Download Nerves: A Physics Problem

Niels Bohr Institute - Membrane Biophysics Group
Nerves: A Physics Problem
Thomas Heimburg - Membrane Biophysics Group
Niels Bohr Institute, University of Copenhagen
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Niels Bohr Institute - Membrane Biophysics Group
Nerves
Luigi Galvani
1737-1798
Hermann v. Helmholtz Archibald V. Hill
1821-1894
1886-1977
Alessandro Volta
1745-1827
Alan L. Hodgkin
1914-1998
Andrew F. Huxley
*1917
Ishiji Tasaki
*1910
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Niels Bohr Institute - Membrane Biophysics Group
exciting nerves by voltage or currents
crayfish motor neuron
extracellular
mV
0.10
0.05
0.00
-0.05
0.00
0.05
0.10
0.15
time [s]
0.20
0.25
0.30
BUT: Nerves can also be excited by
• mechanical means (force)
• cooling (temperature)
• acids (pH)
(These variables were also important for anesthesia)
This is so far unexplained and the existing models don‘t address this! 3
Niels Bohr Institute - Membrane Biophysics Group
The molecular biology picture of a membrane
WHERE IS THE PHYSICS?
what about physical variables, e.g.:
pressure
temperature
volume
entropy
heat
length scales
time scales
... ?
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Niels Bohr Institute - Membrane Biophysics Group
A physical picture for nerve pulses
E. Wilke. 1912. Pflüger‘s Arch.
Curtis&Cole. 1942. J. Physiol.
Hodgkin & Huxley. 1945. J. Physiol.
I want to convince you that nerve pulses are piezoelectric
waves (or sound pulses)
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Niels Bohr Institute - Membrane Biophysics Group
reminder: lipid membranes
can melt
high sensitivity differential
micro-calorimetry
changes in:
• enthalpy: ∆H~35kJ/mol
• volume: ∆V/V~0.04
• area: ∆A/A~0.24 !!!
• thickness: ∆d/d~ -0.16
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Niels Bohr Institute - Membrane Biophysics Group
Some facts about lipid transitions - last weeks
lecture continued
The enthalpy (heat uptake) is proportional to the volume and the
area: This means that heat is released from the membrane when you
compress it
The heat capacity cP is proportional to:
•
•
•
•
volume compressibility
area compressibility
bending elasticity
relaxation times κTV ~ cP
κTA ~ cP
1/K = κbend ~ cP
τrelax ~ cP
This means that membranes are soft in the transition!!!
When membranes are compressed they become soft!
Heimburg. 1998. Biochim.Biophys.Acta. 1415: 147-162 - Halstenberg et al. 1998. Biophys.J. 75: 264-271
Ebel et al. 2001. J.Phys.Chem.B 105: 7353-7360 - Ivanova et al. 2001. Phys. Rev. E 63: 1914-1925
Grabitz et al., 2002. Biophys.J.82: 299-309 - Schrader et al. 2002. J.Phys.Chem.B 106: 6581-6586
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Niels Bohr Institute - Membrane Biophysics Group
measuring the sound velocity
measuring sound velocities in a cavity resonator at 5 MHz:
• Sound velocity c
c=
!
1
κS · ρ
• Sound velocity number u:
(normalized sound velocity)
c − cH2 O
u=
cH2 O · [L]
one can correctly predict sound
velocities from heat capacities
Halstenberg,...,Heimburg,Kaatze. 1998. Biophys.J. 75: 264-271
Schrader,..., Heimburg, Kaatze. 2002. J.Phys.Chem.B 106: 6581-6586
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Niels Bohr Institute - Membrane Biophysics Group
some facts about nerves
•
ion concentrations inside and outside of a nerve are largely different
(e.g. squid axon: 400mM K+ inside and 20mM outside, 400mM Na+
outside and 20mM inside)
•
these concentration differences are responsible for a ‘resting’
potential of the membrane of ~ -70mV (Nernst potential)
•
electrical excitations called ‘action potentials’ can propagate along
nerves (typical velocity 1-100 m/s)
•
myelinated nerves display faster pulses
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Niels Bohr Institute - Membrane Biophysics Group
Hodgkin-Huxley: equivalent circuits
Im
dU
+ gK (U − EK ) + gN a (U − EN a ) + ...
= Cm
dt
currents through membrane, resting potentials for individual ions
gK and gNa are the conductivities of the membrane for K+ and Na+, which
are typically a function of time and voltage. The currents should produce
heat.
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Niels Bohr Institute - Membrane Biophysics Group
Hodgkin-Huxley theory:
• It is based on electrical currents through resistors called ion channels
• It is not a thermodynamic theory - it does not contain ‘volume’, ‘temperature’,
‘entropy’ etc. as variables - nevertheless, resistors should produce heat with a rate
dQ
= U · Im > 0
P =
dt
• The entropy production should always be positive, independent of the direction of
the ion flux
• Therefore, the action potential must be linked to heat production the Hodgkin-Huxley theory is not (!!!) adiabatic / isentropic
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Niels Bohr Institute - Membrane Biophysics Group
thermodynamics of the nerve pulses
•
•
force exerted by a squid axon during action potential
dislocations
Iwasa & Tasaki. 1980.
BBRC 95: 1328
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Niels Bohr Institute - Membrane Biophysics Group
thermodynamics of the nerve pulses
adapted from
Ritchie & Keynes, 1985
• heat release and voltage (actually energy of capacitor)
are in phase
• no net heat release: adiabatic/isentropic!
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Niels Bohr Institute - Membrane Biophysics Group
why is this strange?
•
•
•
•
the action potential seems to be isentropic (no entropy/heat production)
indicating that the physical processes underlying the pulse propagation
are reversible processes
the mechanical changes are in phase with potential changes
the heat changes are in phase with voltage changes
the action potential has rather the properties of a pressure wave/
pulse - may the action potential be a sound wave?

•
•
•
however: the Hodgkin-Huxley theory is clearly non-isentropic
the propagation of the pulse is driven by ion fluxes along gradients (Na+
and K+). It does not contain reversible processes!
an isentropic action potential is inconsistent with the HH-theory
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Niels Bohr Institute - Membrane Biophysics Group
sound velocity as function of density
c2=
1
=c
ρ ⋅ κs
€
sound velocity
Heimburg & Jackson, 2005.
PNAS 102: 9790-9795
Interesting spring properties of membranes:
• the membrane becomes softer upon compression
• frequency dependence of sound velocity nonlinearity
dispersion
possibility of soliton propagation
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Niels Bohr Institute - Membrane Biophysics Group
soliton in a river
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Niels Bohr Institute - Membrane Biophysics Group


$
%


∂ 
∂ ∆ρ
∂
1

∆ρ
=

2
∂t
∂x  ρ · κS ∂x 
& '( )
2
solitons
c=const.
2
∂ 2 ∆ρ
∂
∆ρ
2
= c0
2
∂t
∂x2
normal sound
propagation
c2
2
∂
∂ ∆ρ
=
2
∂t
∂x
!
" 2
#
∂4
2 ∂
∆ρ − h 4
c0 + p∆ρ + q∆ρ
∂x
∂x
$
DPPC LUV, 45°C
width 1 mm for
4
m
h=2 2
dispersion
s
0.20
v = 0.651 · c0
0.15
ΔρA/ρ0A
sound propagation
with nonlinearity
and dispersion
0.10
0.05
€
0.00
-0.10
-0.05
0.00
z [m]
0.05
0.10
propagation
velocity
m
≈ 100
s
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Niels Bohr Institute - Membrane Biophysics Group
comparison with experiment
real nerve
real nerve
adapted from
Ritchie & Keynes 1985
adapted from
Byrne & Tasaki 1981
the properties of our solitons are very similar to
those of the nerve pulse
Heimburg & Jackson, 2005. Proc.Natl.Acad.Sci. USA102: 9790-9795
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Niels Bohr Institute - Membrane Biophysics Group
advantages of the soliton model
• Propagation velocity around 100 m/s - similar than in a
myelinated nerve
• A soliton would automatically produce heat changes and
mechanical displacements in phase with the voltage pulse
(action potential)
• The model explains why nerve pulses can be induced by
cooling or by mechanical perturbations
• It also correctly predicts that a nerve pulse can be inhibited
by heating
• It explains the Meyer-Overton rule and the pressure
reversal of anesthesia quantitatively
• It also provides a key for the inhibition of anesthesia during
inflamation
• None of these features are explained by the HH theory
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