observation and Analysis: Cover Sheet ‘In the Laboratory’ Word Count: 2825 Ian R. Shapiro Division of Chemistry & Chemical Engineering California Institute of Technology Mail Code 127-72 Pasadena, CA 91125 phone: (626)-395-3909 fax: (626)-568-8824 [email protected]C. Patrick Collier (Corresponding Author) Division of Chemistry & Chemical Engineering California Institute of Technology Mail Code 164-30 Pasadena, CA 91125 phone (626)-395-8750 fax: (626)-568-8824 [email protected](Dated: December 18, 2006)
Transcript
Single Molecule Fluorescence Observation and Analysis: Cover Sheet
‘In the Laboratory’
Word Count: 2825
Ian R. ShapiroDivision of Chemistry & Chemical Engineering
California Institute of TechnologyMail Code 127-72
FIG. 3: Doubly-labeled double-stranded DNA sequence, showing donor and acceptor locations
relative to BglI restriction enzyme recognition site. Double stranded DNA identical in sequence to
that shown above but lacking the Texas Red label was also used.
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V FIGURES
E
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E
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FIG. 4: Typical histogram of FRET efficiency (E) values. Bursts were collected from a 100pM
sample of doubly-labeled DNA prepared as described in the experimental section. FRET efficiency
values were calculated from equation 1, and the average value (0.51) closely matched the expected
value calculated by the students in the prelab (0.55), assuming a 14-base-pair separation between
the dyes and taking into account he helical structure of DNA. Excitation was 400µW at 488nm.
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V FIGURES
0.8
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0.2 fra
ctio
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str
icte
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12001000800600400200
time (s)
10s time window
2s time window
FIG. 5: Restriction time course of 20nM DNA containing 200pM doubly-labeled DNA cut by 1U
BglI. For each data point the fraction of unrestricted DNA was calculated by counting bursts from
time windows of either 10-seconds (red triangles) or 2-seconds (blue circles) in duration.
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Single Molecule Fluorescence Observation and Analysis:
Supplemental Materials
Ian R. Shapiro, and C. Patrick Collier
Division of Chemistry and Chemical Engineering,
California Institute of Technology, Pasadena, CA 91125
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Chem 6: Physical Chemistry Laboratory
Single Molecule Fluorescence Spectroscopy
Summary
In this experiment you will use a microscope built on an open opticaltable to observe fluorescence emission from single fluorescent dyes anddye-labeled DNA. The single-molecule methods performed here willpermit the observation of properties otherwise obscured by averagingin ensemble experiments.
1 Introduction
Advances in techniques and instrumentation for optical microscopy over the past 15 yearshave led to the ability to detect and identify individual molecules in real time under am-bient laboratory conditions. Single molecule detection represents a significant advance inmeasurement capabilities that has led to the discovery of new phenomena in many areas inbiology, chemistry and physics. The ability to measure the dynamical properties of singlemolecules offers detailed knowledge that is hidden in bulk measurements due to averaging.This advantage is particularly useful in the study of complex systems. One can measuredistributions of molecular properties directly and determine if the distributions arise fromstatic heterogeneity or are due to dynamic fluctuations. Additionally, single molecule studiescan follow chemical, physical and biological processes in real time, and can capture transientintermediates that would be lost in bulk measurements due to the lack of synchronizationbetween many thousands of molecules.
The major difficulty in detecting signatures of single molecule fluorescence is due tothe background, not the sensitivity of the optical system. A fluorescent burst from a sin-gle molecule must be detected on top of a large background due to fluorescence and lightscattering from the solvent, glass coverslip and optical components. This background canbe minimized by reducing the probe volume since the fluorescence from a single moleculeshould be independent of this volume while the background will be linearly proportional toit. Typically, single molecule fluorescence detection relies on probe volumes of 10−12 L orless.
Confocal microscopy, which can achieve observation volumes as low as 10−15 − 10−16 Lrepresents an optical technique well suited for the observation of single molecule fluorescence.In a conventional wide-field microscope the significant depth of field of the objective resultsin high background intensity due to the collection of photons from planes other than the
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primary focal plane. In confocal microscopy, a pinhole aperture is situated behind theobjective lens at the intermediate image plane. This constrains the optical pathway suchthat only photons emitted from a small 3-dimensional volume pass through to the detectionoptics, as illustrated in figure 1.
True focal plane
}
sample
Pinhole
Intermediate
image plane
Objective lens
]
Detection
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True focal plane
}
sample
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Figure 1: Confocal optical pathway for an objective lens with finite focal length. Only light from the truefocal plane of the objective lens (red rays) can pass through the pinhole aperture at the intermediate imageplane and enter the detection optics. Light from above (blue rays) or below (green rays) the true focal planewill not converge at the intermediate image plane and will therefore fail to reach the detection optics. Formodern infinity-corrected objectives, such as the one we will use in this experiment, the ray paths will besomewhat different, but the basic principle is the same.
The spatial resolution of any optical microscope is ultimately limited by the wavelength ofthe observation light. Light passing through a uniformly illuminated circular aperture resultsin a diffraction pattern with a bright region in the center. This diffraction pattern, called thepoint spread function, defines what is measured by a microscope lens for an infinitely smallpoint-source in the sample. The bright center of the diffraction pattern is referred to as theAiry Disc. The point spread function has an analytical (and nontrivial) three dimensionalshape. It can be calculated from the diffraction pattern of the light rays passing through thevarious lenses of the microscopes optical pathway, as shown in figure 2. The dimensions ofthis diffraction pattern are governed by the numerical aperture (NA) of the objective lens,which is a figure of merit that describes the ability of an objective to gather light:
NA = n0sinθmax (1)
where n0 is the refractive index of the immersing medium (air, water, oil, etc.) andθmax is the half-angle of the maximum cone of light picked up by the objective. The higherthe N.A. of the objective the smaller the point spread function and the better the opticalresolution.
While the lateral (x-y) dimensions of the point spread function can be brought downto very near (and even less than) the wavelength of collected light by the use of a high
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numerical aperture objective lens, in the axial (z) dimension the point spread function ismuch larger when using conventional wide-field optics due to the collection of out-of-focuslight. In confocal microscopy, because the pinhole aperture and laser focus occur at conjugateplanes, the conventional point spread function is squared, resulting in both a modest increasein lateral resolution, and a large reduction of background light collection, as illustrated infigure 2. The resulting probe volume can be approximated as a prolate ellipsoid with minoraxes of diameter 1.22λ/NA (1 Airy) and major axis of diameter 2.5λ/NA.
-1 0
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Figure 2: Conventional (left) and confocal (right) point-spread functions generated by a 1.4 NA objectivelens focusing 488nm laser light.
The size of the confocal pinhole is an important parameter which influences the probevolume and observed signal-to-background. Lowering the pinhole size tightens the probevolume but also decreases the amount of detected light. Increasing the pinhole size permitsthe collection of more photons, but increases the probe volume and can therefore decreasethe signal-to-background ratio. In this experiment you will try a few different pinhole sizesin the range of 1-3 Airy disc diameters.
When a fluorescent molecule transits an excitation volume defined by a focused laserbeam (figure 3) tuned to an optical transition, it will be cycled many times between itsground and excited electronic states. Assuming the molecule emits a photon during each ofthese cycles, the maximum number of photons that can be detected with fluorescence is theratio of the transit time of the molecule in the probe volume with its fluorescence lifetime:
The fluorescence lifetime is important because the molecule must relax back to the groundstate before it can be re-excited. For typical values of τD = 1ms and τf = 1ns, Nmax = 106.This upper limit is seldom reached, however, since even the most photostable molecules tendto decompose before emitting 105 photons. The optical systems used in single molecule
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fluorescence studies typically have detection efficiencies of about 1% or lower, meaning thatbetween 10 and 1000 photons are generally detected when a molecule crosses the laser beam.These photons are detected as bursts, which aids in discriminating single molecule signalsfrom steady-state background fluorescence.
Figure 3: Schematic depiction of the detection of fluorescence bursts from a fluorescent molecule diffusingthrough a confocal observation volume.
The expected transit time of a molecule in the probe volume, as well as the probabilityof finding a single molecule in that volume at a particular time, can be calculated usingthe theory of diffusion controlled reactions. The three-dimensional translational diffusioncoefficient is given by
D =< x2 >
6τx
(2)
where < x2 > is the mean squared shift in particle position and τx is the time in which thedisplacement occurs. If the length of x corresponds to the radius of a spherical observationcavity of radious Rc, an encounter frequency of the particle can be calculated:
τR =1
4πRcDini
(3)
where Di is the particle diffusion coefficient and ni is the particle density. If the probecavity has a radius of 1µm (10−4cm) and if Di = 10−6cm2s−1 (a typical value for smallmolecules in water), a concentration of 10−12M molecules leads to τR = 1s. The averagetime a particle spends inside the spherical cavity is found in a similar way to be
τD =R2
c
3D(4)
or τD = 3ms using the above parameters. The ratio of τD and τR is simply the ratio of thevolumes of the light cavity and the average particle territory. It gives the average probabilityfor finding a molecule inside the probe volume (in this case, 0.003). (A spherical cavity isonly an approximation to the true shape of the 1/e2 Gaussian intensity profile at the focus,which is a elliptical volume element with half axes r and l.) For rapidly diffusing molecules
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in solution, the best experimental approach to detect single molecule fluorescence is to keepthe focused laser spot fixed and monitor fluorescence bursts as individual molecules diffuseinto and out of the probe volume. For slower or immobilized molecules, it makes more senseto scan the excitation volume relative to the sample. Only the former method will be usedin this experiment.
Fluorescence Correlation Spectroscopy
The amount of light emitted from a probe volume is generally proportional to the numberof fluorescent molecules in that volume. Probe volumes much larger than the volume ofthe average trajectory of a single particle may lead to large mean emission intensities, butinformation on the individual molecules will be lost. On the other hand, probe volumessmaller than the volume of a molecules territory will result in much less average fluorescence,but will produce large fluctuations in intensity. Fluorescence Correlation Spectroscopy (FCS)is based on the fact that the number of fluorescent particles in an ultra-small probe volumefluctuates in time, either by diffusion, transitions between fluorescent and non-fluorescentstates, or other chemical reactions. FCS uses an autocorrelation of the deviations in emissionintensity from the average to yield useful kinetic information. For example, the amplitudeof the autocorrelation function is inversely proportional to the number of molecules in theprobe volume, < N >, and the temporal decay of the autocorrelation function is indicativeof the time scale of the fluctuations. Given a time series of fluorescent intensity I(t), thenormalized autocorrelation function G(τ) is given by
G(τ) =< δI(t + τ)δI(t) >
< I(t) >2(5)
where the brackets <> indicate an average over time (usually the full data set). I(t)denotes the fluorescence intensity at time t, and δI(t) is the deviation of the fluorescenceintensity from the average and is given by δI(t) = I(t)− < I >. Intensity fluctuations attime t are multiplied by fluctuations at delayed times t + τ , and the product is integratedover a finite period of time. If the data has some memory, i.e. it is autocorrelated withina timescale τ , then positive fluctuations from the mean will tend to be followed by morepositive fluctuations, and negative by negative. This results in a nonzero value for G(τ). Ifthe data contains no autocorrelation, then positive fluctuations will tend to be followed byboth positive and negative fluctuations with equal probability. The sum of the products ofthese fluctuations will tend to cancel out, yielding a baseline value for the autocorrelation(this baseline is arbitrarily set to 1 by the hardware and software used in this experiment).Intuitively, G(τ) is the probability that a molecule detected in an observation volume attime t will also be detected in that volume at after some delay τ .
Additionally, the cross-correlation between two time series can indicate whether fluctua-tions within one series are correlated to fluctuations within the other. For example, if twocolor dyes are tethered to the same molecule, photons of one color will tend to be detectedat the same time as photons from the other color, and so the cross-correlation of the two
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channel intensities would be above baseline. If the two dyes were not tethered, there wouldbe no cross-correlation, although each individual channel would exhibit autocorrelation.
The autocorrelation function for the specific case of a molecule diffusing through a threedimensional Gaussian intensity profile I(x,y,z) with half axes r and l with
I(x,y,z) = I0e−2(x2+y2)/r2
e−2z2/l2 (6)
is given by
Gdiff(τ) = 1 +1
< N >(1 + (4Dτ/r2))−1(1 + (4Dτ/l2))−
1
2 (7)
where D is the diffusion coefficient and < N > is average the number of particles in theexcitation volume. The correlation function for a fluorescent molecule undergoing reversibleconversion between a bright state and a dark triplet state is given by
Gtrp(τ) = 1 − F + Fe−τ/τtrp (8)
where F is the fraction of dye molecules in the dark triplet state, and τtrp = (kbright +kdark)
−1, where kbright and kdark are the rate constants for conversion to the bright and darkstates, respectively. The full correlation function Gtot(τ) measured by the digital correlatoris the product of Gdiff and Gtrp, equation 9.
Gtot = 1 + [1
< N >(1 + (4Dτ/r2))−1(1 + (4Dτ/l2))−
1
2 (1 − F + Fe−τ/τtrp)] (9)
If the timescales of triplet conversion and diffusion are well separated (by at least twoorders of magnitude), they can be distinguished clearly in the autocorrelation data. Plottedon a log scale, the correlator output has the form depicted in figure 4. The values for < N >,τtrp, τdiff , and F can be calculated from the correlation curve as shown.
Forster resonance energy transfer (FRET)
When a fluorescent molecule absorbs a photon, it undergoes transition to a transient elec-tronically excited state. In the absence of other molecules with which to interact, the excitedelectron releases some of its absorbed energy in small, very fast non-radiative steps, mostlyinto vibrational degrees of freedom. Eventually, due to the constraints of the molecule’senergy manifold, the electron can lose no further energy in these small steps and becomesstuck in a local minimum. After a characteristic delay time τf the electron relaxes to theground state, releasing the remainder of its energy in a single radiative step which generatesan emitted photon of longer wavelength than the initially absorbed photon. If the emissionspectrum of the fluorescent molecule (which represents the probability distribution of elec-tron energies upon relaxation to the ground state) overlaps with the absorption spectrumof another nearby fluorescent molecule, there is some chance that the excited molecule willtransfer its energy to the second molecule. This energy transfer is due to dipole-dipole cou-pling between the two molecules, and is a purely non-radiative transition. The probability
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Figure 4: The autocorrelation function measured by the digital correlator for a dye molecule which is bothrapidly interconverting between dark and bright states, and freely diffusing through a diffraction-limitedconfocal observation volume. Adapted from Haustein and Schwille, Methods 29, 153-166 (2003).
of energy transfer from the donor molecule (D) to the acceptor molecule (A) is dependentupon three factors: the spectral overlap of the donor emission and the acceptor absorption,the separation of the two molecules, and the relative dipole orientations of the donor andacceptor. The closer the two molecules, the greater the spectral overlap, and the more closelytheir dipoles are spatially aligned, the greater the probability of energy transfer. For com-monly used FRET pairs, energy transfer is detectable for distances of less than 80A. Theradius at which energy transfer is 50% probable is termed the Forster radius, R0. At otherseparations R the energy transfer probability is given by equation 10.
E = (1 + (R
R0
)6)−1 (10)
Fluorescence burst analysis
If a single molecule containing a FRET pair transits a confocal observation volume, pho-tons will be detected in two colors with their average ratio being given by equation 10.
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The duration of the transit time, and subsequently the small number of photons collected(typically 10-1000) results in a distribution of calculated values for E. If plotted as a his-togram, the values for E have a Gaussian profile. Additionally, if the separation betweenthe donor and acceptor can fluctuate on timescales faster than the transit time, this canfurther broaden the distribution. However, if multiple molecular species with different D-Aseparations are present witin the sample, and the species either do not interconvert or in-terconvert at timescales longer than the transit time, their relative presence and positionwithin the full population can be resolved. This resolution of subpopulations is an exampleof a measurement made possible by single-molecule techniques which would otherwise beobscured by averaging in a bulk experiment.
For the sample we will use in this experiment, DNA labeled with the dyes Alexa Fluor488 and Texas Red 14 base pairs apart, typical data will look like that shown in figure 5.
E
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Figure 5: Histogram of energy transfer ratios.
2 Instrumentation
In this experiment you will use a homebuilt inverted microscope configured for epifluorescenceFCS using as the excitation source a continuous wave (cw) argon ion laser (Spectra Physics2060 RS). This laser can be tuned to several wavelengths in the visible range. (CAUTION:
this is a Class IV laser, which means it can produce enough power to injure or permanentyblind you. Use extreme care and protect yourself from accidental exposure from scatter orreflections!) For this experiment, the laser will be tuned to 488 nm, where AlexaFluor 488strongly absorbs.
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A schematic illustration of the microscopy setup is shown in figure 6. The laser beam isspatially filtered (for beam homogeneity) expanded and collimated with a simple telescopeand then reflected off a dichroic mirror which is more than 99% reflective at the excitationwavelength, but passes light at wavelengths longer than 497 nm. The fluorescence emissionfrom the samples we will be observing are 500-700nm, and therefore will pass through thedichroic mirror with minimal loss. The reflected laser light then enters the back aperture ofa 60x oil-immersion microscope objective that has a numerical aperture of 1.4. Fluorescenceemitted from the sample exits the objective, passes back through the dichroic mirror, and isfocused by a second lens to form the intermediate image plane where the pinhole is located.Because this second lens has a focal length of 150mm in our experimental setup, comparedwith a conventional tube lens focal length of 200mm (for Nikon objectives), the effectivemagnification of the system is 45x (150
200∗ 60x). An Airy disk of 550nm light at intermediate
image plane therefore has a diameter of 45∗2∗550∗10−9
1.4= 21.5 µm. The pinholes we will use
are in the size range of 25-75 µm, or about 1-3 Airy.
Figure 6: Diagram of the optical pathway in the microscope you will use.
Light passing through the pinhole aperture is then collimated by a second lens, and splitinto red and green wavelengths by a 565nm dichroic mirror. Photons of wavelength lessthan 565nm reflect off the dichroic, pass through a green filter (530/30 bandpass) , andare focused by a final 60mm f.l. lens onto the active element of an avalanche photodiode(detector 1). Photons of wavelength greater than 565nm pass through the dichroic and a
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separate red filter (630/50 bandpass), and are focused onto a second APD (detector 2). Eachindividual photon is converted by the APD to an electrical pulse (‘TTL pulse’) about 2.5Vin amplitude and 33 ns in duration. These electrical pulses are sent to a computer controlledmultichannel scaler (MCS) card and a digital autocorrelator. The MCS card counts TTLpulses from the detector and integrates them within time bins set by the user. We willuse the software MCS-32 to record and save photons counted by the MCS cards. When anAPD generates a TTL pulse, there is a small probability that it will also generate a spurioussecond TTL pulse, called an afterpulse, within a few hundred nanoseconds. This results inan experimental artifact within the correlator data at very short timescales, and can interferewith interpretation of correlator data for τ < 1µs.
The fundamental operations of a digital correlator are:
• counting of photoelectron pulses over sampling time intervals of width t,
• delaying these samples for some integer multiple of t, the lag time τ = k ∗ t,
• multiplying delayed and direct data samples,
• summing these products.
The final 2 steps are typically done for many different delays in parallel. A correspondingnumber of channels are used to keep the results of these computations. Each point in thecorrelation trace is continuously updated in real time using this algorithm to compute G(τ).Correlation date will be collected using the program called Flex5000.
3 Prelab
Recommended Background Reading
• Schwille, et al, Ultrasensitive investigations of biological systems by fluorescence cor-relation spectroscopy. Methods 29, 153-166 (2003)
• Schultz, et al, Single-pair fluorescence resonance energy transfer on greely diffusingmolecules: Observation of Forster distance dependence and subpopulations. Proc.
Nat. Acad. Sci. 96, 3670-3675 (1999)
Prelab Questions
If you have any trouble answering these questions, try a Google search or two using appro-priate search terms, or contact your TA.
1. The hydrodynamic radius of fluorescein in water is 0.4 nm. What is the diffusioncoefficient, D, at 25◦C? The viscosity of water is 0.891 cP.
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2. An FCS experiment yields N = 0.04 for the average number of fluorescein molecules inthe probe volume and a diffusion time of 0.28 ms. Assuming the probe volume can beapproximated by a spherical cavity, what is the effective radius? What is the averagetime between encounters of particles with the cavity? What was the concentration (inmoles/L) used?
3. Based on the expected encounter frequency and residence time from question (2) qual-itatively describe how one would use fluorescence bursts from the multichannel scalerin real time to identify different individual particles crossing the probe volume. Howwould one identify multiple re-crossings into the cavity of the same particle?
4. If the AlexaFluor 488 and Texas Red are spaced by 14 base pairs on the DNA oligomer,what value for E would you expect to see? Use eqn. 10. Keep in mind the helicalnature of DNA. The Forster radius, R0 for AF488/TR is 54A.
5. Experimentally, the effective energy transfer ratio (E) of each fluorescence burst iscalculated using equation 11:
E =(A − bA)
γ ∗ (D − bD) + (AbA)(11)
where A is the acceptor channel signal photon count for that burst, D is the donorchannel count, bA and bD are the acceptor and donor background signals, respec-tively, and γ is a term accounting for the difference in photon collection efficienciesbetween the donor and acceptor channels. γ is the ratio between the fraction of theacceptor emission spectrum collected by the microscope to the fraction of the donoremission spectrum collected by the microscope. Use the following web application toestimate γ, assuming that we will use a 530/30 bandpass filter to collect photons for thedonor channel and a 630/50 bandpass filter to collect photons for the acceptor channel:http://probes.invitrogen.com/resources/spectraviewer/
4 Experimental Procedure
• Obtain sample stocks and buffer from your TA. You will prepare all samples in buffercontaining 25mM Tris, pH 7.5, 100mM NaCl, 10mM MgCl2, and 0.5mM propyl gal-late (to reduce photobleaching). Prepare 0.1nM and 1nM samples of the following:AlexaFluor 488 free dye and AlexaFluor 488 labeled DNA. Prepare a 0.1nM sample ofDNA labeled with both AlexaFluor 488 and Texas Red, as well as a 0.1nM sample ofthis doubly-labeled DNA plus 20nM unlabeled DNA.
• Turn on the water chiller and check for water flow through the ion laser. Turn on ionlaser, set current for 30A and turn off beamlock. Output shutter should be closed andthe aperture set to #6. Allow laser to warm up for at least 15 min. You may need toadjust the laser alignment periodically for the first hour.
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• Clean the optical surface of the 60x objective lens using folded lens tissue paper soakedin acetone. Drag the lens tissue across the lens surface gently and avoid scratching theoptic. Put 1 drop of immersion oil on the objective.
• Place a clean glass coverslip on the stage and mark the surface with orange hi-liter ink.Turn off the room lights, and place a neutral density filter with OD 6.0 in the laserbeam path. Adjust the focus until the immersion oil contacts the bottom surface of thecoverslip. Then, looking through the microscope eyepiece, adjust the focus graduallyuntil you see a single orange spot.
• Plug in the power to the both APDs and open the multichannel scaler (MCS) programon the desktop of the computer. In the MCS program, select device 1 and set the‘trigger to internal, and the pass preset to off. Set a pass length of 1000 bins and a binsize of 1ms. Set the vertical axis to log scale. Select device 2 in the MCS program, anduse the same settings as for device 1, but set trigger to external. This will synchronizethe second MCS with the first MCS card.
• Remove the mirror directing light to the eyepiece, and observe the signals displayedby the MCS traces for both color channels. Carefully adjust the focus of the objective,the position of the pinhole, and the position of each APD to maximize the signal. Thetrick to getting good FCS data is to get the laser excitation focus to match up exactlywith the observation volume defined by the pinhole. Remember that both of these aresituated in three dimensions. With laser attenuation of OD 6.0, you should be able toobtain about 5000 counts/ms in each color channel.
• Obtain one of the clean PDMS wells prepared by your TA, place it on the samplestage, and add 50ul of your first sample. Place a coveslip on top of the PDMS well toprevent buffer evaporation. Reduce the laser attenuation to OD 2.0.
• Check the green channel MCS trace to see if you are collecting discrete fluorescencebursts. Collect an autocorrelation trace for the green channel using the correlatorsoftware with 30s integration time.
• The first data point in the correlation trace is much higher than the trend in the curve.This is caused by afterpulsing in the APD. Afterpulsing is the random generation ofa secondary electron avalanche in the detector caused by the electronics, and occurswithin a few hundred nanoseconds of the primary avalanche generated by the arrivalof an actual photon. This causes a strong false autocorrelation at short times. Whenyou fit the data, you will need to replace the first few data points for correlation timesbelow 1µs with the value at 1µs.
• Save your correlation trace in the data folder on the desktop. If you save more thanonce, you will need to use ‘Save As’ or the original data will be overwritten. Alsocapture an image showing discrete fluorescence bursts from the MCS by hitting thestop button and saving the file in the Ch6 data folder.
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• Vary the laser attenuation between ND2.0 and 4.0, collecting an autocorrelation traceat each power and noting any changes in the intensity of the fluorescent bursts and theratio of the burst intensity to the background intensity.
• Once you have good data for the free AlexaFluor 488 dye, remove the PDMS well fromthe microscope stage and prepare a second sample. For both concentrations of freeAF488 and AF488-labeled DNA, collect autocorrelation traces for a few different laserattenuation values.
• When you proceed to the sample of doubly-labeled DNA, collect autocorrelation tracesand MCS traces for both color channels. Also collect a cross-correlation trace.
• Open the LabView program for this lab and set the bin time to a value between 100µsand 5000µs. Collect fluorescence bursts using this program for 1-5 minutes at a time,and record the saved file names. Load these files in Matlab and process them withthe BurstAnalysis script. Compare the resulting histogram with your expected valuefor E. Collect burst data and perform the burst analysis while varying both the bintime and the laser attenuation. Remember the parameters which yield the best lookingburst analysis data: a relatively smooth histogram centered near E=0.5, with as smalla peak as possible at E=0.
• While keeping these optimal measuremen conditions, prepare a final PDMS well for thesample of doubly-labeled + unlabeled DNA. Before adding the sample to the PDMSwell, add BglI enzyme sufficient to give a concentration of about .02 U/µL (about 1 Utotal) in the sample. Immediately mix the sample, and then load 50µL into the well.Using the LabView program, begin collecting a single 20-minute data series. You canwork up other data in Matlab during this collection.
• Finally, before leaving the lab, remove all neutral density filters from the laser beampath, and use the optical power meter to measure the laser power between the primarydichroic mirror and the microscope objective. Use this value to calculate the laserpower used for each measurement.
5 Analysis and Writeup
• Plot and display all correlator data collected. The correltion data is saved as a textfile– use the data from the two columns directly underneath the label ‘correlation’. Thefirst column is time in units of milliseconds. The second column is the autocorrelation.Cut and paste these columns into whatever graphical analysis program you will use tofit the correlation trace. We use Igor and Matlab which will be available. If you wantto use these programs contact your TA.
• Use your autocorrelation data for each sample to measure the number of moleculesin the probe volume < N >, the diffusion coefficient D, as well as Ftrp and τtrp if
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indications of triplet blinking are observed. Discuss any variation of the autocorrela-tion function with laser excitation intensity. Given the nominal concentration of eachsample, calculate the confocal observation volume and compare your measured valuewith that which would be generated by optimally diffraction-limited optics. Discussany discrepancies. Identify afterpulsing artifacts and consider their influence on themeasured data. What are are other possible sources of error?
• Compare the measured values of D and τtrp for the free AF488 dye and AF488 tetheredto DNA. Discuss any observed differences.
• Similar to the third prelab question, rationalize the appearance of the fluorescenceburst data from the MCS in terms of the average number of molecules detected fromFCS and your best estimates for the residence times and encounter frequencies of theparticle with the probe volume.
• Plot and discuss the auto- and cross-correlation data measured for the doubly-labeledDNA. Use the Matlab script provided by your TA to identify fluorescence bursts andplot the resulting histogram of energy transfer ratios (E). Does the histogram resolveseparate populations of labeled DNA? How does the average observed E compare withthe value you calculated in prelab question 5? Account for any discrepancies.
• Using the Matlab enzyme kinetics script, plot and discuss the observed changes indoubly-labeled DNA over time. Discuss the relationship between time resolution andnoise when analyzing this data.
6 Further Reading
Confocal Microscopy
• Webb, Robert H. Confocal optical microscopy. Rep. Prog. Phys. 59, 427-471 (1996)
Clean standard #1 25mm square coverslips by placing in a teflon holder and immersing in a solutionof freshly-prepared ‘Piranha Solution, which is 70% conc. H2SO4 + 30% conc. H2O2. CAUTION:
fresh piranha solution is highly oxidizing and reacts violently with most organic material. Sonicatethe immersed coverslips for 30 minutes, then rinse thoroughly with MiliQ water. Prepare PDMSholders by curing a ∼4-5mm deep slab of RTV-615 (10:1 A:B) at 80◦C overnight, then cuttinginto ∼5mm squares. Using a standard paper hole puncher, punch a single hole in each PDMSsquare. Rinse with methanol, then place each square on a cleaned coverslip and bond overnightat 80◦C. After bonding, further clean each PDMS well with a 2:1:1 H2O/HCl/H2O2 solution for20 minutes. Rinse with MiliQ H2O, thoroughly dry by blowing with N2, and then place ∼60µl ofneat PEG-Silane in each well. The PEG-Silane may be left in the PDMS well for up to 48 hours.Before use, throughly rinse each well to remove PEG-silane.
Microscope preparation
Alignment of the focused laser spot at the sample plane with the pinhole positioned at the imageplane is accomplished by maximizing the signal collected from a thin layer of fluorescent hi-lighterink on a glass coverslip. While exciting the thin fluorescent layer with very low power 488nmlaser light (∼50nW), adjust the pinhole position iteratively in 3 dimensions until maximum photoncounts are achieved in both color channels. Adjust the position of each APD in 3 dimensions toconfirm that all collected light is focused onto the ∼500µm2 active element. The sudents will repeatthis portion of the alignment procedure, but it is a good idea if the pinhole alignment is alreadyclose. They should have a hands-on experience adjusting the position of the pinhole using the 3-Dmicrometers while observing the optical throughput. However, minimal time (5 minutes) shouldbe spent on this step.
Sample Preparation
If necessary, prepare sample buffer ahead of time. Sample buffer consists of 25mM Tris, pH 7.5,100mM NaCl, 10mM MgCl2. 50mM Propyl Gallate stock should be made up before each lab sessionusing HPLC-grade methanol. Within 24 hours the stock will start to turn yellow and should bediscarded. Prepare or obtain from the -20◦C freezer 2µM stocks of free AF488 dye and labeledDNA. The students will prepare their own samples using these stocks.
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Fitting Autocorrelation Data
In the lab writeup, students are asked to fit the autocorrelation traces to the equation (9) providedin the lab handout:
Gtot = 1 + [1
< N >(1 + (4Dτ/r2))−1(1 + (4Dτ/l2))−
1
2 (1 − F + Fe−τ/τtrp)] (1)
Igor is recommended for performing the fit. The fitting function is nonlinear and involves 6unknowns (N, D, r, l, F, τtrp), and as a result the fitting procedure is somewhat unstable. Igorrequests initial guesses for the unknown parameters, and close guesses improve the likelihood of afit. Figure in the lab handout provides a means to estimate values for N, D, F and τtrp. Initialguesses for r and l are 1.22λ/NA and 2.5λ/NA, respectively, although achievement of these idealvalues for the actual observation volume dimensions is dependent upon use of a 1-Airy pinhole (∼20µm) and precise alignment of the pinhole with the laser focus. In practice r and l may end upbeing larger.
It may be necessary to first perform the nonlinear fit in a piecewise manner by holding somefit parameters constant while allowing Igor to determine the others. For example, hold r, l, N andD at the initially guessed values while allowing Igor to fit F and τtrp . Then, use Igors values forF and τtrp as the initial guesses, and perform the fit for the other parameters. If the collectedautocorrelation data is noisy for small-τ values, exclude the first 5-10 data points from the fit.
The diffusion coefficient for the free AlexaFluor dye is about 6.1e−6cm2s−1, and the diffusioncoefficient for the dye-labeled DNA is about 1.4e−6cm2s−1. However, it is important to note thatthe time units of the autocorrelator data are milliseconds. Whichever units are used for l and r inthe fitting procedure will provide the length units of the diffusion coefficient. The students shouldbe reminded to convert the resulting fit values for D to units of cm2s−1. For Alexa Fluor 488 thetriplet fraction F will vary from about 0.5 at 500µW excitation power to 0.2 at 5µW excitationpower, with τtrp being about 20µs.
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Answers to Prelab Questions
1. Answer: Using the Stokes-Einstein equation: D = kT6πηRH
, we obtain a value of:
1.38e−23m2kgs−2K−1∗298K
6∗π∗.891e−3kgm−1s−1∗4e−10m
= 6e−10m2s−1
2. Answer: Calculate radius: r = (D ∗ τd).5 = (6e−10m2s−1 ∗ .63e−3s).5 = 6e−7m, or 600 nm
Calculate concentration: .04(6e23
∗(10∗6e−7)3) ∼ 3e−10M , or 300 pM
3. Answer:
250
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0
28.128.027.927.827.7
t >> tR
separate molecules
t << tR
same molecule
time
photon
counts
250
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28.128.027.927.827.7
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28.128.027.927.827.7
t >> tR
separate molecules
t << tR
same molecule
time
photon
counts
Figure 1: Cartoon illustration of expected fluorescence burst encounters.
4. Answer: Each base pair constitutes 3.3 A, and so the separation along the DNA backbone is 14∗3.3 =46.2A. Additionally, The dyes are almost exactly one and a half helical turns apart. The diameter ofordinary B-type DNA is 23.7 A. Therefore r (46.22+23.72).5 = 52A. And so E = (1+(52/54)6)−1 = .55
5. Answer: γ = 61.4/48.5 1.3
Figure 2: Screenshot from http://probes.invitrogen.com/resources/spectraviewer
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Matlab script, as provided to students (manuscript p.8), used for identifying fluorescence bursts within a two-color data set and plotting the corresponding histogram of FRET efficiencies. --------------------------------------------------------------------------------------------------------------- green=A152216green; % use appropriate file name for green data % red=A152216red; % use appropriate file name for red data % th=100; % set burst threshold intensity % gamma=1.3; % set gamma value s=size(green); % check number of points in data stream % FRETS=0; % reset FRET count l=0; % reset burst count % for j=1:s(1) % for each bin within the data stream % if green(j)+red(j)>th+gb+rb % if bursts is above threshhold + background% l=l+1; % increment burst count % FRETS(l)=(red(j)-rb)/( gamma*(green(j)-gb) + red(j)-rb ); % calc FRET ratio% end end hist(FRETS,30) % plot histogram % ---------------------------------------------------------------------------------------------------------------
Matlab script, as provided to students (manuscript p.8), used for following the cleavage of a FRET-labeled DNA oligomer undergoing enzymatic restriction. ------------------------------------------------------------------------------------------- green=A152216green; % use appropriate file name for green data % red=A152216red; % use appropriate file name for red data % th=100; % set burst threshold intensity % gamma=1.3; % set gamma value delay=15; % estimated delay time before beginning data collection % s=size(A154630green); % use appropriate filename% bs=.001; % bin size in seconds % window=7000; % number of bins in each observation window% pts=round(s(1)/window); % number of time points which will be collected% FRAC=zeros(pts-1,2); % initialize array of appropriate size % PEAKS=zeros(pts-1,2); % initialize array of appropriate size % for i=1:pts-1 % for each time window % FRAC(i,1)=(i-1)*window*bs+delay; % put time (seconds) into first column of array% PEAKS(i,1)=(i-1)*window*bs+delay FRETS=0; % reset array of FRET values % l=0; % reseat burst count % for j=1+(i-1)*window:1+i*window % for each bin within the time window % if green(j)+red(j)>th+gb+rb % if bursts is above threshhold + background% l=l+1; % increment burst count % FRETS(l)=(red(j)-rb)/( gamma*(green(j)-gb) + red(j)-rb ); %calc FRET ratio% end end fp=0; % fp is # of FRET bursts% for k=1:l % for each element of the FRET array% if FRETS(k)>.20 & FRETS(k)<.90 % check to see if E is within the range for a doubly-labeled DNA% fp=fp+1; % increment FRET burst count% end end FRAC(i,2)=fp/l; % calculate fraction of bursts which are from doubly-labeled DNA% PEAKS(i,2)=l; % keep track of number of bursts counted in that window% end subplot(2,1,1) plot(FRAC(:,1), FRAC(:,2)) % plot timecourse of uncut DNA fraction% subplot(2,1,2) plot(PEAKS(:,1), PEAKS(:,2)) % also plot number of bursts detected within each window% -------------------------------------------------------------------------------------------
