1. Journal Club Meeting Joshua Tokuda 4/19/2011
FCS: Basic Overview and Applications

2. Today’s topics FCS Scheme What are we measuring?
What does the setup look like?
What can we do with FCS

3. Methods for Various Measureable Parameters
Excitation/Emission Spectra
Concentration, local environment, …
Fluorescence Microscopy
Localization, …
Quenching
Local environment, solvent accessibility, …
Fluorescence Lifetime
Dynamic processes, …
Resonance Energy Transfer
Relative distances between probes, …
Anisotropy/Polarization
Rotational diffusion, …
Fluorescence Correlation Spectroscopy
Concentration, translational/rotational diffusion, dynamics, particle photophysics, … …
FCS was one of the first true single molecule techniques!

4. Advantages of FCS
Minimal perturbation  analysis of states closely spaced in free energy
Very small sample region
Fluorescence detection molecular specificity
Wide dynamic range from microseconds to seconds
Amplitude information
Cross-correlation methods

5. Advantages of Single Molecule Studies
Why single molecule?
Obtainable information from bulk measurements are inherently affected by ensemble averaging which may obscure the observation of individual molecular behavior and the direct measurement of kinetics.
Single (or several) Molecule Techniques
Force Spectroscopy
Atomic force spectroscopy
Magnetic, optical tweezers
Electron, (surface enhanced) Raman Microscopy
Fluorescence Spectroscopy
Single molecule detection (SMD): bound to surface
Fluorescence correlation spectroscopy (FCS)
Super-resolution microscopy (STED, PALM, SI, …)
Average result
Distribution

6. Fluorescence Correlation Spectroscopy
What are we measuring? Spontaneous fluctuations of the fluorescence intensity within a defined observation volume … So why is this so powerful?
Gaussian beam
Gaussian focal volume
zone.ni.com
(Schwille, Haustein)

7. Fluorescence Correlation Spectroscopy
Why is this so powerful?
One may make inferences about any process that alters these fluctuations…
Molecular mechanisms that give rise to fluctuations:
Particle movements, conformational changes, chemical/photophysical reactions
…as long as you can model it (more on this soon). I think this takes quite a bit of faith.
Diffusion
Binding events
Hydrodynamic radii
Enzymatic activity
Average concentration
Phase fluctuations
Kinetic chemical reaction rates
Rotational motion
Singlet-triplet dynamics
Protein folding
Conformational dynamics
(Schwille, Haustein)

8. Fluorescence Correlation Spectroscopy
What are we measuring? Spontaneous fluctuations of the fluorescence intensity within a defined observation volume For fluctuations to be noticeable: (1) Reduced concentration (2) Reduced observation volume
Why is this true?
Let’s first take a look at a simple illustration…
(Schwille, Haustein)

9. Simple Illustration
Problem: Jay accidentally released millions of flies while working in the Lis lab and they are now rampant all over campus. Not wanting this incident to tarnish his reputation as the Champion Grand Marshall of the Solar System, Jay has set out to capture his flies by setting up vinegar traps all over campus. Assuming that the flies are now homogenously distributed throughout campus (the numbers fluctuate over seconds, but the average number over minutes stays relatively constant—they seem to like Cornell), he would like know how well his traps are working. Interestingly enough, Jay cannot look at his traps because it makes him sad.
wosound.com

10. Simple Illustration
Problem: Jay accidentally released millions of flies while working in the Lis lab and they are now rampant all over campus. Not wanting this incident to tarnish his reputation as the Champion Grand Marshall of the Solar System, Jay has set out to capture his flies by setting up vinegar traps all over campus. Assuming that the flies are now homogenously distributed throughout campus (the numbers fluctuate over seconds, but the averaging number over minutes stays relatively constant—they seem to like Cornell), he would like know how well his traps are working. Interestingly enough, Jay cannot look at his traps because it makes him sad.
Analogies:
Cornell campus MatTek dish (#1.5, 14mm)
flies fluorescent particles
traps (Jay can’t look in) something that binds and quenches the particles
trap effectiveness disassociation constant

11. Simple Illustration
He quickly finds that it’s really difficult to count the flies in any given area. …but it’s a bit easier to count how many cross the campus boundaries
Analogies:
Cornell campus MatTek dish (#1.5, 14mm)
flies fluorescent substrates
traps (Jay can’t look in) binding protein that quenches
trap effectiveness disassociation constant
counting flies that fluorescence fluctuations
cross borders

12. Simple Illustration
He quickly finds that it’s really difficult to count the flies in any given area. …but it’s a bit easier to count how many cross the campus boundaries Being the smart graduate student he is, Jay decides to instead constrain his observation volume to this conference room since he knows that the flies are homogenously distributed. Now he only needs to pay attention to how many flies pass through the doorway.
Analogies:
Cornell campus MatTek dish (#1.5, 14mm)
flies fluorescent substrates
traps (Jay can’t look in) binding protein that quenches
trap effectiveness disassociation constant
counting flies that fluorescence fluctuations
cross borders
conference room reduced focal volume

13. Simple Illustration
He quickly finds that it’s really difficult to count the flies in any given area. …but it’s a lot easier to count how many cross the campus boundaries Being the smart graduate student he is, Jay decides to instead constrain his observation volume to this conference room since he knows that the flies are homogenously distributed. Now he only needs to pay attention to how many flies pass through the doorway. Furthermore, he knows that if he plays his favorite Beethoven piece (from the clock tower) a fraction of the flies would miss him and die immediately. (Now the fluctuations are very noticeable!)
Analogies:
Cornell campus MatTek dish (#1.5, 14mm)
flies fluorescent substrates
traps (Jay can’t look in) binding protein that quenches
trap effectiveness disassociation constant
counting of flies that fluorescence fluctuations
cross borders
conference room reduced focal volume
fly death by Beethoven reduced concentration
Jay’s measurements help him optimize his traps and he saves the day! Hurray!

14. FCS Theory is Based on Poisson Statistics
Paraphrased from Wikipedia…
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a specified interval (time, space, etc…) if these events occur: (1) with a known average interval and (2) independently of the interval since the last event.
(retrieved 4/16/2011)
f(k, λ) …. probability of k occurrences
k …….….. number of occurrences
λ ……….. expected number of occurrences in
a given interval

15. FCS Theory is Based on Poisson Statistics
Probability that the volume has N fluorophores N
Lakowicz 2006
Lakowicz 2006

16. FCS Theory is Based on Poisson Statistics
The relative fluctuations becomes larger with decreasing particles…
Rhodamine Green
2.3 nM
46 nM
How do we control the volume for our noise?

17. Defining the Observation Volume
How do we control the volume for our noise?
One photon excitation
Two photon excitation
(Confocal setup)
Defined by wavelength, numerical aperture of objective , magnification, pinhole size of aperture
Aperture
Focusing lens
cnx.org
Defined by wavelength, numerical aperture of objective
Focal points
fcsxpert.com

18. FCS Confocal Setup Orange is the new blue Beam expander Laser Laser
Dichroic mirror
Emission
Filter
Correlator card
Lens
(APD)
Avalanche photodiode
Computer
Optical fiber
Schwille, modified!

19. Our FCS Confocal Setup

20. FCS Theory: Fluctuations
How are fluctuations related to what’s happening?
Occupation numbers change more slowly for slowly diffusing situations
We can see this by comparing the intensity at a given time F(t) with the intensity at a later time F(t+τ).
Lakowicz 2006
Lakowicz 2006
How can we analyze this quantitatively?

21. Statistical Correlation
Correlation – A useful tool for analyzing the statistical relationships between two or more random variables or observed data values
scienceaid.co.uk

22. Statistical Correlation
Correlation – A useful tool for analyzing the statistical relationships between two or more random variables or observed data values
Pearson Product-Moment Correlation Coefficient (works for linear relationships)
Both must be non-zero and finite
(Corollary of Cauchy-Schwarz Inequality)

23. Statistical Correlation
Correlation coefficients determined for various relationships between two time series
Wikipedia.org
Example:
X(t) – outdoor temperature Y(t) – indoor temperature
No A/C
Weak A/C
Effective A/C
Over reactive A/C
Really funky A/C
Statistics.laerd.com

24. Statistical Correlation
Autocorrelation – Correlation between one time series and the same series lagged by one (first order) or more (higher order) time units
Some examples, courtesy of Avtar!
Triangle Pulse
Mouse Movements (mimicking light scattering)
A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom.
Wikipedia.org

25. FCS Theory: Fluctuations and Autocorrelation
How do we define fluctuations?
(Assuming constant excitation power)
Temporal average of the fluorescence
Schwille 2003
Fluctuations: deviations from the temporal average (variance)
How can we analyze this quantitatively?
The autocorrelation function of the fluorescence is given by the average value of the products shown below…
t – real time
τ – delay time

26. FCS Theory: Autocorrelation Function
How can we analyze this quantitatively?
Normalized autocorrelation function for fluorescence
t – real time
τ – delay time
Normalized by average fluorescence squared
τ is always relative to an earlier time t, so only τ is relevant
Sometimes this is written as…
Autocovariance of F(t) or rather the
autocorrelation of the fluorescence fluctuations
this is often ignored

27. FCS Theory: Autocorrelation Function
Of course we’re really mainly interested in the fluctuations…
Autocorrelation of fluctuations
When talking about FCS, this is what most people mean by autocorrelation
Remember
How are correlator cards actually calculating autocorrelation?
Counts per bin (fundamental “binsize” down to 12ns)
N = total number of bins
ni = number of counts in ith bin
j·binsize= τ
Warren’s BME 6260 slides

28. FCS Theory: Autocorrelation Function
Sometimes all data is collected first and the autocorrelation is calculated via software
John S. Eid et al. 1999

29. FCS Theory: Autocorrelation Function
Definition of the autocorrelation function
Autocorrelation G(τ)
τ (ms)
To interpret autocorrelation functions, we rely on theoretical predictions of the autocorrelation function arising from fluorescence fluctuations due to different processes
We first need a theoretical description of the fluctuations…

30. FCS Theory: Autocorrelation Function
The theoretical description of these fluctuations can be bit complicated…
κ – overall detection efficiency
Iex(r) – spatial distribution of the excitation energy with the maximum amplitude I0
S(r) – optical transfer function of the objective-pinhole combination (determines spatial collection efficiency)
δσ – fluctuations in the molecular absorption cross-section
δq – fluctuations in the quantum yield
δC(r, t) – fluctuations in the local particle concentration at time t (e.g. because of Brownian motion)
Determining all of these parameters is not practical…
Approximations to the rescue!
This function describes spatial distribution of emitted light.

31. FCS Theory: Autocorrelation Function
Making the fluctuations look more manageable…
This parameter that describes the photon count rate per detected molecule
Now all we need to do is to plug this into our autocorrelation function…

32. FCS Theory: Autocorrelation Function
Autocorrelation function of fluorescence fluctuations
This can be simplified greatly depending on what is held constant (ie. parameters η, or C)

33. FCS Theory: Autocorrelation Function
Spatial Distributions of Light
Fluctuations (due to fluorophore dynamics or concentration)
Time Averaged Fluorescence (normalization)
Let’s first assume that η stays constant and that the particles are freely diffusing in three dimensions.
“The number density autocorrelation term”

34. FCS Theory: Autocorrelation Function
Two final conventions to clean it up…
(1) Relationship between lateral diffusion time τD and diffusion coefficient D
(two dimensional diffusion)
(2) Determination of the effective volume
Lakowicz 2006
Applying these to our autocorrelation function…

35. FCS Theory: Autocorrelation Function
…we finally have the autocorrelation function for one freely diffusing species of molecules
Measuring translational diffusion coefficients is probably the most common application of FCS
Simulated autocorrelation functions for 3D diffusion
N = number of particles
Lakowicz 2006
100 fold difference in D typically corresponds to (10,000 fold in mass)

36. FCS Theory: Autocorrelation Function
Autocorrelation function for 3D diffusion
Veff is usually defined as the volume that contains N fluorophores at a known concentration, the exact shape of the observation profile is unknown.
From G(τ = 0), we can immediately get…
Fitting of this type of non-linear curve is often done with the Levenberg-Marquardt algorithm
Both the diffusion time (τD) and structure parameter (S=r0/z0) describe the shape of the curve and are determined from the fits
research.stowers-institute.com

37. Keeping the big picture in mind…
So far we assumed that the fluctuations are only due to 3D diffusion…
…but of course there are many other processes involved, one important one is intersystem-crossing…
Intersystem-Crossing (triplet state)
Diffusion
Schwille
Observation Volume
Schwille

38. FCS Theory: Accommodating Intersystem-Crossing
Triplet blinking can be described by a simple exponential decay…
T is the triplet fraction
Adding this term to what we had before, we now have…

39. FCS Theory: Other Reversible Processes
The analysis for triplet blinking can be generalized for any fast photophysical process that causes reversible transitions between bright and dark states (flickering). kD B D kB
In the case that the dark state is not completely dark, we simply take into account the molecular emission yields of the two states (ηB and ηD)

40. Making Sense of the Data…
Separation of the dynamics is possible if they occur on different time scales
…But this holds only under the assumption that the diffusion coefficient is unaltered by the other processes.*
Schwille
*One can take these into account as well with a motility term M(τ)… but I will spare you the details!
The basic theme is that you can add and modify terms to make your fits better, but of course you can make anything fit if you add enough parameters (interpretation becomes difficult).

41. Sample: quantum dots in water
Example of a better fit to a more complex model --- but the added complexity (presence of a triplet component) doesn’t make physical sense.
One diffusion constant fit compared to 1 diffusion constant + triplet model. The +triplet model “fits” better, but the improved region of the fit (around 5 ms) is not in the part of the curve normally associated with triplet states.
Sample: quantum dots in water
Warren’s slide BME 6260

42. Cross-Correlation Analysis
Autocorrelation compares a measured signal with itself (at a later time) to look for recurring patterns
Cross-correlation compares two different signals (usually independently measured) to look for any interdependencies (crosstalk).
Nearly any parameter can be subject to cross-correlation analysis, but two common ones are:
(1) Spatial cross-correlation
(2) Dual color cross-correlation
Schwille
Schwille

43. Spatial Cross-Correlation
In this case, the fluctuations between two separate volume elements can be cross-correlated.
Flow velocity =
φ = angle between flow direction and line connecting two foci
Schwille
Since one molecule only correlates with itself, the maximum would be at the average time it takes for the molecule to travel from one detection volume to the other.
Can study flow-/transport-velocity
Schwille

44. Dual Color Cross-Correlation
Two spectrally different fluorophores are excited within the same detection volume using one or two overlapping laser(s) and emissions collected in two separate detection channels.
Schwille
Double-labeled species
Powerful probe for interactions between two different molecular species.
Two differently labeled molecules may move independently at first and then fuse together, or vice-versa.
Complexed molecules will exhibit correlation.
Can also determine the concentration of complexed species from amplitudes of autocorrelation.

45. FCS Techniques
Absolute local concentrations can be determined precisely if Veff is known (may be difficult, also restricted to nanomolar concentrations of less)
Many complications
proteins adhering to surfaces
Photodamage
Molecular brightness is crucial and can be useful
May be able to rate the fluorescence quenching/enhancement of fluorophpore due to changed environment
May be a more sensitive measure of oligomerization than diffusion coefficient (FCCS)
Aggregation measurements are possible
Can be used to determine mobility and molecular interactions
Enables observation of fluorescently tagged molecules in the biochemical pathway of living cells
FRET-FCS, TIRF-FCS, Image Correlation Spectroscopy (ICS), …

46. Summary FCS is: FCS isn’t:
A technique that studies processes correlation analysis of fluorescence intensity fluctuations
Typically done with working conditions:
nM-pM concentrations
Small volumes (approximately 0.1 fL)
~1-100 molecules (single molecule technique)
Very sensitive analytical tool for average number of molecules, diffusion coefficients, e tc…
FCS isn’t:
A technique

47. References
P. Schwille, Introduction to Fluorescence Correlation Spectroscopy. Retrieved April
J. R. Lakowicz, Principles of Fluorescence Spectroscopy, Plenum Press, New York, 1983
N. Thompson, Topics in Fluorescence Spectroscopy: Fluorescence Correlation Spectroscopy, 2002, Volume 1, ,