mitochondrial volume

Dean Pentcheff dean2 at
Tue Sep 21 17:21:05 EST 1993

rogersh at writes:
> How would one go about determining the mitochondrial volume in
>tissue culture cells....unfortunately plant ones.
>Is there a method(s) for doing this ?
>Has any one done it ?
> What are the problems ? (must be loads I expect)
>Simply any information would be really helpful.
> I must say, however, I have no wish to undertake serial sectioning!
>  Hilary Rogers  

There is a whole body of literature dealing with problems like that:
getting three-dimensional information from two-dimensional sections of
structures.  The field is called "stereology."  Depending on the
specifics of your problem, there are all sorts of approaches.

[Late note added in press: oops, _now_ I notice the poster asked about 
 cells in tissue culture, not whole tissue samples... Details of what I
 say later will need to be revised in that light.  I'll leave it as an
 exercise to the Gentle Reader...]

First, I'll assume you just want the relative volume fraction of
mitochondria in the tissue (volume of mitochondria / volume of
tissue):  the "volume density" of mitochondria.  The basic technique
you'd probably use is to take random sections of your tissue (and I
mean random - there are sampling protocols to make sure of this).  On a
subset of the sections, you'll pick a series of microscopic fields.  On
each of those fields, you'll overlay a grid of dots (in the microscope
eyepiece as a reticle, by using a camera lucida focussed on a paper
grid, or by taking photos of the fields and overlaying them with an
acetate sheet).  A count of the number of dots that falls on
mitochondria divided by the count of the number of dots falling on all
the tissue is an estimate of the relative area covered by mitochondria
on the section.  ICBST (It Can Be Shown That) this ratio is also the
relative volume of mitochondria in the volume of the tissue (the volume
density of mitochondria).  That may be good enough for you.

On the other hand, you may want to know the average volume of
individual mitochondria (not just the volume fraction of mitochondria
in the tissue).  One way of getting that number is to get the number of
mitochondria per volume of tissue (the "numerical density" of
mitochondria) as well as the volume density of mitochondria.  Dividing
the volume density of mitochondria by the numerical density of
mitochondria will yield the average mitochondrial volume.

Until very recently, reliable numerical densities were really hard to
get, especially for bizarre non-spherical shapes like mitochondria.
The techniques depended on assumptions about the geometry of the
particles involved.  A number of really nice techniques have recently
been developed, though, that make it much easier and far more reliable
(notably the "disector" and "fractionator", to toss in some jargon).
Once again, these techniques depend on specific sectioning and counting

For the fractionator, one repeatedly splits a tissue sample (again,
using sampling methods carefully designed to avoid statistical bias)
After repeatedly splitting the tissue, you'll be left with a few tiny
tissue blocks.  You'll section those and select a few pairs of adjacent
sections.  Those sections could be "real" physical sections, or you may
be able to come up with a way of optically sectioning the material just
using the microscope.  With those adjacent sections, you'll compare
matched fields using a specific protocol to count particles (this is
the "disector" technique, or its derivative, the "selector").  This
could be done with a pair of adjacent microscopes with drawing tubes,
or by taking photos of matched fields.  Fundamentally, to get estimates
of numerical density without making assumptions about the geometry of
your particles, you are forced to work from at least two sections.
Exhaustive serial sectioning is the worst option (in terms of work).
The fractionator/disector paired technique takes remarkabley few
sections for reliable estimates, and you only need adjacent pairs, not
whole stacks.

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