neurofunctional techniques - moodle@units · neurofunctional techniques lesson 5 14 october 2019...
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Neurofunctional
TechniquesLesson 5
14 October 2019
Revision
Ca2+ diffusion
Ca2+-dependent fluorescence properties
Rough calendar
• October 14-15: Theory (Imaging) + JC (You, 15/10)
• October 21-22: Theory+Revision + Test (22/10) + Imaging devices (Gabriele Baj)
• October 28-29: Mechanobiology 2 + Lab (D. Scaini)
• November 4: No lessons
• November 5: Electrophysiology (M. Gigliano; 14:00-16:00 only!)
• November 11-12: Theory (Optogenetics) + Revision + JC (You)
• November 18: Test
• November 19: No lessons
• November 25-26: Biostatistics (F Cesca)
• December 2: Biostatistics (F Cesca)
• December 3: Behaviour (F. Papaleo)
• December 19: Electrophys (G. Grasselli)
For tomorrow
Printed and read
Ca2+ imaging
Review Ca2+ signaling
Ca2+ indicators
Ca2+ binding
Ca2+ diffusion
Ca2+-dependent fluorescence properties
Simplified models of Ca2+ dynamics
Imaging devises
Applications
Genetically-encoded Ca2+-indicators
Ca2+
We can distinguish 2 major classes:
• Fluorescence resonance energy transfer
(FRET)-based GECIs (e.g. Cameleon family)
• Single-protein indicators (e.g. GCaMP family)
Pros and Cons of GECIs
1) Long-term (days, weeks, months) expression and imaging in vivo
2) Targeting to (i) specific subtypes of neurons or (ii) subcellular locations
Pros and Cons of GECIs
1) Long-term (days, weeks, months) expression and imaging in vivo
2) Targeting to (i) specific subtypes of neurons or (ii) subcellular locations
1) Indicator concentration not known
2) Because (often) based on calmodulin (4 cooperative Ca2+ binding sites)
Ca2+ binding is cooperative (this is not a problem for SMIs; it is being solved
for GICIs too, e.g. tomorrow’s paper)
Difficult to relate ΔF to Δ[Ca2+]
For SMIs loading tedious but concentration known
Independent Ca2+ binding
Law of mass action
Kd = Dissociation constant = [Ca2+] at which 50% of the binding sites have bound Ca2+
Attention: Low Kd = high affinity High Kd = low affinity
The affinity of the indicator should match the expected range of [Ca2+] ‘seen’ by the indicator
Affinity too low (Kd high) not enough sensitivity Affinity too high (Kd low) saturation
Independent vs. cooperative Ca2+ binding
n = 2
Ca2+-binding ratio
For every 100 - 1000 Ca2+ ions entering the neuron, 1 (on average) remains free; the
remaining will be buffered (=bound to proteins) within 10 - 100 μs
Buffering capacity = buffering strength = Ca2+-binding efficiency = Ca2+-binding ratio = κB
κB is obtained by differentiating the above equation for the saturation curve:
Independent Ca2+-binding ratio
[Ca2+] = 0 κB = [B]T/Kd
(It makes sense)
κB decreases when [Ca2+] increases according to the 2 power of [Ca2+]
(It makes sense)
It is important to have a good estimation of κB for both endogenous buffers and added
indicator, in order not to alter the Ca2+ signal.
Cooperative Ca2+ binding ratio
Relationship non-monotonic, making interpretation of fluorescent signals more difficult
Cooperative Ca2+ binding
Ca2+ imaging
Review Ca2+ signaling
Ca2+ indicators
Ca2+ binding
Ca2+ diffusion
Ca2+-dependent fluorescence properties
Simplified models of Ca2+ dynamics
Imaging devises
Applications
Neuronal Ca2+ signaling
MS = -DS
d [ CS ]
dx
Diffusion
Fick’s first law:
Empirical law; but what is the mechanism of diffusion?
Diffusion can be described as a microscopic random walk of molecules that
accounts for diffusion down a gradient according to the Fick’s first law, even
though molecules ‘see’ no force.
Diffusion
Distance from origin
Re
lati
ve c
on
cen
trat
ion
Pro
bab
ility
of
fin
din
g th
e m
ole
cule
μ = 0
Mean-squared displacement = r2 = σ2 = 2Dt
In one dimension:
Diffusion
How far a diffusing molecule will be after a time t?
In one dimension: r = σ = 𝟐𝑫𝒕
In two dimension: r = σ = 𝟒𝑫𝒕
In three dimension: r = σ = 𝟔𝑫𝒕
The sums of random displacements grow as the square root of time
DCa = 220 μm2s-1
Soma
Ø = 10 𝝁m
t = 75 ms
Presynaptic boutons
Ø = 1 𝝁m
t = 0.75 ms
Diffusion
DCa = 220 μm2s-1
The sums of random displacements grow as the square root of time
Intracellular Ca2+ signals can be compartmentalized
Ca2+ diffusion can be either promoted or slowed down by buffers depending on their
mobility Ca2+ indicators may affect not only Ca2+ buffering but also Ca2+ mobility.
Ca2+ imaging
Review Ca2+ signaling
Ca2+ indicators
Ca2+ binding
Ca2+ diffusion
Ca2+-dependent fluorescence properties
Simplified models of Ca2+ dynamics
Imaging devises
Applications
Fluorescent Ca2+ indicator
Fluorescence readout is beneficial because even at low indicator concentration it
allows for high-contrast labeling
How do you make a fluorescent Ca2+ indicator?
It should have two moieties:
• 1 acting as Ca2+ buffer/chelator
• 1 acting as fluorophore
• Ca2+ binding to the chelator moiety must affect some property of the
fluorophore
Question
to read out [Ca2+]i (amplitude, time course, location)
cellular process X = f([Ca2+]i)
Fluorescence Ca2+
Electromagnetic spectrum
Fluo-4 excitation and emission specta
Ca2+-dependent fluorescence changes
Intensity meusurements: Ca2+ bindingincreases (or decreases, not shown)fluorescence (e.g. Fluo & GCaMP series)
Fluorescence rationing: Ca2+ bindingshifts either the absorption (above; e.g.Fura-2) or the emission spectrum (left;e.g. Cameleon)
Fluorescence intensity
How does the fluorescence signal F relate to [Ca2+]i?
QF = quantum yield = photons emitted
photons absorbedΦD = fraction of emitted photons collected by the photodetection system
QD = detector’s quantum efficiency
Iabs = I0 ln(10) ε l [X] = absobed light according to a linear approximation of the
Beer-Lambert law (valid for [X] << 5 - 20 mM)
S = all dye- and setup-specific factors merged in a single proportionality
constant
Fluorescence intensityFor Ca2+ indicators we need to consider separately B and CaB because they have
their own QF and Iabs
Fmin = Sf [B]T
Fmax = Sb [B]T (assuming an increase in F upon Ca2+ binding)
Rf = Dynamic range = Fmax
Fmin
Although useful in vitro this equation is impractical for imaging experiments because
optical path length, total dye concentation, illumination intensity (and therefore Fmax
and Fmin) vary over the field of view. Calibration pixel by pixel unfeasable.
Relative fluorescence change
ΔF/F0 = 𝑭−𝑭
𝟎
𝑭𝟎
ROI 1
Relative fluorescence change
ROI-1
ROI-2
ROI-4ROI-3
ROIb-1
ROIb-2 ROIb-3
ROIb-4
For each ROI:
F = Fobserved - Fbackground
ΔF/F0 = 𝑭−𝑭
𝟎
𝑭𝟎
Average of a time window just before stimolation
Relative fluorescence change
Relative fluorescence change
ΔF/F0 = 𝑭−𝑭𝟎𝑭𝟎