On Fri, 01 Feb 2002 20:42:34 +0100, Edmund Müller <edmund.mueller at freenet.de> wrote:
>Hallo,
>>>Measuring capacity can be somewhat tricky. Exactly what
>>experimental technique are you using?
>>Whole-cell recording in voltage clamp with holding -50 mV and a hyperpolarizing
>step of -10 mV to -60 mV for 20 ms.
>>>What do your data look like?
>>Well, quite classical considering the large axon this cell has: The decaying
>current can very well be approximated biexponential in the form
>>I=Ifast*exp(-t/taufast)+Islow*exp(-t/tauslow).
>>>How are you calculating time constant? How are you calculating
>>capacitance?
>>The time constants I get directly from the above equations. I assume the faster
>belonging to the soma, the slower to the axon. So for the soma I just take the
>first part of the above equation, integrate over time and divide by 10 mV, the
>step used. This should produce the capacity of the cell, shouldn't it?
>>>the neurites. Fourth, because of the cable properties, the area of the
>>neurites (certainly the region within, say, one space constant) must
>>be considered in calculating the area of the cell.
>>Even if I try to neglect that in the above manner? Well how big is the space
>constant for rat hippocampal cells. Since I didn't measure I must guess. Any
>formulas available like space constant= function (diameter axon, etc.)?
>>>Fifth, are you sure
>>your cells are actually the size you say? Where did you get the
>>size information? These are some of the factors you must consider.
>>By taking top view photos of it and approximating an elliptical shape of the
>soma with 9 x 6 micrometers. For the third dimension which I cannot see I
>guessed a rotation symmetric cell so the third dimension is 6 micrometers.
>>I must admit that the cell has a large long axon.
>>Edmund
It has been some time since I did capacitance measurements and
even then, it was in the olden days with microelectrodes. I
hope there is someone on the group who does have experience
measuring cell parameters using patch clamp techniques. But
here is some "book knowledge". Incidentally, the book is the
bible of patch clamping, in case you don't already know that.
The book is "Single-Channel Recording" 2nd Edition, edited by
Sakmann and Neher (Plenum Press, 1995). Chapter 7 by Kevin
Gillis is specifically about "Techniques for Membrane Capacitance
Measurements". Using transient currents from voltage steps
is discussed, but there are other more useful techniques
involving sine waves that seem to produce much more accurate
results. At least, they are discussed at far greatere length.
The essential points are (p. 156) "Techniques for estimating
membrane capacitance... rely on the accuracy of the equivalent
circuit of a cell ... It is important to note that such a simple
model only applies to cells that are approximately spherical
without significant 'neurite-like' membrane projections."
Chapter 2, "Tight-Seal Whole-Cell Recording" by Alain Marty
and Erwin Neher discuss the equivalent circuit model. Here, the
important results are (p. 39) "Brain neurons, for example, have
complicated dendritic arborizations that are not instantly charged
if a square voltage pulse is applied to the soma.". Then on p. 42,
"Whereas Purkinje cells can be satisfactorily modeled with a two-
compartment equivalent circuit, other neurons cannot. In
hippocampal pyramidal cells, for instance, three-exponentials
are needed to model the capcitataive current decay...In such
complex cases a cable analysis may be more appropriate than
a multicompartment model" They refer you to M.B. Jackson,
"Cable analysis with the whole-cell patch-clamp." Biophys.
J. 61:756-766(1992).
The upshot is that it is very definitely NOT true that the
first time constant is the soma and the second the neurite.
Both are complex combinations of the cell resistance and the
patch electrode resistance along with the capacitance. Note
that the cable model ordinarily (always?) assumes that the
soma and the neurite have the SAME time constant! That is,
the apparent two or three or whatever time constants are
merely the fact that you are trying to represent a partial
differential equation with complex boundary conditions with
an ordinary differential equation.
I seem to recall you asking other questions on this group
that indicate that you may be new to a lot of this highly
quantitative work. If so, you really need a lot of help
and advice. At the same time, you are doing some rather
sophisticated experimental procedures. Is there anyone in
you lab that can help you guide you as to the proper
mathematical techniques? If not, and if it is at all possible,
then a few weeks spent in an appropriate laboratory may
be far more valuable than banging your head against the
wall alone in your laboragory for a year (or two or more)
trying to learn the same things. In any event, make sure
you are well familiar with the material in the two chapters
I quoted (and the Jackson paper) before continuing!
