Ryohei's Neuroscience Notes

Group velocity dispersion memo

2006-12-19T20:03:00.000-08:00

Mode-lock pulsed laser has broad wavelength spectrum due to the Heisenberg principle:
Δν τ = τ cΔλ/(λ²)~ 0.44 (FWHM). For 100fs, the wavelength width (Δλ) is ~8nm at 800nm wavelength.

Because light with different wavelength propagates with different velocity, the dispersion of pulsewidth occurs.

Phase shift of light in some material is:

Φ (ω) = n(ω)Lω/c (1)

where L is the length of material, n is the refractive index and c is the speed of light. Φ(ω) can be described as a power seriese as:

Φ(ω) = Φ(ω₀) + (dΦ(ω)/dω) *(ω-ω₀) + (d²Φ(ω)/dω²) * (ω-ω₀)²

The first and seond term does not change the pulse shape. The third term causes pulse broadening. The second order differentiation of Φ can be obtained from equation (1) as:

(d²Φ(ω)/dω²)L^-1 = λ³(2πc²) ^-1 (d²n/dλ²)

The left term is refered to as group velocity dispersion constant, D. Typical value is 100-400 fs^2/cm for silica or BK7 and 1000-2000 fs^2/cm for SF10 or SF11. Pulse broadening is expressed as:

τ_out = τ_in[1 + 7.68*(DL)² τ_in^-4]^1/2
=τ_in[1+205*(DL)² (cΔλ / λ²)⁴]^1/2

Here 7.68 = (2*sqrt(ln2))^4 is to covert gaussian width parameter to FWHM. DL of typical microscope setting is 3,000-10,000 fs². Compensation can be done using a pair of prism with distance of L_prism obtained by:

D_prism = -2L_prismλ³(πc²)^-1(dn/dλ)²

For example, high dispersive materials such as SF-10 or SF-11 have dn/dλ = 40,000-80,000 m^-1 at 800-900nm. Thus, L_prism~30-100cm is required to compensate the dispersion caused by a microscope.

---
Sellmeier equation

λ dependency of dispersive materials can be described as:
n²=1+Σ(A_iλ²)/(λ²-B_i)

A1,A2,A3,B1,B2,B3
SF10 1.61625977 0.25922933 1.07762317 0.0127535 0.05819840 116.607680
SF11 1.73848403 0.31116897 1.17490871 0.0136069 0.06159605 121.922711

References:
V.Iyer et al. J.Biomed.Optic 2006
(http://sensor.bcm.tmc.edu/saglab/pdf/JBO_Iyer.pdf)

Newport web page
(http://www.newport.com/store/genproduct.aspx?id=141161〈=1033&section=Detail
)

Mellesgriot web page
http://www.mellesgriot.com/products/optics/mp_3_1.htm

Wikipedia Sellmeier equation
http://en.wikipedia.org/wiki/Sellmeier_equation

BCP webpage
http://bcp.phys.strath.ac.uk/ultrafast/dictionary/dispersion%20and%20pulse%20broadening/dispersion%20and%20pulse%20broadening.html

Building a 2-photon microscope -- 2

2005-11-10T08:07:00.000-08:00

PMT high voltage power-supply: Using Hamamatsu C4900-1 in combination with 12V powersuply (Power One) is a cost efficient solution. For controlling voltage, one needs a potentiometer (50 ohm).(~$0.2K each).

XYZ-motorized control: I use XY-stage from NEAT (XYR-4040), and Z-axis from Oriental motor (PK266-02A) coupled to microscope focus control. Cables are connected to Sutter MP285. Originally MP285 is for electrode manipulator, but one can ask for modification for the NEAT stage (KS3.4). $7K.

Building 2-photon microscope -- 1

2005-11-01T07:14:00.000-08:00

As I am setting up a 2-photon microscope in my lab, I decided to leave my note here. The system should be significantly cheaper (say, 50%) and probably better than any commercial 2-photon systems, but obviously you need to commit more time and efforts to build.

Materials

- Microscope: I use olympus upright microscope, IX51, because their fluorescence microscope is featured with extremely low background light, so that one can even visualize single molecule without any special setting. I asked them to make a hole (~35 mm) in the side of a filter cube turret, and screw holes around the hole that fits to microconstruction system from Thorlabs. Also, I use a dichroic mirror holder that reflects light to the side (Olympus now provide this cube). This way, we can put photo-multiplier (PMT) to the side of microscope. It should be noted that we need to put PMT as close as possible to the objective to get maximum number of photons in light-scattering tissues. (~$40K)

- mirrors, lens, posts, holders: Thorlabs and Newport (~$1K)

- Optical table: I use big table (12 x 4 feet) that can hold two rigs. Because lasers are so expensive, it is cost effcient to split one laser light and feed into two rigs. It is a little bit tricky to do electrophysiology in two rigs in a table, but still doable. (~$8K)

- Scanner: Cambridge technologies provides fairly good and cheep scanner (6201H). Their lead time is ridiculously long (9 weeks). Their driver board get very hot during opperation. One should not put a lid on this. (~$2K)

- Scan lens: I purchased scan lens for a confocal microscope from Olympus. If one wants to reduce cost, it is good enough with a standard achromatic lens. Singlet lens could also work. (~$1K)

- Machining: One needs to machine an adaptor to connect scanner to the scan lens.

- Cage: One needs complete darkness for 2-photon unlike confocal system. I made a box (size = hight 36''x width 30''x depth 30'') made of angled and slotted bars (McMaster.com, 4664T51) and thin alminum plates (89015K71
). Inside of the cage is black-painted with a car painting spray. Make several holes for wiring and laser light. Metal cage also reduces electrical noise. (~$0.2K)

- Signal amplification and filtering: It is necessary to filter photon signal from PMT with ~300KHz to sample with AD converter. I use stanford amplifier SR-570.(~$2K)

- AD-DA converter: NI6110, National Instruments ($3K). This is both for scan control and data acquisition.

- Photomultiplier: Hamamtsu R3896 Select for QY>20%, Dark Current < 15nA. 4 PMT for 1 microscope. (Gree/red channels for epi/trans fluorescence)

FRAP / FDAP in a dendrite

2005-03-19T21:46:00.000-08:00

FRAP and FDAP
To track diffusion of proteins in a cell, one can tag proteins in a particular region in the cell, and see how they spread from the region. One way to "tag" proteins in a area of interest is to label protein with fluorophores and photo-bleach the fluorophores in the area using a high power laser. From the time course of the fluorescence recovery after the photo-bleaching (FRAP), one can measure the diffusion constant of the protein.One problem of this method is photo-bleaching of fluorophore produces free-radicals in the cell, causing some damages to the cell.

Another way is to tag proteins is photo-activation of photo-activatable fluorophores such as photo-activatable GFP (Fluorescence decay after photoactivation = FDAP). This method should cause less damages to the cell, and give higher signal-to-noise ratio.

FRAP / FDAP in a thin dendrite
When FDAP/FRAP methods are applied in a thin dendrite and whole section of the dendrite is photo-activated (or bleached), the fluorescence change (Δ F) can be expressed as a convolution of 1D-diffusion

Δ F(t, x) ~ t^-1/2 exp(-x²/4dt)

with a square function with the length of the photo-bleaching area (-b/2 < x < b/2). This results the following equation:

Δ F(t, x) ~ 1/2 [erf{(x+b/2)/(4dt)^1/2} - erf{(x-b/2)/(4dt)^1/2}]

Thus, the time course of the fluorescence at the center of the bleaching region is given by

Δ F(t)/ F(0) = erf(b/(16dt)^1/2)

Note that the shape of the curve is very differen from exponential curve.

FRAP/FDAP in spines

The single compartment model can be used when FRAP/FDAP methods are applied in spines. Because the diffusion inside a spine reaches equilibrium quickly and diffusion between spine and dendrite is much slower, the fluorescence change can be expressed as

dF / dt = - 1/τ F
or
Δ F ~ exp(-t/τ)

where τ is the diffusion coupling time constant between a spine and the parent dendrite. τ should be proportional to volume of spine (V), length of the neck and inverse the neck diameter.

Neurons to make decision

2005-02-14T12:29:00.000-08:00

Optical Imaging of Neuronal Populations During Decision-Making (from Kristan's lab)

Understanding how a neuronal network makes a behavioral decision is one of a major goal in neuroscience. In this paper, Briggman et al. imaged the activity of a population of leech neurons using voltage-sensitive dye when the leech makes decision of swimming vs. crawling. They excited the (reduced) animal repeatedly with identical stimuli that stochastically produce crawling and swimming with roughly equal probabilities. Principal component (PC) analysis showed that the activity patterns of the cell population diverge toward two different region in the PC space earlier than the actual response. They identified neurons contributing highly to the discriminant in a linear-discriminant analysis. Interestingly, modulating voltage of one of the identified cells (cell 208) by an electrode biased the decision-making.

Calcium imaging to analyze circuit

2005-02-10T13:07:00.000-08:00

Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex (2005), Ohki K. et al.Nature 433, 597 - 603 (Reid lab.)

Congratulations, Ohki-san!!!!! The column structure in the cortex has fascinated many brain researchers: why are cells that response to similar stimulations clustered to form a column ? Using a combination of bulk loading of AM-calcium sensor and a two-photon microscope, Ohki et al. meausred the orientation selectivity of the visual cortex at a single-cell resolution. The sharpness of the boundary between two orientation columns is almost shocking. Supposedly the input orientation map is much broader as dendritic arbor spreads over hundreds of microns. It would be interesting how a single cell process inputs to "choose" one (or sometimes two) selectivity. Another interesting aspect of the orientation selectivity is that mice have poorly organized structure in contrast to cats. To perform complicated information processing, it may be required for animals to have higher organization of a column.

Spine structural change - Nothing to do with physiology ?

2005-01-28T09:20:00.000-08:00

Today's journal club was about Shrinkage of dendritic spines associated with LTD, Neuron. 2004 Dec 2;44(5):749-57. from Poo's lab.

Blocking of cofilin phosphorylation blocks spine shrinkage without affecting LTD, and blocking PP1 blocks LTD without blocking spine shrinkage. Both are blocked by calcineurin blocker. These suggest the LTD inducing stimulation activates the calcineurin pathway, and the pathway branchs out to produce two different phenomena, LTD and spine shrinkage.

Clearly spine structural change is NOT required by the change in synaptic strength. This is probably the same for LTP and spine enlargement: I heard from several guys that the washout by patch-clamping often blocks selectively the spine enlargement but not LTP.

Then why the spine structure changes ? One possibility is the structural change is just a side effect: because the actin polymerization is regulated by a balance of kinase/phosphatase activity, LTP/LTD inducing stimulation, which changes this balance, can change the sturcture of spines. Or, maybe this is important for late-phase LTP: larger spines can contain more resource to maintain LTP.

Background subtraction in calcium imaging

2005-01-27T08:03:00.000-08:00

"For analysis of calcium transients, the fluorescence background was subtracted from the fluorescence intensity averaged over the line" -- XXX et al., XXXX, 2005

2-photon calcium imaging became popular as a tool to quantify calcium signaling in neurons. In a lot of papers published, fluorescence signal is subtracted by surrouding background fluorescence. However, generally this is a WRONG idea.

----Quote from Yasuda et al., 2004 Science STKE ------
Relating fluorescence and [Ca²⁺] requires subtraction of background from the fluorescence signal. Because neuronal compartments such as spines and boutons are typically smaller than the excitation volume of 2PLSM, the background calculation is complicated. Background fluorescence is commonly estimated by measuring fluorescence far from the spine, F_B. ΔF/F_o is defined by Eq. 12, where F and F_{o, raw} are the raw fluorescence signals during the response and baseline periods.

ΔF/F_o = (F-F_o,raw)/(F_o,raw - F_B)) (Eq.12)

Because the spine volume is smaller than the excitation volume, F, F_o,raw, F_raw, and F_B can be expressed by Eq. 13, where V_sp and V_ex are the spine volume and the excitation volume outside the compartment, b_sp and b_ex are background fluorescence intensities inside and outside the compartment per unit volume, respectively, and f_o and f are the fluorescence intensities from fluorophore in the compartment per unit volume before and after the stimulation.

F = (f+b_sp)V_sp + b_exV_ex
F_{o, raw} = (f_o + b_sp)V_sp+b_exV_ex
F_B=b_ex (V_sp + V_ex)

Because the excitation volume is V_sp+ V_ex, F/F_o is defined by Eq. 14.

ΔF/F_o = (f-f_o)/(f_o-(b_ex-b_sp)) (Eq.14)

Therefore, this type of background subtraction gives the correct value only if b_sp = b_ex, that is, if background is exactly the same inside and outside spine. Unfortunately, this is rarely the case. Under some conditions, depending on the excitation wavelength, spatially heterogeneous background fluorescence is excited. More importantly, it is often the case that small quantities of indicator spilled in the extracellular space during patching produce substantial background fluorescence in the brain slice. In this case, background subtraction always results in an underestimate of F_o and a resulting overestimate of F/F_o. Moreover, this error depends on the size of the compartment; it is larger for smaller compartments. In our view, quantitative measurements demand conditions in which the background is not significantly different from the dark noise of the PMT. If background fluorescence is higher than the dark noise of the PMT, the data are severely compromised for analysis of the amplitudes and time-courses of transient changes in [Ca²⁺].

Effects of coverslip on PSF

2005-01-20T13:16:00.000-08:00

We use water-dip type objective for our two-photon microscopy. However, if there is a coverslip between the objective and the sample, the PSF(Point spread function) is degraded significantly.
This is because the these objectives are not designed for this situation.

The refractive index of water is 1.33, and coverslip is 1.52. Thus if there is a coverslip between a sample and an objective, an incident light is refracted by the coverslip and make a focus at a different point than the focal point without the coverslip. The shift (D) can be calculated as:

D(θ) = a(tanθ - tanθ')/tanθ'

Where N/N' = sinθ / sinθ' (N: refractive index of water, N': of coverslip), and a is coverslip thickness (typically 170 μm).

If optics are at the near-axis, or sinθ ~ tanθ, D does not depend on the incident angle θ. However, for a high NA objective, this is not the case. For example, for NA=0.9 water-dip objective, maximum θ is Asin 0.9/1.33~42^o. In this case the shift D is 42 μm compared to 24 μm at the near axis, the focus position differs by δD~18 μm in z-axis.For NA=0.5, δD~3 μm. Thus, a coverslip degrades PSF significantly.

Therefore, in my opinion, for an in vivo application, one should underfill the backfocal plane with the laser to save laser power.

Pokemon

2005-01-19T13:11:00.000-08:00

These guys can't be serious. They named a proto-oncogene as Pokemon = POK erythroid myeloid ontogenic factor....

Recording from axons

2005-01-14T14:09:00.000-08:00

-Axonal Propagation of Simple and Complex Spikes in Cerebellar Purkinje Neurons J. Neurosci., 25(2):454-463;

-Determinants of Action Potential Propagation in Cerebellar Purkinje Cell Axons
J. Neurosci., 25(2):464-472 (Mike Häusser's lab)

Amazing technique! They performed simultaneous measurements of action potentials at soma of Purkinje Cells and their axon to quantify the reliability of axnal spike propagation. If a cell spikes regularly, the axonal propagation is reliable even when the frequency exceeds 200 Hz. Interestingly, complex spike pattern such as bursts associated with CF activtion causes unreliable propagation. The reliability is determined by inter-spik-interval (for <2ms ISI, the second one is often skipped) and membrane voltage.

2-photon papers (Karel's recommendations)

2005-01-13T13:25:00.000-08:00

"Anyone doing 2-photon should have read and understood these key papers." (Karel)

Key Reviews
Denk, W., and Svoboda, K. (1997). Photon upmanship: why multiphoton imaging is more than a gimmick. Neuron 18, 351-357.

Microscope building
Mainen, Z. F., Maletic-Savatic, M., Shi, S. H., Hayashi, Y., Malinow, R., and Svoboda, K. (1999). Two-photon imaging in living brain slices. Methods 18, 231-239.

Tsai, P. S., Nishimura, N., Yoder, E. J., White, A., Dolnick, E., and Kleinfeld, D. (2002). Principles, design and construction of a two photon scanning microscope for in vitro and in vivo studies. In Methods for In Vivo Optical Imaging, R. Frostig, ed. (CRC Press), pp. 113-171.

Imaging in scattering tissues
Oheim, M., Beaurepaire, E., Chaigneau, E., Mertz, J., and Charpak, S. (2001). Two-photon microscopy in brain tissue: parameters influencing the imaging depth. J Neurosci Methods 111, 29-37.

Lichtman's talk

2005-01-11T14:04:00.000-08:00

Jeff Lichtman gave a talk about competition between axons connecting to a single neuromuscular junction on 1/10 here at Cold Spring Harbor Lab. His group has been imaging axons expressing YFP or CFP, and directly measure the battle between two axons: both axons try to take more synapse area. Interestingly the fate of the competition is determined globally: if a yellow axon loose the battle at one synapse to a blue axon, most likely all of other synapses of the yellow axon also loose to the blue axon. Furthremore, the one loosing battles always innovating more synapses. Thus, it seems like a single axon has only a limited amount of resource, and if one keep winning to have more synapses, the one run out of resources, and start to loose other battles. Interesting questions would be 1) what kind of resource limits the number of synapses and 2) how experience of synapses affect battles. It would be important to measure activity of synapses of winning and loosing axons to solve these questions.

Papers (Neuron 1/6/5)

2005-01-10T07:58:00.000-08:00

-NMDA Receptor-Dependent Activation of the Small GTPase Rab5 Drives the Removal of Synaptic AMPA Receptors during Hippocampal LTD (José Esteban's et al.) Neuron, Vol 45, 81-94

Congratulations, José ! It might be fun to see interactions between Rab5 and the C terminus of rabaptin-5 (last 74 amino acids) using our FLIM system.

-Dendritic Spine Heterogeneity Determines Afferent-Specific Hebbian Plasticity in the Amygdala (Andreas Lüthi et al.) Neuron, Vol 45, 119-131

It is always great to see a paper citing my paper! They identify spines connected by thalamic and cortical affarents by calcium imaging. These spines are functionally and morphologically distinct. it surprises me a bit that one can do this kind of experiment. Looking for a stimulated spine is difficult especially if one stimulates far from a patched neuron. It is a kind of needle-in-haystack problem: only a small fraction of spine is activated to show a rapid and stochastic (some times release probability is less than 0.1) calcium responses.

Cloning note

2005-01-05T07:58:00.000-08:00

I had a chat with my colleague about why Clontech's vectors produce much weaker protein expression than other CMV-based vectors (such as pCI, pcDNA3, pRK5) do, even though they use the same CMV promoter ? It seems like following features of the clontech vectors make them less efficient:
-Clontech vectors use early SV40 polyA signal instead of late SV40 signal. The late SV40 is ~5 times stronger than the early-SV40 (According to Promega note).
-Clontech vectors do not have introns between the promoter and the SV40 polyA signal. It is widely believed the presence of introns is required for optimized protein expression.

Tech note: liquid Lenses

2004-11-02T07:58:00.000-08:00

In a 3D-scanning microscope, it is fairly easy to scan in the xy-plane rapidly using a pair of galvano-mirrors. However, for z-axis scanning, we still rely on a slow stepper motor. An introduction of a liquid lens (discussed in slashdot) by Varioptics might allow a rapid changing of the focus position along the z-axis. The lens is made of water and oil sandwitched by two glass window in a conical structure. According to the article, "the interface between the oil and water will change shape depending on the voltage applied across the conical structure. At zero volts, the surface is flat, but at 40 volts, the surface of the oil is highly convex".

Tech note: Applying dual-colour fluctuation cross-orrelation spectroscopy to cell signaling studies

2004-07-19T08:06:00.000-07:00

Quantitative measurements of dynamics of protein-protein interactions in cells are crucial to understand cell signaling. The fluctuation correlation spectroscopy (FCS) and dual-color fluctuation cross-correlation spectroscopy (FCCS) may open a new way to explore cell signaling mechanisms.

Principles:

1. FCS
FCS measures the fluctuation of fluorescence emitted from a small excitation spot (~0.5 fL) made by a focused laser. When the number of fluorophores in the spot is small, the fluorescence intensity fluctuates due to the in and out movement of the fluorophores (fluctuation size ~ 1/√N. In the case the fluorophores diffuse freely, the fluctuation has the correlation time characterized by the diffusion constant and the size of laser spot. Therefore, by quantifying the correlation time using autocorrelation (or probably Fourier transformation?), the diffusion constant can be obtained. Because the diffusion constant is roughly proportional to the diameter of labeled proteins, this can be a measure of protein binding.

Analytical solution of the autocorrelation is given as follows:

G(τ) = < δ I(t) δ I(t+τ) > / < i ² >

= 1 + 1/[N(1+τ/τ_c) √(1+τ/(g²τ_c)]

where N and τ_c are the average number of fluorescent particle in the volume element and the diffusion time, respectively. q is the ratio of the exp(-2) distance in z-axis and radius in the x-y plane in the confocal space. &tau_c is determined by w_xy²/(4D) where D and w_xy are the diffusion coefficient and the exp(-2) radius. This value is the mean transit time of the molecule in the space.

2. FCCS
The fluctuation of two different fluorophores have interesting characteristics. When two dyes bind together, these dyes move in and out simultaneously, causing the high correlation between these two fluctuations. Therefore, the cross-correlation of the two fluctuation can be a good measure of the interactions between two labeled proteins.

Cross-correlation is defined as
G(τ) = < δI(t)δI(τ+t) > / < i ² >

where r and g indicate signals of different colors. Fraction of binding protein can be obtained as G _rg(0) / G _r(0).

APplication to studies of cellular and synaptic signaling

Both FCS and FCCS work beautifully in cuvette. However, the situation is much more complicated in cells. For example, if two proteins are in the same vesicle, they move together even if they are not bound together. Bacia K. et al. (2002, biophysical J.) used this fact to analyze vesicular movements. Also, slow movements of large organelles containing these proteins can give burst fluorescence, causing a large correlation. Non-mobile fraction of proteins can give some artificial correlations due to photo-bleaching. Thus, great cares have to be taken to interpret the correlation signal. Even with these limitation, Schwille and his colleagues (Kim et al., PNAS 2004) have shown that the techniques are useful to measure interactions between highly mobile signaling proteins in Cells.

Is it possible to apply this technique for the analysis of signaling in neuro-microcompartments such as dendritic spines ? Because dendritic spines are usually smaller than optical resolution, the fluorescence fluctuation is made by fluorophore movement through the narrow necks connecting the spines and their parent dendrite. The time constant of this diffusion coupling is about 0.1-0.8 sec for highly mobile proteins such as GFP. To obtain successful signal-to-noise ratio, the measurements of fluctuation with such the long correlation time can take minutes (hundred times correlation time). For actin associated proteins, because actin-turnover should be ~5 min. time scale, one will need ~hours of imaging without even submicron drift (submicron drift can cause large artificial correlation in this measurement). PSD proteins, forget it. Therefore, the FCS and FCCS applications to studies of synaptic signaling are probably very limited.