Soliton model in neuroscience

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Nonlinear electro-mechanical wave measured in an artificial lipid system Nonlinear electro-mechanical wave observed in single molecule thin film of lipids, using voltage sensitive probes.jpg
Nonlinear electro-mechanical wave measured in an artificial lipid system

The soliton hypothesis in neuroscience is a model that claims to explain how action potentials are initiated and conducted along axons based on a thermodynamic theory of nerve pulse propagation. [1] It proposes that the signals travel along the cell's membrane in the form of certain kinds of solitary sound (or density) pulses that can be modeled as solitons. The model is proposed as an alternative to the Hodgkin–Huxley model [2] in which action potentials: voltage-gated ion channels in the membrane open and allow sodium ions to enter the cell (inward current). The resulting decrease in membrane potential opens nearby voltage-gated sodium channels, thus propagating the action potential. The transmembrane potential is restored by delayed opening of potassium channels. Soliton hypothesis proponents assert that energy is mainly conserved during propagation except dissipation losses; Measured temperature changes are completely inconsistent with the Hodgkin-Huxley model. [3] [4]

Contents

The soliton model (and sound waves in general) depends on adiabatic propagation in which the energy provided at the source of excitation is carried adiabatically through the medium, i.e. plasma membrane. The measurement of a temperature pulse and the claimed absence of heat release during an action potential [5] [6] were the basis of the proposal that nerve impulses are an adiabatic phenomenon much like sound waves. Synaptically evoked action potentials in the electric organ of the electric eel are associated with substantial positive (only) heat production followed by active cooling to ambient temperature. [7] In the garfish olfactory nerve, the action potential is associated with a biphasic temperature change; however, there is a net production of heat. [8] These published results are inconsistent with the Hodgkin-Huxley Model and the authors interpret their work in terms of that model: The initial sodium current releases heat as the membrane capacitance is discharged; heat is absorbed during recharge of the membrane capacitance as potassium ions move with their concentration gradient but against the membrane potential. This mechanism is called the "Condenser Theory". Additional heat may be generated by membrane configuration changes driven by the changes in membrane potential. An increase in entropy during depolarization would release heat; entropy increase during repolarization would absorb heat. However, any such entropic contributions are incompatible with Hodgkin and Huxley model [9]

History

Ichiji Tasaki pioneered a thermodynamic approach to the phenomenon of nerve pulse propagation which identified several phenomena that were not included in the Hodgkin–Huxley model. [10] Along with measuring various non-electrical components of a nerve impulse, Tasaki investigated the physical chemistry of phase transitions in nerve fibers and its importance for nerve pulse propagation. Based on Tasaki's work, Konrad Kaufman proposed sound waves as a physical basis for nerve pulse propagation in an unpublished manuscript. [11] The basic idea at the core of the soliton model is the balancing of intrinsic dispersion of the two dimensional sound waves in the membrane by nonlinear elastic properties near a phase transition. The initial impulse can acquire a stable shape under such circumstances, in general known as a solitary wave. [12] Solitons are the simplest solution of the set of nonlinear wave equations governing such phenomenon and were applied to model nerve impulse in 2005 by Thomas Heimburg and Andrew D. Jackson, [13] [14] [15] both at the Niels Bohr Institute of the University of Copenhagen. Heimburg heads the institute's Membrane Biophysics Group. The biological physics group of Matthias Schneider has studied propagation of two-dimensional sound waves in lipid interfaces and their possible role in biological signalling [16] [17] [18] [19]

Justification

The model starts with the observation that cell membranes always have a freezing point (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. An action potential traveling along a mixed nerve results in a slight increase in temperature followed by a decrease in temperature. [20] Soliton model proponents claim that no net heat is released during the overall pulse and that the observed temperature changes are inconsistent with the Hodgkin-Huxley model. However, this is untrue: the Hodgkin Huxley model predicts a biphasic release and absorption of heat. [9] In addition, the action potential causes a slight local thickening of the membrane and a force acting outwards; [21] this effect is not predicted by the Hodgkin–Huxley model but does not contradict it, either.

The soliton model attempts to explain the electrical currents associated with the action potential 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. Indeed, such nonlinear sound waves have now been shown to exist at lipid interfaces that show superficial similarity to action potentials (electro-opto-mechanical coupling, velocities, biphasic pulse shape, threshold for excitation etc.). [17] Furthermore, the waves remain localized in the membrane and do not spread out in the surrounding due to an impedance mismatch. [22]

Formalism

The soliton representing the action potential of nerves is the solution of the partial differential equation

where t is time and x is the position along the nerve axon. Δρ is the change in membrane density under the influence of the action potential, c0 is the sound velocity of the nerve membrane, p and q describe the nature of the phase transition and thereby the nonlinearity of the elastic constants of the nerve membrane. The parameters c0, p and q are dictated by the thermodynamic properties of the nerve membrane and cannot be adjusted freely. They have to be determined experimentally. The parameter h 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 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. Under restrictive assumptions, there exist periodic solutions that display hyperpolarization and refractory periods. [23]

Role of ion channels

Advocates of the soliton model claim that it explains several aspects of the action potential, which are not explained by the Hodgkin–Huxley model. Since it is of thermodynamic nature it does not address the properties of single macromolecules like ion channel 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 soliton model predicts membrane current fluctuations during the action potential. These currents are of similar appearance as those reported for ion channel proteins. [24] They are thought to be caused by lipid membrane pores spontaneously generated by the thermal fluctuations. Such thermal fluctuations explain the specific ionic selectivity or the specific time-course of the response to voltage changes on the basis of their effect on the macroscopic susceptibilities of the system.

Application to anesthesia

The authors claim that their model explains the previously obscure mode of action of numerous anesthetics. The Meyer–Overton observation 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 proteins 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. [25] 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.

Differences between model predictions and experimental observations

Collision of solitons BBM equation - overtaking solitary waves animation.gif
Collision of solitons

The following is a list of some of the disagreements between experimental observations and the "soliton model":

Antidromic invasion of soma from axon
An action potential initiated anywhere on an axon will travel in an antidromic (backward) direction to the neuron soma (cell body) without loss of amplitude and produce a full-amplitude action potential in the soma. As the membrane area of the soma is orders of magnitude larger than the area of the axon, conservation of energy requires that an adiabatic mechanical wave decrease in amplitude. Since the absence of heat production is one of the claimed justifications of the 'soliton model', this is particularly difficult to explain within that model. [26] [ citation needed ]
Persistence of action potential over wide temperature range
An important assumption of the soliton model is the presence of a phase transition near the ambient temperature of the axon ("Formalism", above). Then, rapid change of temperature away from the phase transition temperature would necessarily cause large changes in the action potential. Below the phase transition temperature, the soliton wave would not be possible. Yet, action potentials are present at 0 °C. The time course is slowed in a manner predicted by the measured opening and closing kinetics of the Hodgkin-Huxley ion channels. [27]
Collisions
Nerve impulses traveling in opposite directions annihilate each other on collision. [28] On the other hand, mechanical waves do not annihilate but pass through each other. Soliton model proponents have attempted to show that action potentials can pass through a collision; [29] however, collision annihilation of orthodromic and antidromic action potentials is a routinely observed phenomenon in neuroscience laboratories and are the basis of a standard technique for identification of neurons. [30] Solitons pass each other on collision (Figure--"Collision of Solitons"), solitary waves in general can pass, annihilate or bounce of each other [31] and solitons are only a special case of such solitary waves. [32]
Ionic currents under voltage clamp
The voltage clamp, used by Hodgkin and Huxley (1952) (Hodgkin-Huxley Model) to experimentally dissect the action potential in the squid giant axon, uses electronic feedback to measure the current necessary to hold membrane voltage constant at a commanded value. A silver wire, inserted into the interior of the axon, forces a constant membrane voltage along the length of the axon. Under these circumstances, there is no possibility of a traveling 'soliton'. Any thermodynamic changes are very different from those resulting from an action potential. Yet, the measured currents accurately reproduce the action potential.[ citation needed ]
Single channel currents
The patch clamp technique isolates a microscopic patch of membrane on the tip of a glass pipette. It is then possible to record currents from single ionic channels. There is no possibility of propagating solitons or thermodynamic changes. Yet, the properties of these channels (temporal response to voltage jumps, ionic selectivity) accurately predict the properties of the macroscopic currents measured under conventional voltage clamp. [33]
Selective ionic conductivity
The current underlying the action potential depolarization is selective for sodium. Repolarization depends on a selective potassium current. These currents have very specific responses to voltage changes which quantitatively explain the action potential. Substitution of non-permeable ions for sodium abolishes the action potential. The 'soliton model' cannot explain either the ionic selectivity or the responses to voltage changes.
Pharmacology
The drug tetrodotoxin (TTX) blocks action potentials at extremely low concentrations. The site of action of TTX on the sodium channel has been identified. [34] Dendrotoxins block the potassium channels. These drugs produce quantitatively predictable changes in the action potential. [33] The 'soliton model' provides no explanation for these pharmacological effects.

Action waves

A recent theoretical model, proposed by Ahmed El Hady and Benjamin Machta, proposes that there is a mechanical surface wave which co-propagates with the electrical action potential. These surface waves are called "action waves". [35] In the El Hady–Machta's model, these co-propagating waves are driven by voltage changes across the membrane caused by the action potential.

See also

Sources

Related Research Articles

<span class="mw-page-title-main">Axon</span> Long projection on a neuron that conducts signals to other neurons

An axon, or nerve fiber, is a long, slender projection of a nerve cell, or neuron, in vertebrates, that typically conducts electrical impulses known as action potentials away from the nerve cell body. The function of the axon is to transmit information to different neurons, muscles, and glands. In certain sensory neurons, such as those for touch and warmth, the axons are called afferent nerve fibers and the electrical impulse travels along these from the periphery to the cell body and from the cell body to the spinal cord along another branch of the same axon. Axon dysfunction can be the cause of many inherited and acquired neurological disorders that affect both the peripheral and central neurons. Nerve fibers are classed into three types – group A nerve fibers, group B nerve fibers, and group C nerve fibers. Groups A and B are myelinated, and group C are unmyelinated. These groups include both sensory fibers and motor fibers. Another classification groups only the sensory fibers as Type I, Type II, Type III, and Type IV.

<span class="mw-page-title-main">Dendrite</span> Small projection on a neuron that receives signals

A dendrite or dendron is a branched protoplasmic extension of a nerve cell that propagates the electrochemical stimulation received from other neural cells to the cell body, or soma, of the neuron from which the dendrites project. Electrical stimulation is transmitted onto dendrites by upstream neurons via synapses which are located at various points throughout the dendritic tree.

<span class="mw-page-title-main">Ion channel</span> Pore-forming membrane protein

Ion channels are pore-forming membrane proteins that allow ions to pass through the channel pore. Their functions include establishing a resting membrane potential, shaping action potentials and other electrical signals by gating the flow of ions across the cell membrane, controlling the flow of ions across secretory and epithelial cells, and regulating cell volume. Ion channels are present in the membranes of all cells. Ion channels are one of the two classes of ionophoric proteins, the other being ion transporters.

<span class="mw-page-title-main">Myelin</span> Fatty substance that surrounds nerve cell axons to insulate them and increase transmission speed

In vertebrates, most neuronal cell axons are encased in myelin. Simply put, myelin insulates axons and increases the rate at which electrical impulses are passed along the axon. The myelinated axon can be likened to an electrical wire with insulating material (myelin) around it. However, unlike the plastic covering on an electrical wire, myelin does not form a single long sheath over the entire length of the axon. Rather, myelin ensheaths the axon in segments: in general, each axon is encased in multiple long myelin sheaths separated by short gaps called nodes of Ranvier.

<span class="mw-page-title-main">Andrew Huxley</span> English physiologist and biophysicist

Sir Andrew Fielding Huxley was an English physiologist and biophysicist. He was born into the prominent Huxley family. After leaving Westminster School in central London, he went to Trinity College, Cambridge on a scholarship, after which he joined Alan Lloyd Hodgkin to study nerve impulses. Their eventual discovery of the basis for propagation of nerve impulses earned them the Nobel Prize in Physiology or Medicine in 1963. They made their discovery from the giant axon of the Atlantic squid. Soon after the outbreak of the Second World War, Huxley was recruited by the British Anti-Aircraft Command and later transferred to the Admiralty. After the war he resumed research at the University of Cambridge, where he developed interference microscopy that would be suitable for studying muscle fibres.

<span class="mw-page-title-main">Action potential</span> Neuron communication by electric impulses

An action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and in some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells.

<span class="mw-page-title-main">Alan Hodgkin</span> English physiologist and biophysicist

Sir Alan Lloyd Hodgkin was an English physiologist and biophysicist who shared the 1963 Nobel Prize in Physiology or Medicine with Andrew Huxley and John Eccles.

<span class="mw-page-title-main">Membrane potential</span> Type of physical quantity

Membrane potential is the difference in electric potential between the interior and the exterior of a biological cell. That is, there is a difference in the energy required for electric charges to move from the internal to exterior cellular environments and vice versa, as long as there is no acquisition of kinetic energy or the production of radiation. The concentration gradients of the charges directly determine this energy requirement. For the exterior of the cell, typical values of membrane potential, normally given in units of milli volts and denoted as mV, range from –80 mV to –40 mV.

<span class="mw-page-title-main">Threshold potential</span> Critical potential value

In electrophysiology, the threshold potential is the critical level to which a membrane potential must be depolarized to initiate an action potential. In neuroscience, threshold potentials are necessary to regulate and propagate signaling in both the central nervous system (CNS) and the peripheral nervous system (PNS).

<span class="mw-page-title-main">Axon hillock</span> Part of the neuronal cell soma from which the axon originates

The axon hillock is a specialized part of the cell body of a neuron that connects to the axon. It can be identified using light microscopy from its appearance and location in a neuron and from its sparse distribution of Nissl substance.

<span class="mw-page-title-main">Pacinian corpuscle</span> Type of mechanoreceptor cell in hairless mammals

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<span class="mw-page-title-main">Hodgkin–Huxley model</span> Describes how neurons transmit electric signals

The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical engineering characteristics of excitable cells such as neurons and muscle cells. It is a continuous-time dynamical system.

<span class="mw-page-title-main">Cable theory</span> Mathematical model of a dendrite

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The squid giant synapse is a chemical synapse found in squid. It is the largest chemical junction in nature.

In neurophysiology, several mathematical models of the action potential have been developed, which fall into two basic types. The first type seeks to model the experimental data quantitatively, i.e., to reproduce the measurements of current and voltage exactly. The renowned Hodgkin–Huxley model of the axon from the Loligo squid exemplifies such models. Although qualitatively correct, the H-H model does not describe every type of excitable membrane accurately, since it considers only two ions, each with only one type of voltage-sensitive channel. However, other ions such as calcium may be important and there is a great diversity of channels for all ions. As an example, the cardiac action potential illustrates how differently shaped action potentials can be generated on membranes with voltage-sensitive calcium channels and different types of sodium/potassium channels. The second type of mathematical model is a simplification of the first type; the goal is not to reproduce the experimental data, but to understand qualitatively the role of action potentials in neural circuits. For such a purpose, detailed physiological models may be unnecessarily complicated and may obscure the "forest for the trees". The FitzHugh–Nagumo model is typical of this class, which is often studied for its entrainment behavior. Entrainment is commonly observed in nature, for example in the synchronized lighting of fireflies, which is coordinated by a burst of action potentials; entrainment can also be observed in individual neurons. Both types of models may be used to understand the behavior of small biological neural networks, such as the central pattern generators responsible for some automatic reflex actions. Such networks can generate a complex temporal pattern of action potentials that is used to coordinate muscular contractions, such as those involved in breathing or fast swimming to escape a predator.

A depolarizing prepulse (DPP) is an electrical stimulus that causes the potential difference measured across a neuronal membrane to become more positive or less negative, and precedes another electrical stimulus. DPPs may be of either the voltage or current stimulus variety and have been used to inhibit neural activity, selectively excite neurons, and increase the pain threshold associated with electrocutaneous stimulation.

Network of human nervous system comprises nodes that are connected by links. The connectivity may be viewed anatomically, functionally, or electrophysiologically. These are presented in several Wikipedia articles that include Connectionism, Biological neural network, Artificial neural network, Computational neuroscience, as well as in several books by Ascoli, G. A. (2002), Sterratt, D., Graham, B., Gillies, A., & Willshaw, D. (2011), Gerstner, W., & Kistler, W. (2002), and Rumelhart, J. L., McClelland, J. L., and PDP Research Group (1986) among others. The focus of this article is a comprehensive view of modeling a neural network. Once an approach based on the perspective and connectivity is chosen, the models are developed at microscopic, mesoscopic, or macroscopic (system) levels. Computational modeling refers to models that are developed using computing tools.

Neural accommodation or neuronal accommodation occurs when a neuron or muscle cell is depolarised by slowly rising current in vitro. The Hodgkin–Huxley model also shows accommodation. Sudden depolarisation of a nerve evokes propagated action potential by activating voltage-gated fast sodium channels incorporated in the cell membrane if the depolarisation is strong enough to reach threshold. The open sodium channels allow more sodium ions to flow into the cell and resulting in further depolarisation, which will subsequently open even more sodium channels. At a certain moment this process becomes regenerative and results in the rapid ascending phase of action potential. In parallel with the depolarisation and sodium channel activation, the inactivation process of the sodium channels is also driven by depolarisation. Since the inactivation is much slower than the activation process, during the regenerative phase of action potential, inactivation is unable to prevent the "chain reaction"-like rapid increase in the membrane voltage.

An action potential pulse is a mathematically and experimentally correct Synchronized Oscillating Lipid Pulse coupled with an Action Potential. This is a continuation of Hodgkin Huxley's work in 1952 with the inclusion of accurately modelling ion channel proteins, including their dynamics and speed of activation.

References

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  17. 1 2 Shrivastava, Shamit; Schneider, Matthias (18 June 2014). "Evidence for two-dimensional solitary sound waves in a lipid controlled interface and its implications for biological signalling". Journal of the Royal Society Interface. 11 (97): 20140098. doi:10.1098/rsif.2014.0098. PMC   4078894 . PMID   24942845.
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  28. ↑ Tasaki, Ichiji (1949). "Collision of two nerve impulses in the nerve fiber". Biochim Biophys Acta. 3: 494–497. doi:10.1016/0006-3002(49)90121-3.
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  32. ↑ Shrivastava, Shamit; Kang, Kevin; Schneider, Matthias F (30 Jan 2015). "Solitary shock waves and adiabatic phase transition in lipid interfaces and nerves". Physical Review E. 91 (12715): 012715. arXiv: 1411.2454 . Bibcode:2015PhRvE..91a2715S. doi:10.1103/PhysRevE.91.012715. PMID   25679650. S2CID   12034915.
  33. 1 2 Hille, Bertil (2001). Ion channels of excitable membranes (3. ed. ed.). Sunderland, Massachusetts: Sinauer. ISBN   9780878933211.
  34. ↑ Catterall, WA (2014). "Structure and function of voltage-gated sodium channels at atomic resolution". Experimental Physiology. 99 (1): 35–51. doi:10.1113/expphysiol.2013.071969. PMC   3885250 . PMID   24097157.
  35. ↑ El Hady, A., Machta, B. (2015). "Mechanical surface waves accompany action potential propagation". Nature Communications . 6: 6697. arXiv: 1407.7600 . Bibcode:2015NatCo...6.6697E. doi:10.1038/ncomms7697. PMID   25819404. S2CID   17462621.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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