December 9, 2004

At the December 3, 2004 UK-California Stem Cell Symposium, here at CHLA, I got to thinking about how many dimensions can be examined in a light microscopy experiment. The list that I came up with can be summarized as:

xyztiλτθρηN$

where:

xy       XY dimensions of a 2D image

z          Z dimension (axial; multiple planes of focus

t            Time (timepoints within a dataset; also developmental or organism time)

i            Intensity (amplitude of signal = photon flux ... possibly due to changes in absorption)

λ          Lambda: Wavelength (transmission, reflectance, excitation, emission spectra)   

               For fluorescence spectra, see http://www.mcb.arizona.edu/ipc/fret/default.htm        

τ            Tau: Fluorescence lifetime

θ            Theta: Rotational lifetime (how molecules spin)

ρ             Polarization (birefringence; fluorescence polarization & anisotropy)

η             Refractive index

N             Number of replicates (sample size) needed for statistical significance. 

$             Money to buy and run all of the equipment needed.

I propose there is a direct correlation between the quantity of $ and the number of other dimensions you can work in. The limit being 0,0.

For my purposes, Lambda () includes color, i.e. RGB color or 1,2,3 etc number of images. 

Terms for which I do not have good symbols for: 

* phase - as in Zernike phase contrast (or Nomarski or Smith DIC). 

* how (or whether) to distinguish between brightfield/DIC/phase etc and fluorescence.

* how (or whether) to make distinctions between 1, 2, 3 etc photon excitation (fluorescence) as well as between 2nd, 3rd, etc harmonic generation (SHG, THG, etcHG). 

* multiple stage positions and/or stage tiling (acquire images from greater than field of view)

* measurements (changes in "specimen dimensions", orientation) 

* dry mass (re: Graham Dunn DRIMAP - is this a measurement image or a dimension?)

* retardance (i.e. Polscope birefringence imaging).

* multichannel ratio - i.e. ratiometric FRET or Fura-2 signals. 

* lens type(s) - i.e. plan apochromat, plan fluorite, plan achromat, (non-plan) lenses, and the new Super-apo, VC (violet corrected) apo's etc. 

* Magnification? - it is very easy to change magnification on many microscopes, for example, the electronic zoom on a confocal laser scanning microscope. Too low or high a magnification, and you will fail to satisfy Nyquist sampling theorem. Note that there are times when you should "fail Nyquist", such as in using high zoom to make objects very large for sub-pixel centroid finding (i.e. single particle tracking).

* Resolution? - All microscope objective lenses are engraved on the barrel with both magnification and numerical aperture (NA). If a study does not report lens type, magnification, and NA -- and while we're at it, intermediate magnification and pixel dimensions - how is anyone supposed to (1) know how well the microscope should be performing, and (2) replicate the experiment. For that matter, if the settings were not documented, how does someone know they are repeating an experiment even on the same hardware? Hopefully resolution is kept constant (at the optimal settings, i.e. Koehler illumination for standard brightfield microscopy), but I wouldn't count on it. 

* Illumination "dimensions"? Multi-line lasers change relative output depending on power used. Argon ion lasers have little output at 458 nm at minimum power, respectable output at higher power (at highest power they tend to die quickly, after which they of course have zero power until more $ is pumped into them); Xenon flash lamps have distinct spectra at low vs high power; arc lamps frost over with age (mostly an Intensity effect).  

* Detector "dimensions"? Quantum efficiency, detector temperature, exposure time(s), all impact light collection efficiency, background noise, and signal to noise ratio (SNR). To paraphrase Clinton/Gore 1992: "it's the SNR stupid" that dictates performance. 

* Reagent dimensions? What happens if you run out of a production lot of antibodies or serum in the middle of an experiment? Clearly, temperature, humidity, osmolality, perfusion rate, oxygen tension (partial oxygen pressure), CO2 concentration, ionic composition, and more, are potential variables. These could vary on purpose (your experiment: pre vs post stimulus) or unintentionally (room drafts, temperature changes, etc).

Any additions (or subtractions?) from this list are welcome. Please email comments to me at gmcnamara@chla.usc.edu and geomcnamara@earthlink.net 

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