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