"r norman" <rsnorman_ at _comcast.net> wrote in message
news:p4ih9v45tu7damae50i6p2r11livvs1b1f at 4ax.com...
| On Fri, 11 Apr 2003 18:47:27 -0400, Jake <jtrexel at ix.netcom.com>
|| >How do I parameterize these equations
| >using time as the dependent
| >variable ? v is for voltage, alpha
| >is the alpha symbol and I have 3
| >separate equations for alpha (n, h and n).
| > I also want to be able to
| >plot them together.
| >alpha(m)(v) = 4*exp(1-0.0556(v+65)
| >alpha(h)(v) = 1/(1+exp-0.1(v+35))
| >aplah(n)(v) = 0.125*exp(-0.0125*v + 65)
| >These are the Hodgkin-Huxley equations.
|| I think you may not be understanding the
| H-H equations correctly, or else or are
possibly not asking the question correctly. Then
| again, I may be misunderstanding your question.
|| The alpha's and beta's in the H-H equations
| are not functions of time. They vary with voltage,
| as you show. But the alphas and betas are,
| in fact, parameters in differential equations for
| m, n, and h. That is where time enters:
| dm/dt = alpha-m * (1-m) - beta-m * m
|| It doesn't really mean much to plot the alphas
| and betas vs time. On the other hand, plotting
| m, n, and h vs time is useful because
| they have a physical interpretation in terms
| of activation and inactivation
All such can be reduced to energy-flow, which can be further reduced
ti 'instaneous energy-gradient ['instantaneous' energy vector field],
which is the only 'proper' way to do it because there's no such thing
as 'time' in physical reality, and this is especially important
within nervous systems in which everything that has been referred to
as "time" occurs as a function of energy-flow.
[It's the same within the rest of physical reality, but Physicists
just don't get-it [yet]].
What's been referred to as "time" is nothing more than a mental
construct that's been used to order discussions of energy-flow. The
mental consturct works against understanding, however, instead of
The problem inherent shows up when the 'time'-ordering is replaced
with any linear numerical "counting" method.
Such doesn't work because, to correspond rigorously to physical
reality, the 'units' have to be variables - which exposes 'time' as
an encumbering "absurdity" through which energy-flow is commonly
addressed in an absurdly-convoluted way.
Why not just calculate the energy-flow, and reap the rewards of
understanding [and applications] inherent in doing so?
ken [K. P. Collins]