Poster for Gomadingen 2006

1
So you think you know how anesthetics works?
(How anesthetics influence the density pulse in
a cylindrical system) Yes Please read on for a
different view. --- No Please read on and
hopefully learn a little. Kaare Græsbøll, Andrew
D. Jackson, Benny Lautrup, Heiko Seeger, and
Thomas Heimburg.Department of Bio membranes,
Niels Bohr Institute University of Copenhagen
Denmark
The Hodgkin-Huxley Model.
What is all the fuzz about? Regard the following
pictures of a small collection molecules. There
is huge variety in the selection, nevertheless
they all act as anesthetics.
The compressibility of the system is calculated
from heat capacity
The currently commonly accepted nerve model is
the Hodgkin-Huxley Model (HHM). This is an
entirely electrical model based on the
assumption of the nerve membrane to be regarded
as an electrical impenetrable membrane with
embedded protein channels to transmit ions and
thereby current.
Non-linear properties of the nerve membrane
(picture left) in phase transition regime sustain
stable density waves Solitons. (picture right)
From compressibility data solitons are calculated
using the soliton equation. As apparent from the
graph on solitons, soliton shape is dependent on
the velocity of the soliton. Using data, width
and energy profiles as function of velocity has
been calculated for the different anesthetic
concentrations.
Action of Anesthetics.
The link between the Meyer-Overton Rule, which
states that the solubility of a drug in lipids
the membrane decides the anesthetics strength,
and the Soliton model, which key feature is
non-linear properties of the compressibility
during phase transition, is Melting point
depression.
Width of solitons as a function of soliton
velocity. To send max information along a nerve.
The width of soliton must be minimum, for all
data this happens at app. 120 m/s.
The nerve signal - an electrical pulse - travels
along the nerve, driven by opening and closing of
ion channels (picture) which allows ions to flow
through the channels due to concentration
differences of ions on the in- and outside of the
nerve.
This simple relation states that the depression
of the melting point of a given substance, M, is
directly proportional to the concentration of a
substance, A, which is only dissolved in the
liquid phase.
Collection of molecules that will act as
anesthetics.
The common property of these drugs where
discovered more than a hundred years ago by C.E.
Overton The strength of all anesthetics is
proportional to the solubility of the anesthetic
in lipids. Also all substances dissolvable in
lipids acts as anesthetics proportional to their
solubility.
The HHM include Sodium, Potassium and Leak
current channels which combines into a delicate
electric circuit, that is repeated along the
nerve.
This physical mechanism is responsible for
melting the ice on our pavements when salt is
tossed. And also it changes the melting point of
nerve membranes, thereby changing the properties
of the compressibility, and so affecting the
solitons which carry the nerve signal!
Energy of solitons as a function of soliton
velocity. If nerve signals travels at 120 m/s,
the energy cost is twice in the most anesthetized
nerve compared to no anesthetic.
The combined circuit is governed by ten coupled
differential equations, the primary one
describing the circuit
The solubility of anesthetics in oil as a
function of anesthetics strength is linear in a
log-log system. This relation is known as the
Meyer-Overton Rule.
Experiments.
To investigate whether the assumption of melting
point depression is viable in a bio-membrane, and
how it affects the compressibility. Experiments
where conducted on this Micro Calorimeter.
Apparently it cost more energy to send a soliton
in an anesthetized membrane, if that energy is
not available is not available no signal can be
sent!
where n, m, and h are given by the other nine
equations. In the HHM anesthetics act by binding
to these ion channels and thereby blocking them.
It is very difficult to explain how the channels
can have binding sites for all anesthetics!
To sum it up.
There is a lot of good reasons to revise the
existing view on how nerves function. A new model
for nerves was proposed by Heimburg and Jackson,
and this project has so far shown how anesthetics
might trivially work within that new model. Lots
of more anesthetics will have to be tested in a
similar way, so that the relation to the
Meyer-Overton Rule can be firmly established and
hence demonstrates that this model works for all
anesthetics.
One would assume that these old finding was
easily incorporated in the modern understanding
of how nerves function, since nerves are where
anesthetics works. This is not the case and
that is what the fuzz is about.
Experiments where performed using pure DPPC-lipid
membranes and 1-octanol as anesthetic.
The Soliton Model.
The action of anesthetics is more easily
implemented in a new model for nerves proposed by
T. Heimburg and A. Jackson (2005) The Soliton
Model (SM). The SM is based on a soliton wave in
the nerve membrane, that is a density pulse that
does not change shape or velocity as it travels,
ergo it does not lose energy, it is an adiabatic
wave. The soliton equation is a wave equation
with a dispersion term.
Nerves.
Nerves come in many varieties, but they are all
cells and as such share characteristics with
other cells, in interest for nerve models is the
cell membrane, which consist of lipids and
proteins.
Literature Hodgkin and Huxley, J. Physiol. 1952
117, 500-544 C.E. Overton, Studien die Narkose,
1901 Heimburg and Jackson, PNAS, vol 102, no 28,
9790-9795, 2005
Want to comment on this poster? Mail me on
grasboll_at_nbi.dk Or talk to me in person (picture).
where r is the density of the membrane, and k is
the compressibility. The key feature is that k
displays nonlinear properties in the phase
transition regime of a bio-membrane, this allows
solitons.
Heat capacity profiles of DPPC with increasing
amount of anesthetic. This data shows how
anesthetics perform melting point depression on a
lipid membrane. When fitting to theory the
correlation coefficient is rr 0.998.