Soliton model
Encyclopedia
The Soliton model in neuroscience
is a recently developed model that attempts to explain how signals are conducted within neuron
s. It proposes that the signals travel along the cell's membrane
in the form of certain kinds of sound
(or density
) pulses known as soliton
s. As such the model presents a direct challenge to the widely accepted Hodgkin-Huxley model
which proposes that signals travel as action potential
s: voltage-gated ion channel
s in the membrane open and allow ion
s to rush into the cell, thereby leading to the opening of other nearby ion channels and thus propagating the signal in an essentially electrical manner.
of the University of Copenhagen
. Heimburg heads the institute's Membrane Biophysics Group and as of early 2007 all published articles on the model come from this group.
(the temperature below which the consistency changes from fluid to gel-like) only slightly below the organism's body temperature, and this allows for the propagation of solitons. It has been known for several decades that an action potential traveling along a neuron results in a slight increase in temperature followed by a decrease in temperature. No net heat is released during the overall pulse. The decrease during the second phase of the action potential is not explained by the Hodgkin-Huxley model (electrical charges traveling through a resistor
always produce heat), but traveling solitons do not lose energy in this way and the observed temperature profile is consistent with the Soliton model. Further, it has been observed that a signal traveling along a neuron results in a slight local thickening of the membrane and a force acting outwards; this effect is not explained by the Hodgkin-Huxley model but is clearly consistent with the Soliton model.
It is undeniable that an electrical signal can be observed when an action potential propagates along a neuron. The Soliton model explains this as follows: the traveling soliton locally changes density and thickness of the membrane, and since the membrane contains many charged and polar
substances, this will result in an electrical effect, akin to piezoelectricity
.
where
is time and 
is the position along the nerve axon. 
is the change in membrane density under the influence of the action potential, 
is the sound velocity of the nerve membrane, 
and 
describe the nature of the phase transition and thereby the nonlinearity of the elastic constants of the nerve membrane. The parameters 
, 
and 
are dictated by the thermodynamic properties of the nerve membrane and cannot be adjusted freely. They have to be determined experimentally. The parameter 
describes the frequency dependence of the sound velocity of the membrane (dispersion relation
). The above equation does not contain any fit parameters. It is formally related to the Boussinesq approximation (water waves)
for solitons in water canals. The solutions of the above equation possess a limiting maximum amplitude and a minimum propagation velocity that is similar to the pulse velocity in myelinated nerves. There also exist periodic solutions that display hyperpolarization and refractory periods.
proteins on a molecular scale. It is rather assumed that their properties are implicitly contained in the macroscopic thermodynamic properties of the nerve membranes. The model is therefore neither in conflict with the action of membrane proteins nor with pharmacology. The soliton model predicts membrane current fluctuations during the action potential. These currents are of similar appearance as those reported for ion channel proteins. They are thought to be caused by lipid membrane pores spontaneously generated by the thermal fluctuations, which are at the core of the soliton model.
holds that the strength of a wide variety of chemically diverse anesthetics is proportional to their lipid
solubility, suggesting that they do not act by binding to specific protein
s such as ion channels but instead by dissolving in and changing the properties of the lipid membrane. Dissolving substances in the membrane lowers the membrane's freezing point, and the resulting larger difference between body temperature and freezing point inhibits the propagation of solitons. By increasing pressure, lowering pH
or lowering temperature, this difference can be restored back to normal, which should cancel the action of anesthetics: this is indeed observed. The amount of pressure needed to cancel the action of an anesthetic of a given lipid solubility can be computed from the soliton model and agrees reasonably well with experimental observations.
Neuroscience
Neuroscience is the scientific study of the nervous system. Traditionally, neuroscience has been seen as a branch of biology. However, it is currently an interdisciplinary science that collaborates with other fields such as chemistry, computer science, engineering, linguistics, mathematics,...
is a recently developed model that attempts to explain how signals are conducted within neuron
Neuron
A neuron is an electrically excitable cell that processes and transmits information by electrical and chemical signaling. Chemical signaling occurs via synapses, specialized connections with other cells. Neurons connect to each other to form networks. Neurons are the core components of the nervous...
s. It proposes that the signals travel along the cell's membrane
Cell membrane
The cell membrane or plasma membrane is a biological membrane that separates the interior of all cells from the outside environment. The cell membrane is selectively permeable to ions and organic molecules and controls the movement of substances in and out of cells. It basically protects the cell...
in the form of certain kinds of sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
(or density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
) pulses known as soliton
Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
s. As such the model presents a direct challenge to the widely accepted Hodgkin-Huxley model
Hodgkin-Huxley model
The Hodgkin–Huxley model is a mathematical model that describes how action potentials in neurons are initiated and propagated....
which proposes that signals travel as action potential
Action potential
In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
s: voltage-gated ion channel
Voltage-gated ion channel
Voltage-gated ion channels are a class of transmembrane ion channels that are activated by changes in electrical potential difference near the channel; these types of ion channels are especially critical in neurons, but are common in many types of cells....
s in the membrane open and allow ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s to rush into the cell, thereby leading to the opening of other nearby ion channels and thus propagating the signal in an essentially electrical manner.
History
The Soliton model was developed beginning in 2005 by Thomas Heimburg and Andrew D. Jackson, both at the Niels Bohr InstituteNiels Bohr Institute
The Niels Bohr Institute is a research institute of the University of Copenhagen. The research of the institute spans astronomy, geophysics, nanotechnology, particle physics, quantum mechanics and biophysics....
of the University of Copenhagen
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
. Heimburg heads the institute's Membrane Biophysics Group and as of early 2007 all published articles on the model come from this group.
Justification
The model starts with the observation that cell membranes always have a freezing pointMelting point
The melting point of a solid is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at standard atmospheric pressure...
(the temperature below which the consistency changes from fluid to gel-like) only slightly below the organism's body temperature, and this allows for the propagation of solitons. It has been known for several decades that an action potential traveling along a neuron results in a slight increase in temperature followed by a decrease in temperature. No net heat is released during the overall pulse. The decrease during the second phase of the action potential is not explained by the Hodgkin-Huxley model (electrical charges traveling through a resistor
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
always produce heat), but traveling solitons do not lose energy in this way and the observed temperature profile is consistent with the Soliton model. Further, it has been observed that a signal traveling along a neuron results in a slight local thickening of the membrane and a force acting outwards; this effect is not explained by the Hodgkin-Huxley model but is clearly consistent with the Soliton model.
It is undeniable that an electrical signal can be observed when an action potential propagates along a neuron. The Soliton model explains this as follows: the traveling soliton locally changes density and thickness of the membrane, and since the membrane contains many charged and polar
Chemical polarity
In chemistry, polarity refers to a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. Polar molecules interact through dipole–dipole intermolecular forces and hydrogen bonds. Molecular polarity is dependent on the difference in...
substances, this will result in an electrical effect, akin to piezoelectricity
Piezoelectricity
Piezoelectricity is the charge which accumulates in certain solid materials in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure...
.
Formalism
The soliton representing the action potential of nerves is the solution of the partial differential equationPartial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
where
is time and is the position along the nerve axon. is the change in membrane density under the influence of the action potential, is the sound velocity of the nerve membrane, and describe the nature of the phase transition and thereby the nonlinearity of the elastic constants of the nerve membrane. The parameters , and are dictated by the thermodynamic properties of the nerve membrane and cannot be adjusted freely. They have to be determined experimentally. The parameter describes the frequency dependence of the sound velocity of the membrane (dispersion relationDispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....
). The above equation does not contain any fit parameters. It is formally related to the Boussinesq approximation (water waves)
Boussinesq approximation (water waves)
In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation...
for solitons in water canals. The solutions of the above equation possess a limiting maximum amplitude and a minimum propagation velocity that is similar to the pulse velocity in myelinated nerves. There also exist periodic solutions that display hyperpolarization and refractory periods.
Role of ion channels
The Soliton model explains several aspects of the action potential, which are not explained by Hodgkin-Huxley. Since it is of thermodynamic nature it does not address the properties of single macromolecules like ion channelIon channel
Ion channels are pore-forming proteins that help establish and control the small voltage gradient across the plasma membrane of cells by allowing the flow of ions down their electrochemical gradient. They are present in the membranes that surround all biological cells...
proteins on a molecular scale. It is rather assumed that their properties are implicitly contained in the macroscopic thermodynamic properties of the nerve membranes. The model is therefore neither in conflict with the action of membrane proteins nor with pharmacology. The soliton model predicts membrane current fluctuations during the action potential. These currents are of similar appearance as those reported for ion channel proteins. They are thought to be caused by lipid membrane pores spontaneously generated by the thermal fluctuations, which are at the core of the soliton model.
Application to anesthesia
The authors claim that their model explains the previously obscure mode of action of numerous anesthetics. The Meyer-Overton observationAnesthesia
Anesthesia, or anaesthesia , traditionally meant the condition of having sensation blocked or temporarily taken away...
holds that the strength of a wide variety of chemically diverse anesthetics is proportional to their lipid
Lipid
Lipids constitute a broad group of naturally occurring molecules that include fats, waxes, sterols, fat-soluble vitamins , monoglycerides, diglycerides, triglycerides, phospholipids, and others...
solubility, suggesting that they do not act by binding to specific protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
s such as ion channels but instead by dissolving in and changing the properties of the lipid membrane. Dissolving substances in the membrane lowers the membrane's freezing point, and the resulting larger difference between body temperature and freezing point inhibits the propagation of solitons. By increasing pressure, lowering pH
PH
In chemistry, pH is a measure of the acidity or basicity of an aqueous solution. Pure water is said to be neutral, with a pH close to 7.0 at . Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline...
or lowering temperature, this difference can be restored back to normal, which should cancel the action of anesthetics: this is indeed observed. The amount of pressure needed to cancel the action of an anesthetic of a given lipid solubility can be computed from the soliton model and agrees reasonably well with experimental observations.
Sources
- On the (sound) track of anesthetics, press release University of Copenhagen, 6 March 2007 An elementary introduction.