Transcript Journal Club

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
Methods
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.
Average result
•
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, …)
Distribution
http://www.eng.utah.edu/~lzang/images/Lecture_17_NSO
M-single-molecule.pdf
Fluorescence Correlation Spectroscopy
What are we measuring?
Spontaneous fluctuations of the fluorescence intensity within a defined
observation volume
Gaussian beam
Gaussian focal volume
zone.ni.com
… So why is this so powerful?
(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
•
•
•
•
•
Diffusion
Hydrodynamic radii
Average concentration
Kinetic chemical reaction rates
Singlet-triplet dynamics
•
•
•
•
•
•
Binding events
Enzymatic activity
Phase fluctuations
Rotational motion
Protein folding
Conformational dynamics
(Schwille, Haustein)
…as long as you can model it (more on this soon). I think this takes quite a bit of faith.
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.
wosound.com
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.
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
flies
traps (Jay can’t look in)
trap effectiveness
MatTek dish (#1.5, 14mm)
fluorescent particles
something that binds and quenches the particles
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
flies
traps (Jay can’t look in)
trap effectiveness
counting flies that
cross borders
MatTek dish (#1.5, 14mm)
fluorescent substrates
binding protein that quenches
disassociation constant
fluorescence fluctuations
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
flies
traps (Jay can’t look in)
trap effectiveness
counting flies that
cross borders
conference room
MatTek dish (#1.5, 14mm)
fluorescent substrates
binding protein that quenches
disassociation constant
fluorescence fluctuations
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…
Normalized Fluorescence Intensity
1.06
Normalized Fluorescence Intensity vs Time
Rhodamine Green
1.04
1.02
2.3 nM
1
46 nM
0.98
0.96
0.94
0.92
0.9
0
100
200
300
400
Time (s)
How do we control the volume for our noise?
500
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
Focal points
fcsxpert.com
Defined by wavelength,
numerical aperture of
objective
FCS Confocal Setup
Beam expander
Orange is the new blue
Laser
Laser
Emission
Filter
Lens
Optical fiber
Dichroic
mirror
Correlator card
(APD)
Avalanche
photodiode
Computer
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
How can we analyze this quantitatively?
Lakowicz 2006
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…
this is often ignored
Autocovariance of F(t) or rather the
autocorrelation of the fluorescence fluctuations
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 of Rhodamine Green (Joanna's Data)
Autocorrelation G(τ)
1.12
1.10
1.08
1.06
1.04
1.02
1.00
1.E-04
1.E-02
1.E+00
1.E+02
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…
1.E+04
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…
Intersystem-Crossing (triplet state)
…but of course there are many other processes
involved, one important one is intersystemcrossing…
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).
B
kD
kB
D
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).
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.
1:10,000 TDA
(120611.asc)
2.5
Sample: quantum
dots in water
2.0
1.5
1.0
1-comp diff
2
D = 0.0794 um /ms
N = 0.4895
0.5
1-comp. diff + triplet
2
D = 0.0300 um /ms
N = 0.9864
F = 0.5058 (blinking fraction)
lifetime = 0.1501 ms
0.0
-0.5
0.001
0.01
0.1
1
delay (ms)
10
100
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
Schwille
(2) Dual color cross-correlation
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:
– 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
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•
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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,