Raster Image Correlation Spectroscopy and Number and Brightness Analysis

Transcription

1 Raster Image Correlation Spectroscopy and Number and Brightness Analysis 15 Principles of Fluorescence Course Paolo Annibale, PhD On behalf of Dr. Enrico Gratton

2 lfd Raster Image Correlation Spectroscopy We can have a combination of very high time resolution with sufficient spatial resolution. Major benefits of RICS: It can be done with commercial laser scanning microscopes (either one or two photon systems) It can be done with analog detection, as well as with photon counting systems, although the characteristic of the detector must be accounted for (time correlations at very short times due to the analog filter) RICS provides an intrinsic method to separate the immobile fraction It provides a powerful method to distinguish diffusion from binding How does it work?

3 lfd Raster Scanning Pixel time Start here Line time + retracing time

4 Spatial correlation Temporal information hidden in the raster-scan image: the RICS approach lfd Situation 1:slow diffusion Slower diffusion Faster diffusion Situation : fast diffusion Pixel

5 lfd How is the spatial correlation done? (,) (,55) (x,+y) (,55) Image 1 x Image 1 shifted Matrix 1 Matrix Operation: Spatial Correlation Results In the x direction PLUS In the y direction (,,) (,1,1) (,,)...(,17,17) ( 1, 1,) (1,1 1,1) (1, 1,)...(1,171,17) One number is obtained for x and y and is divided by the average intensity squared

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7 lfd How to use a stack of images? (,) (,55) FRAME #1 Spatially correlate each frame Individually then take the average of all the frames (,) (,55) (,) (,55) (,) (,55) (,) (,55) (,) (,55) FRAME #1 FRAME #1 FRAME #1 FRAME #1 FRAME #1

8 lfd The RICS approach: -D spatial correlations In a raster-scan image, points are measured at different positions and at different times simultaneously G RICS If we consider the time sequence, it is not continuous in time If we consider the pixel sequence, it is contiguous in space In the RICS approach we calculate the -D spatial correlation function (similarly to the ICS method of Petersen and Wiseman) I( x, y) I( x, y ) (, ) 1 I( x, y) The variables and represent spatial increments in the x and y directions, respectively -D spatial correlation can be computed very efficiently using FFT methods. To introduce the RICS concept we must account for the relationship between time and position of the scanning laser beam.

9 lfd The RICS approach for diffusion The dynamic at a point is independent on the scanning motion of the laser beam G RICS (, ) S(, ) xg(, ) Consider now the process of diffusion. The diffusion kernel can be described by the following expression P( r, t) 1 (4Dt) 3/ exp( r ) 4Dt FAST There are two parts: (1) the temporal term, () the spatial Gaussian term SLOW For any diffusion value the amplitude decreases as a function of time and the width of the Gaussian increases as a function of time

10 lfd 1 1 ) ( 4 1 ) ( 4 1 ), ( z l p l p w D w D N G At any position, the ACF due to diffusion takes the familiar form: τ p and τ l indicate the pixel time and the line time. The correlation due to the scanner movement is: ) ) ( 4 (1 ] ) ( ) [( exp ), ( w D w r w r S l p Where r is the pixel size. For D= the spatial correlation gives the autocorrelation of the PSF, with an amplitude equal to /N. As D increases, the correlation (G term) becomes narrower and the width of the S term increases. RICS: space and time relationships Digman et al. Biophys. J., 5 Spatial correlation Faster diffusion Pixel Slow diffusion AutoCorrelation plot (log averaged) Tau (s) 14e-6 14e-5 14e-4 14e-3 14e- G(t)

11 RICS Simulations of three different diffusion rates: Box size=3.4µm sampling time: 1) 3µs/pixel ) 8µs/pixel 3) 4µs/pixel D =.1 µm /s (membrane proteins) D = 5. µm /s (4 nm beads) D = 9 µm /s (EGFP)

12 g() g() lfd Horizontal and Vertical fits: Simulations of beads 3 frames, 18x18pixels, 8s/pix, size of pixels=3nm Horizontal ACF Vertical ACF D = 1 D = 1 D = 1 D = D = 1 D = 1 D = 1 D = ( m) In SIMFCS ( m) Brown et al, JMI, 7

13 lfd How to Setup the Laser Scanning Confocal Microscope Scan Speeds (s/pixel): 4s for fast molecules D >1m /s 8-3s for slower molecules D= 1 m /s-1m /s 3-1s for slower molecules D=.1 m /s-1m /s Pixel Size: 3-4x smaller than the Point Spread Function (PSF~3nm) Molecular Concentrations Same conditions as conventional FCS methods

14 Courtesy of Jay Unruh lfd Common Errors in RICS Scanning Too Slow (1 us/pixel, D = 3 um /s) Pixels are separated too much relative to PSF (pixel size = w =.3 um)

15 y-coordinate RICS: Fits to spatial correlation functions Olympus Fluoview3 LSM x-coordinate EGFP in solution Spatial ACF 18x18, 4 s/pixel, 5.4 ms/line,.3 m/pixel Fit to Spatial ACF D = 15 ± 1 m /s Digman et al. Biophys. J., 5

16 D (m /s) g() average What ROI size to use? How many frames to acquire? x56 18x18 64x64 3x3 1nM megfp ROI size Size of ROI square (pixels) 1nM megfp Number of Frames Analyzed 5 frames 1 frames 75 frames 5 frames 5 frames 1 frames 1 frame Brown et al, JMI, 7

17 Concentration via RICS Obtaining concentration from RICS Fluorescein in 1mM TRIS ph 9 y =.86x R = Concentration via Absorbance (nm) Brown et al, JMI, 7

18 lfd How we go from solutions to cells? In cells we have an immobile fraction The -D-spatial correlation of an image containing immobile features has a very strong correlation pattern We need to separate this immobile fraction from the mobile part before calculating the transform How is this achieved?

19 lfd Does noise from the detectors correlate? In a truly immobile bright region, the intensity fluctuates according to the Poisson distribution due to shot noise. The time correlation of the shot noise is zero, except at time zero. The spatial correlation of the intensity at any two pixels due to shot noise is zero, even if the two points are within the PSF. If we subtract the average intensity and disregard the zero timespace point, the immobile bright region totally disappear from the correlation function Attention!!!! This is not true for analog detection, not even in the first order approximation. For analog detection the shot noise is time (and space) correlated. Photon counting: ACF of a bright immobile particle Analog detection: ACF of a bright immobile particle t t

20 lfd Formula used to subtract background: y x Spatial Correlation Average intensity of each pixel on the overall stack: I i ( x, y) I( x, y) Subtract the average I( x, y) Spatial Correlation of entire image After subtracting image The intensity of each pixel minus the average intensity from entire stack for each pixel: However, this yields negative values. A scalar must be added : Spatial correlation before subtracting background a I ICS( F ( x, i y)) where F ( x, i y) I ( x, y) I( x, y) i a

21 Intensity lfd How to subtract immobile features from images? Intensity profile Pixels

22 Intensity Intensity Immobile feature Pixels line Average of the image including the immobile part Average of the sea of molecules only Intensity after removal Intensity before removal Pixels line

23 Intensity lfd Subtraction of moving average End of the analysis Start the analysis Frames

24 lfd Moving average operation on frames: Frame #5 Average between = Matrix1 Matrix A scalar average is then added Operation is repeated for frame #6 - average between -11 frame #7 - average between 3-1

25 y-coordinate y-coordinate Example of the Removal of Immobile Structures and Slow Moving Features lfd x-coordinate Spatial ACF No removal Spatial correlation-average What is left after removal Spatial ACF With removal Fit using 3-D diffusion formula Pixel size =.9μm Pixel time= 8 μs Line time = 3.15 ms Wo =.35 μm G1() =.6 D1 = 7.4 μm /s G() =.3 D =.54 μm /s Bkgd = -.115

26 G() lfd Small Molecule Cytosolic Protein Conclusions Transmembrane Protein RICS Large Protein Aggregates (s) Line msec Pixel sec t=3 t= t=1 t= t=n T-ICM Sec to min FCS Line Scan Temporal correlation RICS Temporal ICM Techniques Time Res. Spatial Res. Used to Study Temporal-ICM sec <.5 m Protein aggregates Transmembrane proteins RICS sec-msec ~ m Soluble proteins Binding interactions Line-RICS msec <.5 m Soluble proteins Binding interactions

27 lfd Summary of RICS Measures dynamic rates from the sec-sec time scale Anyone with a commercially available instrument can use it Immobile structures can be filtered out and fast fluctuations can be detected RICS has high spatial and temporal resolution The range of these dynamic rates covers a wide range from immobile to cytosolic diffusions (.1-3um /s) Other types of processes and interactions are also measured Line scanning is essential for determination of binding process and complements the RICS analysis

28 Existing Methods to determine protein concentration and aggregation of proteins in cells 1. Calibration of the free fluorophore based on intensity A INTENSITY 31,5counts/sec B 93,75 counts/sec Average intensity of MEF cells expressing Paxillin-EGFP If free EGFP at 1nM gave 3, counts/sec then the conclusion would be that : A =1nM B = 3nM However, it doesn t give you the size distribution Only concentration is given

29 . Förster resonance energy transfer (FRET) This method is very sensitive to detect the formation of pairs.

30 3. Image correlation Spectroscopy (ICS) However, the events must be slow >1sec (no movement during one frame) and the aggregates must be large. Petersen and Wiseman:Biophys J. 1999

31 The Number and Brightness (N&B) analysis Purpose: Provide a pixel resolution map of molecular number and aggregation in cells Method: First and second moment of the fluorescence intensity distribution at each pixel Source: Raster scanned image obtained with laser scanning microscopes TIRF with fast cameras Spinning disk confocal microscope Output: The N and B maps, B vs intensity D histogram Tools: Cursor selection of pixel with similar brightness Quantitative analysis of center and std dev of the e and n distribution Tools for calibration of analog detectors Tutorials: mathematical background, data import, analysis examples (our web site)

32 Frequency Frequency Intensity (kcps) Intensity (kcps) How to distinguish pixels with many dim molecules from pixels with few bright molecules? Average first moment) k i K k i at pixel k Time (s) k at pixel j Time (s) Variance s cond moment) i ( k i K k ) s 19.4 khz 19.4 khz Given two series of equal average, the larger is the variance, the less molecules contribute to the average. The ratio of the square of the average intensity (<k> ) to the variance (s ) is proportional to the average number of particles <N>. * Originally developed by Qian and Elson (199) for solution measurements.

33 Calculating protein aggregates from images This analysis provides a map of <N> and brightness (B) for every pixel in the image. The units of brightness are related to the pixel dwell time and they are counts/dwell time/molecule. k i K k i s i ( k i K k ) B k N s k N k s s = Variance <k>= Average counts N = Apparent number of molecules B = Apparent molecular brightness K = # of frames analyzed

34 G() Selecting the dwell time To increase the apparent brightness we could increase the dwell time, since the brightness is measured in counts/dwell time/molecule. Increasing the dwell time decreases the amplitude of the fluctuation..4 1 s dwell time 1 ms dwell time Time(s)

35 What contributes to the variance? Variance due to particle number fluctuations Variance due to detector shot noise n s s d n n The measured variance contains two terms, the variance due to the particle number fluctuation and the variance due to the detector count statistics noise s s n These two terms have different dependence on the molecular brightness: s d s n s n n d (for the photon counting detector) Both depend on the intrinsic brightness and the number of molecules. We can invert the equations and obtain n and n is the true number of molecules is the true molecular brightness

36 1 s s s s k n n k k k B d d n How to Calculate n and This ratio identifies pixels of different brightness due to mobile particles. The true number of molecules n and the true molecular brightness for mobile particles can be obtained from k k n s k k s If there are regions of immobile particles, n cannot be calculated because for the immobile fraction the variance is = <k>. For this reason, several plots are offered to help the operator to identify regions of mobile and immobile particles. Particularly useful is the plot of NvsB.

37 Variance Quadratic dependence of the variance on particle brightness nm EGFP in solution as a function of laser power y = 4.431x x Intensity (c/dwelltime/molecule) n s n -photon excitation using photon counting detectors

38 Variance/intensity B Identification of mobile and immobile molecules Mobile Increase the concentration but laser power stays the same Increase the laser power EGFP 1 Immobile Intensity 1. Slide Counts/s If we change the laser power, a plot of the ratio variance/intensity vs intensity can distinguish the mobile from immobile fraction. The two curves are for different pixel integration times.

39 B B The effect of the immobile part: with photon counting detectors Fluorescent beads in a sea of 1nM Fluorescein. Variance/ntensity Intensity B map x=. y=. #pixels= in= Monomer-octamer serie 4 3 Selecting fluorescein intensity Selecting beads intensity Immobile intensity 3

40 Brightness and number of molecules can be measured independently n B EGFP in solution D histogram 1 15 Brightness vs laser intensity (counts/s/molecule) intensity Number of particles vs concentration Concentration (nm) (counts/s/molecule) Counts/pixel 1 Brightness vs concentration Concentration (nm)

41 What are the parameters for analog systems?

42 Detector Noise in Analog Systems Additional considerations with analog detection systems: digital levels are recorded (instead of photon counts) an offset is typically present additional detector variance at low currents s d offset = analog offset S = digital levels per photon = variance of analog detector k s d n Sn d offset s n N B B S B S If we fix the PMT settings (voltage and gain), then S and s should not change and need only be determined once.

43 Number of times Detector characterization Analog detector response (dark current) TChart 1, Amplifier Gaussian noise (s ) 1, 1, Exponential distribution of digital levels (S) 1 Offset Digital levels

44 Number of times Detector characterization Photon counting detector response (dark current) 1,, TChart 1, 1, 1, (counts/second)

45 Solution experiments: using analog detectors Recovery of n and e in the analog system for nm EGFP in solution n vs laser n vs laser power y = 7E-5x Laser power Laser power 6 In the analog system, the recovery of relative values is good, for absolute values the calibration is more problematic. The best obtained so far is within a factor of Courtesy of Valeria Vetri

46 EGFP in CHO-k1 (1-Photon LSM) homogenous Brightness & heterogeneous Number of Molecules n Map of Number of molecules A C Average intensity 5 B 6 4 Map of molecular Brightness Intensity (digital levels) D CHOk1 MEF (counts/s/m) Intensity (digital levels)

47 Summary of N&B N&B distinguishes between number of molecules and molecular brightness in the same pixel The acquisition for the N&B can be done with a commercial Laser Scanning Microscope (LSM) and the same data used for RICS can be used to map N and B. The Immobile fraction can be separated since it has a Brightness value =1 The N&B analysis of paxillin at adhesions shows large aggregates of protein during disassembly.