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

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

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!

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

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 http://www.eng.utah.edu/~lzang/images/Lecture_17_NSOM-single-molecule.pdf

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)

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)

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)

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

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

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

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

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!

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

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

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?

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

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!

Our FCS Confocal Setup

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?

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

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)

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

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 http://cnyack.homestead.com/files/aconv/convau1.htm Mouse Movements (mimicking light scattering) http://mach7.bluehill.com/proteinc/autocorrelation.html A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. Wikipedia.org

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

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

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

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

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…

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.

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…

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)

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”

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…

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)

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

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

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…

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)

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).

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

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

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

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.

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), …

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

References P. Schwille, Introduction to Fluorescence Correlation Spectroscopy. Retrieved April 2011. www.biophysics.org/Portals/1/PDFs/Education/schwille.pdf J. R. Lakowicz, Principles of Fluorescence Spectroscopy, Plenum Press, New York, 1983 N. Thompson, Topics in Fluorescence Spectroscopy: Fluorescence Correlation Spectroscopy, 2002, Volume 1, 337-378,